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Dosimetry von in Radiotherapy

jANIZED BY I lO-OPERATIO

ViENrORGANIZED IN CO-OPEF

INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1988

The cover picture shows dose measurements at a 50 MeV medical accelerator. Photo taken by R olf Eklund, University o f Urnea.

DOSIMETRY IN RADIOTHERAPY

PROCEEDINGS SERIES

DOSIMETRY IN RADIOTHERAPY

PROCEEDINGS OF AN INTERNATIONAL SYMPOSIUM ON DOSIMETRY IN RADIOTHERAPY

ORGANIZED BY THE INTERNATIONAL ATOMIC ENERGY AGENCY

IN CO-OPERATION WITH THE WORLD HEALTH ORGANIZATION

AND HELD IN VIENNA, 31 AUGUST - 4 SEPTEMBER 1987

In tw o volum es

VOLUME 1

INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA, 1988

DOSIMETRY IN RADIOTHERAPY IAEA, VIENNA, 1988

STI/PUB/760 ISBN 92-0-010088-0

© IAEA, 1988

Permission to reproduce or translate the information contained in this publication may be obtained by writing to the International Atomic Energy Agency, Wagramerstrasse 5, P.O. Box 100, A-1400 Vienna, Austria.

Printed by the IAEA in Austria February 1988

FOREWORD

In developed countries with a comprehensive cancer programme, more than h alf o f all cancer patients, or roughly one in eight o f the population, will receive radiotherapy, either alone or in conjunction with other therapeutic modalities. In developing countries, as communicable diseases are gradually being controlled, cancer and other non-communicable diseases are becoming important public health problems. However, at present, cancer control is included in the health programmes of only a very limited number of developing countries and radiotherapy facilities exist in only approximately 60% of these countries.

International studies have consistently emphasized the close link between good clinical results and high accuracy in the determination of the absorbed dose, i.e. the energy absorbed per unit mass. The figure o f ± 5 % for the dose to the tumour has been suggested but today this is still very difficult to achieve, being composed of several independent steps. For more than fifteen years the IAEA in co-operation with WHO has run a postal dose intercomparison service for radiotherapy hospitals, mainly in developing countries. In all, about 650 hospitals worldwide have been served. Although a significant improvement has been registered during the last few years, still about 30% of the hospitals are not able to reach the desired goal of +5% of the prescribed dose in water.

Furthermore, it is essential that there should be consistency in dose determination between different parts o f the world in order that meaningful comparison of treatment results can be made. The IAEA/WHO Network of Secondary Standard D osim etry Laboratories was established about 10 years ago as an instrument for improving the coherence and accuracy of dosimetric measurements in radiation therapy. These laboratories should help to bridge the gap between primary measurement standards and users. The network now includes about 60 laboratories, 46 of them in developing countries.

A series of symposia on dosimetry in medicine and biology have been held by the IAEA in co-operation with WHO; the last one on “ Biomedical Dosimetry: Physical Aspects, Instrumentation and Calibration” was held in Paris in 1980. The present Symposium was the first one focussing on “ Dosimetry in Radiotherapy” . Among the 138 participants from 34 different countries were representatives from several of the National Radiation Standards Laboratories as well as radiotherapists and physicists from hospitals, research institutes and international organizations.

The 48 papers presented orally and the 37 papers presented as posters reflected the different steps in the calibration chain such as the calibration standards established by the National Standards Laboratories and the conversion of the reading of calibrated instruments to the desired quantity, i.e. absorbed dose to water at a

reference point in the user’s beam at the radiotherapy clinic. The programme further examined the procedures necessary for optimization of the treatment of the patient, such as treatment planning methods, dose distribution studies, new techniques of dose measurement, improvements in the physical dose distributions/conformation therapy and special problems involved in total body treatments. Results o f quality assurance in radiotherapy were presented from local hospitals as well as from national and international studies.

One theme that ran through the Symposium was the resurgence of problems that were thought to have been solved long ago, a striking example being the dosimetry of orthovoltage X-ray beams. Investigations on related parameters presented by three different groups showed varying results, leading to an animated discussion which will probably continue for some years.

In the 1980s several national Protocols or Codes of Practice for the dosimetry of high energy photon and electron beams have been issued. The first international Code of Practice, prepared by the IAEA and appearing just before the Symposium, undertook the responsibility of being the first international approach regarding consistency in stopping power data. Most of the national protocols or revisions of protocols appearing after 1986 are based on the same set of physical data as the IAEA protocol. Thus a greater consistency in absorbed dose determination all over the world is on the way to being achieved. Nevertheless, problem areas still exist, principally in electron beams where experiments have shown that inadequate characterization of beam quality could involve an uncertainty of as much as 2 %.

Several standards laboratories are actively pursuing the establishment of standards in the quantity of absorbed dose to water as a result of improvements in the theoretical and experimental aspects of realizing this quantity. In particular, calorimetric determination of absorbed dose has now reached a very high level of precision and, furthermore, water calorimeters are now the subject of intense research activity. This work will lead to an even more precise knowledge of the correction factors required when using ionization chambers. At one national physical laboratory, a new calibration service is being offered for high energy X-radiation, the calibration of ionization chambers in absorbed dose to water, with the purpose of decreasing uncertainties and reducing the risk of computational errors.

Results from dose intercomparison services for cobalt-60 therapy centres in some countries demonstrated that a considerable improvement in the determination of absorbed dose to water can be achieved by an active follow-up of unsatisfactory results and consultations with the hospitals. The Secondary Standard Dosimetry Laboratories can play a major role in these efforts.

The ability to transfer the absorbed dose in a water phantom in an X-ray or gamma ray beam to the patient has improved considerably during the last decades. New diagnostic techniques are available allowing the acquisition of patient data in three dimensions, and three dimensional treatment planning may be performed, enabling optimization of the treatment. This optimization is also facilitated by the progress in the determination of the dose distribution, e.g. with small radiation fields.

These developments were reflected in the Symposium and recognized as very encouraging, as it might now be possible to deliver a dose to the target volume which is within + 5 per cent of the prescribed dose.

For radiotherapy centres with limited resources, it is encouraging to notice that even on a cheap personal computer, advanced treatment planning systems may be applied.

The Symposium ended with a session on conformation therapy and the new generation of radiation therapy equipment, thus completing an encapsulation of the activities in the 1980s in the field of dosimetry in radiotherapy.

EDITO R IA L N O TE

The Proceedings have been edited by the editorial staff o f the IAEA to the extent considered necessary fo r the reader’s assistance. The views expressed remain, however, the responsibility o f the named authors or participants. In addition, the views are not necessarily those o f the governments o f the nominating Member States or o f the nominating organizations.

Although great care has been taken to maintain the accuracy o f information contained in this publication, neither the IAEA nor its Member States assume any responsibility fo r consequences which may arise from its use.

The use o f particular designations o f countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status o f such countries or territories, o f their authorities and institutions or o f the delimitation o f their boundaries.

The mention o f names o f specific companies or products (whether or not indicated as registered) does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement or recommendation on the part o f the IAEA.

The authors are responsible fo r having obtained the necessary permission fo r the IAEA to reproduce, translate or use material from sources already protected by copyrights.

Material prepared by authors who are in contractual relation with governments is copyrighted by the IAEA, as publisher, only to the extent permitted by the appropriate national regulations.

CONTENTS OF VOLUME 1

DETERMINATION OF ABSORBED DOSE (Sessions I and II)

Consistency in stopping power ratios for dosimetry (IAEA-SM-298/97) ....... 3P. A ndreo

The Standard DIN 6800: Procedures for absorbed dose determinationin radiology by the ionization method (IAEA-SM-298/31) ............................ 13K. Hohlfeld

Outline of the Italian Protocol for photon and electron dosimetryin radiotherapy (IAEA-SM-298/38) ..................................................................... 23R.F. Laitano

Determination of absorbed dose to water in clinical photon beams using a graphite calorimeter and a graphite-walled ionization chamber (IAEA-SM-298/77) .................................................................................................. 37A .H .L . A albers, E. Van D ijk, F.W. W ittkämper, B.J. M ijnheer

Fundamental measurement of absorbed dose in water for cobalt-60gamma rays: Procedure and experimental instrumentation(IAEA-SM-298/28) ................................................................... .............................. 49D .C . M osse, M. C anee, M. C hartier, J. D aures, A. O strowsky,J .P . Simoën

The high energy dosimetry system Göttingen — Twelve years controlledaccuracy and stability (IAEA-SM-298/104) ........................................................ 75B. M arkus, G. K asten

Extension of the Spencer-Attix cavity theory to the 3-media situationfor electron beams (IAEA-SM-298/81) ............................................................... 87A.E. Nahum

Dependence of some dosimetric parameters on beam sizein an irradiated phantom (IAEA-SM-298/8) ...................................................... 117J R. Cunningham, M. Woo

Dosimetry of orthovoltage X-ray beams (IAEA-SM-298/78) ............................. 129B.J. M ijnheer, L .M . Chin

Perturbation correction factor for X-rays between 70 and 280 kV(IAEA-SM-298/34) ....................... ......................................................................... 141U. Schneider, B. G rossw endt, H .M . K ram er

Determination of ionization chamber kerma correction factors for measurements in media exposed to orthovoltage X-rays(IAEA-SM-298/45)................................................................................... ................. 149M. K ristensen , P. H jortenberg, J. W. Hansen, M. Wille

Perturbation correction factors in ionization chamber dosimetry(IAEA-SM-298/69) .................................................................................................. 175B. N ilsson, A. M ontelius, P. A ndreo, B. Sorcini

Perturbation correction factors for the plane-parallel chamber NE 2534(IAEA-SM-298/82) .................... ............................................................................. 187R. G ajew ski, J. Izewska

DOSIMETRY IN BRACHYTHERAPY (Session III)

Modern developments in brachytherapy dosimetry (IAEA-SM-298/99) ......... 197A. D utreix

Comparaison des distributions de dose en curiethérapie interstitielleautour de sources continues et discontinues (IAEA-SM-298/23) .................. 213A. B ridier, H. Kafrouni, J .-P . H oulard, A. D utreix

Dosimétrie des sources solides d’iode 125 modèle 6711 (IAEA-SM-298/26) . 229 J.R . Isturiz P ineda, A. D utreix

Characterization of m Cs low dose rate sources for brachytherapy anddose algorithm verification (IAEA-SM-298/41) ................................................ 237A.M . D i N allo, L. Begnozzi, V. Panichelli, M. Benassi, G .A. Lovisolo

Clinical dosimetry of brachytherapy sources in tissue equivalent phantom(IAEA-SM-298/37) .................................................................................................. 247G. A rcovito , A. P ierm attei, F. Andreasi B assi, C. Bacci

Clinical application of computer dosimetry in radiotherapy of carcinomaof the uterine cervix (IAEA-SM-298/79) ............................................................ 261A.A. E l-M asry, A. O. Badib, M .Y. Gouda, M.F. Nooman,N .M . El-G ham ry

Quality assurance in gynaecological brachytherapy (IAEA-SM-298/58) ......... 275C.H. Jones

Poster Presentations

Dosimetry in 192Ir brachytherapy using pre-calculated tables(IAEA-SM-298/95P) .................................................... ......................................... 291G. H orgas, V. Lokner, B. P rokrajac, S. Spaventi

Organ doses from radiotherapy for cervical cancer usingMonte Carlo calculations (IAEA-SM-298/18P) ................................................ 293N. P etoussi, M. Zankl, G. W illiams, R. Veit, G. D rexler

Control o f occupational exposure in the use of afterloading systemsby means of controlled areas and systems of work (IAEA-SM-298/54P) .. 295D. Gifford, T.J. G odden, D. K ear

Low dose rate brachytherapy techniques: Staff exposure doses(IAEA-SM-298/57P) ................................................................................ .............. 297C.H. Jones, W. Anderson, R. D avis, A .M . B idm ead, S.H. Evans

Protección radiológica en curieterapia. Análisis de riesgos y controlde funcionamiento (IAEA-SM-298/74P) ............................................V. Anceña, P . Lorenz, G. M arti, P. O rtiz

299

EXTERNAL THERAPY DOSIMETRY (Session IV)

Calculation of electron contamination in a 60Co therapy beam(IAEA-SM-298/48) ................................................................................................. 303D .W .O . R ogers, G .M . E wart, A.F. B ielajew , G. Van D yk

Influence de l’os sur la distribution de dose dans les faisceaux d ’électrons(IAEA-SM-298/22) .................................................................................................. 313F. B idault, P. A letti, A. D utreix

Analysis of energy distribution by depth dose curves and its applicationto the dosimetry of fast electrons (IAEA-SM-298/88) ................................... 329G. Christ, F. Niisslin

Computer assisted film electron dosimetry: 3-D isodose curve(IAEA-SM-298/90) .................................................................................................. 341M. Lazzeri, L. A zzarelli, S. C esaro, M. Chimenti, O. Salvetti

Dosimetry of small X-ray radiation fields (IAEA-SM-298/42) ........................ 355L. B ianciardi, L. D ’A ngelo, F .P. G entile, M. Benassi, A. S. G uerra

Méthode générale d ’optimisation de la distribution des isodosesen radiothérapie par faisceaux de petites dimensions (IAEA-SM-298/27) .. 365D. Lefkopoulos, J.-Y . D evaux, J .-C . R oucayrol

Poster Presentations

Determination of electron ranges in water from those in solids(IAEA-SM-298/32P) ............................................................................................... 379B. G rosswendt, M. R oos

Dose distribution study of soft X-rays and extension of the application of short distance röntgen therapy to advanced skin cancer(IAEA-SM-298/75P) ............................................................................................... 381У. Skoropad

Dosimetry of rotational total-skin radiotherapy with electrons(IAEA-SM-298/6P) .................................................................................................. 383K. M uskalla, A. Stratmann, U. Quast

Chairmen of Sessions ............................................................ -...................................... 385Poster Rapporteurs ........................................................................................................ 385Secretariat of the Symposium ..................................................................................... 385

DETERMINATION OF ABSORBED DOSE

(Sessions I and II)

Chairmen

H. SVENSSONSweden

A. DUTREIXFrance

IAEA-SM-298/97

In v ite d Paper

C O N SISTEN C Y IN STO PPING PO W ER R A T IO S FO R D O S IM E T R Y

P. ANDREO*Sección de Física,Hospital Clínico Universitario,Zaragoza, Spain

Abstract

C O N S IS T E N C Y IN S T O P P IN G P O W E R R A T IO S F O R D O S IM E T R Y .O rg a n iz a t io n s f o r m e d ic a l p h y s ic s in d i f f e r e n t c o u n tr ie s h av e p u b lis h e d r e c o m m e n d a t io n s

fo r t h e d o s im e try o f h ig h e n e rg y p h o to n a n d e le c tr o n b e a m s u s e d in r a d io th e r a p y . In m o s t o f

th e m n o a t t e n t io n h a s b e e n fo c u s e d o n th e c o n s is te n c y o f th e re c o m m e n d e d s to p p in g p o w e r

ra t io s w i th th o s e u s e d in s ta n d a rd la b o ra to r ie s f o r th e c a l ib ra t io n o f io n iz a t io n c h a m b e r s . A

rev iew o f th e b a sic d a ta b e in g u s e d in d o s im e try p r o to c o ls a n d s ta n d a rd la b o ra to r ie s is p re s e n te d ,

s tre s s in g th e d if f e r e n c e s b e tw e e n p r o to c o ls p u b lis h e d b e fo re a n d a f te r 1 9 8 6 . In a d d i t io n , o th e r

s o u rc e s o f in c o n s is te n c y in th e d o s im e tr ic c h a in a re d iscu ssed .

1. INTRODUCTION

During the last few years several organizations for medical physics have published recom m endations for the dosimetry of high energy photon and electron beams used in radiotherapy. In m ost of them no attention has been paid to the consistency of the recommended numerical data with those being used in the standard laboratories to provide calibration factors for ionization chambers. Each dosimetry protocol included the most recent data avilable at the time o f publication, the result being more updated protocols; however, there were no consistent links with the standard laboratories or even with the ‘international dosimetry com m unity’ regarding stopping power ratio data.

After the publication of the ICRU Report on stopping powers for electrons and positrons [1], CCEM RI(I) [2] recommended that as o f the beginning of 1986 Primary Standard Dosimetry Laboratories (PSDLs) should adopt this new set o f values together w ith o ther basic physical data. However, these recommendations did not affect by themselves the general lack of consistency among PSDLs and hospital users, the situation being not very different from that already in existence.

* P resen t add ress: D ep artm en t o f R ad iation Physics, T h e K aro lin ska Institu te and

U niversity o f S tockho lm , S tockho lm , Sw eden.

3

4 ANDREO

The need for a consistent set o f stopping power data both in the standard laboratories and in radiotherapy dosimetry was already pointed out by Svensson in 1984 [3]. Later on it was suggested [4, 5] tha t the recom m endations of CCEM RI(I) [2] should also be included in the dosimetry protocols. The Code o f Practice prepared by the International Atomic Energy Agency (IAEA) [6 ] has been the first international approach regarding consistency in stopping power ratios. O ther protocols as well as updates o f existing ones have been published since the beginning o f 1986; m ost o f them are based on practically the same set of basic physical data as those o f the IAEA protocol. The actual situation in dosim etry seems to have finally overcome the lack o f consistency already m entioned, although there are still a few cases where inconsistencies remain.

A review o f the basic data being used in standard laboratories and dosimetry protocols will be presented in this paper, stressing the differences between the protocols published before and after 1986.

There are also some difficulties in the proper selection o f stopping power ratios for photon and electron beams that in some cases produce im portant discrepancies between ionom etric and chemical dosimetry. These are usually related to the specification of a param eter to describe the quality o f therapeutic beams and then select the corresponding stopping power ratio to com pute the absorbed dose to water from a measured quantity. Although on most occasions there were no data available to properly account for the assignment of stopping power ratios to beam quality, it is true that this lack o f consistency adds uncertainty to the last step in the dosimetric procedure. Some recent developments will be discussed to show that this problem has been solved for photon beams [7]. However, there is still an im portant lack o f inform ation regarding the dosimetry of electron beams, where energy and angular spread play an im portant role that existing data do not take into account.

2. IMPORTANCE OF CONSISTENCY IN STOPPING POWER RATIOS

The different steps in the absorbed dose determ ination, when high energy photon and electron beams are used in radiotherapy, include a set o f different physical constants and correction factors. Already at the beginning o f the calibration chain, stopping power ratios must be used at the standard laboratories to determ ine exposure or air kerma. The same quantity must be introduced by the user in different steps when the absorbed dose is to be determined.

There are also some other physical constants and factors that depend on stopping power values. For instance, the quantity W/e is based on experimental determ inations tha t assume certain stopping power ratios (see e.g. Refs [6 , 8 ]). Some other quantities and correction factors (g, katt) are based on calculations using stopping power data, and other necessary factors also include stopping

IAEA-SM-298/97 5

TABLE I. D IFFERENT STEPS IN THE DOSIMETRIC CHAIN WHERE STOPPING POWER RATIOS ARE INTRODUCED3

P lace S te p P h y s ic a l c o n s ta n ts an d fa c to rs

S ta n d a rd la b o ra to r ie s x,Kair swa!l, air W /e g

H o sp ita l

( c h a m b e r fa c to r ) ND k m W /e k att

H o sp ita l

( a b s o rb e d d o s e d e te r m in a t io n ) Dw sw ater, air Pu

a S y m b o ls fo llo w IC R U [9 ] a n d IA E A [ 6 ] n o ta t io n .

TABLE II. STOPPING POWER DATA USED IN DIFFERENT STEPS OF THE DOSIMETRIC CHAIN BY DOSIMETRY PROTOCOLS PUBLISHED BEFORE 1986a

P r o to c o lN A C P

[ 1 1 , 1 2 ]А А РМ

[1 3 ]

S E F M

[1 4 ]

H P A

[1 5 , 16]

C h a m b e r fa c to rs sb g 64 gBG 80 jBGeo sb G82

P h o to n d o s im e tr y s BG<* gSA 80 sSA so sBG82

E le c t ro n d o s im e try sS A 80 SSA 82 ss a 80 sS A 82

3 V alues u s e d a t s ta n d a r d la b o ra to r ie s w e re d e riv e d f ro m R ef . [1 0 ] (see n o te s ) .

Notes:

sBG B ra g g -G ra y s to p p in g p o w e r r a tio s , p r im a r y s p e c tru m (see IC R U R e p o r t 35 [9 ] ) .

sSA S p e n c e r - A t t ix s to p p in g p o w e r ra t io s , to t a l s p e c tru m (see IC R U R e p o r t 35 [9 ] ) .

6 4 B e rg e r a n d S e l tz e r 1 9 6 4 e le c tr o n s to p p in g p o w e rs ; ‘o ld ’ I-v a lu e s , S ( S te r n h e im e r ) [1 0 ] .8 0 B e rg e r a n d S e l t z e r 1 9 8 0 e le c tr o n s to p p in g p o w e rs ; ‘n e w ’ I-v a lu e s , S (S te r n h e im e r -P e ie r ls ) .

D a ta in c lu d e d in IC R U R e p o r t 35 [9 ] .

8 2 B e rg e r a n d S e l tz e r 1 9 8 2 e le c t r o n s to p p in g p o w e rs ; ‘n e w ’ I-v a lu e s , 5 (S te r n h e im e r - B e r g e r -

S e ltz e r ) [1 7 ] . D a ta in c lu d e d in IC R U R e p o r t 3 7 [1 ] .

6 ANDREO

power ratios in the existing form ulations (km, pu). Table I shows the different steps where stopping powers are introduced.

It is obvious that systematic errors may occur if different sets o f values are used along the whole procedure. Nevertheless, until 1986, standard laboratories based their calibrations on the old values o f Berger and Seltzer published in 1964 [ 1 0 ], whereas most o f the dosimetry protocols published at that time were based on a different set o f values derived under different evaluations o f the density effect and different I-values (both o f which are im portant parameters for calculating stopping powers), and using different approaches to evaluate s-ratios, e.g. Bragg-Gray or Spencer-A ttix ratios [9]. The situation is shown in Table II.It is surprising that until recently this lack of consistency between standard laboratories and users of different dosimetry protocols has not received more attention. The agreement reached between laboratories in different countries was excellent for 60Co gamma ray beams (see e.g. Ref. [18]) and many countries had uniform dosimetry among the users of a given protocol; however, there was no connection between these groups, which produced a weak link in the dosimetry chain. Furtherm ore, within a given protocol, a m ixture o f data was employed, shown in Table II.

3. CONSISTENCY OF THE PRESENT SITUATION

It is well known that stopping powers for electrons have been subject to revision over recent years. The re-evaluation o f the density effect, together with a better knowledge o f I-values [1, 17] has led to im portant changes for some materials used in dosimetry. Graphite, for instance, the most common material for the walls o f ionization chambers, now presents a 1% difference for the ratio sgraphite; air compared with the previous value at the energy o f 60Co.Some of the above mentioned physical quantities will also have to be modified owing to their dependence on stopping power ratios [8 ].

CCEM RI(I) [2] recommended the beginning o f 1986 as the date when standard laboratories should adopt the new set o f values. The aim was again to use a consistent set o f data in all laboratories to retain the excellent agreement on 60Co standards, but these recom m endations were not addressed to the users o f different dosimetry protocols. If general consistency is considered, the situation was not better than that shown in Table II, except for updating o f data at the laboratories.

As early as 1984 Svensson [3] pointed out this lack of consistency but, unfortunately, none o f the protocols published at that time took his ideas into consideration. When the IAEA undertook the task of elaborating an international dosimetry protocol, the importance o f the consistency o f the data to be included was stressed from the beginning. An Advisory Group Meeting, held in March 1985 [5], decided that the IAEA Code o f Practice [6 ] should include the recommendations o f CCEM RI(I) [2], Even if this was a natural consequence of the aim of an

IAEA-SM-298/97 7

international docum ent, addressed both to the SSDLs’ network supported by the IAEA and to users in different countries, the practical result was that for the first time an im portant effort had been made to overcome the Jack o f consistency along the whole dosimetric chain regarding numerical data. Several authors have since then supported this consistent approach [4 ,19] and, during 1986 and 1987, some countries published new dosimetry protocols [20-22], updated existing ones [23], or prepared recommendations, stressing the importance of consistency and including a new set o f data.

4. OTHER SOURCES OF INCONSISTENCY

Even if the basic stopping powers for electrons are taken from the latest re-evaluation published by the ICRU [1], the last step in the dosimetric procedure, namely com putation o f the absorbed dose to water from a measured quantity using w ater/air stopping power ratios, still deserves some attention regarding consistency.

In the strict sense, a com plete electron spectrum at the point o f measurem ent would be needed in order to determ ine the water to air stopping power ratio for the beam being used. In practice this procedure is unrealistic and a simpler approach that relates the quality of the beam to a given stopping power ratio value is commonly used in all existing dosim etry protocols. Nevertheless, most o f the protocols published before 1986 are based on rather inconsistent assignments o f stopping pow er ratios to a given beam quality.

4.1. Photon beams

It can be seen in Table III tha t w ith the exception of the Code o f Practice issued by the HPA [15], there is a certain similarity in all the protocols published before 1986 regarding the specification of the quality of photon beams. The dose or ionization ratio at two different depths is to be measured keeping the source- surface distance (SSD = 1 m) or the source-cham ber distance (SCD = 1 m) constant, with the field size defined at the surface or at the detector level, respectively.

On the o ther hand, the bremsstrahlung spectrum used to calculate electron spectra and to com pute stopping power ratios, and the type o f calculations to derive s-ratios, are substantially different. NACP [11], for example, used Bragg- Gray stopping power ratios taken from ICRU [24] that were determined for thin targets using crude approxim ations, but no connection was established with the beam quality descriptor. А АРМ [13] used Spencer-A ttix stopping power ratios giving an approxim ate relationship with dose ratios, but their values were based on independent approxim ate calculations for the two quantities. SEFM [14]

8 ANDREO

TABLE III. SPECIFICATION OF THE QUALITY OF PHOTON BEAMS AND BREMSSTRAHLUNG SPECTRA USED TO COMPUTE STOPPING POWER RATIOS IN THE DIFFERENT DOSIMETRY PROTOCOLS PUBLISHED BEFORE 1986 (SEE TEXT)

P r o to c o lP h o to n b e a m q u a li ty d e s c r ip to r

S p e c tru m u s e d to c o m p u te

s to p p in g p o w e r ra t io s

N A C P [1 1 ] E x p e r im e n ta l io n . ra t io s

a t S S D = 1 m

T h in ta rg e ts

A A P M [1 3 ] E x p e r im e n ta l d o se ra t io s

a t SC D = 1 m

T h in ta rg e t + e x p e r im e n ta l

S E F M [1 4 ] E x p e r im e n ta l io n . r a t io s

(a s N A C P )

T h in ta rg e ts

H P A [1 5 ] N o m in a l M V M o n o e n e rg e tic

( h i1 ‘e f fe c t iv e ’)

used the same dose ratios as NACP [11] and Spencer-A ttix s-ratios, bu t again there was no relation between the two quantities.

A new set o f water/air stopping power ratios was prepared for the IAEA protocol [7]. This time, both energy deposition and electron spectra as a function o f depth were calculated by the Monte Carlo m ethod for one and the same beam using the data recommended by CCEM RI(I) [2]. This allowed consistent determ ination o f the photon beam quality (dose ratio at two depths) and the Spencer-A ttix stopping power ratios, ensuring a strict relationship between the two quantities. The procedure was performed for a large set o f bremsstrahlung spectra available for different clinical accelerators as well as for calculated thick target spectra covering the range o f clinical photon beams. Together w ith a complete set o f chamber dependent wall correction factors (km and pu ) [25], these new data have been included in the IAEA protocol [6 ] providing consistency along the various steps o f the dosimetric procedure.

The same consistent approach, with minor differences regarding some of the recommended values for certain parameters, has been adopted in the new dosimetry

protocols and updates published since 1986 and referred to above [20-23]. It has to be pointed out that NACP is preparing a revision of its actual protocol to update the numerical data according to the general consistency described here. AAPM, on the contrary, will not yet adopt the stopping power ratios discussed here as it is claimed that the ‘revised values are no t likely to affect significantly dose determ inations for X-ray beams’ [26].

IAEA-SM-298/97 9

Practically all the dosimetry protocols mentioned in the preceding section are in agreement with the recommended values for the water/air stopping power ratios in electron beams. A doption o f the values of Berger and Seltzer as given in the AAPM protocol completes the consistency for all the beams used in radiotherapy.

The same is true for the specification of some types o f ‘quality index’ in electron beams, where the half-value depth, R s0, is related to the mean electron energy at the phantom surface, E0 . The mean energy is used together with the depth of measurement, z, to select the corresponding value o f the water/air stopping power ratio. Small discrepancies exist in the different dosimetry protocols regarding the practical determ ination of R 50 (compare, for instance NACP [11] with AAPM [13]), but the differences in the final swater air values are o f little importance when the same data se t is used.

Johansson and Svensson [27] pointed out that E0 and z were not adequate parameters to select swater air in electron beams w ith a given spectral width. The experimental results o f Mattsson [28] (see also Ref. [29]) have confirmed this, showing that use o f s-ratios derived for monoenergetic and monodirectional beams was adequate for beams with a certain energy and angular spread, but not for ‘clean’ beams. This dem onstrates that some type of inconsistency remains.

In order to investigate this discrepancy, different calculations have been performed using the Monte Carlo m ethod. Calculated swater ajr for beams w ithout energy and angular spread do not show significant differences from the Berger and Seltzer values, especially for the electron beam energies more commonly used in radiotherapy. (E 0 less than 20 MeV.) On the o ther hand, the inclusion of energy and angular spread in the calculations [30, 31] has confirmed that R 50 is not simply related to the mean energy o f the spectrum at the phantom surface, but that the calculated variation o f swater air at the depth of the maximum absorbed dose is never as large as the 2 % figure reported by Mattsson. This has been confirmed even for beams with an extreme energy and angular spread. Further work is being done to explain the influence of the characteristics o f the beams on the w ater/air stopping power ratios.

4.2. Electron beams

5. CONCLUSIONS

The inclusion o f the recom m endations o f CCEM RI(I) in protocols for the dosimetry of high energy electron and photon beams has considerably improved the consistency o f the dosimetric chain. Use of a common set of stopping power data in dosimetry eliminates systematic errors existing in most o f the protocols published before 1986. International agreement is now quite satisfactory.

10 ANDREO

Despite this overall consistency, the dosimetry o f electron beams still requires further investigation to explain the discrepancies that exist between theory and experiments. Additional work in both fields will provide a better understanding o f the underlying phenomena and will lead to an improvement in electron dosimetry.

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R a d io th e r . O n c o l., to b e p u b lis h e d .[9 ] IN T E R N A T IO N A L C O M M IS S IO N O N R A D IA T IO N U N IT S A N D M E A S U R E M E N T S ,

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R e p o r t 3 5 , B e th e s d a , M D ( 1 9 8 4 ) .[ 1 0 ] B E R G E R , M .J ., S E L T Z E R , S .M ., T a b le s o f e n e rg y lo sses a n d ra n g e s o f e le c tr o n s an d

p o s i t ro n s , N A S -N R C P u b lic a t io n 1 1 3 3 : 2 0 5 -2 6 8 , N a t io n a l A c a d e m y o f S c ie n c e s -N a tio n a l

R e s e a rc h C o u n c i l, W a s h in g to n , D C (1 9 6 4 ) .

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th e r a p y b e tw e e n 1 a n d 5 0 M eV , A c ta R a d io l., O n c o l. 19 ( 1 9 8 0 ) 5 5 .

[1 2 ] N O R D IC A S S O C IA T IO N O F C L IN IC A L P H Y S IC S , E le c tro n b e a m s w ith m e a n e n e rg ie s

a t th e p h a n to m s u rfa c e b e lo w 15 M eV , A c ta R a d io l ., O n c o l. 2 0 (1 9 8 1 ) 4 0 1 .

[1 3 ] A M E R IC A N A S S O C IA T IO N O F P H Y S IC IS T S IN M E D IC IN E , A p r o to c o l f o r th e

d e te rm in a t io n o f a b s o rb e d d o s e f r o m h ig h -e n e rg y p h o to n a n d e le c t r o n b e a m s , M ed .

P h y s . 1 0 ( 1 9 8 3 ) 7 4 1 .

[1 4 ] S O C IE D A D E S P A Ñ O L A D E F IS IC A M E D IC A , P r o c e d im ie n to s r e c o m e n d a d o s p a ra

la d o s im e tr ía d e f o to n e s y e le c tr o n e s d e e n e rg ía s c o m p re n d id a s e n t r e 1 M eV y 5 0 M eV

e n r a d io te r a p ia d e h a c e s e x te rn o s , S E F M P u b lic a t io n N o . 1, M ad r id ( 1 9 8 4 ) .

[1 5 ] H O S P IT A L P H Y S IC IS T S ’ A S S O C IA T IO N , R ev ise d C o d e o f P ra c tic e f o r th e d o s im e try

o f 2 to 2 5 M V X -ra y , a n d o f c a e s iu m -1 3 7 a n d c o b a l t -6 0 g a m m a -ra y b e a m s , P h y s . M ed.

B io l. 2 8 ( 1 9 8 3 ) 1 0 9 7 .

[1 6 ] H O S P IT A L P H Y S IC IS T S ’ A S S O C IA T IO N , C o d e o f P ra c tic e f o r e le c tr o n b e a m d o s im e try

in r a d io th e r a p y , P h y s . M ed . B io l. 3 0 ( 1 9 8 5 ) 1 1 6 9 .

IAEA-SM-298/97 11

[1 7 ] B E R G E R , M .J ., S E L T Z E R , S .M ., S to p p in g P o w e rs a n d R an g e s o f E le c tro n s a n d P o s i t ro n s ,

R e p o r t N B S IR 8 2 -2 5 5 0 , N a t io n a l B u re a u o f S ta n d a rd s , G a i th e rs b u rg , M D ( 1 9 8 2 ) .[1 8 ] N A T E L , M .T ., L O F T U S , T .P ., O E T Z M A N N , W ., C o m p a r is o n o f e x p o s u r e s ta n d a rd s fo r

60C o g a m m a ra y s , M e tro lo g ia 11 ( 1 9 7 5 ) 17 .[1 9 ] R O G E R S , D .W .O ., R O S S , C .K ., S H O R T T , K .R . , B IE L A JE W , A .F ., C o m m e n ts o n th e

60C o g r a p h i te /a i r s to p p in g p o w e r r a t io u s e d in th e A A P M T G 2 1 p r o to c o l , M ed . P h y s . 13

( 1 9 8 6 ) 9 6 4 .

[ 2 0 ] M IJN H E E R , B .J ., A A L B E R S , A .H .L ., V IS S E R , A .G ., W IT T K A M P E R , F .W ., C o n s is te n c y

a n d s im p lic i ty in th e d e te r m in a t io n o f a b s o rb e d d o s e in h ig h -e n e rg y p h o to n b e am s: A n e w

c o d e o f p ra c t ic e , R a d io th e r . O n c o l. 7 ( 1 9 8 6 ) 3 7 1 .

[21] SW IS S S O C IE T Y O F R A D IA T IO N B IO L O G Y A N D R A D IA T IO N P H Y S IC S , D o s im e try

o f H ig h E n e rg y P h o to n a n d E le c t r o n B eam s: R e c o m m e n d a t io n s (M ay 1 9 8 6 ) .

[2 2 ] O u tl in e o f th e I ta l ia n P r o to c o l f o r P h o to n a n d E le c tro n D o s im e try in R a d io th e r a p y ,

S u b c o m m itte e f o r B asic D o s im e try , C o m m it te e f o r D o s im e try S ta n d a rd iz a t io n in

R a d io th e r a p y , I ta l ia n A s s o c ia tio n o f B io m e d ic a l P h y s ic is ts (A IF B ) (M a y 1 9 8 7 ).

[2 3 ] S O C IE D A D E S P A Ñ O L A D E F IS IC A M E D IC A , S u p le m e n to a l d o c u m e n to S E F M

N o . 1 -1 9 8 4 : P r o c e d im ie n to s r e c o m e n d a d o s p a ra la d o s im e tr ía d e f o to n e s y e le c tr o n e s de

e n e rg ía s c o m p re n d id a s e n t r e 1 M eV y 5 0 M eV e n r a d io te ra p ia d e h a c e s e x te r n o s , S E F M

P u b lic a t io n N o . 2 , M a d r id ( 1 9 8 7 ) .

[2 4 ] IN T E R N A T IO N A L C O M M IS S IO N O N R A D IA T IO N U N IT S A N D M E A S U R E M E N T S ,

R a d ia t io n D o s im e try : X -ra y s a n d G a m m a R a y s w i th M a x im u m P h o to n E n e rg ie s b e tw e e n

0 .6 a n d 5 0 M eV , IC R U R e p o r t 1 4 , B e th e s d a , M D (1 9 6 9 ) .

[2 5 ] A N D R E O , P ., N A H U M , A .E ., B R A H M E , A ., C h a m b e r -d e p e n d e n t w a ll c o r r e c t io n fa c to rs

in d o s im e try , P h y s . M ed . B io l. 31 ( 1 9 8 6 ) 1 1 8 9 .

[2 6 ] S C H U L Z , R .J . , R e p ly to c o m m e n ts o f R o g e rs e t a l., M ed . P h y s . 13 ( 1 9 8 6 ) 9 6 5 .

[2 7 ] JO H A N S S O N , K .A ., S V E N S S O N , H ., D o s im e tr ic I n te rc o m p a r is o n a t th e N o rd ic R a d ia t io n

T h e ra p y C e n te rs . P a r t I I , C o m p a r is o n b e tw e e n D if f e r e n t D e te c to r s a n d M e th o d s , T h e s is

K .A . J o h a n s s o n , U n iv e rs ity o f G o th e n b u rg , S w e d e n ( 1 9 8 2 ) .

[2 8 ] M A T T S S O N , L .O ., C o m p a r is o n o f d i f f e r e n t p r o to c o ls fo r th e d o s im e tr y o f h ig h -e n e rg y

p h o to n a n d e le c tr o n b e a m s , R a d io th e r . O n c o l. 4 ( 1 9 8 5 ) 3 1 3 - 3 1 8 .

[2 9 ] S V E N S S O N , H ., A N D R E O , P ., C U N N IN G H A M , J . , H O H L F E L D , K ., “ C o d e o f p ra c tic e

fo r a b s o r b e d d o s e d e te r m in a t io n in p h o to n a n d e le c tr o n b e a m s ” , R a d io th e r a p y in D e v e lo p in g C o u n tr ie s (P ro c . S y m p . V ie n n a , 1 9 8 6 ) , IA E A , V ie n n a ( 1 9 8 7 ) 3 3 3 .

[3 0 ] A N D R E O , P ., N A H U M , A .E ., “ In f lu e n c e o f in i t ia l e n e rg y s p re a d in e le c tr o n b e a m s o n th e d e p th -d o s e d is t r ib u t io n a rid s to p p in g p o w e r r a t io s ” , P ro c . X IV IC M B E a n d

V I I P , E s p o o , M ed . B io l. E n g . C o m p u t . 23 S u p p l. 1 ( 1 9 8 5 ) 6 0 8 .[3 1 ] A N D R E O , P ., B R A H M E , A ., N A H U M , A ., In f lu e n c e o f e n e rg y a n d a n g u la r s p re a d o n

d e p th d o s e s a n d s to p p in g p o w e r r a t io s f o r e le c tr o n b e a m s , W o rk in p ro g re s s .

IAE A-SM-298/31

THE STANDARD DIN 6800: PROCEDURES FOR ABSORBED DOSE DETERMINATION IN RADIOLOGY BY THE IONIZATION METHOD

K. HOHLFELDPhysikalisch-Technische Bundesanstalt,Braunschweig,Federal Republic of Germany

Abstract

T H E ST A N D A R D D IN 6 8 0 0 : P R O C E D U R E S F O R A B SO R B E D D O S E D E T E R M IN A T IO N IN

R A D IO L O G Y B Y T H E IO N IZ A T IO N M E T H O D .

In the F ed era l R epub lic o f G erm any , the Physika lisch -T echn ische B undesansta lt (PT B ) as the

national P rim ary S tandard D o sim etry L ab o ra to ry has developed p rim ary standards o f abso rbed dose to

w ater. T hus it is possib le to c a lib ra te therapy leve l dosim eters d irec tly in a w a ter phan tom to ind icate

abso rbed dose in g ray . T h e S tandard C om m ittee on R ad io logy (N orm enausschuß R ad io log ie) in the

F ed era l R epublic o f G erm any decided tha t in th e field o f dosim etry fo r rad ia tio n th e rap y , exposu re

should be rep laced on ly by ab so rbed dose to w a ter in a w a ter phan tom . A w ork ing g ro u p has been

estab lished to rev ise the S tandard D IN 6800 ‘D o sism eßverfah ren in d e r rad io log ischen T echn ik —

Ion isa tionsdosim e trie ’ acco rd ing ly . In th is new concep t one quantity is u sed exclusive ly from the

p rim ary standard to the u s e r’s instrum ent. A d ra ft o f the rev ised stan d ard w ill soon be availab le .

1. INTRODUCTION

The Physikalisch-Technische Bundesanstalt (PTB) at Braunschweig as the national Primary Standard Dosimetry Laboratory (PSDL) of the Federal Republic of Germany and the Normenausschuß Radiologie (NAR) as the Federal German standard committee on radiology in close co-operation decided that only the absorbed dose to water in a water phantom should be used as measurand in the dosimetry for radiation therapy. This quantity replaces the quantity Standard- Ionendosis, which is equal to exposure. On the one hand, this decision had the effect of strengthening the efforts of the PTB to establish primary standards of absorbed dose to water in the whole range of photon and electron radiation. On the other hand, the NAR set up a working group to revise the standard DIN 6800, part 2[l], incorporating the new concept of using exclusively one quantity from the primary standard to the user's instrument.

This procedure eliminates uncertainties associated with the conversion of a calibration factor in terms of exposure or air kerma free in air into a calibration factor in terms of absorbed

13

14 HOHLFELD

dose to water in a water phantom. The simplicity and clarity of the concept which can be seen from the use of only one fundamental relation reduce the probability of errors by the user.

The absorbed dose, D , at a point in the phantom, where the reference point of the ionization chamber is located, is given by the relation

D = к • N • M w

where M is the indicated value of the ionization dosimeter, N is the calibration factor in terms of absorbed dose to water and к is the product of the correction factors. These correction factors take into account all effects owing to influence quantities deviating from their reference values and can, in principle, be determined experimentally by comparing the ionization dosimeter with the primary standard under the relevant conditions. As, up to now, these experimental determinations have not been completed, calculated correction factors are also given.

2. MEASUREMENT CHAINThe PTB as the national standard laboratory has developed pri

mary standards of absorbed dose to water which for high energy photon and electron radiation are based on the known energy imparted by electrons in a ferrous sulphate solution [2], whereas in the X-ray energy range an extrapolation ionization chamber in a graphite phantom forms the main part of the standard measuring device [ з ] . In addition to this, currently investigations on the water absorbed dose calorimeter and the heat defect of water are being carried out [4 ].

Secondary standard dosimeters are calibrated in a water phantom under reference conditions in a Co-60 gamma radiation beam and additional measurements are performed in filtered X-ray beams.

By means of these secondary standards the calibration is transferred to

- the manufacturers of the dosimeters- the German Calibration Service (DKD - Deutscher Kalibrier

dienst )- the dosimetry laboratories of the verification authorities.

In the Federal Republic of Germany the Verification Law [5] subjects each ionization dosimeter used in the treatment of patients with external photon radiation beams with energies up to3 MeV to special procedures: first, in a type-test at the PTB ithas to be shown that the requirements for approval for verification [6] stated by the PTB are fulfilled. Secondly, before being taken into use, the stated calibration factor of the individual ionization dosimeter must be shown to be within given limits. This verification must be repeated at certain time intervals.

Although the Verification Law does not apply to high-energy radiation, it provides the framework within which the Standard DIN 6800 describes details of the dosimetric procedures.

IAEA-SM-298/31 15

3. CALIBRATION FACTOR, REFERENCE CONDITIONS AND CORRECTION FACTORS

The calibration factor of the ionization dosimeter in terms of absorbed dose to water is the ratio of the conventionally true value of the water absorbed dose and the indication of the dosimeter under calibration conditions. These calibration conditions fix the set of values of all influence quantities and circumstances, for which the calibration factor is valid without any further corrections. Influence quantities are those quantities which are not the object of the measurement but influence the measured value, e. g. temperature, humidity, air pressure, line voltage, dose rate, radiation quality. Up to now, there have been different calibration factors of an ionization chamber for different X-ray qualities. Radiation quality is now treated like the other influence quantities. Co-60 gamma radiation is taken as the reference radiation, measurements at other radiation qualities do need a correction factor. This formal treatment results in only one calibration factor for an ionization dosimeter. Correction factors are related only to one influence quantity, varying within its rated range, while all other influence quantities are fixed at their calibration values.

A slight difference exists in the treatment of the geometrical conditions which relate to the change in radiation quality. These reference conditions are stated in Table I. Calibration conditions

TABLE I. GEOMETRICAL REFERENCE CONDITION FOR THE CALIBRATION OF IONIZATION DOSIMETERS AND FOR THE DETERMINATION OF CORRECTION FACTORS FOR THE QUALITY OF PHOTON AND ELECTRON BEAMS a)

Radiation quality: Reference depth Focus-surface Field size atnuclide, generating in phantom distance phantom surfacepotential, energy (cm) (cm) (cm)

Co-60 gamma radiation Photon radiation: 0.1 - 10 MV > 10 MV

Electron radiation: 1 < E 0 < 5 MeV5 < EP’ < 10 MeV

10 < EP’ < 20 MeV20 < EP’„ < 50 MeV

- P , 0

100 10 X 10; 10 0

510

,100

R100100

ororОГ

i b)b),b)

1 0 0 1 0 X 1 0 ; 1 0 Ú1 0 0 1 0 X 1 0 ; 1 0 0

1 0 0 1 2 X 1 2 ; 1 2 $1 0 0 1 2 X 1 2 ; 1 2 0

1 0 0 2 0 X 2 0 ; 2 0 0

1 0 0 2 0 X 2 0 ; 2 0 0

a) E . is the most probable energy of the electrons at the phantom sur-p, иface, is the depth of dose maximum.

b) The greater depth is to be chosen.

16 HOHLFELD

f o r s u c h q u a n t i t i e s a s t e m p e r a t u r e , a i r p r e s s u r e an d h u m i d i t y a r e t h e v a l u e s 20° C , 1013 hP a a n d 50% r e l a t i v e h u m i d i t y , r e s p e c t i v e l y .

The c a l i b r a t i o n f a c t o r i s s t a t e d f o r c o m p l e t e s a t u r a t i o n . The d i r e c t i o n o f t h e i n c i d e n t r a d i a t i o n beam i n r e l a t i o n t o t h e i o n i z a t i o n ch am b e r h a s t o be i n d i c a t e d by t h e m a n u f a c t u r e r i f t h e r e s p o n s e o f t h e i o n i z a t i o n ch am be r d e p e n d s on i t . As p h an to m m a t e r i a l o n l y w a t e r i s p r o v i d e d f o r by t h e s t a n d a r d . I f f o r c o n v e n i e n c e t h e c a l i b r a t i o n p r o c e d u r e i s c a r r i e d o u t i n a p l a s t i c ph a n to m , a ny p o s s i b l e d e v i a t i o n i n t h e c a l i b r a t i o n f a c t o r o f t h e i o n i z a t i o n ch a m b e r t y p e h a s t o be shown by c o m p a r i s o n w i t h a c a l i b r a t i o n c a r r i e d o u t i n a w a t e r p h a n to m . T h i s e f f e c t was s t u d i e d e x p e r i m e n t a l l y f o r t h e t y p e s o f i o n i z a t i o n c h a m b e r s commonly e m p lo ye d i n t h e F e d e r a l R e p u b l i c o f Germany a n d c o r r e c t i o n f a c t o r s r e f e r r i n g t o t h i s e f f e c t w e re e v a l u a t e d [7] . I f , i n t h e c a s e o f n o n - w a t e r t i g h t i o n i z a t i o n c h a m b e r s , an y p r o t e c t i v e s h e e t s o r h o l d e r s a r e t o be u s e d , t h e w a l l t h i c k n e s s i n t h e r e g i o n o f t h e s e n s i t i v e vo lume o f t h e i o n i z a t i o n ch a m b e r i s l i m i t e d t o 1 mm. I f t h e c a l i b r a t i o n h a s b e e n p e r f o r m e d u s i n g t h e p r o t e c t i v e s h e e t s , t h e s e m u s t be a p p l i e d a l s o when m e a s u r e m e n t s a r e c a r r i e d o u t .

The c a l i b r a t i o n p r o c e d u r e and t h e e x p e r i m e n t a l d e t e r m i n a t i o n o f t h e e n e r g y d e p e n d e n c e o f t h e r e s p o n s e o f t h e i o n i z a t i o n ch a m b e r a r e d e s c r i b e d i n t h e s t a n d a r d . I t i s r e commended t h a t a t t e n t i o n be p a i d t o t h e more d e t a i l e d g u i d a n c e o f t h e P T B - P r U f r e g e l n [8] w h i c h a r e t o be a p p l i e d i n t y p e - t e s t i n g f o r a p p r o v a l f o r v e r i f i c a t i o n a nd f o r t h e v e r i f i c a t i o n m e a s u r e m e n t i t s e l f .

4. DETERMINATION OF THE WATER ABSORBED DOSE IN PHOTON AND ELECTRON BEAMS

The e f f e c t o f i n f l u e n c e q u a n t i t i e s u n d e r m e a s u r i n g c o n d i t i o n s d e v i a t i n g f ro m t h e c a l i b r a t i o n c o n d i t i o n s i s t a k e n i n t o a c c o u n t by t h r e e d i f f e r e n t k i n d s o f c o r r e c t i o n s : c o r r e c t i o n f a c t o r s , a d d i t i v e c o r r e c t i o n s and e f f e c t i v e p o i n t o f m e a s u r e m e n t . The a d d i t i v ec o r r e c t i o n s a r e n e e d e d , f o r e x a m p l e , f o r l e a k a g e c u r r e n t s ; i n g e n e r a l , t h e y p l a y a m i n o r r o l e . A l l c o r r e c t i o n f a c t o r s t a k e t h e v a l u e 1 . 0 0 0 a t t h e c a l i b r a t i o n c o n d i t i o n s . The p r o d u c t o f t h e m o s t i m p o r t a n t c o r r e c t i o n f a c t o r s f o r p h o t o n r a d i a t i o n and e l e c t r o nr a d i a t i o n , r e s p e c t i v e l y , h a s t h e f o l l o w i n g fo r m s

f o r p h o t o n s : к = k n • к * к • к • k_ • k_ * кQ <j s p T F z

f o r e l e c t r o n s : к = к * к • к • к * k m E ç s p T

w h e r e t h e к . r e l a t e t o t h e f o l l o w i n g i n f l u e n c e q u a n t i t i e s

q u a l i t y o f t h e p h o t o n r a d i a t i o n a t t h e p o i n t o f i n t e r e s t i n t h e w a t e r ph an to me n e r g y o f t h e e l e c t r o n s a t t h e p o i n t o f i n t e r e s t i n t h e w a t e r phan tom a i r d e n s i t y i n c o m p l e t e s a t u r a t i o n p o l a r i t y o f t h e ch am be r v o l t a g e

IAEA-SM-298/31 17

к ^ - t e m p e r a t u r e e f f e c tk_ - f i e l d s i z epk^ - d e p t h i n t h e pha n to m

I n t h e f o l l o w i n g , o n l y t h o s e c o r r e c t i o n f a c t o r s a r e c o n s i d e r e d i n more d e t a i l t h a t a p p l y o n l y t o t h e f o r m a l i s m o f t h e DIN s t a n d a r d o r whose e v a l u a t i o n d i f f e r s f r o m t h a t i n o t h e r p r o t o c o l s , c o d e s o r r e c o m m e n d a t i o n s . 1

4.1 Evaluation of the polarity correction factorThe c a l i b r a t i o n f a c t o r o f a n ' i o n i z a t i o n ch a m b e r r e l a t e s t o a

g i v e n p o l a r i t y o f t h e chambe r - v o l t a g e a n d i n c o r p o r a t e s t h e i n f l u e n c e o f t h i s e f f e c t . The same h o l d s f o r t h e c o r r e c t i o n f a c t o r s к a n d к i f e x p e r i m e n t a l l y d e t e r m i n e d f o r an i n d i v i d u a l

у bi o n i z a t i o n c h a m b e r .

I n t h e c a s e t h a t o n l y t y p e - s p e c i f i c o r c a l c u l a t e d к and кQ и

v a l u e s a r e a v a i l a b l e , t h e d e v i a t i o n o f t h e p o l a r i t y e f f e c t u n d e r m e a s u r i n g c o n d i t i o n s f ro m t h a t u n d e r r e f e r e n c e c o n d i t i o n s c a n be a l l o w e d f o r by t h e c o r r e c t i o n f a c t o r , k ^ . The f o l l o w i n g r e l a t i o n

s h i p i s a p p r o x i m a t e l y v a l i d f o r k^ i f t h e i o n i z a t i o n c u r r e n t i s

m e a s u r e d a t b o t h p o l a r i t i e s o f t h e ch a m b e r v o l t a g e :

k p = [ (M1 + M2 )/Ml ] 1 [ ( M1 + M2 )/Ml ]

i s t h e i n d i c a t e d v a l u e a t t h e u s u a l p o l a r i t y , M„ i s t h e i n d i c a t e d v a l u e a t t h e o p p o s i t e p o l a r i t y . The i n d e x Co r e l a t e s t h ed e n o m i n a t o r t o t h e c a l i b r a t i o n c o n d i t i o n s a t C o - 60 gamma r a d i a tion.

4.2 Displacement effectWith t h i m b l e t y p e i o n i z a t i o n c h a m b e r s t h e r e f e r e n c e p o i n t i s

s i t u a t e d a t t h e c e n t r e o f t h e ch am be r vo lu me on t h e ch a m b e r a x i s . Wi th p l a n e - p a r a l l e l i o n i z a t i o n c h a m b e r s t h e r e f e r e n c e p o i n t i s c h o s e n a s t h e c e n t r e o f t h e f r o n t s u r f a c e o f t h e i o n i z a t i o n vo lum e . By c h o o s i n g t h i s f o r t h e l a t t e r , t h e p e r t u r b a t i o n e f f e c t i s v e r y s m a l l i f a n a d e q u a t e g u a r d r i n g i s u s e d . F o r t h i m b l e t y p e i o n i z a t i o n c h a m b e r s t h e d i s p l a c e m e n t e f f e c t i s t a k e n i n t o a c c o u n t by t h r e e d i f f e r e n t s t e p s :

( 1 ) The d i s p l a c e m e n t e f f e c t f o r Co - 60 gamma r a d i a t i o n i n t h e e x p o n e n t i a l p a r t o f t h e d e p t h d o s e c u r v e i s a l r e a d y c o n t a i n e d i n t h e c a l i b r a t i o n f a c t o r a f t e r c a l i b r a t i o n w i t h t h i s r a d i a t i o n q u a l i t y i n a w a t e r ph an to m a t a d e p t h o f 5 cm.

( 2 ) Unde r t h e r e f e r e n c e c o n d i t i o n s , a c c o r d i n g t o T a b l e I ( f o r p h o t o n r a d i a t i o n t h e r e f e r e n c e d e p t h o f 5 cm i s s i t u a t e d i n

18 HOHLFELD

TABLE II. VALUES OF THE CORRECTION FACTOR, к , OF COMMERCIALLY AVAILABLE IONIZATION0 \

CHAMBERS FOR X-RAYS UP TO 280 kV GENERATING POTENTIAL0 '

Radiation Correction factor, к , V

of ionization chamber type

quaii ty

PTW23331 PTW23332 PTW233641 Farmer2571 NPL2561 Capin.PR06

T 100 1.025 1.069 1.012 1.003

T 120 1.04 - - 1.049 1.008 -

T 140 1.008 1.045 1.025 1.048 1.005 0.994

T 150 1.000 - - 1.035 1.001 0.991

T 200 0.998 1.002 0.999 1.025 1.001 0.994

T 250 0.998 - - 1.018 1.001 -

T 280 0.996 0.996 0.994 1.014 1.001 1.001

a) Radiation qualities according to the specification in [8] . The к values were

measured at the PTB and are mean values of several specimens. The spread of the

individual к values is comparable with the variation of the к values with the

radiation quality.

TABLE III. CALCULATED VALUES OF THE CORRECTION FACTOR, к , FOR HIGH ENERGY PHOTON

RADIATIONa ) 5

Radiation

quality, 0

Referencedepth

(cm)

Correction factor, k^, chamber type

of the

PTW23332 PTW233641 PTW23331 NE2561 NL’2571

Co-60 5 1.000 1.000 1.000 1.000 1.000

0.59 5 0.997 0.997 0.997 0.998 0.998

0.62 5 0.995 0.995 0.995 0.996 0.996

0.65 5 0.991 0.991 0.991 0.994 0.993

0.68 5 0.987 0.987 0.987 0.991 0.981

0.70 10 0.985 0.985 0.985 0.989 0.9880.72 10 0.981 0.981 0.981 0.985 0.984

0.74 10 0.976 0.976 0.976 0.981 0.9800.76 10 0.971 0.971 0.971 0.976 0.975

0.78 10 0.963 0.963 0.963 0.969 0.967

a) The radiation quality is expressed as radiation quality index Q = M2o^M 10 exceP t for the reference radiation quality Co-60 gamma radiation.

IAEA-SM-298/31 19

t h e s l o p e o f t h e d e p t h d o s e c u r v e , f o r e l e c t r o n s t h e r e f e r e n c e d e p t h i s t h e maximum R-^q q ) ■ t h e d i s p l a c e m e n t e f f e c t i s

a l l o w e d f o r i n t h e c o r r e c t i o n f a c t o r s k.. ( z = 5 cm) an d

k E (R100>*

(3 ) When t h e d e p t h s o r d e p t h r a n g e s d e v i a t e f r o m t h e a b o v e ment i o n e d , t h e p e r t u r b a t i o n e f f e c t i s c o r r e c t e d by a s h i f t o f t h e m e a s u r i n g p o i n t .

4.3 Absorbed dose determination in photon radiation beamsThe e n e r g y d e p e n d e n c e o f t h e r e s p o n s e o f i o n i z a t i o n c h a m b e r s i s

i n f l u e n c e d m a i n l y by

( 1 ) t h e p h o t o n i n t e r a c t i o n c o e f f i c i e n t s a n d e l e c t r o n s t o p p i n g p ow er s o f t h e i o n i z a t i o n ch a m b e r w a l l , c e n t r a l e l e c t r o d e , d e t e c t o r m a t e r i a l a i r and p ha n to m m a t e r i a l w a t e r ,

( 2 ) t h e p e r t u r b a t i o n o f t h e p h o t o n r a d i a t i o n f i e l d by t h e i o n i z a t i o n ch a m b e r w a l l , c e n t r a l e l e c t r o d e and s t e m ,

(3 ) t h e p e r t u r b a t i o n o f t h e p h o t o n r a d i a t i o n f i e l d by t h e c a v i t y o f t h e i o n i z a t i o n ch a m b e r .

The e n e r g y d e p e n d e n c e i s c o r r e c t e d f o r by t h e f a c t o r к .

Chan ges i n t h e s p e c t r a l f l u e n c e d i s t r i b u t i o n a n d t h e d i r e c t i o n a l d i s t r i b u t i o n o f t h e p h o t o n f i e l d i n t h e p h a n t o m , p r e d o m i n a n t l y i n t h e p h o t o n e n e r g y r a n g e up t o a b o u t 30 0 keV, l e a d t o a d e p e n d e n c e o f t h e r e s p o n s e on t h e p a r a m e t e r s f i e l d s i z e a nd d e p t h i n t h e ph an to m .

4.3.1 Correction factors for X-rays with generating potential up to 1 MV and gamma radiation

I n t h i s p h o t o n e n e r g y r a n g e a c a l c u l a t i o n o f t h e c o r r e c t i o n f a c t o r s p r o v e d i m p o s s i b l e owi ng t o a l a c k o f a c k n o w l e d g e d t h e o r e t i c a l m od e l s t a k i n g i n t o a c c o u n t t h e ab o v e m e n t i o n e d i n f l u e n c e s .T h e r e f o r e , t h e c o r r e c t i o n f a c t o r s к (Q f o r Q u a l i t y ) a r e d e t e r

gímined e x p e r i m e n t a l l y by c o m p a r i n g t h e i o n i z a t i o n ch a m b e r w i t h t h e s t a n d a r d a t t h e PTB i n t h e c o u r s e o f a t y p e - t e s t m a n d a t o r y f o r t h e r a p y d o s i m e t e r s i n t h e F e d e r a l R e p u b l i c o f Ge rmany . R e s u l t s a r e g i v e n i n T a b l e I I . The c o r r e c t i o n f a c t o r s k^ f o r f i e l d s i z e and к f o r d e p t h i n t h e ph an to m a r e e v a l u a t e d c o r r e s p o n d i n g l y [ 9 ] .

4.3.2 Correction factors for high-energy photon radiationV a l u e s o f к f o r h i g h - e n e r g y p h o t o n r a d i a t i o n s h o u l d a l s o be

Qd e r i v e d e x p e r i m e n t a l l y . F i r s t r e s u l t s a r e b e i n g e v a l u a t e d . Howe v e r , a s t h e s e a r e n o t y e t c o m p l e t e , t h e k n v a l u e s h a v e b e e n c a l c u l a t e d . From t h e f o r m a l i s m o f t h e IAEA I n t e r n a t i o n a l Code [ l o ]and t h a t o f t h e DIN s t a n d a r d t h e r e l a t i o n

20 HOHLFELD

c a n e a s i l y be d e r i v e d u s i n g t h e e q u a t i o n s f o r t h e a b s o r b e d d o s e t o w a t e r f o r C o - 60 gamma r a d i a t i o n a n d t h e r a d i a t i o n q u a l i t y , Q. The r a d i a t i o n q u a l i t y i s e x p r e s s e d by t h e q u a l i t y i n d e x , Q, d e f i n e d a s t h e r a t i o o f t h e i n d i c a t e d v a l u e s , ^ 20 ’ ^ ° m

w a t e r pha n to m a n d , M . a t 10 cm d e p t h , t h e s o u r c e - c h a m b e r - d i s t a n -

c e b e i n g c o n s t a n t a t 100 cm and t h e f i e l d - s i z e a t 10 crn x 10 cm 20(TPRi q ) . The v a l u e s s h o u l d be t a k e n f r o m t h e manu a l s u p p l i e d by

t h e m a n u f a c t u r e r . I n T a b l e I I I t h e к v a l u e s c a l c u l a t e d a c c o r d i n gV

t o t h e a b ov e r e l a t i o n a r e shown f o r i o n i z a t i o n c h a m b e r s commonly u s e d i n t h e F e d e r a l R e p u b l i c o f Germany and w h ic h ha v e p a s s e d a t y p e - t e s t a t t h e PTB. Where k^ v a l u e s a r e n o t a v a i l a b l e , t h e

me t ho d b a s e d on t h e IAEA f o r m a l i s m i s p r e s e n t e d i n an a p p e n d i x t o t h e s t a n d a r d . The d i f f e r e n c e i n t h e t r e a t m e n t o f t h e e f f e c t i v e p o i n t o f m e a s u r e m e n t i s t a k e n i n t o a c c o u n t .

4.3.3 Correction factor for high-energy electron radiationThe c o r r e s p o n d i n g c o r r e c t i o n f a c t o r , к , f o r e l e c t r o n r a d i a t i o n

- hi s o b t a i n e d s i m i l a r l y . Where e x p e r i m e n t a l k^ v a l u e s a r e n o t s t a t e d by t h e m a n u f a c t u r e r i n t h e i n s t r u c t i o n s f o r u s e , k^ m u s t be c a l c u l a t e d . F o r t h i s p u r p o s e k„ i s s p l i t i n t o two f a c t o r s , k* an d k ” .b h. hк d e p e n d s o n l y on t h e v a r i a t i o n o f t h e s t o p p i n g pow er r a t i o ,

w i t h t h e s p e c t r a l d i s t r i b u t i o n o f t h e e l e c t r o n e n e r g y a t t h e

p o i n t o f i n t e r e s t a n d i s g i v e n by t h e r e l a t i o n

k E = s " (E , z ) / s (Co) w, a o ’ w , a

The s t a n d a r d s u p p l i e s v a l u e s o f s û (E , z ) i n a t a b l e d e p e n d i n g onw, a оt h e mean i n i t i a l e n e r g y , E , o f t h e e l e c t r o n s a t t h e ph an to m s u r f a c e and d e p t h , z , i n t h e ph a n to m . E i s c a l c u l a t e d f r om t h e h a l f - v a l u e d e p t h , t h e m e a s u r e d i o n d o s e c u r v e . A s c a l i n g

o f t h e d e p t h , z , u s i n g t h e c a l c u l a t e d a nd t h e m e a s u r e d p r a c t i c a l r a n g e i s r ecommended a s i n t h e IAEA I n t e r n a t i o n a l Code o f P r a c t i c e [ l 0 ] . The s e c o n d f a c t o r , k ^ , d e p e n d i n g on t h e t y p e o f i o n i z a t i o n ch a m b e r h a s r e g a r d t o t h e d i m e n s i o n s and t h e m a t e r i a l o f t h e i o n i z a t i o n c h a m b e r , ki? i s d e f i n e d by t h e e q u a t i o n

h*

IAEA-SM-298/31 21

w h er e p c o r r e c t s f o r t h e d i f f e r e n c e s i n s c a t t e r i n g o f p r i m a r y e l e c t r o n s i n t h e w a t e r and t h e a i r c a v i t y ¡JLÍ] and c a n be t a k e n i n goo d a p p r o x i m a t i o n f rom t h e f i t - f o r m u l a [12]

p (E , r ) = 1 - b • r - e x p ( - c E ) u z z

w i t h b = 0 . 2 1 5 5 cm ^ and с = 0 . 1 2 2 4 MeV ^ .

р ^ (С о ) h a s t h e same m ea n i n g a s i n t h e IAEA I n t e r n a t i o n a l Code

o f P r a c t i c e and к (Co) i s n e e d e d f o r t h e d i f f e r e n c e s i n t h e e f f e c - rt i v e p o i n t o f m e a s u r e m e n t w i t h e l e c t r o n s an d Co- 60 gamma r a d i a t i o n and c a n be e a s i l y c a l c u l a t e d by t h e r e l a t i o n

к (Co) = 1 + 0 . 0 3 r r

w he re r i s t h e i n n e r i o n i z a t i o n c h a m b e r r a d i u s i n cm.

5. ABSORBED DOSE DETERMINATION USING PLANE-PARALLEL IONIZATION CHAMBERS CALIBRATED IN ELECTRON BEAMS

C a l i b r a t i o n o f t h e i o n i z a t i o n ch a m b e r i n a h i g h - e n e r g y e l e c t r o n beam e x h i b i t s a d v a n t a g e s w i t h r e s p e c t t o t h e e n e r g y d e p e n d e n c e o f kg and к i n t h e h i g h - e n e r g y r a n g e o f t h e p h o t o n a n d e l e c t r o n beams and a l s o w i t h r e s p e c t t o i n f l u e n c e s o f t h e i n d i v i d u a l geomet r i c a l p r o p e r t i e s o f t h e i o n i z a t i o n c h a m b e r [13] . T h i s p r o c e d u r e , a l s o d e s c r i b e d i n t h e d r a f t s t a n d a r d , h a s b e e n d e v e l o p e d by Markus p . 4 ,1 5 3 a nd h a s b e e n w i d e l y a d o p t e d i n t h e F e d e r a l R e p u b l i c o f Ge rmany . A g r a p h i t e d o u b l e e x t r a p o l a t i o n ch a m b e r s e r v e s a s a p r i m a r y s t a n d a r d t o m e a s u r e t h e a i r a b s o r b e d d o s e u n d e r B r a g g - G r a y c o n d i t i o n s i n a g r a p h i t e ph an to m . A b s o r b e d d o s e t o w a t e r i s a r r i v e d a t by means o f t h e s t o p p i n g p ow er r a t i o , s (E ) . T h i s

W t cl Is

s t o p p i n g po w e r r a t i o , e v a l u a t e d by c o m p a r i s o n o f t h e i o n i z a t i o n m e a s u r e m e n t and f e r r o u s s u l p h a t e d o s i m e t r y , d e p e n d s o n l y on t h e mean r e m a i n i n g e n e r g y o f t h e e l e c t r o n s a t t h e p o i n t o f m e a s u r e m e n t . I t c a n e a s i l y be d e t e r m i n e d by e l e c t r o n r a n g e m e a s u r e m e n t s [ l 6 , 1 7 3 . Howeve r , c o m p r e h e n s i v e i n t e r c o m p a r i s o n s o f t h e two met h o d s d e c r i b e d h a v e n o t y e t come t o h a n d .

REFERENCES[1] DIN 6 8 00 , T e i l 2 . , D o s i s m e ß v e r f a h r e n i n d e r r a d i o l o g i s c h e n

T e c h n i k - I o n i s a t i o n s d o s i m e t r i e , ß e u t h V e r l a g GmbH, B e r l i n an d C o lo g n e ( 1 9 8 0 ) .

[2] FEIST, H . , D e t e r m i n a t i o n o f a b s o r b e d d o s e t o w a t e r f o r h i g h e n e r g y p h o t o n s an d e l e c t r o n s by t o t a l a b s o r p t i o n o f e l e c t r o n s i n f e r r o u s s u l p h a t e s o l u t i o n , P h y s . Med. B i o l . 27 (1 9 82 ) 1 435 .

[3] SCHNEIDER, U . , D o s i s m e s s u n g e n f ü r P h o t o n e n s t r a h l u n g m i t E n e r g i e n b i s 1 . 3 MeV, P h y s i k a l i s c h - T e c h n i s c h e B u n d e s a n s t a l t , B r a u n s c h w e i g , P T B - B e r i c h t D o s - 6 ( 1 9 8 1 ) .

22 HOHLFELD

[4] HOHLFELD, K . , KRAMER, H. M. , ROOS, M. , SELBACH, H. J . , Two e x p e r i m e n t a l m e t h o d s f o r d e t e r m i n i n g t h e h e a t d e f e c t o f w a t e r , IAEA-SM-298/29 , t h e s e P r o c e e d i n g s .

[5] ENGELKE, B . A . , OETZMANN, W., D ie E i c h p f l i c h t f ü r T h e r a p i e d o s i m e t e r , S t r a h l e n t h e r a p i e 163 (1 9 8 7 ) 94 .

[6] A n f o r d e r u n g e n d e r P h y s i k a l i s c h - T e c h n i s c h e n B u n d e s a n s t a l t an T h e r a p i e d o s i m e t e r m i t I o n i s a t i o n s k a m m e r n f ü r d i e Z u l a s s u n g z u r E i c h u n g vom 1 . S e p t e m b e r 1 9 82 , P T B - M i t t . 93 (1 9 8 2 ) 17 6 .

[7] ENGELKE, B . A . , OETZMANN, W., D ie K a l i b r i e r u n g und E i c h u n g d e r T h e r a p i e d o s i m e t e r i n n i c h t - w a s s e r ä q u i v a l e n t e n Umgebungsm a t e r i a l i e n , P T B - M i t t . 97 ( 1 9 8 7 ) , i n p r e s s .

Q3j P T B - P r ü f r e g e l n , Band 16 , T h e r a p i e d o s i m e t e r m i t I o n i s a t i o n s kammern f ü r P h o t o n e n s t r a h l u n g m i t E n e r g i e n u n t e r h a l b von 3 MeV, P h y s i k a l i s c h - T e c h n i s c h e B u n d e s a n s t a l t , B r a u n s c h w e i g and B e r l i n ( 1 9 8 4 ) .

£9] SCHNEIDER, U . , GROSSWENDT, B . , " D o s i s m e s s u n g e n im Ph an tom b e i k o n v e n t i o n e l l e r R ö n t g e n s t r a h l u n g (70 kV b i s 300 kV) m i t I o n i s a t i o n s k a m m e r n u n t e r B e d i n g u n g e n , d i e von den B e z u g s b e d i n g u n g e n a b w e i c h e n " M e d i z i n i s c h e P h y s i k 86 ( v . KLITZING, L . , E d . ) , D e u t s c h e G e s e l l s c h a f t f ü r M e d i z i n i s c h e P h y s i k , Lübeck ( 1 9 8 6 ) .

[ lO] A b s o rb e d Dose D e t e r m i n a t i o n i n P h o t o n and E l e c t r o n Beams - An I n t e r n a t i o n a l Code o f P r a c t i c e , IAEA, V i e n n a , i n p r e s s .

[ l l j ICRU ( I n t e r n a t i o n a l Commis s ion on R a d i a t i o n U n i t s a n d Measur e m e n t s ) , R a d i a t i o n D o s i m e t r y : E l e c t r o n Beams w i t h E n e r g i e sBe tw een 1 and 50 MeV, ICRU P u b l i c a t i o n s , B e t h e s d a , ICRU R e p o r t 35 ( 1 9 8 4 ) .

[ 12 ] HOHLFELD, K . , ROOS, M. , " D o s i s m e ß v e r f a h r e n m i t z u r A n z e i g e d e r W a s s e r - E n e r g i e d o s i s k a l i b r i e r t e n I o n i s a t i o n s k a m m e r n " , M e d i z i n i s c h e P h y s i k 86 ( v . KLITZING, L . , E d . ) , D e u t s c h eG e s e l l s c h a f t f ü r M e d i z i n i s c h e P h y s i k , Lübeck ( 1 9 8 6 ) .

£133 ROOS, M. , HOHLFELD, K . , SCHNEIDER, M. , TRIER, J . O . , V a r i a t i o n o f r e s p o n s e o f i o n i z a t i o n c h a m b e r s a t h i g h e n e r g i e s , ( P r o c . Wor ld C o n g r . Med. P h y s . and B iom ed . E n g n g . ) S . 2 7 . 1 1 , MPBE 1982 e . V. Hamburg.

[ l 4 j MARKUS, В . , E i n e p o l a r s i e r u n g s e f f e k t - f r e i e G r a p h i t - D o p p e l - e x t r a p o l a t i o n s k a m m e r z u r A b s o l u t d o s i m e t r i e s c h n e l l e r E l e k t r o n e n , S t r a h l e n t h e r a p i e 150 (1 9 7 5 ) 3 07 .

[15] MARKUS, B . , E i n e P a r a l l e l p l a t t e n - K l e i n k a m m e r z u r D o s i m e t r i e s c h n e l l e r E l e k t r o n e n und i h r e Anwendung, S t r a h l e n t h e r a p i e 152 (1 9 76 ) 517 .

[l6[] MARKUS, B . , KASTEN, G . , Zum K o n z e p t d e s m i t t l e r e n B r e m s v e r mögens und d e r m i t t l e r e n E l e k t r o n e n e n e r g i e i n d e r E l e k t r o n e n d o s i m e t r i e , S t r a h l e n t h e r a p i e 159 (1 9 8 3 ) 567 .

[ 17З MARKUS, B . , KASTEN, G . , "Zum K o n z e p t d e s m i t t l e r e n Brems ve rm ö g e n s i n d e r E l e k t r o n e n d o s i m e t r i e " , M e d i z i n i s c h e P h y s i k 84 (SCHMIDT, T h . , E d . ) , S t ä d t i s c h e s K l i n i k u m N ü r n b e r g ( 1 9 8 4 ) .

IAEA-SM-298/38

OUTLINE OF THE ITALIAN PROTOCOL FOR PHOTON AND ELECTRON DOSIMETRY IN RADIOTHERAPY

R.F. LAITANOCommittee for the Standardization

of Dosimetry in Radiotherapy,Italian Association of Biomedical Physicists (AIFB),CRE Casaccia,ENEA,Rome,Italy

Abstract

OUTLINE OF THE ITALIAN PROTOCOL FOR PHOTON A ND ELECTRON DOSIMETRY IN RADIOTHERAPY.

The paper is a condensed version o f the Italian text o f the Italian Association of Biomedical Physicists (AIFB) Protocol for dosimetry o f photon and electron beams with maximum energies ranging from 1 to 40 MeV. One o f the main features that characterizes this Protocol is the adoption o f a single type o f ionization chamber for dosimetry, at reference conditions, o f photon beams and of electrons with Eq > 5 M eV. Moreover, the set o f physical parameters adopted is taken from the most recent and consistent data so far available. The reference ionization chamber adopted in the Protocol is a graphite homogeneous chamber designed at ENEA. For electron beams with E0 < 5 MeV the use o f any good quality plane-parallel chamber is recommended.

Introduction

About two years ago, the Italian Association of Biomedical

Physicists (AIFB) designated a Committee for the standardization of dosimetry

in radiotherapy with the task of preparing a general dosimetry protocol

covering the following subjects: (1) basic dosimetry, (2) clinical dosimetry,

(3) computerized dosimetry, (4) quality assurance.

Four sub-committees were appointed to develop a protocol on each

of these subjects. The first part of this programme was recently completed

with the preparation of the protocol for basic dosimetry that is confined to

the dosimetric procedures under reference conditions.

23

24 LAIT ANO

Ш Aluminum

Chamber dimensionsInternal diameter 4 mmInternal length 20 mmWall thickness 0.5 mmCollecting e lectrode diameter 0.9 mmCollecting e lectrode length 19 mmBuildup thickness 25 mmWaterproofing sheath thickness 0.5 mmCollecting volume Q24 cm3

Chamber materialsATJ Graphite, p = 1.79g/cm3lwall,collecting electrode,buildup cap) Rexolite® ( insulator)Aluminum (stem)PMMA (w aterproofing sheath)

Stem size Diameter Length Thickness

Maximum polarizing voltageLeakage curren t (typ ica l)

5 mm 25 cm 0.5 mm

± 200 V 3x1015 A

FIG. I . Characteristics o f the ENEA cylindrical chamber recommended in the Italian Protocol o f Dosimetry in Radiotherapy.

IAEA-SM-298/38 25

This paper is a condensed version of the Italian text of the AIFB

Protocol. It adopts a set of updated and consistent physical parameters for

the dosimetry of photon and electron beams with maximum energies between 1 and

40 MeV.

The AIFB considered it convenient to adopt in the Protocol a

single type of reference chamber (except for electrons with 1 * 5 MeV). The

recommendations of the Protocol can thus be followed in a much simpler way,

reducing also the sources of error in current practice. In addition, any

future change that the AIFB would deem necessary in the physical parameters

related to the chamber can easily be made known to all the chamber users.

The Italian text of the protocol contains a section on uncertainty

evaluation and 2 Appendices dealing with the generalities on the formalism and

the recommended procedures for Fricke dosimetry. Owing to lack of space, these

parts are not reported in the present paper.

Section I. Instrumentation

(a) Reference chamber

The protocol recommends for each radiotherapy centre a cylindrical

ionization chamber specifically designed for this purpose at ENEA |1|; the

scheme is shown in Fig.l. This chamber will be used as a local standard for

dosimetry at the user reference conditions. Absorbed dose determination by the

reference chamber can be performed with photon beams having maximum energies

above 1 MeV and with electron beams having mean energies, E0 , greater than 5

MeV.

The reference chamber can easily be adapted to the majority of

good quality commercial electrometers.

The reference chamber is calibrated at the ENEA Primary Standard

Dosimetry Laboratory (PSDL) which directly furnishes a calibration factor,

(see Section III), in terms of absorbed dose to air from an exposure or air

kerma calibration at the 60-Co gamma ray quality.

(b) Ionization chamber for electrons with £„==■ 5 MeV

26 LAIT ANO

Radiation treatment by electron beams with E ^ 5 MeV is not frequently

performed. Wherever a dosimetry of such electron beams is required, a plane-

parallel coin shaped chamber is recommended. This chamber should be of the

guarded type with a thin front window and an electrode spacing not greater

than 2 mm. Good quality chambers with those features are commercially

available.

Calibration of the plane-parallel chambers is performed at the ENEA

PSDL or, whenever possible, in the radiotherapy centre by using the reference

cylindrical chamber as a standard and according to the procedure referred to

in Section III.2.

(c) Complementary dosimeters and field instruments

Fricke (ferrous-sulphate) dosimeters and calorimeters, where

available, should be used as independent methods to compare the results

obtained with the ionization chamber. For TLD, semi-conductor detectors and

other dosimeters used for various types of measurements (other than absorbed

dose) it is only necessary to periodically check their response stability.

Section II. Determination of the radiation quality

(a) Electron beams

The most relevant electron beam parameters which are specifically

needed for the application of this Protocol are the mean energy at the phantom

surface, E0, the mean energy, Ez at the depth z in phantom, the half-value

range, RgQ and the practical range, R^.

The value of E0 is determined by the equation

(1)

IAEA-SM-298/38 27

The constant С = 2.33 should be used for range and energy

determinations obtained from depth dose curves |2,3|.

However, the determination of and then of E„ from depth

ionization curves is more direct and, to apply Eq.(l) also to depth ionization

curves, the value С = 2.38 should be used |4|.

The range R can be determined by measuring the depth ionization

distributions. Differences between the R values so obtained and that obtainedP

by depth dose distributions are considered negligible for practical

dosimetry|5|. The measurement of range parameters (Rgp. R ) requires use of

the effective point of measurement (see Section III) for the cylindrical

chamber or to use a plane-parallel chamber below 5 MeV.

The depth ionization curves for the determination of the parameters in

Eq.(l) should be obtained from measurements at a fixed source-chamber distance

(SCO). This procedure requires particular care |6| and, where this method is

not applied, a fixed source-surface distance (SSD) can be used provided that

the beam divergence corrections are applied, multiplying the ionization values

2 2by (SSD + z) /(SSD) , where z is the depth at the effective point of

measurement of the chamber in the phantom.

The mean energy, E^, at the depth z can be determined in a number of

ways which differ in their degree of approximation |7|.

The expression

E2 = I „ ( 1 - z / R ) ( 2 )

can be used for approximate evaluations of E^ |8| and taking into account that

this approximation gets worse at high energies and large depths. Wherever more

accurate determinations of E^ are required it is recommended that reference be

made to the Monte Carlo calculations of Ë 19 1.z

Range measurements should be always made with large field sizes of at

least 12 cnrx 12 cm for E0-15 MeV and of at least 20 cm x 20 cm for E0> 15 MeV

|10|.

(b) Photon beams

The quantity that this protocol recommends for specifying

20the MV X-ray quality is the ratio, TPR^, of the ionization measured at 20 cm

28 LAITANO

Table I. Factors, F^, that convert (through N ) the chamber reading

into absorbed dose to water, as a function of the photon beam quality

Beam quality

(TPRi q ) Fx

Co-60 1.1230.53 1.126

0.56 1.122

0.59 1.121

0.62 1.118

0.65 1.116

0.68 1.113

0.70 1.110

0.72 1.1060.74 1.101

0.76 1.096

0.78 1.088

0.80 1.057

0.82 1.069

depth to that measured at 10 cm, in a water phantom at a constant

source-detector distance and with 10 cm x 10 cm field size at the chamber

position.

The stopping power ratios used in the factors F^ (Section III and

Table I) refer to tissue-phantom ratios (TPRs) that are determined |11|

according to their definition of ratios between absorbed doses at two given

depths. When the ionization ratio, as recommended here, is considered instead? 0

of the dose ratio, an uncertainty of less than 1% on TPRj'g could be

introduced. This uncertainty, however, results in negligible changes when

transferred to stopping power ratios.

Section III. Determination of absorbéd dose to water

III.1. Photon beams with E > 1 MeV and electron beams with E > 5 MeVmax

(a) Generalities on the formalism

The expressions of the absorbed dose to water (w) at the reference

depth in the water phantom and with the reference chamber positioned at its

IAEA-SM-298/38 29

effective point of measurement are, for electrons of quality E (i.e. energy

E0) and photons of quality X, respectively

D (P . J = M N F (3)w eff D E

D (P ,,) = M N. Fv (4)w eff D X

where M is the chamber reading (at the user's beam) corrected to the standard

ambient conditions and for the ion recombination effect; is the absorbed

dose to air calibration factor of the reference chamber; F and F are theL Л

factors which convert (through N^) the chamber reading into absorbed dose to

water for electrons (E) and photons (X),respectively.

The calibration factor, N

gamma ray calibration quality as

The calibration factor, N^, is determined by the ENEA-PSDL at the 60-Co

ND = NK n-g) (L/Ç)* iM )l katt (5)

where the correction factor, , which includes the factor ß (i.e. the

quotient of absorbed dose by the collision fraction of kerma in the chamber

wall), accounts for photon attenuation and scattering in the chamber wall

(including the build-up cap); is the air kerma calibration factor; the

other factors have the usual, well known meaning (a and с stand for air and

graphite, respectively).

The conversion factors, F ,, F^ are given respectively by

Fx ■ <L/e )A x px 161

Fr “ ' C Ü ' i ,7)

The perturbation factor Pv is given byЛ

■*(L/e )a - < r e n /e >cw + (i- « ) ( l/е>1

Px - ----------------------------------------- (8)

( L /ç ) Z

30 LAIT ANO

For photons (Eqs.6,8), the mean restricted stopping powers are

taken from Andreo and Brahme |11| and Andreo, Nahum and Brahme J121 ; the

energy absorption coefficients are taken from Cunningham |13|. The values of

q ( , which represents the fraction of ionization due to the electrons

originated in the chamber wall (Eq.8), are calculated from the data of

Lempert, Nath and Schulz |14|.

The stopping powers for electrons (Eq.7) are taken from AAPM |15|.

The factors P^, that account for the electron fluence perturbation due to the

presence of the chamber in water, are based on the experimental determinations

by Johansson et al. |16|. The P^ values adopted in this protocol are based on

the determinations of those authors but, to express F^ as a function of E„ and

z, it was necessary to obtain P . as a function of E0 and z. This was made by

means of Eq.(2) in which the practical range in water, R , was obtained from

the equation |7|Г

R = -0.11 + 0.505 E - 0,0003 E 2 (9)p po po

where the most probable energy E was replaced by E0.

The value of the reference chamber calibration factor (Eq.5) is NQ

= 0.988 Nk , whith g = 3.2>10'3 |17|, (L/ç )® = 0.998,- = 1-001 |12|

and the factor к = 0.992, as calculated from the data of Nath and Schulz d 1 1

|18|. The factor has a typical value of about 11.6 cGy/nC with W/e =

33.97 J/C, for dry air |19|.

20The conversion factors F (as a function of TPR ) and F_ (as a

_ x l o tfunction of E„ and z) are reported in Tables I and 11 a, respectively.

- Chamber reading

The chamber reading should be corrected for ion recombination loss

(for both continuous and pulsed beams) according to the two-voltage method

1201 and for ambient conditions.

Leakage current and polarity effects should be also corrected if

greater than 0.5%.

IAEA-SM-298/38 31

The expressions of the absorbed dose to water (Eqs.3,4) are valid

only if the effective point of measurement, ^eff « displaced from the

chamber centre, P., towards the source by a distance z(P„)-z(P _,) = d . The ° 0 eff r

recommended values of d for the reference cylindrical chamber are:r

d = 0.5 r for electron beams r

d^ = 0.75 r for photon beams

where r= 2 mm is the chamber radius.

Strictly speaking, the effective point of measurement varies with

depth and, at the plateau region where the maximum dose occurs, it would

coincide with the chamber centre. The d^ values reported above are to be

intended as average values that are only used for convenience at all energies

of interest, at all depths beyond the maximum dose depth, d , and also atmax

d .max

For plane-parallel chambers the effective point of measurement is

taken at the inside surface of the chamber front face.

- Effective point of measurement

- Reference depth

The reference depth for photon beams should be on the descending

part of the depth dose curve. Accordingly, the recommended reference depths

(measured from the surface of the phantom to the reference point of the

chamber) for photons in a water phantom and with a field size of 10 cm x 10 cm

at the reference depths are:

20- 5 cm, for the beam qualities: 60-Co gamma ray and TPR < 0.70

20- 10 cm, for the beam quality: TPR > 0.70

For electron beams with E0 energies (MeV), the reference depths in

water, with a field size of 10 x 10 cm at the phantom surface, are given by:

Table lia. Factors, F^, that convert (through N^) the (cylindrical) chamber reading into

absorbed aose to water, as a function of the electron energies, E0(MeV) and depth z (cm) .

R (cm) is calculated according to Eq.(8)

E. 40 30 25 20 18 16 14 12 10 9 8 7 6 5

Rz P

19.6 14.8 12.3 9 .9 8 .9 7.9 6 .9 5.9 4 .9 4 .4 3.9 3 .4 2 .9 2 .4

0.1 0 .913 0.929 0.941 0.951 0.957 0.963 0.971 0 .978 0 .986 0.990 0.995 1.001 1.008 1.0170 .2 0.914 0.930 0.942 0.952 0 .958 0.964 0.971 0 .978 0 .986 0.991 0.996 1.002 1.009 1.0190 .3 0 .915 0.931 0.943 0 .953 0.959 0.965 0.971 0.979 0 .987 0.991 0.997 1 .030 1.011 1.0200 .4 0.916 0.932 0.944 0.954 0 .960 0.966 0.972 0 .980 0 .988 0.993 0.999 1.005 1.012 1.0230 .5 0 .917 0.933 0.945 0 .955 0.961 0.967 0 .974 0 .980 0 .989 0.993 1.000 1.006 1.015 1.0260 .6 0 .918 0 .934 0 .946 0.956 0 .962 0.968 0 .975 0.982 0 .990 0.995 1.001 1.008 1.018 1.0300 .8 0 .920 0.936 0 .948 0.957 0.964 0.969 0 .976 0.984 0.993 0 .998 1.005 1.013 1.023 1.0371.0 0.922 0 .938 0.950 0.959 0.965 0.972 0 .978 0 .986 0.996 1.001 1.008 1.018 1.030 1.0451.2 0.924 0 .940 0.951 0.961 0.967 0.973 0.981 0 .988 0.999 1.005 1.013 1.023 .1.036 1.0531 .4 0 .925 0 .942 0 .952 0.963 0 .970 0.976 0 .983 0.991 1.002 1.010 1.019 1.030 1.044 1 .0601.6 0.927 0.944 0.953 0.966 0.971 0.978 0.985 0.994 1.006 1.014 1.023 1.037 1.052 1 .0681 .8 0 .929 0.945 0.954 0.967 0.974 0.980 0 .988 0.997 1.010 1.019 1.029 1.044 1.059 1.0752 .0 0.930 0.947 0 .955 0.969 0 .975 0.983 0 .990 1.000 1.014 1.023 1.036 1.051 1.066 1.0822 .5 0 .934 0 .952 0 .960 0 .974 0.981 0 .988 0.997 1.008 1.026 1.038 1.054 1.067 1.0833 .0 0 .938 0.955 0.964 0 .979 0 .986 0.993 1.004 1.018 1.039 1.052 1.067 1.082 1.0903 .5 0.941 0.957 0.969 0.984 0.991 1.000 1.012 1.029 1.053 1.066 1.0794 .0 0 .944 0.960 0.973 0 .989 0.997 1.008 1.022 1.042 1.065 1.0784 .5 0 .948 0.964 0 .978 0 .994 1.003 1.015 1.032 1.055 1.0785 .0 0.951 0.968 0.981 0 .999 1.010 1.025 1.043 1.0685 .5 0 .954 0.972 0 .986 1.005 1.017 1.034 1.056 1.0786 .0 0 .958 0.977 0 .990 1.011 1.026 1.045 1.0687 .0 0 .962 0.984 1.001 1.027 1.044 1.0628 .0 0.967 0 .993 1.014 1.046 1.0619 .0 0.976 1.002 1.025 1.064 1.0761 0.0 0.983 1.012 1.039 1.07512.0 0.997 1.034 1.06514.0 1.013 1.06216.0 1.031 1.0661 8.0 1.0502 0 .0 1.059

LA

ITA

NO

IAEA-SM-298/38 33

Table lib. Factors, F ., that convert (through

chamber reading into absorbed dose to water, ài

electron energies E0 (MeV) and depth z (err

taken at d^^. (cm) is calculated according to Eq.

) the plane-parallel

a function of the

The z values shall be

(8 )

EoR

OEPTH P

1.0

0.4

2.0

0.9

3.0

1.4

4.0

1.9

5.0

2.4

0.0 1.116 1.097 1.078 1.059 1.0400.1 1.124 1.101 1.081 1.061 1.042

0.2 1.131 1.106 1.084 1.064 1.044

0.3 1.135 1.112 1.089 1.067 1.046

0.4 1.136 1.117 1.093 1.071 1.050

0.5 1.122 1.098 1.076 1.054

0.6 1.126 1.103 1.080 1.058

0.8 1.133 1.113 1.090 1.067

1.0 1.121 1.099 1.076

1.2 1.129 1.108 1.085

1.4 1.133 1.117 1.095

1.6 1.124 1.104

1.8 1.130 1.112

2.0 1.133 1.120

2.5 1.131

- dmax

for E„ < 5

- dmax

or 1 cm (1) for 5 4 E0 < 10

- dmax

or 2 cm (1) for 10 $ m| о 20

- dmax

or 3 cm (1) for 20 $ Eo 40

- Phantom

Water phantoms are recommended for use in this Protocol. Plastic

phantoms can be used for checks of constancy of the radiation beam parameters

20(e.g. in water TPR-|g )• Plastic phantoms can also be used for range

parameter measurements at electron energies below 5 MeV . In this case depths

in plastic, Zp.|, should be scaled to depths in water, *м»Ьу the expression

Pi<ro/p y i r o / p )

Pi

(1) The depth chosen shall be the largest.

34 LAIT ANO

where r0 is the continuous slowing down approximation range 17]. For electron

irradiation, a conductive material (e.g. A-l50) should be used for the plastic

phantom |21|. Alternatively, a plastic phantom should be composed of several

sheets with thicknesses ranging from 0.2 to 1 cm.

The standard size recommended for the water phantom (both for

photons and electrons) is a 30 cm cube.

III.2.Electron beams with energies E0é 5 MeV

This Protocol recommends the use of a plane-parallel chamber for

absorbed dose determination with electron beams of E„6 5 MeV.

The absorbed dose to water at the effective point of measurement is

given by

D (P ,,) = H N. F. (10)w eff D,p E

where the absorbed dose to air calibration factor, N„ , for the planeD,p Kparallel chamber is determined in an indirect way, i.e., according to the

procedure described in NACP |22|.

The values of F . are reported in Table II b and in this case they

coincide with the mass stopping power ratios, as the factor P^ (Eq.6) is

assumed to be equal to one for plane-parallel chambers.

The value of N^ p can be determined by the user, if the user's

experimental facilities allow that. Where this is not possible, the

plane-parallel chamber calibration is made at the ENEA PSDL.

References

(1) LAITANO R.F., GUERRA A.S., QUINI M., Physica Medica 3 2 (1987).

(2) BRAHME A., SVENSSON H., Med. Phys. 3 (1976) 95.

(3) BERGER M.J., SELTZER S.M., Natl. Bur.Stand. Internal Report No. 82-

2451 (1982).

IAEA-SM-298/38 35

(4) WU A., KALEND A.M., ZWICKER R.O., STERNICK E.S., Med. Phys. JJ_ (1984)

871.

(5) SVENSSON H., HETTINGER G., Acta Radiol. Ther. Phys. Biol. JO (1971) 369.

(6) SCHULZ R.J., MELI, J., Med. Phys. 11 (1984)872.

(7) ICRU (INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS) -

ICRU Report 35 (1984).

(8) HARDER D., Symposium on High-Energy Electrons, (Zuppinger A., Poretti G.,

Eds.), Springer-Verlag, Berlin (1965) 260.

(9) ANDREO P., BRAHME A., Med. Phys. 8 (1981) 682.

(10) LAX I., BRAHME A., Acta Radiol.,Oncol. J9 (1980) 199.

(11) ANDREO P., BRAHME A., Phys. Med. Biol. 3J (1986) 839.

(12) ANDREO P., NAHUM A., BRAHME A., Phys. Med. Biol. 3J П986) 1189.

(13) CUNNINGHAM J.R., Absorbed dose determination in photon and electron

beams. An International code of practice (Table 8.5) IAEA Vienna (1987)

in press.

(14) LEMPERT G., NATH R., SCHULZ R.J., Med. Phys JO (1983) 1.

(15) Task Group 21, Radiation Therapy Committee, AAPM, Med. Phys. JO (1983)741.

(16) JOHANSSON K.A., MATTSSON L.O., LINDBORG L., SVENSSON H., National

and International Standardization of Radiation Dosimetry (Proc. Symp.

Atlanta, 1977) IAEA, Vienna (1978).

(17) CCEMRI (I)/85-18 (COMITE CONSULTATIF POUR LES ETALONS DE MESURE

DES RAYONNEMENTS IONISANTS (Section I), BIPM, Sèvres, Document

CCEMRI (D/85-18, (1985).

(18) NATH R., SCHULZ R.J., Med. Phys. 8 (1981) 85.

(19) CCEMRI(D/85-8 (COMITE CONSULTATIF POUR LES ETALONS DE MESURE DES

RAYONNEMENTS IONISANTS (Section I), BIPM, Sèvres, Document

CCEMRI(I)/85-8 (1985).

(20) WEINHOUS M.S., MELI J.A., Med. Phys. JJ_ (1984) 846.

(21) MATTSSON L.O., SVENSSON H., Acta Radiol.,Oncol. 23 (1984) 393.

(22) NACP (NORDIC ASSOCIATION OF CLINICAL PHYSICS), Acta Radiol.,Oncol.

20 (1981) 401.

IAEA-SM-298/77

DETERMINATION OF ABSORBED DOSE TO WATER IN CLINICAL PHOTON BEAMS USING A GRAPHITE CALORIMETER AND A GRAPHITE-WALLED IONIZATION CHAMBER

A.H.L. AALBERS, E. VAN DIJK Dosimetry Section,National Institute of Public Health

and Environmental Hygiene (RIVM),Bilthoven

F.W. WITTKÄMPER, B.J. MIJNHEER Radiotherapy Department,The Netherlands Cancer Institute

(Antoni van Leeuwenhoekhuis),Amsterdam

Netherlands

Abstract

DETERMINATION OF ABSORBED DOSE TO WATER IN CLINICAL PHOTON BEAMS USING A GRAPHITE CALORIMETER AND A GRAPHITE-WALLED IONIZATION CHAMBER.

The absorbed dose to water has been determined from calorimetric absorbed dose measurements in graphite. Clinical photon beams with maximum energies from 1 to 25 MeV were used. The calorimetric data have been converted into absorbed dose to water using an NE 2561 ionization chamber as a transfer device. A different approach to derive absorbed dose to water from the calorimetric data is based on a calculation method, applying mass energy absorption coefficient ratios and O’Connor’s scaling theorem. The results obtained with the two methods have been compared with absorbed dose to water values derived from ionization chamber measurements and analysed according to the Dutch Code of Practice. The values for absorbed dose to water derived with the graphite calorimeter and using the two conversion methods are within 1.7% o f absorbed dose to water values obtained from the ionometric data.

1. INTRODUCTION

In 1980 Hofmeester [1] determined absorbed dose to water

values with a graphite calorimeter at 13 accelerators in 11

different hospitals in The Netherlands. In addition, he measured

the absorbed dose to water using a graphite-walled ionization

37

38 AALBERS et al.

chamber. For the analysis of his ionization chamber data he

applied the ICRU recommended С -values [2] as well as the NACP

protocol [3]. Recently, protocols have been published, or are in

preparation, giving a consistent set of recommended conversion

and correction factors. It seemed, therefore, worthwhile to

analyse his data again using these most recent recommendations as

given, for instance, in the new Dutch Code of Practice [4].

The calorimetric data need a conversion from absorbed dose

to graphite into absorbed dose to water which can be done in two

different ways. The first method applies a transfer system as

suggested in ICRU Report 14 [2]. A thin-walled ionization chamber

was used as a transfer device and intended to act as a Bragg-Gray

cavity in both media. In the second method the absorbed dose to

graphite is converted directly by means of a calculation method

which involves a scaling of the depth and field size according to

electron densities. The method is based on the scaling theorem of

0 Connor [5]. Because the theorem is derived for situations where

the dominant mode of interaction is Compton scattering [7], it

can be applied to clinical megavoltage photon beams, as has been

discussed by O'Connor and several other authors [6,8,9]. It is

the purpose of this paper to compare absorbed dose to w ater

values using both conversion techniques of the calorimetric data,

with the ionometric results.

2. MATERIALS AND METHODS

2.1. Analysis of the calorimetric measurements

In the first method, using an ionization chamber as a transfer

device, the absorbed dose to water, D , can be related to thew

absorbed dose to graphite, Dgr . by the equation :

D = D Mw Sw,air ^Pd^w ^Pwall^w ^

Mgr sgr,air ^ d ^ g r ^Pwall^gr

IAEA-SM-298/77 39

where M is the reading of the ionization chamber corrected for

temperature, pressure and recombination, s is the restricted mass

stopping power ratio according to the Spencer-Attix theory, p^ is

the displacement correction factor and Pw a ^ corrects for the

difference in composition between the ionization chamber wall and

the medium in which the chamber is positioned. Equation (1) has

b e e n applied using : (a) values for the mass stopping power

ratios as calculated by Andreo and Brahme for electron spectra at

the reference depth generated by photon beams in a water phantom

[10], (b) values for the displacement correction factor derived

from depth ionization curves in water and graphite for fixed

source-to-chamber distances as measured by Hofmeester and by

assuming that the effective point of measurement is located at a

fraction of 0.75 of the chamber radius proximal to its centre,

(c) values for (p equal to unity and values for (p4twall'gr ^ J rwall w

calculated according to the Dutch Code of Practice.

The determination of the absorbed dose to water from the

graphite calorimeter data using the s c a l i n g m e t h o d can be

described as follows: First the dimensions of the irradiation

geometry used in the calorimetric experiment were transferred to

a corresponding geometry in water by scaling the depth and the

field size with the electron densities of graphite and water. A

value of 1.62 is obtained for the ratio of electron densities,. 3

if a density of 1.8 g»cm for the graphite of the calorimeter

and phantom material is assumed. The equivalent depth and field

size in water will be denoted by d and s, respectively. The

absorbed dose in water at the equivalent depth can be expressed

by :

D (d,s) = D (d , s ) • (S /P)w • S, (d,s) (2)w 4 ' gr 4 r’ tc' v en' 'gr h v ' v '

i “ wwhere ( V*en /Р ) r is. the ratio of mean mass energy-absorption

coefficient of water to that of graphite and the factor S^ takes

into account the change in a b s o r b e d dose to w a t e r due to

variation with field size of scattered radiation originating in

the accelerator head. is defined as the ratio of the output in

air for a given field to that for a reference field and is a

40 AALBERS et al.

f u n c t i o n o f t h e c o l l i m a t o r s e t t i n g o f t h e l i n e a r a c c e l e r a t o r .

F r o m t h i s d o s e v a l u e t h e a b s o r b e d d o s e t o w a t e r a t t h e r e f e r e n c e

d e p t h ( d r ) a n d r e f e r e n c e f i e l d s i z e ( s r ) c a n b e c a l c u l a t e d

a c c o r d i n g t o t h e e q u a t i o n :

s 1 PDD(d ,s )D (d s ) - D (d.s) . ----------- . -------(3 )

Sh (do ,s) PDD(d.s)

w h e r e S, i s t h e t o t a l s c a t t e r c o r r e c t i o n f a c t o r o f t h e s c a l e d h . p

f i e l d s i z e r e l a t i v e t o t h a t f o r t h e r e f e r e n c e f i e l d a t t h e d e p t h

o f max imu m d o s e d Q a n d t h e l a s t f a c t o r r e p r e s e n t s t h e r a t i o , o f

p e r c e n t a g e d e p t h d o s e s a t d e p t h d i n w a t e r a n d t h e r e f e r e n c e

f i e l d , f o r w h i c h d i m e n s i o n s 10 cm x 10 cm w e r e c h o s e n t o t h a t a t

d e p t h d i n w a t e r a n d a n e q u i v a l e n t f i e l d s i z e o f s cm x s cm.

I n o r d e r t o d e t e r m i n e a n d m e a s u r e m e n t s w e r e p e r f o r m e d

b o t h i n a i r a n d i n w a t e r , r e s p e c t i v e l y , u s i n g e x p e r i m e n t a l

t e c h n i q u e s a s d i s c u s s e d f o r i n s t a n c e b y Kahn e t . a l . [ 1 1 ] . The

h e a d s c a t t e r c o n t r i b u t i o n ( S ^ ) i s d e t e r m i n e d b y m e a s u r i n g t h e

o u t p u t o f t h e l i n e a r a c c e l e r a t o r i n a i r f o r t h e e q u i v a l e n t f i e l d

s i z e r e l a t i v e t o t h e r e f e r e n c e f i e l d . F o r t h e s a m e f i e l d s i z e s

a b s o r b e d d o s e m e a s u r e m e n t s w e r e p e r f o r m e d i n a w a t e r p h a n t o m

r e l a t i v e t o a f i e l d s i z e o f 10 cm x 10 cm t o d e r i v e t h e t o t a l

s c a t t e r c o r r e c t i o n f a c t o r (S , ) . T h e t o t a l s c a t t e r a n d t h eh , p

s c a t t e r c o n t r i b u t i o n o f t h e l i n e a r a c c e l e r a t o r h e a d c a n b e

s e p a r a t e d b y d e f i n i n g t h e p h a n t o m s c a t t e r c o r r e c t i o n f a c t o r (S )

a c c o r d i n g t o t h e e q u a t i o n :

\ p ( d .s )S ( d . s ) - - Ü i £ ------------ ( 4 )

Sh ( d ’ s )

Sp a l l o w s f o r t h e q u a n t i f i c a t i o n o f t h e i n - p h a n t o m s c a t t e r

component. From the measurements of S, and S, values of S haveh h . p pb e e n c a l c u l a t e d u s i n g e q u a t i o n ( 4 ) . w h i c h a r e c o m p a r e d w i t h d a t a

g i v e n i n BJR S u p p l . 1 7 [ 1 5 ] .

IAEA-SM-298/77 41

T h e i o n o m e t r i c d a t a f r o m H o f m e e s t e r w e r e c o n v e r t e d t o

a b s o r b e d d o s e t o w a t e r a c c o r d i n g t o t h e r e l a t i o n g i v e n i n t h e

D u t c h Code o f P r a c t i c e [ 4 ] :

2.2 Analysis of the ionometric measurements

D - M • N„ • С (5 )W K. w, u

w h e r e M i s t h e c o r r e c t e d i o n i z a t i o n c h a m b e r r e a d i n g , N„- i s t h eК

a i r k e r m a c a l i b r a t i o n f a c t o r a n d С i s t h e a i r k e r m a t ow , ua b s o r b e d d o s e t o w a t e r c o n v e r s i o n f a c t o r . I n t h e D u t c h Code o f

P r a c t i c e Cw v a l u e s a r e g i v e n f o r t h e g r a p h i t e - w a l l e d i o n i z a t i o n

c h a m b e r , u s e d i n t h i s s t u d y a n d o t h e r r e f e r e n c e c h a m b e r s a s a

f u n c t i o n o f t h e q u a l i t y i n d e x . I ^ q / I j _ q : r e l a t i v e

i o n i z a t i o n s m e a s u r e d a t 2 0 a n d 1 0 cm d e p t h i n w a t e r ,

r e s p e c t i v e l y , a t f i x e d s o u r c e - d e t e c t o r d i s t a n c e f o r a 1 0 cm x 10

cm f i e l d s i z e a t t h e g e o m e t r i c a l c e n t r e o f t h e d e t e c t o r .

2 . 3 . C a l o r i m e t e r m e a s u r e m e n t s

T h e g r a p h i t e c a l o r i m e t e r e m p l o y e d i n t h e e x p e r i m e n t o f

H o f m e e s t e r [ 1 ] was c o n s t r u c t e d a c c o r d i n g t o a d e s i g n b y Domen a n d

L a m p e r t i [ 1 2 ] a n d c o n s i s t e d o f t h r e e ( n e s t e d ) b o d i e s : c o r e ,

j a c k e t a n d s h i e l d i n a g r a p h i t e medium. The t e m p e r a t u r e r i s e o f

t h e c o r e d u r i n g i r r a d i a t i o n i s p r o p o r t i o n a l t o t h e a b s o r b e d d o s e

i n t h e c o r e a n d was m e a s u r e d i n t e r m s o f a r e s i s t a n c e c h a n g e o f a

m i c r o t h e r m i s t o r . S i m u l t a n e o u s l y , a d d i t i o n a l e l e c t r i c a l p o w é r was

s u p p l i e d t o t h e s h i e l d i n o r d e r t o c o m p e n s a t e f o r t h e d e p t h - d o s e

g r a d i e n t . T h e r e s p o n s e o f t h e c o r e t h e r m i s t o r was c a l i b r a t e d b y

r e l e a s i n g a w e l l known am o u n t o f e l e c t r i c a l e n e r g y i n t h e c o r e .

T h e m e a s u r e m e n t s w e r e p e r f o r m e d a t a d e p t h a s c l o s e a s p o s s i b l e_ 2

t o t h e r e f e r e n c e d e p t h o f 5 g - c m i n g r a p h i t e , a p p l y i n g a f i e l d

s i z e o f 10 cm x 10 cm a t t h e s u r f a c e o f t h e p h a n t o m . The c o r e o f

t h e c a l o r i m e t e r w a s p o s i t i o n e d a t t h e i s o c e n t r e . A r e f e r e n c e _ 2

d e p t h o f 7 g ' c m w a s u s e d f o r t h e r a d i a t i o n q u a l i t i e s w i t h

maximum X - r a y e n e r g i e s o f 1 6 , 18 a n d 25 MeV, r e s p e c t i v e l y . M o r e

d e t a i l s of the c a l o r i m e t r i c m e a s u r e m e n t s are provided by

Hofmeester [1].

2.4. Ionization chamber measurements

The ionization chamber used in the experiments of Hofmeester

was a graphite-walled NE 2561 chamber. A Delrin build-up cap was

used during the calibration in air in the Co gamma-ray beam of

the N a t i o n a l Standards Laboratory (RIVM). The measurements

performed by Hofmeester were done at three different depths

around the appropriate reference depth in both graphite and

water, for a field size of 10 cm x 10 cm at the surface of the

phantom and applying the same source detector distance as in the

calorimetric measurements.

The determinations of and S^ were performed with a 0.1

cm^ ionization chamber. For the S, measurements this cylindricalh -2

chamber was surrounded by a cap of brass of about 3 g-cm to

provide electronic equilibrium. It is assumed that determined

for this thickness of material is equal to that at the reference

depths.

4 2 AALBERS et al.

3. RESULTS AND DISCUSSION

Two sets of absorbed dose to water values have been derived

from the calorimetric data. For convenience we will refer to the

conversion method using the NE 2561 c h a m b e r as a t r a n s f e r

instrument as "transfer method" and to the method involving the

0 Connors scaling theorem as "scaling method". Figure 1 shows

the ratio of absorbed dose to water derived from the calorimetric

measurements using the transfer method to that determined from

the ionization chamber measurements and analysed according to the

Dutch Code of Practice. The data are given in figure 1 as a

function of the quality index.

According to Hofmeester [1], an uncertainty of 0.7% (one

standard deviation) can be estimated for the absorbed dose to

IAEA-SM-298/77 43

1. 0Б/*чL Ф

Ло 1 .04 _с Ü

о 1.02■нV

>01 1.00 L <D 4>ОЕ 0 .98L О

° 0 .96

>□0.34

0. 55 0 . 6 0 0 . 65 0 . 7 0 0 . 75 0 . 8 0 0.85

Q u a l i t y I n d e x

FIG. I . Absorbed dose to water as a function o f the quality index, determ ined with the graphite calorimeter and analysed with the transfer m ethod norm alized to values measured with an N E 2561 ionization chamber and analysed according to the Dutch Code o f Practice.

water determinations using the transfer method. By presenting the

da t a as the ratio Dw (cal) / Dw (ion) the uncertainty in the

io n o m e t r iсa 1 ly d e r i v e d v a l u e s has to b e . i n c l u d e d . T h i s

contribution arises mainly from the air kerma calibration factor

N^. The combined uncertainty amounts to about 1% (1 SD) and is

indicated by the error bars given in figure 1. Relatively large

discrepancies can be observed between the two data sets presented

in figure. 1. The maximum deviation in the results amounts to

1.7%. The average difference was found to be 0.6% with a standard

deviation of 0.9%.

The fluctuations in the results given for contiguous quality

index points suggest the presence of an uncertainty independent

of the quality index. A possible cause might be found in the

relatively large time intervals between the c a l o r imetrically

absorbed dose determination and the m e a s u r e m e n t s w i t h the

i o n i z a t i o n chamber in the graphite phantom. Obviously, the

44 AALBERS et al.

l .06ЛС ®

АО 1.04

X оС.2 1- 02 ЧУ

> о~ 1 .00 L Ф *>ФЕ 0.98•нL О

j 0.96 %□

0.940.55 0.60 0.65 0.70 0.75 0.00 0.85

Q u a l i t y I n d e x

FIG. 2. Absorbed dose to water as a function o f the quality index, determined with graphite calorimeter and analysed with the scaling method norm alized to values m easured with an N E 2561 ionization chamber and analysed according to the Dutch Code o f Practice.

1.05

1.04 -

1 .0 3 -

U. a>^ 1 . 0 2 -

Q.1Л

1 .01 -

1 . 0 0 -

0.99

■***■ = Sp □ = NPSF

ж

□

■*-* * ° □* * #

D

CD

0.55 0.60 0.65 0.70 0.75 0.80Quality Index

0.85

FIG. 3. The phantom scatter correction fac to r (Sp) and the norm alized peak scatter fa c to r (NPSF) given as a function o f the quality index. Sp has been determined a t dose maximum fo r the equivalent fie ld , relative to a 10 cm x 10 cm field . The values fo r the N PSF have been taken from the British Journal o f Radiology, Suppl. 17, fo r the same equivalent f ie ld sizes.

IAEA-SM-298/77 45

accelerator stability is important here and the value of 0.3%,

a d o p t e d by H o f m e e s t e r for the unc e r t a i n t y of the monitor

stability, might be underestimated. According to Johansson [13],

this uncertainty is 0.5%, one standard deviation. This value is

in better agreement with the observed discrepencies in the data

given in figure 1 .

Figure 2 compares the calorimetric data analysed according

to the scaling method with the data derived from the ionometric

measurements in the water phantom. As can be seen from this

figure the differences are rather small: 1.0% at maximum. The

average difference amounts to 0 .1% with a standard deviation of

0 . 7 % . V a l u e s f o r t h e m e a n m a s s e n e r g y - a b s o r p t i o n

coefficient ratio of graphite to water have been calculated as a

function of the quality index from data given in the draft IAEA

protocol [14]. For values of the quality index up to about 0.71

(corresponding to a maximum X-ray energy of about 8 MeV) the

ratio of mean mass energy-absorption coefficients is fairly

constant. This ratio varies about 1.2% from this constant value

for variation in the quality index to 0.785 (corresponding to a

maximum X-ray energy of 25 MeV). The scaling theorem assumes that

radiation interacts by the Compton effect only. Therefore, the

scaling theorem does not hold rigorously for photon energies,

where pair production cannot be neglected. However, for the

photon energies employed in this study the results indicate that

deviations which may arise from differences in pair production in

water and graphite are probably not very large.

Figure 3 shows some r e s u l t s for the p h a n t o m s c a t t e r

c o r r e c t i o n f a c t o r o b t a i n e d at dose maximum in water from

measurements according to the experimental procedure described in

the previous section. The results are plotted as a function of

the quality index. Also shown in this figure are values for the

normalized peak scatter factor (NPSF) taken from the British

Journal of Radiology, Suppl.17 [15]. The NPSF value could be

related to the quality index, by deriving the latter quantity

from percentage depth dose data given in BJR, Suppl.17, and using

a formalism described by Mijnheer et al. [16]. Note that the NPSF

equals the phantom scatter correction factor by definition. Good

46 AALBERS et al.

agreement can be observed up to a quality index of about 0.71.

Above this value both sets of data tend to show a different

behaviour with respect to increasing quality index, which has to

be investigated further.

4. CONCLUSIONS

From the results presented in figures 1 and 2 it can be

c o n c l u d e d that the absorbed dose to water derived from the

scaling method gives a somewhat b e t t e r a g r e e m e n t w i t h the

ionometric data than the results obtained with the transfer

method. The calorimetric absorbed dose to water using the scaling

method involves only measurements in the radiation beam with a

graphite calorimeter. Therefore, possible errors introduced by

changing the measurement geometry, replacing the phantom material

and l o n g time i n t e r v a l s b e t w e e n the m e a s u r e m e n t s , i.e.

accelerator stability can be avoided. The results presented here

support the conclusion that, within the accuracy of measurements

and calculations, the scaling theorem can be used to convert

absorbed dose in graphite to absorbed dose in water for the

clinical photon beams used in this investigation. Comparison of

the ionometric data with the results for both methods of analysis

of the calorimetric data shows no difference larger than 1.7%.

These findings provide evidence that consistent results can be

achieved by applying the most recent values for the physical

parameters as used, e.g. in the Dutch Code of Practice.

REFERENCES

[1] HOFMEESTER, G.H., Calorimetric determination of absorbed

dose in water for 1 - 2 5 MeV X-rays, Biomedical Dosimetry:

Physical Aspects, Instrumentation, Calibration (Proc. S y m p .

Paris, 1980), IAEA Vienna (1981) 235.

IAEA-SM-298/77 47

[2] ICRU (International Commission on Radiations U n i t s and

Measurements), Radiation Dosimetry: X Rays and Gamma Ray

with Maximum Photon Energies between 0.6 and 50 MeV, Report

14, ICRU Publications, Bethesda, MD, USA (1969)

[3] NACP (Nordic Association of Clinical Physics), Procedures in

e x t e r n a l r a d i a t i o n therapy between 1 and 50 MeV, Acta

Radiol.Oncol. 19 (1980) 55.

[4] M I J N H E E R , B . J . , A A L B E R S , A .H .L ., V IS S ER , A . G. and

WITTKAMPER, F.W. , C o n s i s t e n c y and s i m p l i c i t y in the

d e t e r m i n a t i o n of absorbed dose to water in high-energy

photon beams: a new Code of Practice, Radiother. Oncol. ]_(1986) 371.

[5] O C O N N O R , J.E., The variation of scattered X Rays w i t h

density in an irradiated body, Phys.Med.Biol. 1 (1956) 352.

[6] O ’CONNOR, J.E., The density scaling theorem a p p l i e d to

lateral electronic equilibrium, Med.Phys. JLl (1984) 678.

[7] PRUITT,J.S., LOEVINGER, R., The photon-fluence s c a l i n g

theorem for Compton-scattered radiation, Med.Phys. 9 (1982)

176.

[8 ] KUTCHER, G.J., SUNTHARALINGAM, N., Equivalent depths for

photon beam calibrations at high energies, Med.Phys.6 (1979)

339 (abstract).

[9] SONTAG, M.R. .CUNNINGHAM, J.R., The equivalent tissue-air

ratio method for making absorbed dose calculations in a

heterogeneous medium, Radiology 129 (1978) 787.

[10] ANDREO, P., BRAHME A., Stopping power data for high energy

photon beams, Phys.Med.Biol. 31 (1986) 839.

48 AALBERS et al.

[11] KAHN, F.M., SEWCHAND, W., LEE, J., WILLIAMSON, J.F.,

Revision of tissue-maximum ratio and scatter-maximum ratio

concepts for Cobalt 60 and higher energy X-ray beams,

Med.Phys. 7 (1980) 230.

[12] D O M EN , S . R., LA MP E R T I , P.J., He a t - 1 os s -c o m p e n s a t e d

calorimeter: theory, design and performance,

J.Res.Natl.Bur.Stand. 78A (1974) 595.

[13] JOHANSSON, K.A., Studies of different methods of absorbed

dose determination and a dosimetric intercomparison at the

N o r d i c r a d i o t h e r a p y ce ntres, Thesis, U n i v e r s i t y o f

Gothenburg, Sweden (1982).

[14] IAEA (International Atomic Energy Agency), Code of practice

for absorbed dose determinations in photon and electron

beams, in press.

[15] BJR (British Journal of Radiology), Central axis depth dose

data for use in radiotherapy. Suppl.17 (1983) 131.

[16] MIJNHEER, B.J., WITTkXm PER, F.W., AALBERS, A.H.L., VAN DIJK,

E. , E x p e r i m e n t a l v e r i f i c a t i o n of the a i r k e r m a to

absorbed dose conversion factor С , Radiother .Oncol. 8w , u —

(1987) 49.

IAEA-SM-298/28

FUNDAMENTAL MEASUREMENT OF ABSORBED DOSE IN WATER FOR COBALT-60 GAMMA RAYS: PROCEDURE ANDEXPERIMENTAL INSTRUMENTATION

D.C. MOSSE, M. CANCE, M. CHARTIER,J. DAURES, A. OSTROWSKY, J.P. SIMOËN Laboratoire de métrologie des rayonnements ionisants, CEA, Centre d’études nucléaires de Saclay, Gif-sur-Yvette,France

Abstract

FUNDAM EN TAL M EASUREM ENT OF A BSO RBED DOSE IN WATER FOR COBALT-60 GAMMA RAYS': PRO CEDURE AN D EXPERIM ENTAL INSTRUM ENTATIO N.

The work is concerned w ith the set-up o f a new standard expressed in term s o f absorbed dose to water, at 5 g -cm ' 2 depth in a water phantom placed in a cobalt-60 gamma-ray field. The phantom is a parallelepiped w ith d im ensions 30 cm X 30 cm X 20 cm. The irradiator is o f the ‘A lcyon’ type , suitable for cobalt therapy applications. The procedure is based on a transfer m ethod using three suitable dosim etry system s, nam ely: an ionom etric system (using a 0 . 6 cm 3

radiotherapy ion ization cham ber o f the NE 2571 type), a spectrophotom etry system based on the Fricke solution , and an ESR spectrom etry system based on alanine. These system s are calibrated using the national primary standard o f absorbed dose, w hich is the graphite calorimeter. The dosim etric interpretation o f m easurem ent results rests on a strict form alism , dealing in generalized term s w ith the cavity theory and w ith th e perturbations, inherent to the measurement procedure.

1 - INTRODUCTION

The absorbed dose i s the main q u a n t i t y o f i n t e r e s t i n the

many areas where d os im e try a p p l ie s , e . g . , m e d ic in e , h e a l th phy

s ic s and the r a d ia t i o n p ro c e s s in g o f f o o d s t u f f s . Any s tandard

o f absorbed dose sh o u ld , i n v iew o f i t s ve ry n a tu re , be s p e c i

f i e d in terms o f r a d ia t i o n f i e l d q u a l i t y , and n a tu re , geometry

and d im ensions o f th e m a te r ia l s p re s e n t a t th e p o in t o f i n t e

r e s t , o r c lo s e by. In the f i e l d s o f a p p l i c a t i o n m entioned above,

49

50 MOSSE et al.

w a te r i s th e p re fe r r e d re fe re n c e medium [ 1 ] , and c o b a l t - 6 0 pho

to n r a d ia t i o n i s w id e ly used. I t w as , t h e r e f o r e , a n a tu ra l d e c is io n

f o r LMRI1 to des ign and b u i l d a new s ta nd a rd o f absorbed dose

i n w a te r f o r c o b a l t -6 0 pho tons, which would supp lement the

e x i s t i n g s tandards o f th e l a b o r a to r y . T h is s ta nd a rd i s s p e c i

f i e d a t a depth o f 5 g -cm"2 i n a w a te r phantom and i s l i n k e d to

th e n a t io n a l s tanda rd o f absorbed dose, i . e . , the g ra p h i te ca

l o r i m e t e r , and us ing a p p ro p r ia te t r a n s f e r systems [ 2 ] .

T h is new s ta nd a rd w i l l have d i r e c t a p p l i c a t i o n s i n th e

areas m entioned above ; f u r t h e r , i t shou ld make i t p o s s ib le to

d e te rm ine the hea t d e fe c t i n w a te r by comparison w i th a w a te r

c a lo r im e t e r , which i s a p o s s ib le s tandard f o r absorbed dose in

w a te r .

The purpose o f t h i s paper i s to d e s c r ib e th e p rocedure

a dop ted , to s p e c i f y th e fo rm a lism and to p re s e n t the experim en

t a l means used as w e l l as the data c o l l e c t e d . The a n a ly s is and

t h e o r e t i c a l i n t e r p r e t a t i o n o f th e data w i l l be covered i n ano

th e r paper.

2 - EXPERIMENTAL PROCEDURE

Our expe r im en ta l procedure i s based on th e use o f a g ra p h i

te c a lo r im e t e r as a s tanda rd o f absorbed dose f o r c o b a l t 60

p h o to n s , i n a s s o c ia t io n w i th d o s im e t r ic t r a n s f e r systems w i th

a p p r o p r ia te c h a r a c t e r i s t i c s , i . e . , io n o m e try , chemical dosime

t r y u s in g fe r r o u s s u l f a t e , and a la n in e ESR s p e c t ro m e try . The

genera l method in v o lv e s the fo l lo w in g fo u r s teps :

a ) - C a lo r im e te r measurements a re made a t th re e d i f f e r e n t

depths in a g r a p h i t e phantom cen te red on th e c o b a l t - 6 0 beam.

1 LMRI : L a b o r a t o i r e de M é t ro lo g ie des Rayonnements I o n i s a n t s .

IAEA-SM-298/28 51

T h is g iv e s th re e re fe re n c e va lu es o f th e absorbed dose in g ra

p h i t e , (D g )r e f , a t th re e p o in t s " i " a long th e beam a x is .

b) - Each t r a n s f e r dosemeter " j " i s then i r r a d i a t e d under id e n

t i c a l c o n d i t i o n s , a t th e th re e depths " i " in th e g ra p h i te

phantom. T h is y i e l d s th re e re a d i n g s , © ^ , which a re assumed

t o be c o r re c te d f o r n o n -d o s im e t r ic param eters s p e c i f i c o f the

measurement te c h n iq u e used.

T h is o p e r a t io n , j o in e d w i th the f i r s t one, c o n s t i t u t e s

th e c a l i b r a t i o n in terms o f absorbed dose i n g r a p h i t e , o f dose

m eter " j " a t p o in t " i " in th e g r a p h i t e phantom ; th e c a l i b r a

t i o n f a c t o r i s thus equal to th e r a t i o (D g )r e f ^ g ’ '-’ •

c ) - Each dosemeter " j " i s a ls o i r r a d i a t e d under th e same

c o n d i t io n s , i n th e w a te r phantom c e n te re d on th e beam a x is , a t

th e re fe re n c e depth o f 5 g - c n T ^ T h i s y i e l d s a c o r r e c te d re a d in g

c J iJwater•

The dose i n w a te r , a t th e same p o in t and i n th e absen

ce o f th e dosem ete r, D^â»tJr , would be d e r iv e d from th e r e l a t i o n

s h ip :

n i J = m b - 0 ^ water k water m

- . ' *W ‘ i p

where

. k g ,J i s th e o v e r a l l d o s im e t r ic c o r r e c t io n f a c t o r s p e c i f i c to

d o s e m e te r " j " i r r a d i a t e d a t depth " i " in th e g r a p h i t e phantom

52 MOSSE et al.

t h i s f a c t o r accoun ts f o r the la c k o f e q u iva le n ce o f the mate

r i a l s o f th e w a l l and o f the d e te c to r medium in the c a v i t y , to

th e su r ro u n d in g medium ( g r a p h i t e ) .

• ^ w a te r1 s t l ie o v e r a l l d o s im e t r ic c o r r e c t io n f a c t o r s p e c i f i c to

dosemeter " j 1' , i r r a d i a t e d a t th e depth o f r e fe re n c e in th e wa

t e r phantom ; t h i s f a c t o r accounts f o r the la c k o f e q u iva le n ce

o f th e dosemeter m a te r ia l s to th e s u r ro u n d in g medium ( w a te r ) .

The t h e o r e t i c a l i n v e s t i g a t i o n o f t h i s f a c t o r i s cove

re d i n S e c t io n 3.

d) - The re fe re n c e va lue o f absorbed dose in w a te r ,

(Dwater) r e f , a t the depth o f 5 g -cm "^ , i s the w e igh ted average o f

D waterva1 u es> th rough the r e l a t i o n s h i p :

( DwaterVef = i , j P i , j 1 Dwater

where

i j » и - 1 <3)

and p j j i s a no rm a l ized w e ig h t in g f a c t o r which takes i n t o ac

co u n t th e expe r im en ta l data r e la t e d to depth " i " and dosemeter

" j " . For example, t h i s f a c t o r may be taken as p ro p o r t io n a l to

th e r e c ip r o c a l o f v a r ia n c e .

E xp ress ion s (1 ) and (2 ) le a d to the f o l lo w in g r e l a

t i o n s h ip between (Dwater) r e f and ( ° g ) r e f :

i n \ ^ n ! n M c / b water ^ water I A Ï' water r e f i , j P i , j g r e f ■ • ~ t— H )

g ’ g ’

j

IAEA-SM-298/28 53

3 .1 - T h e o re t ic a l c o n s id e r a t io n s on absorbed dose measurements

The purpose o f t h i s S e c t io n i s to p re s e n t the genera l

fo rm a l is m o f th e c o r r e c t io n f a c t o r s used in r e l a t i o n s h ip s (1 )

and ( 4 ) . In a l l absorbed dose measurements, the b a s ic problem

a r is e s from two m a jo r c o n s t r a in t s [ 3 ] :

. f i r s t , the ve ry n a tu re o f the q u a n t i t y to be measured

[ 4 ] : p o in t q u a n t i t y , d e f in e d in a volume e lem ent o f

th e m a te r ia l c o n s id e re d , which i s a f f e c t e d by the

c o m p o s i t io n o f a d ja c e n t m a t e r ia l s ,

. second, the f a c t t h a t i t i s r a r e l y p o s s ib le to measure

d i r e c t l y the energy im p a r te d to the m a te r ia l o f

i n t e r e s t ; t h i s r e q u i r e s the i n t r o d u c t i o n o f a fo r e ig n

" d e t e c t o r " m a te r ia l i n t o the medium.

For i l l u s t r a t i o n purposes, the most genera l fo rm o f dose

m eter c o n s is ts o f a w a l l , made o f m a te r ia l "w " , and a c a v i t y

filled with detector material"d" , p i aced i n a medium " m " ( F i g . l ) .

Throughout the f o l l o w in g , the c a v i t y w i l l be assumed to be

o f any s iz e , whereas the w a l l i s assumed to be too t h i n to en

su re th e re a l o r t r a n s i e n t e q u i l i b r i u m o f th e charged secondary

p a r t i c l e s s e t in m o t ion in medium "m " .

The i r r a d i a t i o n o f th e dosemeter r e s u l t s in an energy de

p o s i t i o n in th e d e te c to r medium, which i s measured by the asso

c ia t e d in s t r u m e n t a t io n . The th e o ry o f the measurement o f

.absorbed dose aims a t e s t a b l i s h in g a p h y s ic a l r e l a t i o n s h i p b e t

ween th e average absorbed dose, <Dcj>c a v , w i t h i n the d e te c to r

m a te r ia l i n the c a v i t y , and the dose, Dm, w hich e x is t s a t the

c e n te r o f the dosemeter c a v i t y when c a v i t y m a te r ia l " d " and

3 - FORMULATION

54 MOSSE et al.

in te r fa c e V

in te r fa c e Z

m aterial “d"

m aterial "w"

m aterial "m"

<Dd>cav

<1/001 >*

<kcol >z *

FIG . 1. S ch em a tic p resen ta tio n o f th e m ea su rem en t o f a bsorbed dose, D m , in a m e d iu m ‘m ’.

w a l l m a te r ia l "w" a re re p la c e d by th e s u r ro u n d in g medium "m"

( F ig . 1 ) , i . e . , i n the absence o f the dosemeter.

In g e n e ra l , th e th e o ry o f absorbed dose measurement i s

based on th e p ro p e r ty o f a d d i t i v i t y o f doses in the c a v i t y

[ 5 , 3 , 6 ] . Thus, th e average dose, <Dd>c a v . i s equal to the sum

o f th re e component average doses :

<Dd>cav <Dd,m>cav + <Dd ,w >cav + <Dd ,d >cav (5)

IAEA-SM-298/28 55

where <Dd,m>c a v > ^ d . w ^ a v and ^ d . d ^ a v a re th e average a b so rbed doses in th e c a v i t y f i l l e d w i th m a te r ia l " d " , r e s u l t i n g

f rom the charged secondary p a r t i c l e s genera ted i n m a te r ia l s

"m " , "w" and " d " , r e s p e c t i v e l y . The t h e o r e t i c a l a n a ly s is p resen

te d in th e f o l lo w in g paragraphs ( r e l a t i o n s h ip s 17, 22, 27 and

31) shows t h a t each o f these th re e average doses i s p r o p o r t i o

nal to the dose Dm to be measured :

R e la t io n s (5 ) to (8 ) lead to the e x p re s s io n o f th e absorbed

dose in "m " , Dm, as a f u n c t io n o f th e t o t a l average dose in

th e d e te c to r medium "d " in th e c a v i t y :

where " k " i s th e o v e r a l l d o s im e t r ic c o r r e c t io n f a c t o r (1 ) which

accoun ts f o r th e la c k o f e q u iv a le n c e o f th e w a l1/ d e t e c t o r mate

r i a l s , to the s u r ro u n d in g medium. Thus we have :

3.2 - Analysis of the components of the average dose in the

< ld,m>cav ^m • (6 )

<Dd,w>cav Dm • h2 (7)

<Dd ,d >cav - Dm • h3 (8)

(9)

(10)

cavi ty

For conven ience in th e f o r m u la t io n , the average mass c o l

l i s i o n s to p p in g power o f e le c t r o n s , u s u a l ly d e s ig n a te d as

Sco i / P , w i l l be sym bo lized by S ; i n the same way, th e average

56 MOSSE et al.

mass energy a b s o rp t io n c o e f f i c i e n t f o r pho tons , y er¡ /P , w i l l be

sym bo lized by M.

The f o l lo w in g a n a ly s is o f th e components <Dd m>c a v ,

<Dd,w >c a v 5 <Dd ,d >cav o f the average absorbed dose <0d>c a v ,

r e l i e s on th e f o l lo w in g assumptions [ 5 , 7, 8 ] :

. f o r an e le c t r o n f lu e n c e i n c id e n t on a medium, the r e l a

t i v e v a r i a t i o n o f absorbed dose in th e medium w i l l be re p re s e n

te d by a f u n c t io n u ( x ) ,

. f o r a photon f lu e n c e in c id e n t on a medium, the v a r i a

t i o n o f absorbed dose in the medium, r e l a t i v e to the c o l l i

s io n kerma a t the e n t ra n c e , w i l l be re p re s e n te d by th e p ro d u c t

o f a f u n c t io n v ( x ) by the f a c t o r J3 d e f in e d [ 9 , 10] as the r a t i o

o f dose to c o l l i s i o n kerma when the secondary e le c t r o n s a re in

t r a n s i e n t e q u i l i b r i u m ,

. the c o l l i s i o n kerma, Kco , i s d e f in e d from th e kerma К

by r e l a t i o n :

Kco1 = K . ( l - g ) (11)

where g i s th e r a d ia t i o n y i e l d o f secondary e le c t r o n s ; th ro u g h

o u t the f o l l o w in g g w i l l be assumed to be c o n s ta n t f o r a g iven

medium and f o r a g ive n photon energy ,

. th ro u g h o u t the f o l l o w in g , i t i s assumed t h a t in th e am

b ie n t medium “ m " , w i t h o u t th e dosem ete r, the t r a n s ie n t e q u i l i

b rium o f secondary e le c t r o n s i s ach ieved a t any p o in t o f the

v o lu m e .d e f in e d by th e c lo se d s u r fa c e z' (see F ig . 1 ) .

IAEA-SM-298/28 57

a) - Expression of component <Dc/ m>cav

The average absorbed dose <D(j jm>cav due to e le c t r o n s s e t

i n m o t io n in medium "m" i s l i n k e d to the average absorbed dose

<Dd m>E a t i n t e r f a c e z , th rough the average va lue

<ud m>c a v ’ th e f u n c t io n ud m(x ) i n th e c a v i t y :

<Dd,m>cav = <Dd,m> E • <ud,m>cav

A t i n t e r f a c e E, th e average doses <Dd m>^ i n th e c a v i t y

"d " and <DW m>2 i n th e w a l l "w" a re r e s u l t s o f the same e le c

t r o n f lu e n c e ; they a re th us r e la t e d by :

■ 's2;:>e из)where (S ^ ’ |]J)£ i s the r a t i o o f th e average mass c o l l i s i o n s to p

p in g powers f o r m a te r ia l s "d " and " w " , d e f in e d on th e energy

d i s t r i b u t i o n o f secondary e le c t r o n s genera ted in medium "m"

and p re s e n t a t i n t e r f a c e Z.

I f uw m i s th e r e l a t i v e v a r i a t i o n between in t e r f a c e S and

o f the dose i n "w" by secondary e le c t r o n s o r i g i n a t i n g from

<^w,m>Z < )w,m>Z ’ • uw,m

As in th e case o f r e l a t i o n s h i p ( 1 3 ) , dose <DW , can

be d e r iv e d from :

58 MOSSE et al.

L e t ßm be th e r a t i o [ 9 , 10] o f » to th e average

c o l l i s i o n kerma in m a te r ia l "m" a t th e same in t e r f a c e

E ' w i th dosemeter p re s e n t (see F ig , 1) ; we have

<Dm m> v , = < K £ 0 l > * . ßm ( 1 6 )m,m E* m z* m 1 '

By com bin ing r e l a t i o n s h ip s (12 ) th rough ( 1 6 ) , we o b ta in

th e f o l lo w in g e q u a t io n , from which <Dd m>cav can be d e r iv e d :

( 1 7 )

< )d,m>cav = ^ m ^ Z * - • ^ m ’ m^Z»’ ^w )m ^Z* uw,m ■ <ud,m>cav

bj - Expression of component <Drf w>cav

The average absorbed dose due to e le c t r o n s s e t in m o t io n

i n th e w a l l "w " , <0 (1 w>c a v , i s re 1 a te d the average absorbed

dose £ i n "d " a t i n t e r f a c e E th rough the average v a lu e

<ud ,w >cav o f U n c t i o n u<j w( x ) w i t h i n th e c a v i t y :

<Dd,w>cav = <Dd,w> z • <ud ,w >cav

A t i n t e r f a c e E , th e average doses <0^ w>£ in th e c a v i t y

"d " and <DW w> £ i n th e w a l l "w" a re r e s u l t s o f the same e le c

t r o n f lu e n c e ; they a re thus r e la t e d by :

< ° d , w > ¡ : ■ <“ „ , » > i • ‘ ^ S ’ i ( 1 9 )

where (S¿¡’ ^ ) £ i s the r a t i o o f th e average mass c o l l i s i o n s to p

p in g powers f o r m a te r ia l s "d " and " w " , d e f in e d on th e energy

d i s t r i b u t i o n o f secondary e le c t r o n s genera ted in th e w a l l "w"

and p re s e n t a t i n t e r f a c e E .

IAEA-SM-298/28 59

Based on th e assum ptions adop ted , the f o l l o w in g e q u a t io n

l i n k s th e average absorbed dose <DW w> ^ to the average c o l l i

s io n kerma i n m a te r ia l "w" a t i n t e r f a c e s ' ;

<D» , w > ¡: • « 5 o 1 > £ . ( 2 0 )

A t i n t e r f a c e E ‘ , th e average c o l l i s i o n kermas <к £ о1>е >

i n th e w a l l "w" and <K^o1>^, i n th e medium "m" a re r e s u l t s o f

th e same photon energy f lu e n c e ; they a re thus r e l a t e d by :

< С Ь Ё. = < C 4 . • «S i 21 '

where Mjjj i s th e r a t i o o f th e average mass energy a b s o rp t io n

c o e f f i c i e n t s f o r m a t e r ia l s "w" and "m " .

By com b in ing r e l a t i o n s h ip s (18 ) th rough ( 2 1 ) , we a r r i v e a t

the f o l l o w in g e x p re s s io n f o r <Dd w>cav :

( 2 2 )

<^d ,w >cav = ^ m ^ E ’ • ®w • • ^ w ’ XpE • vw • <ud,w>cav

c) - Expression of component <° >с/>сау

Based on th e assum ptions adop ted , the average absorbed

dose <Dd d>cav 1S r e ^a te d to th e average c o l l i s i o n kerma

a t i n t e r f a c e E th rough the average v a lu e in th e ca

v i t y , <vd>c a v , o f f u n c t io n v d ( x ) :

« d . d ' c a » * < K 5 ° b S • ° d ■ " V c a v (23)

60 MOSSE et al.

I n th e same way as i n r e l a t i o n s h i p ( 2 1 ) , the average kermas

<Kd0 l> Z and <Kw0 l> E a re 1 inked ЬУ th e f o l lo w in g r e l a t i o n s h i p :

<|/COl>* - <|/COl>* <Kd > Z " <Kw >Z (24)

I f < ^ w >Z / < ^ w>z. 1S the r a t i o o f average photon energy

f lu e n c e s in th e w a l l m a te r ia l a t i n t e r f a c e s Z a n d Z ' , the ave

rage c o l l i s i o n kerma <K^01 >£ a t i n t e r f a c e Z can be expressed as

a f u n c t io n o f the average c o l l i s i o n kerma a t i n t e r

fa ce Z ' :

< C > * = < K « b * . . 1 1 * 4 (25)< V i .

As in th e case o f r e l a t i o n s h ip ( 2 1 ) , the average kermas

« $ < > 4 , and <K^o1> | , a re l i n k e d by th e e q u a t io n :

< K £ o l > z* , . К ( 2 6 )

Combining r e l a t i o n s h ip s (23) th rough ( 2 6 ) , <Dd d>Cav can be

d e r iv e d from :

*

<Dd , d >cav = <Km01 ^ > • ßd ‘ Mm • — * <Vd>cav' < V z >

3 .3 - F in a l r e l a t i o n s h i p between Dm and <D£|>cav

R e la t io n s h ip s ( 1 7 ) , ( 2 2 ) and (27) show t h a t th e t o t a l average

dose i n th e c a v i t y , <D(i >c a v , (e q u a t io n 5 ) , may be expressed as

IAEA-SM-298/28 61

a f u n c t io n o f th e average c o l l i s i o n kerma in medium "m“ , a t

i n t e r f a c e £ ' w i th dosemeter p re s e n t , <K£o1> £ , . The f i n a l s tage

t h e r e f o r e c o n s is ts in d e r i v i n g th e r e l a t i o n s h i p between t h i s

kerma and the absorbed dose in m a te r ia l "m" in th e absence o f

th e dosem eter, Dm, (see F ig . 1 ) .

a ) - Relationship between and Dm

The average c o l l i s i o n kerma in "m " , a t i n t e r f a c e e ' ,

<Km0 l> Z’ ( see ^ 9 - D ’ s l inked to the average c o l l i s i o n kerma,

<Km0 l> 2> a t t l ie same s u r fa c e > wllen th e volume occup ied by the

dosemeter i s f i l l e d w i t h m a te r ia l "m " , by th e r e l a t i o n :

< C 4 * . ■ < ° 4 , • (28)S V

where the symbolism used f o r photon energy f lu e n c e s ^ i s id e n

t i c a l to the one used f o r c o l l i s i o n kermas.

The average c o l l i s i o n kerma in homogeneous medium, a t

i n t e r f a c e E‘ , <KC£ 1> i s r e la t e d to the c o l l i s i o n kerma

i n "m" a t C, th e p o in t o f i n t e r e s t , ( K ^ o l ) c , th rough the r a t i o

< ^ m> Z 1 I ^ m^C Photon energy f lu e n c e s a t z' and a t С :

« S 01>Î' ■ ( C ' l c • (23)! Ф т > с

L e t ßm be the r a t i o [ 9 , 10] a t p o in t С o f Dm, th e absorbed

dose to be d e te rm in e d , to th e c o l l i s i o n kerma (K£o 1 ) c :

62 MOSSE et al.

Thus, th e average c o l l i s i o n kerma can be e xp res

sed th rough r e l a t i o n s h i p s ( 2 8 ) , ( 2 9 ) , (30 ) as a f u n c t io n o f Dm, the

absorbed dose to be de te rm ined :

<KS 0 l > I ' ° Dm • — ■ > 1 3 1 1

b) - Expression of the overall correction factor к

E q ua t io n (9 ) in t ro d u c e s " k " , th e o v e r a l l d o s im e t r ic c o r

r e c t i o n f a c t o r , which accounts f o r th e la c k o f e q u iva len ce o f

m a te r ia l "w" and "d " to th e am b ien t medium "m" :

^m " < 0 d > c a v • ^

In e qu a t io n (10 ) the " k " f a c t o r i s expressed as a fu n c

t i o n o f the th re e f a c t o r s h^,. h2 and h j , r e s p e c t i v e ly , d e f in e d

as th e r a t i o s o f <Dd y c a v , <DdîW>cav and <Dd>d>cav to Dm :

Components h-^, h2 and hß can be d e r iv e d by combin ing (17 ) and

( 3 1 ) , (22 ) and ( 3 1 ) , (27 ) and (3 1 ) .

IAEA-SM-298/28 63

Tab le I . PARTICULAR EXPRESSIONS FOR COMPONENTS h b h2 AND h3

OF THE OVERALL DOSIMETRIC CORRECTION FACTOR " k " .

Assumption S p e c i f i c r e l a t i o n s h ip s

- a -

xw <<Rw

( u l t r a t h i n

wal 1 ) h3 (see r e l a t i o n 34)

V >Rw

( t h i c k w a l l )

hx = О

h2 = <ud ,w >cav •

h3 (see r e l a t i o n 34)

x d < < Rd

(B ragg-G ray

cav i t y )

hl ~ uw,m • • ^ w ’ m^ z ’m 'E *

vw ■ (S .M )“ . ( S 2 '« ) y .'m ■ ^ w . w ' Z - { W j

h3 = 0

x « R w , w and

x « R , d d( id e a l dosemeter)

hl - ( sm)m^C

h2 = 0

h3 = 0

a. xw and Xçj a re th e w a l l and c a v i t y th ic k n e s s e s , r e s p e c t i v e l y ;

R i s th e range o f secondary e le c t r o n s

64 MOSSE et al.

3 ,4 - P a r t i c u l a r cases

C e r ta in p a r t i c u l a r cases may occur in p r a c t i c e , where ex

p re s s io n s f o r hls h2 and h3 can be s i m p l i f i e d . They a re g ive n

i n Tab le I .

4 - EXPERIMENTAL PROCEDURES

The p rocedures fo l lo w e d fo r e s t a b l i s h in g th e re fe re n c e i n

te rm s o f absorbed dose in w a te r a re p resen ted i n S e c t io n 2.

4 .1 - L a b o ra to ry f a c i l i t i e s

The e xpe r im en ta l work in v o lv e d [ 2 ] us ing the L a b o r a to r y ’ s

" c o b a l t № 2" beam f a c i l i t y , c o n s i s t i n g o f an "A lc y o n " ty p e ,

c o b a l t th e ra p y u n i t and a " C o l l i r e " c o l l i m a t o r . The l a t t e r de

f i n e s a h o r iz o n ta l c o n ic a l beam w i th a d iam e te r o f 8 .7 cm a t one

m eter from the source.

The g ra p h i te phantom i s i n th e shape o f a r e c ta n g u la r

b lo c k . The en tran ce s u r fa c e , w i th d im ens ions 30 cm x 30 cm, i s

c e n te re d on the beam and p e rp e n d ic u la r to i t s a x is . Phantom

depth a long the c e n t e r l i n e i s 20 cm. The phantom fe a tu r e s a

c e n t r a l c y l i n d r i c a l p a r t , 18 cm in d ia m e te r , c o n s is t in g o f

in te rc h a n g e a b le d is k s w i th v a r io u s th ic k n e s s e s . A l l th e t r a n s

f e r dosemeters used in th e p rocedure a re in s e r t e d and cen te re d

i n such d is k s , which a re i n d i v i d u a l l y b u i l t f o r each dosemeter.

The w a te r phantom s iz e and shape a re the same as above.

I t s s t r u c t u r e i s a 15 mm t h i c k p o ly m e th y l -m e ta c r y la te (PMMA)

w a l l . The e n trance window, c y l i n d r i c a l i n shape, i s 12 mm in

d ia m e te r w i th 4 mm th ic k n e s s . For measurement pu rposes , the

IAEA-SM-298/28 65

phantom i s f i l l e d w i th w a te r and th e dosemeters a re c e n te re d on

th e beam a x is .

The g r a p h i t e c a lo r im e te r used in our expe r im en ts i s the

p r im a ry s ta nd a rd o f absorbed dose f o r c o b a l t 60 photons [1 1 ,

12, 1 3 ]. The c a lo r im e t e r i t s e l f c o n s is ts o f th re e g r a p h i t e e le

m en ts , i n c lu d in g th e abso rber which i s a c e n t r a l l y lo c a te d d isk

16 mm i n d ia m e te r and 3 mm t h i c k .

Three t r a n s f e r dosemeter systems were used : a s m a l l ,

t h i n - w a l l e d i o n i z a t i o n chamber, fe r r o u s s u l f a t e dosemeters ( o f

th e F r i c k e ty p e ) and a la n in e dosemeters processed by an e le c

t r o n s p in resonance measurement te c h n iq u e (ESR).

The NE 2571 i o n i z a t i o n chamber i s o f th e c y l i n d r i c a l -

ta p e re d ty p e , f e a t u r in g an in t e r n a l volume o f 0 .6 cm3 and 0 .36 mm

w a l l t h ic k n e s s . When used f o r measurements in s id e th e phantom,

th e chamber i s p ro te c te d by a ve ry t h i n p l a s t i c i n s u l a t o r .

The F r i c k e dosemeter [1 4 ] i s th e second t r a n s f e r system.

The fe r r o u s s u l f a t e s o lu t i o n i s h e ld in f l a t c y l i n d r i c a l

c o n ta in e rs made o f PMMA w i th 0 .8 mm w a l l t h ic k n e s s . A d d i t io n a l

caps o f the same m a t e r i a l , w i th 1, 2 o r 3 mm th ic k n e s s a re

p la c e d on th e dosemeter when making measurements in the w a te r

phantom. The i n t e r n a l c a v i t y o f th e chemical dosemeter i s

25.7 mm in d ia m e te r and 6 mm t h i c k ; the volume a v a i l a b le f o r

th e F r i c k e s o lu t i o n i s thus 3 .1 cm3 .

The t h i r d t r a n s f e r dosemeter system i s based on alanine

ESR sp e c t ro m e try [ 1 5 ] . The d e te c to r m a te r ia l i s L -a la n in e

a m in o -a c id , i n th e form o f a ve ry f i n e powder. For measurement

purposes , th e powder i s h e ld i n f l a t , c y l i n d r i c a l PMMA c y l i n

ders w i th 1 mm w a l l th ic k n e s s . The i n t e r n a l c a v i t y i s 16 mm in

d ia m e te r w i th 2 mm th ic k n e s s ; i t s volume i s th us 0 .4 cm3 .

66 M OSSE et al.

T ab le I I . REFERENCE VALUES OF ( D j ) r e f IN THE GRAPHITE PHANTOM

i x/mm Xg/(g.cm“2) ( D j ) r e f / (G y .h -1 )

- a - - b - - с - - d - e -

1 983.9 2.741 38.99

2 1000.0 5.512 35.26

3 1011.8 7.522 32.44

a. i d e n t i f i c a t i o n o f measurement p o in t i n g ra p h i te phantom.

b. d is ta n c e from th e source to measurement p o in t " i " i n th e ho

mogeneous phantom.

c . mass per u n i t area a t measurement p o in t " i " i n g r a p h i t e -

e q u iv a le n t medium [ 1 ] .

d. absorbed d o s e ra te in g r a p h i t e , measured a t p o in t " i " o f the

homogeneous g ra p h i te phantom, as o f 0 1 /0 1 /8 5 a t 0 .0 0 h.

e. u n c e r t a i n t i e s a s s o c ia te d w i th (D’ ) r e f [ 1 ] :

. e s t im a te d r e l a t i v e s tanda rd d e v ia t io n ( ty p e A

u n c e r t a in t y ) : 0 .032 %

. e v a lu a te d r e l a t i v e s tandard d e v ia t io n ( ty p e В

u n c e r t a in t y ) : 0 .242 %

. compound r e l a t i v e s tandard d e v ia t io n : 0 .244 %.

Tab le I I I . TRANSFER

IAEA-SM-298/28

DOSEMETER READINGS IN THE

67

GRAPHITE PHANTOM

i

- a -

j

- b -

x/mm

- с -

X g / ( g . c m " 2 )

- d -

( 4 j J ) *

- e -

1 982.3 2.405 - 2 .8998x lO -1 0 A

1 2 983.4 2.298 0.15497 h ' 1

3 983.9 2.757 2 .1 8 1 2 xlO-3 h ' 1

1 998.3 5 .179 - 2 .6 3 2 5 x l0 _10A

2 2 1000.0 5.054 0.13995 h _1

3 1000.0 5.535 1 . 9675X10"3 h _1

1 1010.4 7.184 - 2.4310X10“ 10A

3 2 1011.8 7.077 0.12889 h ' 1

3 1011.8 7.535 1 . 8173X10-3 h " 1

a. i d e n t i f i c a t i o n o f measurement p o in t i n th e g r a p h i t e phantom.

b. t r a n s f e r dosemeter i d e n t i f i c a t i o n (1 : i o n i z a t i o n chamber ;

2 : F r i c k e - t y p e dosemeter ; 3 : a la n in e dosem e te r) .

c . d is ta n c e from th e source to th e e f f e c t i v e measurement p o in t

o f th e t r a n s f e r dosemeter ( th e e f f e c t i v e measurement p o in t

o f th e i o n i z a t i o n chamber i s lo c a te d fo rw a rd o f th e geome

t r i c a l c e n te r , a t a d is ta n c e equal to 0 .5 t im es the i n t e r n a l

r a d iu s o f th e a i r c a v i t y [ 1 ] ) .

d. mass per u n i t a rea a t the e f f e c t i v e measurement p o in t o f

th e t r a n s f e r dosem ete r, i n g r a p h i t e - e q u iv a le n t medium (see

" c " above).

e. re a d in g s c o r r e c te d f o r n o n -d o s im e t r ic pa ram e te rs , expressed

as o f 0 1 /0 1 /8 5 a t 0 .00 h ( a s s o c ia te d u n c e r t a in t ie s a re g i

ven in T a b le V ) .

Tab le IV . TRANSFER DOSEMETER READINGS IN THE WATER PHANTOM

68 MOSSE et al.

j

- a -

A xw/mm

- b -

x/mm

- с -

X . / ( g . cm 2) water 3

- d -

J i z ) *^water'

- e -

1 0 .36 998.4 5.078 2 .4 8 4 9 x l0 - 10 A

2 0 .8 1000.0 4 .993 0.13330 h " 1

2 1.8 1000.0 4.974 0.13464 h ' 1

2 2 .8 1000.0 4 .595 0.13499 h’ 1

2 3 .8 1000.0 4.936 0.13457 h ' 1

3 1.0 1000.0 4.981 1.9096X10-3 h“ 1

a. t r a n s f e r dosemeter i d e n t i f i c a t i o n (1 : i o n i z a t i o n chamber ;

2 : F r i c k e - t y p e dosemeter ; 3 : a la n in e dosem ete r) .

b. th ic k n e s s o f dosemeter w a ll i n th e case o f t r a n s f e r i n th e

w a te r phantom.

c . d is ta n c e from th e source to the e f f e c t i v e measurement p o in t

o f the t r a n s f e r dosemeter ( th e e f f e c t i v e measurement p o in t

o f the i o n i z a t i o n chamber i s lo c a te d fo rw a rd o f th e geome

t r i c a l c e n te r , a t a d is ta n c e equal to 0 ,5 t im es the in t e r n a l

r a d iu s o f th e a i r c a v i t y [ 1 ] ) .

d. mass per u n i t area a t the e f f e c t i v e measurement p o in t o f the

t r a n s f e r dosemeter, i n w a t e r -e q u iv a le n t medium (see "c "

above) .

e. re a d in g s c o r re c te d f o r n o n -d o s im e tr ic pa ram ete rs , expressed

as o f 0 1 /0 1 /8 5 a t 0 .00 h. (a s s o c ia te d u n c e r t a in t ie s a re

g iv e n in ta b le IV ) .

IAEA-SM-298/28 69

Table V. Uncertainties associated with the measurement of ratio

j

- a - - b - - С -

1 0 .003 % 0.152 %

2 0.139 % 0.120 %

3 0 .173 % 0.164 %

a. i d e n t i f i c a t i o n o f t r a n s f e r dosemeter (1 : i o n i z a t i o n cham

ber ; 2 : F r ie k e - t y p e dosemeter ; 3 : a la n in e dosem ete r) .

b. e s t im a te d r e l a t i v e s ta nd a rd d e v ia t io n o f measured r a t i o

-p*.c . e v a lu a te d r e l a t i v e s ta nd a rd d e v ia t io n o f measured r a t i o

< А К ) * / ( ^ 4 ) * .water ' v g

4 .2 - E xp e r im e n ta l data

The re fe re n c e va lues o f absorbed dose i n g r a p h i t e ,

Í Dg) r e f » measured a t p o in t " i " u s in g th e g r a p h i t e c a lo r im e te r

a re shown in Tab le I I .

The " j " t r a n s f e r dosemeters a re c a l i b r a t e d under quasi

i d e n t i c a l c o n d i t io n s a t the th re e depths " i " in th e g ra p h i te

phantom. Tab le I I I shows re a d in g s >j ) * c o r re c te d f o r the

70 MOSSE et al.

n o n -d o s im e t r ic param eters s p e c i f i c to th e measurement te c h n iq u e

used, b u t n o t y e t f o r la c k o f a d ju s tm e n t in dosemeter p o s i t i o

n ing w i t h i n th e g r a p h i t e phantom. F o l lo w in g c a l i b r a t i o n in the

g r a p h i t e phantom, th e t r a n s f e r dosemeters a re i r r a d i a t e d in the

w a te r phantom. Tab le IV shows re a d in g s <d(jàter)*, c o r re c te d

f o r th e n o n -d o s im e t r ic param eters s p e c i f i c to th e measurement

te c h n iq u e used, b u t n o t y e t f o r la c k o f a d jus tm e n t in dosemeter

p o s i t i o n i n g w i t h i n th e w a te r phantom. Table V shows the unce r

t a i n t i e s a s s o c ia te d w i th r a t i o s ( o ^ ater) ’

5 - CONCLUSION

In t h i s f i r s t r e p o r t , we have d e s c r ib e d th e p ro c e d u re , the

fo rm a l is m and the expe r im en ta l equ ipm ent, r e q u i r e d f o r s e t t i n g

up a re fe re n c e f o r absorbed dose i n w a te r in a c o b a l t - 6 0 Y ray

beam. The b as ic r e s u l t s o f measurement a re a ls o p resen ted :

they concern th e e xpe r im en ts perform ed w i th the g r a p h i t e c a lo

r im e te r - which c o n s t i t u t e s the p r im a ry s tanda rd in s t ru m e n t f o r

absorbed dose - and w i th th e th re e t r a n s f e r in s t ru m e n ts chosen

( i . e . , th e i o n i z a t i o n chamber, th e F r i c k e dosemeter and the

a lan ine /E S R dosem e te r) . The q u a l i t y o f these r e s u l t s appears to

be s a t i s f a c t o r y and adapted to th e goal o f th e program, c o n s i

d e r in g th e h igh le v e l o f accuracy ach ieved w i th each o f the

fo u r d o s im e try systems used. I t i s then p o s s ib le to c o n s id e r

th e second s tep which w i l l concern th e t re a tm e n t o f th e data

o b ta in e d , in o rd e r to d e r iv e the re fe re n c e va lu e o f absorbed

dose i n w a te r .

T h is w i l l be the s u b je c t o f a second r e p o r t , i n which each

s e t o f data s h a l l be co ns ide red w i th the c h a r a c t e r i s t i c s o f the

dosemeter in v o lv e d , i n th e frame o f th e fo rm a lism adopted f o r

e s t im a t in g th e complex d o s im e t r ic c o r r e c t io n f a c t o r s to be

IAEA-SM-298/28 71

a p p l ie d i n such measurements. The absorbed dose va lu e s o b ta in e d

w i th th e th re e t r a n s f e r dosemeters w i l l then be compared in

te rm s o f independen t u n c e r t a i n t i e s , and i f no s i g n i f i c a n t b ia s

i s fo u n d , th e f i n a l v a lu e w i l l be d e r iv e d by c a l c u l a t i o n o f the

w e ig h te d mean.

R E F E R E N C E S

[ 1 ] Comité F ra n ç a is "Mesure des Rayonnements I o n i s a n t s ,

Recommandations pour la mesure de la dose absorbée en r a

d io t h é r a p ie , 1986, Rapport CFMRI n° 2 " , monographies du

Bureau N a t io na l de M é t r o lo g ie , E d i t i o n s CHIRON, P a r is .

[ 2 ] ZITOUNI, Y . , C o n t r ib u t i o n à l ' é t a b l i s s e m e n t d 'u ne r é fé r e n

ce de dose absorbée dans l ' e a u pour le s photons du

c o b a l t - 6 0 , thèse n° 50, U n iv e r s i t é Paul S a b a t ie r (S c ie n c e s ) ,

Toulouse ( F ra n c e ) , 7 j u i l l e t 1986.

[ 3 ] SIMOEN, J . P . , G é n é ra l i s a t io n de la th é o r ie de la c a v i t é au

cas des n e u tro n s . A p p l i c a t i o n au c a lc u l de l a s e n s i b i l i t é

d 'u n d o s im ê t re , B iom ed ica l d o s im e try : p h y s ic a l a s p e c ts ,

i n s t r u m e n t a t io n , c a l i b r a t i o n , I AEA-SM-249 /48 , ( 4 5 -6 0 ) ,

P a r is , 27-31 o c to b re 1980, IAEA Vienna (1981 ).

[ 4 ] INTERNATIONAL COMMISSION ON RADIATION UNITS AND

MEASUREMENTS, R a d ia t io n Q u a n t i t i e s and U n i t s , ICRU Report

33, (19 80 ) .

[ 5 ] BURLIN, T . E . , A genera l th e o ry o f c a v i t y i o n i z a t i o n ,

B r i t i s h Jo u rna l o f R ad io logy 39 (1 9 6 6 ) , 727-734.

72 MOSSE et al.

[ 6 ] SHIRAGAI, A . , NODA, Y . , MARUYAMA, T . , Some r e l a t io n s h ip s

between d o s im e t r ic q u a n t i t i e s i n photon and e le c t r o n

beams, Japanese Jou rna l o f A p p l ie d P h y s ic s , 2 ^ ( 3 ) , March

1982, 523-528.

[ 7 ] GREENING, J . R . , The concep t o f kerma and i t s r e l a t i o n s

h ip s , Chap. 6 , i n Fundamentals o f R a d ia t io n D os im e try ,

Medica l Phys ics Handbooks _15, 2nd e d i t i o n (1 9 8 6 ) , Adam

H i lg e r L td .

[ 8 ] BATHO, H .F . , R e la t io n s h ip s between exposure , kerma and

absorbed dose i n a medium exposed to m egavoltage photons

f rom an e x te rn a l so u rce , 1968, Phys ics i n M ed ic in e and

B io lo g y , 13 ( 3 ) , (1 9 6 8 ) , 335-346.

[ 9 ] ROESCH, W.C., A c o r r e c t io n f o r r a d ia t i o n n o n - e q u i l i b r iu m ,

Report BNWL-SA-1014, W ash ington , D.C. (June 19-22 , 1967).

[ 1 0 ] LOEVINGER, R . , A fo rm a l is m f o r c a l c u la t i o n o f absorbed do

se to a medium from photon and e le c t r o n beams, medica l

Phys ics 8 ( 1 ) , (Jan /Feb . 1981) , 1-12.

[ 1 1 ] CAUMES, J . , Mesures d o s im é tr iq u e s fondam enta les dans un

fa is c e a u de RX de 35MV en vue de la d é te rm in a t io n du re n

dement ra d io c h im iq u e G(Fe3 + ) du d os im è tre au s u l f a t e f e r

r e u x , thèse n° 2206, 5 mars 1979, U n v e rs i té Paul S a b a t ie r

de Toulouse (S c ie n c e s ) .

[ 1 2 ] MOSSE, D . , D é te rm in a t io n des c o n s ta n te s r a d io m é tro lo g iq u e s

G(Fe3+) e t Wa^r /e dans un fa is c e a u d ’ é le c t r o n s de 35 MeV,

thèse n° 2295, 26 novembre 1979, U n iv e r s i t é Paul S a b a t ie r

de Toulouse (S c ie n c e s ) .

IAEA-SM-298/28 73

[ 1 3 ] MOSSE, D . , CANCE, M ., STEINSCHADEN, K . , CHARTIER.M.,

OSTROWSKY, A . , SIMOEN, J . P . , D é te rm in a t io n du rendement du

d o s im è tre au s u l f a t e f e r r e u x dans un fa is c e a u d 'é le c t r o n s

de 35MeV, 1982, Phys ics in M ed ic ine and B io lo g y , 7J_ ( 4 ) ,

583-596.

[ 1 4 ] GUIHO, J . P . , SIMOEN, J . P . , C o n t r ib u t io n à la conna issance

des co n s ta n te s fondam enta les W e t G in t e r v e n a n t dans le s

mesures de dose absorbée , 10-14 march 1975, i n t e r n a t i o n a l

Symposium on Advances in B iom edica l D o s im e try ,

IAEA-SM-1 9 3 /7 1 , V ienna.

[1 5 ] MOSSE, D .C ., Le système d o s im é t r iq u e de ré fé re n c e à

Г a la n in e du LMRI, 1987, Note CEA ( to be p u b l is h e d ) .

IAEA-SM-298/104

THE HIGH ENERGY DOSIMETRY SYSTEM GÖTTINGEN — TWELVE YEARS CONTROLLED ACCURACY AND STABILITY

B. MARKUS, G. KASTEN Abteilung Klinische Strahlenbiologie

und Klinische Strahlenphysik,Zentrum Radiologie,Georg-August-Universität Göttingen,Göttingen,Federal Republic of Germany

Abstract

THE HIGH ENERGY DOSIMETRY SYSTEM GÖTTINGEN - TWELVE YEARS CONTROLLED ACCURACY AN D STABILITY.

The high energy dosimetry system Göttingen is the first and so far only absolute measuring system o f ionization dosimetry for high energy electrons and photons in practical use and performs direct calibrations in electron and photon beams. It consists o f a graphite double extrapolation chamber as the primary standard, a small parallel-plate chamber as a secondary standard and field dosimeter chamber, and a ferrosulphate dosimeter as a transfer dosimeter. The estimate o f the Bragg-Gray dose of air, Da, in the graphite chamber (phantom) is ‘absolute’. The dose to water, D w, at the same point is Dw = swa-Da. The accuracy o f the system is given — apart from the fact o f direct instead o f мСо or 2 MV calibration with a number o f semi-empirical correction factors — by that o f all magnitudes needed and correction factors gained experimentally by the system itself and reduced to general physical and dosimetric constants. The relative mass stopping power, sw a, is experimentally evaluated combining ionization and ferrosulphate dosimetry, and essentially given by the product o f the dosimetric constants W-G-e . Except for air density and saturation losses, corrections are included in the calibration factor, also for field perturbation. The simplicity o f the system is first given by the choice o f the reference energies: Ep 0, the most probable energy at the surface, and Er the residual energy at depth z. sw a if referred to Er depends only on this one parameter for all initial energies and usual spectra between Er = 2 and 42 MeV and depths z < 0 .8 Rp. swa (Er) is simple to calculate by an interpolation formula to better than ±0.3%. Another simplifying factor is the energy independence o f the air dose calibration factor, and a pertinent small polarity effect o f < 0 .5 %. The latter is valid also for high energy photon beams, at least between 8 and 42 MeV. An analogous procedure as for electrons can be applied. A comparison o f the long term stability o f the primary/secondary and the primary/ferrosulphate standards shows random deviations o f < 0 . 1 and < 0 .2 , respectively. The total uncertainty o f ±1.8% for a water dose in a low Z phantom at points with full or restricted particle equilibrium the authors consider further fulfilled.

The high energy dosimetry system Göttingen is so far the only absolute measuring system of ionization dosimetry for high energy electrons and photons in practical use and performs direct calibrations in electron and photon beams. It consists o f a graphite double extrapolation chamber as the primary standard, a small parallel-plate

75

76 MARKUS and KASTEN

FIG. 1. Principle o f the absolute measurement o f a ir dose J. Collected ion charge A Q in A V equals compensating charge CK-AU K. E = zero electrometer.

FIG. 2. Cross-section (scheme) o f adjustable cylindrical measuring volume and collector area o f the graphite double extrapolation chamber. Side wall norm ally removed. M easures in mm [1].

chamber (‘electron chamber’) as a secondary standard and field dosimeter chamber, and a Fricke ferrosulphate dosimeter as a transfer dosimeter [1-4]. The estimate of the Bragg-Gray dose of air, Da, in the graphite chamber or graphite phantom, transferred to the parallel-plate chamber, is ‘absolute’. From this the dose to water, Dw, at the same point is given by Dw = sw a -D,,.

The air dose is measured according to the equation

a qJ = lim —----- ( 1 )

Д ш — о A m a

Da = (W/e)-J (2)

IAEA-SM-298/104 77

For measurement schemes and chamber construction see Figs 1,2. Essential are pure graphite chamber material, nearly homogeneous construction with very few other materials, negligible electrostatic and polarity effects, and double-volume extrapolation axially and radially to zero.

The accuracy of J (С/kg) determined with the primary standard is ±1.15% [1].Figure 3 shows an example of measured extrapolation curves for 15 MeV elec

trons at different depths. The steepness defines the grade of transient and full particle equilibrium, the latter existing at a graphite depth of 2.19 mm, the former below this depth [1].

The parallel-plate chamber (‘electron chamber’) constructed of Plexiglas (PMMA) is of the small volume (0.06 cm3) and small collector volume type [2, 5] (for principal cross-section see Fig. 4) which defines the main features: small electrostatic and polarity influences, small dependence on beam direction and on beam energy of the calibration factor [2]. The chamber is watertight if used with its water protection cap of 1 mm water equivalent. The only changes in the construction after the first year of experience were an improved chamber cable and a larger (6 mm as opposed to 5 mm) measuring volume diameter which was of advantage in minimizing the polarity effect. The dose reproducibility lies within ±0.5% . The equipment comprises a radioactive Sr-control device, its ionization current being part of the calibration protocol.

Using the calibration protocol and following the application manual, no further corrections are necessary besides saturation losses and air density, especially not for field perturbation.

An essential feature of the system is the manner of obtaining the water dose from the air dose at a specific point (depth) of interest in a phantom. Provided a certain electron energy at the surface is given with a sufficiently narrow energy distribution, the local value of the stopping power ratio may be referred to the mean electron energy, E, at depth, z, depending on the energy at the surface. swa then becomes a function of the two variables E(z=0) and z. So a two-dimensional matrix, sw a(E0,z), is an essential part of many recommended protocols in electron dosimetry. (Sometimes E0 is replaced by the measured practical range, Rp, of the individual electron beam.) Herein lies the difference and the simplification of our system.

We introduce another energy, the ‘residual energy’, Er, at depth z, as well as the most probable energy at the surface Ep0. Er in contrast to E is linearly dependent on depth and leads to the one-parametric form of the stopping power ratio, sw a(Er), for every initial energy and every depth in the whole range of application, at least EPi0 = 5 ... 42 MeV, z = 0 ... 0.8 Rp.

The cause is the linear relation of Er to the ‘residual range’, Rr, analogous to Ep0 and Rp [6, 7]. As shown in Fig. 5

R r = R p - z (3)


FIG. 5. Residual electron range Rr = Rp - z for the residual energy Er o f two different electron energies E¡, E2 in the depths z¡, z2.

E r (MeV)

FIG. 6. Experimental relative mass stopping power, sw a, as a function o f residual energy Er for different energies Ep 0. Insert: Interpolation formula (Trier [9]).

IAEA-SM-298/104 79

FIG. 3. Example o f measured and extrapolated values AQ/AV and Q/V as a function o f electrode distance d o f the graphite double extrapolation chamber for different depths in graphite t. EPi0 = 15.0 MeV [I].

В 2 1 s aT

-30*-т а

-30*-

FIG. 4. Parallel-plate chamber. Geometrical cross-section (A), water protection cap (B), distance ring (C) [2].

We apply the range-energy relation [8] ‘to the electrons at depth, z, with a residual range, Rr’

Rp-p(Z/A) = 0.285 Ep>0 - 0.137 (4a)

Rr-p(Z/A) = 0.285 Er - 0.137 (4b)

Substituting Rp and Rr in Eq. (3):

- Er = Epo — 3.51(Z/A)-p-z w (5a)

= Ep 0 - 1.955z for water (5b)

The application is shown in Fig. 6: swa(Er) for initial energies Ep0 of 5.03 ...42.83 MeV coinciding in a single curve for different depths (Er).


M e a s u re m e n t d e p th (c m g ra p h ite )

FIG. 7. Coinciding depth dose distributions in graphite measured by graphite double extrapolation chamber, parallel-plate ('electron') chamber and ferrosulphate. Ep 0 = 15.07 MeV [2].

IAEA-SM-298/104 81

90

80

70

60

100

TJS 50

< 40

30

20

10

0\

J ___ V-0 1 2 3 4 5 6 7 8

M e a su re m e n t d e p th (c m w a te r)

FIG. 8. Coinciding depth dose distributions in water, measured by parallel-plate (‘electron ’) chamber and ferrosulphate.

Values of the relative mass stopping power, sw a,, were determined experimen-tally combining absolute ionization and ferrosulphate dosimetiy [1] for the variouspoints, Er(Epo,z), as indicated [3, 6].

Dw = (W /e)-J-sw,a (6)

Dw = const(G-e)"1 (7)

— swa = const(W ■ G • e)'1 (8)1

The measured values of sw a may be interpolated by the formula in Fig. 6 to better than ±0.3% [9]. They coincide quite well with theoretical values [10], which are less than 1% smaller for higher energies (Er > 10 MeV) [3]. Furthermore, this sw a has been proved by application to dose measurements in various low Z materials in the same energy range: in graphite by a standard extrapolation chamber, ferrosulphate dosimetry in thin layers (1 mm) and by a parallel-plate chamber. An example for 15.07 MeV is shown in Fig. 7 [2]. Further comparisons have been made in water, tissue-equivalent phantom mass M3 [11] and Plexiglas. Figure 8 shows an example

1 The numerical values applied for W/e, G, e are according to ICRU Report 35 (1984).


E0 (M eV )

FIG. 9. Coinciding linear range-energy relation with different materials (graphite, Plexiglas, M3, water). Correlation coefficient r = 0.9999 [7].

P late s e p a ra tio n d (m m )

FIG. 10. Example o f measured values A Q/AV and Q/V as a function o f electrode distance d for different depths in graphite. Photon peak energies 8, 16, 30, 42 MV [4]. (Note: coinciding extrapolation to zero within every radiation quality, contrary to electrons, Fig. 3.)

IAEA-SM-298/104 83

of the dose distribution of 15 MeV in water measured with a parallel-plate chamber and a ferrosulphate dosimeter.

The calculation of equivalent depths for the determination of Ep 0 in various low Z materials follows Eq. (4a). Examples are shown in Fig. 9 for water, M3, Plexiglas and graphite. From this

One point still deserves attention in connection with the choice of Er and Ep 0 as the characteristic and reference energies in our system: it remains insensitive also to higher energy losses in the primary beam (for example, in foils). These energy losses cause complications if mean energies are used instead. If the thickness of lead foils is increased manifold as is sometimes possible with betatrons (for example, 0.4 mm lead to 1.2 mm at 42 MeV, 0.25 mm to 1.2 mm at 30 MeV, 0.1 mm to0.6 mm at 15 MeV) in conjunction with drastic energy losses of several MeV, all the measured values of sw,a for the new Ep 0 and Er coincide perfectly with the expected values [7]. This signifies a further essential simplification in practical dosimetry over the whole range of energies available for radiotherapy.

With regard to the long term stability we performed comparisons within our calibration chain, the primary standard together with three independent dosimeters: an electron chamber with the appropriate Sr-check device, an N-chamber (0.6 cm3, PTW-Freiburg) with Ra and Sr-check devices, and a stabilized ferrosulphate dosimeter [12]. The results given by random samples between the primary versus secondary standard and versus ferrosulphate (i.e. experimental swa) are the following:

(z-p-Z/A), = (z-p-Z/A)2 (9)

Reproducibility

1976-1987

Primary standard Primary standard

Secondary standard Ferrosulphate

Random samples: Single swa-values:

Differences <0.1% Standard deviation <0.2%

Single values versus interpolation formula (Er = 2 ... 42 MeV):

Max. deviation <0.3%


FIG. 11. Experimental stopping power ratio (s^ J q fo r different radiation qualities Q o f high energy photon radiation [4]. Eg = peak energy; QI = quality index.

D e p th (c m P lexig las)

FIG. 12. Coinciding depth dose distributions in graphite, water, M3, Plexiglas measured by a graphite double extrapolation chamber or parallel-plate (‘electron’) chamber and ferrosulphate dosimeter. Depth scaling: (Z/A)-p-z. Photon peak energy 42 MV [4].

In addition, the reproducibility of the secondary standard versus ferrosulphate was measured with the result that the deviations for 90% of all repetitions (n = 77) lay below 0.5%, the maximum deviation being 0.8%.

Finally, the calibration stability of the electron chamber could be proved in about 42 chambers recalibrated after practical use up to 4 times after 1 to 8 years. The maximum deviation per year for 76% of the chambers was below 0.3%, for all chambers being below 0.7% (except one: 0.94%).

IAEA-SM-298/104 85

The applicability of this system to X-rays of at least 8 to 42 MV for estimating the dose to water has been proved [4]. As for electrons, the air dose under Bragg- Gray conditions is determined absolutely and the parallel-plate chamber becomes calibrated. In contrast to electron radiation, the energy spectrum in depths below the maximum of dose remains fairly constant (see Fig. 10) and sw a becomes a depth independent function for a radiation quality Q: (sw a)Q instead of sw a(Er). Figure 11 shows (sW 3 ) q as a function of quality index Q = 12о/1ю- The perturbation correction is included in the calibration factor as for electrons. The calibration factor for the air dose was found constant as for electrons in the energy range of our measurements.

The accuracy of a dose measurement with this method for a given radiation quality Q is the same as for electrons, ± 1.8 %. An additional uncertainty comes from the estimate of Q if another radiation quality is used.

As for electrons, we have compared the depth doses in graphite by the primary standard, the electron chamber and ferrosulphate, and also in water, M3, and Plexiglas by electron chamber and ferrosulphate. The depth dose curves coincide if the depth is transformed in the same manner as for electrons by the equation (z-p-Z/A), = (z -/o-Z/A)2, i.e. via electron density with good approximation. An example for 42 MV betatron photon radiation is shown in Fig. 12.

REFERENCES

[1] MARKUS, В., Eine polarisierungseffekt-freie Graphit-Doppelextrapolationskammer zur Absolutdosimetrie schneller Elektronen, Strahlentherapie 150 (1975) 307.

[2] MARKUS, B., Eine Parallelplatten-Kleinkammer zur Dosimetrie schneller Elektronen und ihre Anwendung, Strahlentherapie 152 (1976) 517.

[3] MARKUS, B., KASTEN, G., Absolute Ionisationsdosimetrie schneller Elektronen oberhalb von 15 MeV, Strahlentherapie 159 (1983) 435.

[4] MARKUS, B., KASTEN, G., “ Absolute Ionisationsdosimetrie ultraharter Röntgenstrahlung mittels Graphit-Doppelextrapolationskammer und ‘Elektronenkammer’ ” , Medizinische Physik 1983 (SCHÜTZ, J., Ed.), Hüthig-Verlag, Heidelberg (1984) 341.

[5] MARKUS, B., “ Ionization chambers, free of polarity effects, intended for electron dosimetry” , Dosimetry in Agriculture, Industry, Biology and Medicine (Proc. Symp. Vienna, 1972), IAEA, Vienna (1973) 463.

[6] MARKUS, В., KASTEN, G., Zum Konzept des mittleren Bremsvermögens und der mittleren Elektronenenergie in der Elektronendosimetrie, Strahlentherapie 159 (1983) 567.

[7] MARKUS, B., KASTEN, G., “ Zum Konzept des mittleren Bremsvermögens in der Elektronendosimetrie. Eine Fortsetzung und Entgegnung” , Medizinische Physik 1984 (SCHMIDT, Th., Ed.), Hüthig-Verlag, Heidelberg (1985).

[8] MARKUS, B., Energiebestimmung schneller Elektronen aus Tiefendosiskurven, Strahlentherapie 116 (1961) 280.

[9] TRIER, O., in Kohlrausch, Praktische Physik, 23rd edn, Par. 9 .8.6.3, Stuttgart (1985).[10] BERGER, M., SELTZER, S.M ., in Radiation Dosimetry. Electrons with Initial Energies

between 1 and 50 MeV, ICRU Report 21, ICRU, Washington, DC (1972).


[11] MARKUS, В., Über den Begriff der Gewebeäquivalenz und einige “ wasserähnliche” Phantomsubstanzen für Quanten von 10 keV bis 100 MeV sowie schnelle Elektronen, Strahlentherapie 101 (1956) 111.

[12] MARKUS, B., KASTEN, G., “ Kann die Eisensulfat-Dosimetrie zu einer Präzisionsmethode entwickelt werden?” , Medizinische Physik 1986 (von KLITZIKG, L., Ed.), Deutsche Gesellschaft für Medizinische Physik, Lübeck (1986) 233.

IAEA-SM-298/81

E X T E N S I O N O F T H E S P E N C E R - A T T I X C A V I T Y T H E O R Y T O T H E 3 - M E D I A S I T U A T I O N F O R E L E C T R O N B E A M S

A.E. NAHUMJoint Department of Physics,Royal Marsden Hospital

and Institute of Cancer Research,Sutton, Surrey,United Kingdom

Abstract

EXTENSION OF THE SPENCER-ATTIX CAVITY THEORY TO THE 3-MEDIA SITUATION FOR ELECTRON BEAMS.

The Spencer-Attix cavity theory is extended to the case of a non-medium equivalent dosimeter wall for electron irradiation. An expression is derived for the case of a thick wall in which all the 5-rays depositing energy in the cavity are generated. An approximate expression is given for a new quantity ^ed.waii.c = Dmed/Dc for an intermediate wall thickness, consisting of the weighted sum of the s-ratios for the ‘thick’ and ‘thin’ wall cases. This is cast in the form of a correction factor to the conventional S-A s-ratio and contains the quantities 4ы,с^т^,с> swaii,c/swaii.c and t, the proportion of the 6-ray cavity dose from wall-generated ¿-rays, for which an expression containing a cutoff energy related to the wall thickness, Awa]1, is given. Values of these quantities are given for wall materials ranging from A-150 plastic (I = 65.1 eV) through water (I = 75.0 eV) to aluminium (I = 166 eV) for 5, 10 and 20 MeV electrons as a function of depth, Awall and S-A cavity cutoff, Дс, derived from electron fluence spectra generated using the EGS4 user code FLURZ. The predictions of the theory are compared with an experiment involving graphite and aluminium walled chambers in a 20 MeV electron beam. The correct trend is predicted, but the closeness of the agreement depends critically on the values chosen for Дс and Awa„. Correction factors to the s ^ Krair-values given in dosimetry protocols to be applied to two commercially available thimble chambers, with A-150 and C-552 walls, respectively, are given; these do not deviate from unity by more than 0.5% for 10 MeV electrons at the reference depth. The limitations inherent in this simple theory, such as its restriction to wall thicknesses that do not significantly disturb the primary electron fluence, and the neglect of ¿-ray scattering differences between wall and cavity material, are discussed. The new theory should be viewed as a predictor of the order of magnitude of ‘wall’ effects rather than yielding exact numbers.

1 . INTRODUCTION

The S p e n c e r - A t t ix t h e o r y [ l ] i s c u r r e n t l y th e m ost s o p h is t ic a t e d w ay o f e v a lu a t in g th e s to p p in g -p o w e r r a t i o f o r d e t e c t o r s t h a t can b e t r e a t e d as B ra g g -G ra y c a v i t i e s . Thus

®med “ ^ c a v s m e d ,c a v

87

88 NAHUM

w h e re and D c a v a r e th e ab so rb e d d o ses in th e u n d is tu rb e dmedium and th e r a d i a t i o n - s e n s i t i v e e le m e n t o f th e d e t e c t o r r e s p e c t iv e ly , and s m e d ,c a v i s th e S p e n c e r - A t t ix s to p p in g -p o w e r r a t i o . The c o n d i t io n w h ic h m ust be f u l f i l l e d f o r i t s v a l i d i t y i s

The detector should be such that the fluence of charged partic les entering the cavity should be the same as that present at the same position In the undisturbed medium.

T h is i n t u r n im p lie s t h a t

1 ) The d e t e c t o r i s " s m a l l” , and

2 ) The r a d i a t i o n - s e n s i t i v e e le m e n t o f th e d e t e c t o r , h e r e a f t e r r e f e r r e d t o as th e c a v i t y , s h o u ld b e made o f one m a t e r ia l o n ly and a n y w a l l p re s e n t s h o u ld be m e d iu m -e q u iv a le n t .

I n th e c a s e o f p h o to n beam s, c o n d i t io n 1 ) im p l ie s t h a t th e ra n g e o f th e c h a rg e d p a r t i c l e s m ust b e v e r y much g r e a t e r th a n th e mean c h o rd le n g th in th e c a v i t y . The o n ly p r a c t i c a l d o s im e te r f u l f i l l i n g t h i s c o n d i t io n i s th e a i r - f i l l e d i o n i s a t i o n cham ber. I n th e c a s e o f e le c t r o n beam s, even f o r v e r y s m a l l a i r c a v i t i e s , f u l f i l l i n g l ) i s p r o b le m a t ic a l due t o th e la r g e s c a t t e r in g d i f f e r e n c e s b e tw e e n th e w a t e r - l i k e medium and th e a i r . T h is i s h a n d le d b y in t r o d u c in g a p e r t u r b a t io n f a c t o r [ 2 ] . T h is ty p e o f c o r r e c t io n t o th e p r im a r y e le c t r o n f lu e n c e w i l l n o t b e f u r t h e r m e n tio n e d i n w h a t f o l lo w s .

The io n cham bers i n common use i n t h e a b s o lu te d o s im e try o f m e g a v o lta g e p h o to n and e le c t r o n beams do n o t g e n e r a l ly f u l f i l c o n d i t io n 2 ) , i . e . m e d iu m -e q u iv a le n t w a l l . F o r p h o to n beams t h i s d e v ia t io n i s c o r r e c te d i n t h e v a r io u s n a t io n a l and i n t e r n a t i o n a l d o s im e try p r o t o c o ls [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 1 0 , 1 1 , 1 2 ] u s in g th e a p p ro x im a te A lm o n d-S ven sson e x p r e s s io n [ 1 3 ] . In th e c a s e o f e le c t r o n beams th e S A - r a t io i s a p p l ie d d i r e c t l y , th u s n e g le c t in g a n y d i f f e r e n c e s b e tw e e n S—r a y g e n e r a t io n and s lo w in g -d o w n i n th e medium and i n th e a c t u a l w a l l m a t e r ia l . As t h e v a s t m a jo r i t y o f 6 - r a y s h a v e v e r y s h o r t ra n g e s th e n even f o r v e r y t h in - w a l le d a i r - c a v i t i e s m ost o f th e e - r a y s d e p o s it in g e n e rg y in th e a i r c a v i t y w i l l h a v e o r ig in a t e d i n th e w a l l r a t h e r th a n th e medium ( F i g . l ) .

I n th e p r e s e n t w o rk S -A t h e o r y i s e x te n d e d t o ta k e a c c o u n t i n an a p p ro x im a te m anner o f th e e f f e c t o f th e m a t e r ia l in th e w a l l o f th e d o s im e te r on i t s re s p o n s e i n e le c t r o n beam s. The new t h e o r y i s e v a lu a te d f o r one p a r t i c u l a r e x p e r im e n t w h e re th e

e f f e c t o f a non-m edium e q u iv a le n t w a l l was c l e a r l y shown t o be s i g n i f i c a n t [ 1 4 ] and d a t a i s g iv e n t o e n a b le th e e x p r e s s io n s to b e e v a lu a te d f o r th e w a l l m a t e r ia ls coimnonly used i n th e io n cham bers em ployed i n e l e c t r o n beam d o s im e tr y .

IAE A-SM-298/81 89

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FIG. I. Schematic o f the 3-media situation fo r a dosimeter with a non-medium equivalent wall irradiated by electrons.

2 . THEORY

2 . 1 The S p e n c e r - A t t ix c a v i t y i n t e g r a l

The b a s ic e x p r e s s io n i n S -A t h e o r y cam b e w r i t t e n as [ 2 , 1 5 , 1 6 ]

I * [ф‘ ° ‘ ( Л =»с С5<А=>/Р> (2>

C

w h ere л»Dç < ) i s th e a b s o rb e d d o s e t o th e c a v i t y ,

[ ♦ t o t ] i s th e t o t a l , i . e . p r im a r y + a l l g e n e r a t io n s E с

o f 8 - r a y s , e le c t r o n f lu e n c e i n th e c a v i t y , d i f f e r e n t i a l

i n e n e r g y ,

( L / p ) ü c i s th e mass c o l l i s i o n s to p p in g p o w er i n th e

c a v i t y , r e s t r i c t e d t o lo s s e s le s s th a n Дс ,

i s th e ( u n r e s t r i c t e d ) n a s s c o l l i s i o n

s to p p in g p o w er i n t h e c a v i t y a t e n e r g y A ç , and

Aj, i s a c u t - o f f e n e rg y r e la t e d t o th e mean c h o rd

le n g th i n t h e c a v i t y [ l ]

T he second te rm i s t h e com ponent o f a b s o rb e d d o s e i n t h e c a v i t y d ue t o s o - c a l le d " t r a c k - e n d s " [ 1 5 , 1 6 ]

90 NAHUM

The B ra g g -G ra y c o n d i t io n im p l ie s t h a t [<*^o t ] c c a n b e

r e p la c e d b y [ ♦ E ° t ] roe<j» t h e e le c t r o n f lu e n c e p r e s e n t i n th e un

d is t u r b e d m edium . R e p la c in g " c " b y "med” f o r t h e s to p p in g p o w ers y i e l d s t h e a b s o rb e d d ose t o th e medium and th e n

SA3 raed ,c “ g» ( 3 >

Dc (Д с)

} * 1* T ( Í ° ' U S W ' C 0 1 . C * °

A m ore c o n v e n ie n t n o t a t io n f o r th e SA c a v i t y i n t e g r a l can be d e f in e d b y w r i t i n g Equ( 3 ) as

^ m e d ^ c 1 ( * m e d '^ in e d '^ c )s SA = ------------------- = ------------------------------------------ ( 4 )Шви i О nSA / & \ * SA / ж, t a \

c 1 (♦ m e d 'Lc ' Ac>

w h e re th e I a ( ....... ) r e p r e s e n ts th e sum o f t h e i n t e g r a l o v e r th ef lu e n c e s p e c tru m and th e t r a c k - e n d te r m .

I n g e n e r a l , [ ♦ e ^ lm e d f o r a u n ifo rm medium can b e o b ta in e dfro m a c o m b in a t io n o f a n a l y t i c a l te c h n iq u e s and M o n te -C a r lo s im u la t io n p r o v id e d t h a t th e in c id e n t f lu e n c e i s known in

e n e r g y and a n g le [ 1 6 , 1 7 , 1 8 ] . Thus v a lu e s o f s p ä t e r , a i r h a v e

b e e n com puted f o r m o n o e n e rg e tic e le c t r o n beam s i n w a te r [ 5 , 1 5 ] . I n th e c a s e o f a non-m edium e q u iv a le n t w a l l i t i s n o t v a l i d

t o r e p la c e [ * ^ o t ] c i n Equ( 2 ) b y i d e a l l y a M o n te -

C a r lo s im u la t io n o f t h e e x a c t d e t e c t o r g e o m e try w o u ld b e needed [ c f . 19 f o r a C o -6 0 b e a m ]. The a p p ro a c h ta k e n i n t h i s w o rk i s t o f i n d an a p p ro x im a te e x p re s s io n f o r th e r a t i o 0 ^ / 0 ^ as a f u n c t io n o f w a l l m a t e r ia l and th ic k n e s s b a s e d on a s im p le 2 -c o m p o n en t m o d e l a n a lo g o u s t o t h a t u sed t o h a n d le th e e f f e c t o f a non-m edium e q u iv a le n t w a l l i n p h o to n beams [ 1 3 ] .

2 .2 T he t h i c k w a l l c a s e

C o n s id e r t h e s i t u a t i o n i l l u s t r a t e d i n F i g . 2 . The w a l l th ic k n e s s i s su ch t h a t th e w h o le o f th e S - r a y com ponent o f th e e le c t r o n f lu e n c e a t th e p o s i t io n o f th e c a v i t y i s g e n e ra te d in th e w a l l . I t i s f u r t h e r assumed t h a t t h e r e i s a p p ro x im a te

IAEA-SM-298/81 91

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FIG. 2. Schematic o f a thick walled dosimeter in a medium irradiated by electrons showing point X at the centre o f the wall.

6 - r a y e q u i l i b r iu m i n th e c e n t r e o f th e c a v i t y ; t h i s i s a gooda p p ro x im a t io n i n e le c t r o n beams e x c e p t c lo s e t o th e s u r fa c e[s e e b e lo w and a ls o 2 , 2 0 , 2 1 , 2 2 ] . The d ose t o th e w a l l a tp o in t X w i l l th e n b e g iv e n b y i n t e g r a t i n g t h e p r o d u c t o f th e

p r ip r im a r y e le c t r o n f lu e n c e [Ф Е and t h e ( u n r e s t r i c t e d )

s to p p in g p o w e r o v e r a l l e n e r g ie s p r e s e n t í

BG г p r i° w a l l “ j d e i^ E l w a l l ( S/ P > w a l l ( 5 )

о

w h ic h w i l l b e r e p r e s e n te d b y

BG pp^ w a l l ” 1 ( * w a l l ' ^ w a l l )

S i m i l a r l y , t h e d o s e a t X i n t h e u n d is tu rb e d m edium can b e w r i t t e n as

80 Rr®med ” 1 (* m e d '^ m e d )

The a s s u m p tio n i s now made t h a t t h e ’‘t h i c k " w a l l d o e s n o t d is t u r b t h e p r im a r y e le c t r o n f lu e n c e . T hu s c a n b er e p la c e d b y i n E q u (5 ) and

- lB G < l e l l ( t )

® w a l l “ lB G ( “ w a ll ' s w a l l )

92 NAHUM

u s in g th e n o t a t io n f o r th e u n r e s t r ic t e d s to p p in g -p o w e r r a t i o e s t a b l is h e d i n [ 2 ] .

I t i s now r e q u ir e d t o r e l a t e 0 C t o Dw a l l . T he S A - r a t io f o r c u t o f f Aç i s a p p r o p r ia t e . The t o t a l f lu e n c e s p e c tru m i n t h e c a v i t y i n t e g r a l s h o u ld s t r i c t l y b e a c o m b in a tio n o f th e p r im a r y f lu e n c e i n t h e u n d is tu rb e d medium and t h e 6 - r a y f lu e n c e g e n e ra te d b y t h i s p r im a r y f lu e n c e i n th e " t h ic k " w a l l . H o w eve r, su ch a f lu e n c e i s n o t r e a d i l y o b t a in a b le . In s t e a d , t h e t o t a l f lu e n c e f o r m e d iu m = w a ll a t an e q u iv a le n t d e p th w i l l b e u s e d , w h e re th e e q u iv a le n c e i s t h a t w h ic h w o u ld g iv e th e same v a lu e

o f s m e d ,w a ll* Я # В

= E ^ a i i ' l c / ^ L . ( 7 )

® w all 1 ( ^ w a l l '^ - w a l l '^ c )

= [ в » „ ( ¿ c ) ] *с - w a l l ^

i n d i c a t i n g t h a t th e f lu e n c e s p e c tru m i n t h e c a v i t y i n t e g r a l s i s t h a t f o r m e d iu m = w a ll.

C o m b in in g E q s . ( 6 ) and ( 7 ) , o ne o b ta in s

[£ма| . L bg 1 L sa ( Jl ° c J t h i c k w a l l l « e d . w a l l j L w a l l , с ^ J < >

*m ed * w a l l

T h is e x p r e s s io n i s a n a lo g o u s t o t h a t f o r a t h ic k - w a l le d cham beri n a p h o to n beam [ 1 3 , 2 3 ] w h e re one h a s [Me r i / p lmed w a l l i n s te a dC BG '

o f 5 m e d ,w a ll-

The e v a lu a t io n o f t h e tw o s to p p in g -p o w e r r a t i o s i n E q u . ( 8 ) w o u ld , in p r a c t i c e , b e c o m p lic a te d b y th e n e c e s s it y o f c h o o s in g a d e p th when c o m p u tin g e q u iv a le n t t o t h a t o f t h e d e p th o ft h e d e t e c t o r i n th e m edium . T h is p ro b le m c a n b e a v o id e d ,

в лh o w e v e r . T he q u a n t i t y s m e d ,w a l l ca n b e e x p re s s e d as

_ S3 0 1. m e d ,w a ll .

*m ed. m e d ,c j

*m ed

SBGw a l l , r

*med( 9 )

p r i p r iI t h a s b een s t a t e d ab o ve t h a t = “V a i l o r d e r t o bec o n s is t e n t w i t h th e B ra g g -G ra y a s s u m p tio n . Thus u s in g E q u . ( 9 ) th e e x p r e s s io n f o r th e t h i c k w a l l c a s e can be r e c a s t as

IAEA-SM-298/81 93

vmedt h ic k w a l l

5BG med, с

med

<*> w a l l . с сBG

.sw a l l , c

( 1 0 )

w a l l

I t can b e n o te d now t h a t b o th th e s - r a t i o s i n th e second s q u a re b r a c k e t on th e r . h . s . a r e t o b e e v a lu a te d u s in g th e f lu e n c e s p e c tru m i n th e same m edium , i . e . I t w i l l b e shown i n

w h a t f o l lo w s t h a t t h i s r a t i o d ep en d s o n ly w e a k ly on d e p th andr P r i ih e n c e on th e e x a c t sh ap e o f th e j

a v o id s th e p ro b le m o f e x a c t ly m a tc h in g th e s p e c t r a i n th e w a l l and i n th e m edium .

s p e c tru m , w h ic h th u s

p r im a r y f lu e n c e

2 .3 The w a l l - l e s s c a s e

F o r th e o p p o s ite e x tre m e t o t h a t i n s e c t io n 2 . 2 , t h a t o f th e v a n is h in g ly t h i n w a l l , th e a b s o rb e d d ose r a t i o , medium t o c a v i t y , i s g iv e n b y

'med

n o - w a l l

SAs m e d ,c (Ac^ (1 1 )

med

w h ic h i s th e s t r a ig h t f o r w a r d S -A r a t i o e v a lu a te d o v e r th e t o t a l f lu e n c e s p e c tru m i n th e medium a t th e d e p th o f th e d e t e c t o r .

2 . 4 The in t e r m e d ia t e c a s e

The a s s u m p tio n i s now made t h a t th e d ose r a t i o , medium t o c a v i t y , a p p r o p r ia t e t o th e c a s e o f an a r b i t r a r y w a l l th ic k n e s s can b e a p p ro x im a te d b y

( 1 2 )

.я е й

w a l l

■ned + u - оt h i c k w a l l

'med

n o - w a l l

w h ere « i s th e f r a c t i o n o f th e s - r a y c a v i t y d ose due t o 6 - r a y s g e n e ra te d i n th e w a l l . T h is s im p le 2-co m p o n e n t m o d el i s a n a lo g o u s t o th e A lm o n d-S ven sson t h e o r y [ 1 3 ] f o r a p h o to n beam w h e re p a r t o f th e d ose comes fro m p h o to n i n t e r a c t i o n i n th e d e t e c t o r w a l l .

R e p la c in g t h e tw o d ose r a t i o s i n E q u . ( 1 2 ) b y E q s . ( lO ) and( 1 1 ) ,

a - . ] = e s

w a l l

BGmed, с

SAsw a l l , c <Ac >

SBGw a l l , с

+ ( 1 - 6 ) s 3* (Д с) m ed,с

( 1 3 )

94 NAHUM

w h e re th e s u b s c r ip ts and <t>wa1 i h a v e b e e n o m it te d ; i t w i l lb e assumed i n w h a t f o l lo w s t h a t t h e f i r s t s u b s c r ip t a f t e r "s " d e n o te s th e medium i n w h ic h Ф - i s t o b e co m p u ted .

G e n e r a l ly in e le c t r o n d o s im e tr y th e q u a n t i t y c i sa v a i l a b l e . I t i s t h e r e f o r e c o n v e n ie n t i f th e new e x p r e s s io n i s r e c a s t i n th e fo rm o f a c o r r e c t io n f a c t o r t o t h i s q u a n t i t y . F u r th e rm o re , th e m e d iu m - to -c a v ity d ose r a t i o w i l l b e e x p re s s e d as a new s to p p in g -p o w e r r a t io «

SA3 sm e d ,w a l l ,с

med

w a l l

and th e n

SA3s m e d .w a l l .c _ _ f e m e d .с

„ SAw a l l . с (^ с ^

s SA m e d ,с

.S A / А \ . m e d ,с w a l l , с

I t i s r e a d i l y seen t h a t t h e k e y q u a n t i t y i s th e s S A / s BG r a t i o f o r m e d iu m - to -c a v i ty and f o r w a l l - t o - c a v i t y . P o r th e c a s e o f w a ll= m e d iu m , t h e above e x p r e s s io n re d u c e s t o u n i t y as i t m ust d o .

2 .5 An e x p r e s s io n f o r e

Tft»e new q u a n t i t y « can be e s t im a te d b y c a l c u la t in g th e ” l o c a l " c a v i t y d ose ( i . e . lo s s e s le s s th a n &c ) fro m t h e f lu e n c e

o f 6 - r a y s t h a t o r i g i n a t e i n th e w a l l , [ *§ ! ] . i t w i l l b ew a l l

assumed t h a t th e s e 6 - r a y s h a v e a maximum e n e rg y r e l a t e dt o th e w a l l t h ic k n e s s . A l l Б- r a y s p r e s e n t i n th e c a v i t y w i t h e n e r g ie s b e tw e e n A ^ j^ i £<->/2, th e maximum p o s s ib le 6 - r a ye n e r g y , w i l l b e assumed t o o r i g i n a t e fro m t h e m edium .

A q u a n t i t y I e ( * ^ a i i # i - c ,û c ) w i l l b e d e f in e d as

fAw a l l

1 (^wall'^-c'^wall'^c) “ J (Aç, w a l l w

( s ( * c > / P > c o l , c * c ( 1 5 )

w h ic h i s t h e S -A c a v i t y i n t e g r a l , b u t o v e r t h e 6 - r a y f lu e n c e o n ly ; th e t h i r d q u a n t i t y i n I ( . . . ) i s t h e u p p e r l i m i t o f th e i n t e g r a l . Thus

[♦ * ] ( L / p ) +L EJ A „ ,C

IAEA-SM-298/8I 95

l S ( <t'w a l l 'f-c>Aw a ll> Ac )« = « ( 1 6 )

1 ( <few a l l , í - c '^ y ,2 ' Ac^

The d e n o m in a to r i s th e 6 - r a y dose c o r re s p o n d in g t o th e t h i c k w a l l c a s e , i . e . Д у ^ ц = Eç/2 .

3 . Q UAN TITIES REQUIRED TO EVALUATE Sj¡j£d/W an >c

3 . 1 The f lu e n c e s p e c tru m , 4»g

The e le c t r o n f lu e n c e , d i f f e r e n t i a l i n e le c t r o n e n e r g y , f o r p r i

t h e p r im a r y e le c t r o n s , <t>E and f o r p r im a r y and a l l g e n e r a t io n s

o f 6 - r a y s , *E 0 t , i s r e q u ir e d i n o r d e r t o e v a lu a t e t h e c a v i t y t h e o r y i n t e g r a l s g iv e n i n th e p re c e d in g s e c t io n s . T he " t o t a l " s p e c tru m i s r e q u ir e d down t o Дс , f o r w h ic h 10 k e V i s s u f f i c i e n t l y lo w f o r th e s iz e s o f a i r vo lu m es i n io n cham bers i n p r a c t i c a l u s e . I n t h e o r y th e lo w e r l i m i t i n e v a lu a t in g

BGs i s z e r o b u t th e c o n t r ib u t io n t o t h e d ose i n t e g r a l s fro m e le c t r o n s w i t h e n e r g ie s le s s them 10 k e V i s e n t i r e l y n e g l i g i b l e . Thus th e same l i m i t s u f f i c e s i n b o th c a s e s .

D e p th -d e p e n d e n t and <*^rL f o r e le c t r o n beams гигеg e n e r a l ly o b ta in e d fro m M o nte C a r lo s im u la t io n [ 2 , 1 6 , 1 7 , 1 8 ] , w h e re th e c u t o f f f o r e le c t r o n t r a n s p o r t i s ch o sen w i t h re g a rd t o t h e s i z e o f t h e re g io n s o v e r w h ic h th e f lu e n c e i s s c o re d . H ie f lu e n c e s p e c tru m b e lo w t h i s c u t o f f e n e r g y , g e n e r a l ly o f th e o r d e r o f 0 . 5 MeV, i s o b ta in e d fro m a s e p a r a te d e p th - in d e p e n d e n t a n a l y t i c a l c a l c u la t io n [ 1 5 , 1 6 , 1 7 , 2 4 ] . H o w eve r, th e s e M o n te -C a r lo t r a n s p o r t c o u p le d w it h d e p th - in d e p e n d e n t e x te n s io n co d es a r e p r e s e n t ly r e s t r i c t e d t o w a t e r , w h e re a s i n t h i s w o rk we r e q u i r e f lu e n c e s p e c t r a f o r a l l th e m e d ia used f o r io n cham ber w a l ls and a ls o f o r a lu m in iu m . C o n s e q u e n tly , new

c o m p u ta tio n s o f <t>g0 t and * j h a v e b e e n p e r fo rm e d , u s in g th e c o u p le d e le c t r o n -p h o t o n M o n te -C a r lo co d e s y s te m EGS4 [ 2 5 ] w h ic h

a l lo w s c o m p le te f l e x i b i l i t y r e g a r d in g t h e m edium . T he EGS4 u s e r co d e FLURZ d e v e lo p e d b y B ie la je w and R o g ers [ 2 6 ] f o r g e o m e tr ie s w it h c y l i n d r i c a l sym m etry , was u s e d . FLURZ s c o re s f lu e n c e as th e sum o f th e e le c t r o n t r a c k le n g th s d iv id e d b y t h e vo lum e o f t h e r e g io n o f i n t e r e s t i n u s e r - s e le c t e d e n e rg y b in s . Thep a r t i c u l a r v e r s io n o f FLURZ u sed i n t h i s w o rk a l lo w e d a maximum o f 2 0 e n e rg y b in s and 12 g e o m e t r ic a l r e g io n s , th e l a t t e r b e in g s e m i - i n f i n i t e s la b s o v e r s m a ll d e p th i n t e r v a l s p e r p e n d ic u la r t o t h e beam d i r e c t i o n . T he s o u rc e c o n s is te d o f a p a r a l l e l beam o f m o n o e n e rg e tic e le c t r o n s . T he s c o r in g g e o m e try th u s c o rre s p o n d e d t o th e f lu e n c e e x i s t i n g o v e r s m a l l d e p th i n t e r v a l s on th ec e n t r a l a x is o f a b ro a d p a r a l l e l beam . FLURZ d oes n o t

96 NAHUM

TABLE I

P a ra m e te rs u sed i n t h e c o m p u ta t io n o f [ $ £ 0 t ( EQ,z) ] me¿| and

[ 4 i ^ o , z ^m ed

a . EGS4 p a ra m e te rs .

AE = 0 .5 1 2 MeV; AP = 0 .0 1 0 MeV i n a l l th e PEGS4 d a t a s e ts u s e d .ECUT = 0 .5 1 2 MeV ; PCUT = 0 .5 1 2 MeV

b . FLURZ p a ra m e te rs .

N o. o f e n e rg y b in s = 20

N o . o f g e o m e t r ic a l r e g io n s = 12

D e p th n o .

l23456

V C 0

0 . 0 - 0 . 0 5 0 . 0 5 - 0 . 1 0 0 . 1 0 - 0 . 1 5 0 . 1 5 - 0 . 2 0 0 . 2 0 - 0 . 3 0 0 . 3 0 - 0 . 4 0

D e p th n o .

789

101112

z / r 0

0 . 4 0 - 0 . 5 0 0 . 5 0 - 0 . 6 0 0 . 6 0 - 0 . 7 0 0 . 7 0 - 0 . 8 0 0 . 8 0 - 1 . 0 0 1 .0 0 - 1 .2 0

( rQ v a lu e s f o r th e d i f f e r e n t m a t e r ia ls g iv e n i n T a b le I I I ) .

C . ENERGY INTERVALS IN CAVITY THEORY INTEGRAL EVALUATION.

i E > TM IN - FLURZ e n e rg y b in s u sed d i r e c t l y .

i i E < TM IN - F L U R Z -d e r iv e d Ф- v a lu e s i n t e r p o la t e d t oc o rre s p o n d t o e q u a l lo g i n t e r v a l s , e n e rg y h a lv e d in 10 i n t e r v a l s , as i n [ 1 6 ] .

Eg (M e V ) TM IN (M e V )

5 0 .2 0 4 710 0 .5 0 4 22 0 1 .0 0 8 5

IAEA-SM-298/81 97

in c o r p o r a t e a n y d e p th —in d e p e n d e n t e x te n s io n o f th e f lu e n c e s p e c tru m b e lo w th e e le c t r o n t r a n s p o r t c u t o f f , ECOTKE. Thus ECUTKE was s e t t o Ю k e V ( i . e . ECUT = 0 .5 2 1 MeV i n EGS4 t e r m in o lo g y ) w h ic h r e s u l t e d i n e x t r e m e ly lo n g s im u la t io n s ( o f t h e o r d e r o f 3 s p e r h i s t o r y on a M icro V A X I I ) f o r 10 MeV e l e c t r o n s .

T he r e l a t i v e l y s m a ll num ber o f e n e rg y b in s i n FLURZ, 2 0 ,t o c o v e r t h r e e d eca d es o f e n e rg y fro m EQ t o 10 k e V , m ean t t h a tr e l a t i v e l y w id e b in s h ad t o b e u sed b e lo w a b o u t l-J te V , w h e re th es to p p in g p o w er v a r ie s r e l a t i v e l y r a p i d l y w i t h e n e r g y . Thus th ei n d i v i d u a l v a lu e s o f and a i r a s a f u n c t io n o f EQand z c a n n o t b e c o n s id e re d t o b e a c c u r a te t o b e t t e r them ± 1%.A d iv id i n g e n e r g y , T M IN , was c h o s e n . Above T M IN , th e f lu e n c ev a lu e s c o r re s p o n d in g t o t h e FLURZ e n e rg y b in s w e re u sedd i r e c t l y i n E q u (2 ) e tc ? b e lo w T M IN , ♦ j . - v a lu e s c o r re s p o n d in g t oe q u a l lo g a r i t h m ic e n e rg y i n t e r v a l s , su ch t h a t 10 i n t e r v a l sc o v e re d a f a c t o r 2 i n e n e rg y [a s i n 1 6 ] , w e re i n t e r p o l a t e d fro mth e FLURZ v a lu e s . As a r e s u l t o f t h i s p ro c e d u re , th e r e l a t i v e дд BGv a r i a t i o n i n S and S as a f u n c t io n o f Дд e t c and th e

r a t i o s a r e e x p e c te d t o b e a c c u r a te t o b e t t e r them0.1% .

One p o t e n t i a l p ro b le m w i t h t h e c u r r e n t v e r s io n o f FLURZ i s t h a t ea ch e le c t r o n s t e p le n g t h i n a g iv e n r e g io n o f i n t e r e s t i s a llo w e d t o c o n t r ib u t e t o o n ly one e n e rg y b i n , t h e one c o n t a in in g t h e e n e r g y o f th e e le c t r o n a t t h e m id - p o in t o f th e s te p [ 3 0 ] . I f an e l e c t r o n lo s e s an a p p r e c ia b le f r a c t i o n o f i t s e n e rg y i n a s t e p le n g t h , th e n p a r t s o f t h e s t e p le n g t h s h o u ld c o n t r ib u t e t o s e v e r a l a d ja c e n t e n e rg y b in s ; t h i s h as b een d is c u s s e d in d e t a i l i n [ 1 6 ] . I n o r d e r t o re d u c e t h e e f f e c t o f t h i s a p p ro x im a te m ethod o f b in n in g , t h e maximum f r a c t i o n a l e n e rg y lo s s a l lo w e d i n an e le c t r o n s t e p , ESTEPE [ 2 7 , 2 8 ] , was s e t e q u a l t o 0 . 0 4 , a v a lu e lo w e r th a n t h a t r e q u ir e d t o f a i t h f u l l y m o d e l e le c t r o n t r a n s p o r t . F o r th e same re a s o n , th e im p ro ved e le c t r o n t r a n s p o r t a lg o r i t h m PRESTA [ 2 9 ] w h ic h a l lo w s v e r y la r g e e le c t r o n s t e p le n g t h s , h a s n o t b e e n e m p lo ye d , a lth o u g h i t s use w o u ld h a v e le d t o c o n s id e r a b ly re d u c e d co m p u tin g t im e s .

The p a ra m e te rs u sed i n t h e c o m p u ta t io n o f 4^ o t and *]?r i a r e sum m arised i n T a b le I .

The v a lu e s o f ♦ E * and eire c o r r e l a t e d i . e . th e y w e recom puted fro m th e same s e t o f e le c t r o n h i s t o r i e s . E le c t r o n s o r i g i n a t i n g fro m b re m s s tra h lu n g p h o to n s w e re d e s ig n a te d 'p r im a r y ' b y s e l e c t i n g t h i s o p t io n i n FLURZ. T h is i s c o n s is t e n t w i t h d e f in in g s®0 so t h a t i t cam a ls o b e u sed f o r p r im a r y p h o to n beams [ 1 6 ] .

No s p e c i f i c b en ch m arks o f u s e r co d e FLURZ h a v e b een p u b lis h e d t o d a t e . C o n s e q u e n t ly , f o r t h e c a s e o f 20 MeV

BG одe le c t r o n s i n w a t e r , t h e q u a n t i t i e s O ^ t e r an d D ^ t e r ( дс “

10 k e V ) com puted a c c o rd in g t o E q s . ( 2 ) and ( 5 ) a t a l l tw e lv e

98 NAHUM

Оoáwfe

DEPTH s / c m

F/G. 5. Comparison of three different computations of absorbed dose for broad, parallel 20 M e V

electron beam in water: ------ from INHOM, 10 000 histories;-----------is D ^ ater (Ac = 10 keV) fromEq. (3) using [Ф'е!wmr from FLURZ, 10 000 histories;....... is D^,erfrom Eq. (6) using [<Pf"Iwa,„fromFLURZ, same 10 000 histories as for ф10' (see Table I for details of EGS4 parameters and depths etc;

Table III for stopping-power data used).

d e p th s ( see T a b le I ) h a v e b e e n com pared t o th e a b s o rb e d d ose com puted u s in g u s e r co d e INHOM [ 3 1 ] . I n b o th c a s e s , ю ООО h i s t o r i e s w e re e x e c u te d . T h e se h i s t o r i e s w e re n o t c o r r e l a t e d , h o w e v e r , i . e . th e randean num ber se q u e n c es d i f f e r e d . T he s t a t i s t i c a l u n c e r t a i n t i e s on th e IN H O M -d e riv e d d ose v a lu e s w e re le s s th a n ±1% (o n e S . D . ) f o r d e p th s 1 t o 1 0 , ±1% f o r d e p th 11 an d ±2% f o r d e p th 1 2 . The u n c e r t a i n t i e s on th e FLURZ - d e r i ve d

S A “B Gv a lu e s o f ¿ V a te r an^ ^ w a t e r 3X 0 ^ е ваше o r d e r * The same

EGS4 d a t a s e ts [ 2 5 ] w e re u sed i n t h e tw o c o m p u ta t io n s . Thus th e same s to p p in g -p o w e r d a t a was in v o lv e d i n c o m p u tin g e n e rg y lo s s e s g o v e rn in g e le c t r o n t r a n s p o r t an d i n e v a lu a t in g th e c a v i t y i n t e g r a l s .

IAEA-SM-298/81 99

The v a lu e s o f O u a t e r ' ^ w a t e r 311x3 ^ w a t e r a t th e 12 deP th i n t e r v a l s a r e shown i n F ig u r e 3 . T he d e v ia t io n fro m u n i t y o f

t h e r a t i o D SA/ D INHOM i s n e v e r s t a t i s t i c a l l y s i g n i f i c a n t and o n ly v a r ie s b e tw e e n 0 .9 8 7 and 1 .0 0 2 f o r d e p th s l t o 9 . The

r a t i o 0 BG/ 0 I№IOM i s s i g n i f i c a n t l y g r e a t e r th a n u n i t y a t d e p th s1 t o 4 . T h is i s an e x p r e s s io n o f t h e la c k o f e v e n a p p ro x im a te 6 - r a y e q u i l ib r iu m c lo s e t o th e s u r fa c e [ 2 0 ,2 2 ] due t o th e i n i t i a l fo rw a rd t r a j e c t o r y o f 6 - r a y s w i t h a p p r e c ia b le ra n g e s , f t i i s i s e n t i r e l y a n a lo g o u s t o th e b u i ld - u p r e g io n in h ig h -e n e r g y p h o to n b eam s. C l e a r l y Eqs ( 5 ) and ( 6 ) a x e n o t v a l i d i n t h i s r e g io n o f 6 - r a y n o n - e q u i l ib r iu m n e a r t h e s u r f a c e and

th u s th e t h e o r y f o r medium с i s n o t e x p e c te d t o a p p ly a tsuch d e p th s .

H i i s e x c e l l e n t a g re e m e n t b e tw e e n a b s o rb e d d ose v a lu e s com puted i n th e s e t h r e e v e r y d i f f e r e n t ways s t r o n g ly s u g g e s ts t h a t FLURZ c o r r e c t l y com putes t h e t o t a l and p r im a r y e le c t r o n f lu e n c e s fro m t h e e le c t r o n h i s t o r i e s .

TABLE II

A c o m p a ris o n b e tw e e n t h e d ose d ue t o " s to p p e rs " i n INHOM and t h e t r a c k - e n d te r m i n t h e S p e n c e r - A t t ix c a v i t y d o s e ; 20 MeV e le c t r o n s i n w a t e r , 10 0 0 0 h i s t o r i e s (s e e T a b le I f o r EGS4 p a r a m e te r s ) .

D e p thN o.

STOPPERS DOSE

(E C U TK E =10keV )

£¿3TOP w a te r

(MeV-g_ ’ cm2 )

TRACK-END DOSE

(Д с = 1 0 k e V )

¿ Г-Ew a te r(MeV-g_1-cm2 )

^ S a te r

rjSTOP‘■'water

^ S a te r

^ w a te r

1 .0971< ±1% .0 9 9 4 1 .0 2 4 .0 5 32 .1 0 2 4 ¿ .1 0 4 2 1 .0 1 8 .0 5 33 .1 0 6 0 .1 0 7 4 1 .0 1 3 .0 5 34 .1 0 7 8 .1 0 9 1 1 .0 1 2 .0 5 45 .1 1 0 8 .1 1 3 1 1 .0 2 1 .0 5 46 .1 1 0 6 .1 1 7 7 1 .0 2 7 .0 5 47 .1 1 9 0 .1 2 1 5 1 .0 2 1 .0 5 58 .1 2 3 0 .1 2 4 3 1 .0 1 1 .0 5 59 .1 2 3 6 .1 2 4 4 1 .0 0 6 .0 5 5

10 .1 1 6 2 .1 1 5 4 0 .9 9 3 .0 5 511 .0 7 1 ±1% .0 7 1 1 .0 0 .0 5 712 .0 1 1 ±2% .0 1 2 1 .0 5 .0 6 4

100 NAHUM

ûwall/MeV

FIG. 4. Fraction of the 6-ray cavity dose, for A, = 10 keV, from 5-rays generated in the wall, e, as a function of A wall, evaluated from Eqs (15), (16) and (17) for с = air with fluence spectra from

F L U R Z runs, 5000 histories, for depth No. 7 (see Tables I and III). 20 M e V electrons in water (-----------) and in aluminium (-------); 10 M e V electrons in water (----------- ) and aluminium (...........).

3 .2 The t r a c k - e n d te r m and " s to p p e rs "

The v a lu e o f ECOTKE was s e t t o lO k e V when e x e c u t in g INHOM i n o r d e r t o com pare t h e dose com ponent due t o " s to p p e r s " , i . e . th o s e e le c t r o n s t h a t h a v e f a l l e n b e lo w ECUTKE i n e n e rg y an d a x e assum ed t o d e p o s it t h e i r r e s id u a l e n e r g y ’ on th e s p o t ’ , w it hедth e t r a c k —end te r m i n (A q * 1 0 k e V ) w h ic h i s th e secondt e r n on th e r . h . s . i n th e n u m e ra to r i n E q u ( 3 ) . T h e s e tw o q u a n t i t i e s a r e g iv e n i n T a b le I I f o r t h e 10 ООО- h i s t o r y ru n s o f INHOM and FLURZ d e s c r ib e d a b o v e . The tw o q u a n t i t i e s a r e g e n e r a l ly w i t h i n 2% o f e a c h o t h e r , w i t h b e in g c o n s is t e n t lys l i g h t l y h ig h e r . T h is i s t o be e x p e c te d as t h e 's t o p p e r s ' w i l l h a v e e n e r g ie s s l i g h t l y b e lo w 10 k e V w h e re a s th e ' t r a c k - e n d s ' i n th e SA c a v i t y i n t e g r a l a r e d e f in e d a s h a v in g an e n e rg y e x a c t ly e q u a l t o Др.

3 .3 The dose f r a c t i o n fro m w a l l - g e n e r a t e d 6 - r a y s ,e

E q u (1 6 ) h a s b een e v a lu a te d f o r E0 » 20 and 10 MeV, » 10 k e V , med » w a t e r and med • a lu m in iu m , с = a i r a s a f u n c t io n o f

Awa2 j . . The 6 - r a y f lu e n c e , w as o b ta in e d fro m

IAEA-SM-298/81 101

*n ie d e p th -d e p e n d e n c e o f e was fo u n d t o b e v e r y e m a i l . Ther e s u l t s гиге p l o t t e d i n F ig u r e 4 f o r z / r Q = 0 . 4 - 0 . 5 . T h ese

osov a lu e s can b e u sed f o r e i n e v a lu a t in g s m e d ,w a l l ,c a t “ У

d e p th w h ere th e t h e o r y i s v a l i d ( s e e S e c t io n 3 . 1 ) ; t h e e x a c t v a lu e f o r e u sed i s g e n e r a l ly n o t c r i t i c a l .

F ig u r e 4 shows t h a t th e 6 - r a y d ose i s p r e d o m in a n t ly due t o lo w -e n e r g y 6 - r a y s ; b e tw e e n 60 and 70% o f t h i s d o s e i s d u e t o 6 - r a y s w it h e n e r g ie s le s s th a n 1 0 0 k e V , a l th o u g h th e maximum

6 - r a y e n e rg y i s t h e o r e t i c a l l y e q u a l t o EQ/2ri . e . 5 o r 10 MeV i n F ig u r e 4 . T he v a lu e o f « i s n o t d e f in e d f o r < Дс .

T he f r a c t i o n o f th e t o t a l d o s e , ( ^ = 10 k e V ) , due t oa l l 6 - r a y s , i . e . * E^/ï, was fo u n d t o b e v i r t u a l l yin d e p e n d e n t o f d e p th and e n e r g y , v a lu e s f o r EQ= 1 0 and 20 MeV b e in g 0 .2 3 and 0 . 2 4 r e s p e c t iv e l y i n w a t e r . T h is r a t i o can b e e s t im a te d fro m

0:BG* 1 - A v c

S c o l , c

TABLE I I I

D e t a i l s o f th e m e d ia f o r w h ic h s ^ d , a i r < ^ ^ m e d ^ i r h a s b een c a lc u la te d ? d a t a fro m [ 3 2 ] e x c e p t f o r f i n a l co lu m n ; E0 i s in M6V; v a lu e s f o r a i r a ls o in c lu d e d .

P i r 0 ( E0 ) S o u rce o f

M a t e r i a l (g-cm- 3 ) ( e V ) (cm ^g-1 ) d e n s i t ye f f e c t d a t a

WATER 1 .0 0 0 7 5 .0 2 .5 5 ( 5 ) [ 3 3 ]4 .9 6 ( 1 0 ) [ 3 3 ]9 .3 0 ( 2 0 ) [ 3 3 ]

ALUMINIUM 2 .6 9 9 1 6 6 .0 3 .0 9 ( 5 ) [ 3 3 ]5 .8 6 ( 1 0 ) [ 3 3 ]

1 0 .5 6 ( 2 0 ) [ 3 3 ]

A—15 0 PLASTIC 1 .1 2 7 6 5 .1 5 .0 5 ( 1 0 ) [ 3 3 ]C—552 PLASTIC 1 .7 6 0 8 6 .8 5 .6 1 ( 1 0 ) [ 3 3 ]GRAPHITE 1 .7 0 0 7 8 .0 5 .6 6 ( 1 0 ) [ 3 3 ]POLYSTYRENE 1 .0 6 0 6 8 .7 5 .1 6 ( 1 0 ) [ 3 3 ]PMMA 1 .1 9 0 7 4 .0 5 .5 2 ( 1 0 ) [ 3 3 ]

A IR 1 . 2 0 5 E -0 3 8 5 .7

102 NAHUM

TABLE IV

The q u a n t i t y s £ £ d / a i r ( ЛС V smed> a i r - f o r Ac = io k e V and Д ^ г о к е У , f o r med = m a t e r ia ls l i s t e d i n T a b le I I I ; 10 MeV e le c t r o n s ; d e p th n o .7 ;Д С= Ю k e V and Ac = 2 0 k e v .

M a t e r i a l = med I ( e V )

s SAmed,

Ac ( k e V ) = 10

/ s BG a i r m e d ,a ir

20

A -1 5 0 6 5 .1 1 .0 0 9 2 1 .0 0 6 9P o ly s ty r e n e 6 8 .7 1 .0 0 7 2 1 .0 0 5 3PMMA 7 4 .0 1 .0 0 4 3 1 .0 0 2 9W a te r 7 5 .0 1 .0 0 4 0 1 .0 0 3 0G r a p h ite 7 8 .0 1 .0 0 1 6 1 .0 0 0 7C -5 5 2 8 6 .8 0 .9 9 8 2 0 .9 9 8 2A lu m in iu m 1 6 6 .0 0 .9 7 0 4 0 .9 7 6 3

MEAN EX CITATIO N ENERGY, I , / e V m ed

FIG. 5. Ratio = 10 keV) / ^ , 01> as a function of the mean excitation energy, Imed;

A - A-150 plastic, Py - Polystyrene, Pa - P M M A , W - Water, G - Graphite (p = 1.70 g -cm'3), C¡ - C-552 plastic, Al - Aluminium; 10 M e V electrons; Depth No. 7 (see Tables I and III).

IAEA-SM-298/81 103

TABLE V

T he q u a n t i t y sm e d ia i r <Ac ) / sme d .a i r ' f o r Ac = 1 0 k e V ' f o r ^ = w a t e r and med = a lu m in iu m , f o r 5 , 10 and 20 MeV e le c t r o n s ;d e p th n o . 7 .

E0( M eV)

SSA / в « 5 m ed, a i r med, a i r

med = w a t e r a lu m in iu m

5 1 .0 0 4 6 0 .9 7 2 910 1 .0 0 4 0 0 .9 7 0 420 1 .0 0 2 0 0 .9 6 7 4

w h e re t h e r e s t r i c t e d t o u n r e s t r ic t e d s to p p in g -p o w e r r a t i o i s e v a lu a te d a t th e mean p r im a r y e le c t r o n e n e rg y a t d e p th z , Ez .

3 . 4 The c r a t i o

3 . 4 . 1 V a r i a t i o n w i t h medium

The r a t i o o f th e S p e n c e r - A t t ix t o th e u n r e s t r ic t e d (B G ) s to p p in g -p o w e r r a t i o , a p p e a r in g i n t h e f i n a l e x p r e s s io n , E q u (1 4 ) , f o r wai i /C h a s b een co m p u ted , f o r с = a i r , f o rt h e m a t e r ia ls m ost com m only u sed f o r th e w a l ls o f th im b le and p la n e —p a r a l l e l (p a n c a k e ) io n ch am b e rs , as w e l l as f o r a lu m in iu m , w h ic h r e p r e s e n ts an e x t r e m e ly n o n ^ w a te r l i k e m a t e r i a l . The m a t e r ia ls eure l i s t e d in T a b le I I I t o g e t h e r w i t h t h e i r mean e x c i t a t i o n e n e r g ie s ( I - v a l u e s ) , d e n s i t i e s and th e s o u rc e o f th e p a ra m e te rs f o r th e e v a lu a t io n o f th e d e n s i t y e f f e c t .

FLURZ was e x e c u te d f o r E0 - 10 MeV, a c c o rd in g t o T a b le I , f o r a l l th e m e d ia l i s t e d in T a b le i l l , f o r 5 0 0 0 h i s t o r i e s .

T a b le i v c o n t a i n s t h e v a lu e s o f a i r i ^ c “ 10 k e V ) / sm e d ,a iro b t a in e d , f o r d e p th n o . 7 ( z/rQ = Ó .4 - 0 . 5 ) . T he v a lu e s a r e g iv e n t o 5 s i g n i f i c a n t f ig u r e s as t h e r e i s an u n c e r t a in t y o f o n ly ± 0 .0 0 0 1 due t o t h e s t a t i s t i c a l n a tu r e o f t h e c a l c u la t io n o f <&£.. The d ep en d en ce o f t h i s r a t i o on In ^ a i s c l e a r l y ' d e m o n s tra te d i n F ig u r e 5 . T he SA/BG r a t i o i s g r e a t e r them u n i t y f o r Ijjjg^ < l a i r and le s s th a n u n i t y f o r I j ^ > I ^ j . « as was shown i n [ 2 2 ] . A l t e r n a t i v e l y , t h e c lo s e n e s s o f th e SA/BG -m ed, a i r r a t i o t o u n i t y can b e u sed a s a m easu re o f th e a i r - e q u iv a le n c e o f th e medium w i t h r e g a r d t o 6 - r a y e f f e c t s i n e le c t r o n beam s.

104 NAHUM

D E P T H , z / í 1 о

FIG. 6. Ratio ssmAed%air(Ac = 10 keV)//^dalr as a function of depth, z/r0, for 20 M e V electrons in

med = water (OJ and med = aluminium (A); [4>g']med and [<tf¿i]med from 5000 history runs of F L U R Z (see Tables I and III).

TABLE V I

SAThe S p e n c e r - A t t ix s to p p in g -p o w e r r a t i o , a i r ( Лс ) , a s af u n c t io n o f c u t o f f e n e rg y Дс f o r 20 MeV e le c t r o n s ; d e p th no .7 ; f o r med = w a te r and med = a lu m in iu m ( n o te t h a t th e chan g e in

S Asined a i r wi^ h дс i s e x p e c te d t o b e a c c u r a te t o a t l e a s t f o u r s i g . f i g s . b u t n o t t h e a b s o lu te v a lu e s ) .

Дс ( k e v ) s SA w a t e r , a i r

s SA A l , a i r

10 1 .0 0 5 7 0 .8 1 0 120 1 .0 0 4 8 0 .8 1 5 030 1 .0 0 4 1 0 .8 1 7 450 1 .0 0 3 6 0 .8 2 0 170 1 .0 0 3 3 0 .8 2 1 7

10 0 1 .0 0 2 9 0 .8 2 3 1150 1 .0 0 2 4 0 .8 2 4 7200 1 .0 0 2 0 0 .8 2 5 8

IAEA-SM-298/81 105

FLURZ was a ls o e x e c u te d a t E0 » 5 and 2 0 MeV f o r w a te r and a lu m in iu m . V a lu e s o f th e SA/BG r a t i o , f o r Aç = 10 k e V , a t d e p th n o . 7 , f o r EQ - 5 ,1 0 and 20 MeV a r e g iv e n i n T a b le V f o r th e s e tw o m e d ia . The s t a t i s t i c a l u n c e r t a i n t i e s a r e a s f o r th eед олd a t a i n T a b le I V . T h e re i s a v e r y g r a d u a l d e c re a s e i n s /s w it h in c r e a s in g E0 .

The d e p th v a r i a t i o n , f o r EQ *= 20 MeV, i s p l o t t e d i n F ig u r e 6 . The ano m alo us b e h a v io u r a t s m a ll d e p th s w h e re a_¿r i sn o t m e a n in g fu l ( s e e S e c t io n 3 . 1 ) i s c l e a r l y e v id e n t . A t d e p th s

SA BGaw ay fro m th e s u r fa c e th e v a r i a t i o n i n s /s i s n e g l i g i b l e m w a t e r , and in c r e a s e s b y a b o u t 0 .8 % a t m ost i n a lu m in iu m . The d a t a i n F ig u r e 6 ta k e n t o g e t h e r w i t h th e d a ta i n T a b le V

СД or* —s u g g e s t t h a t s /s ca n b e e x p re s s e d as a f u n c t io n o f Ez, th e mean p r im a r y e le c t r o n e n e rg y a t d e p th z, in d e p e n d e n t o f EQf p ro v id e d t h a t z/rQ > 0.25.

3 . 4 . 3 v a r i a t i o n w i t h Ac

The d a t a g iv e n in s e c t io n s 3 . 4 . 1 t o 3 . 4 . 3 h a v e b een o b ta in e d f o r Дс = 10 k e V . The v a lu e o f Дс i s r e la t e d t o th e s i z e o f th e c a v i t y . A 10 k e V e le c t r o n h a s a c s d a ra n g e , rQ, o f2 . 4 mm i n a i r . T h is i s a lo w e r l i m i t f o r th e s m a l le s td im e n s io n o f th e a i r c a v i t i e s e n c o u n te re d i n p r a c t i c a l in s t r u m e n ts . G e n e r a l ly th e e x a c t v a lu e o f Д„ i s n o t c r i t i c a l

ОДi n e v a lu a t in g a - r f o r m e d ia w i t h I - v a l u e s c lo s e t o t h a t o fa i r (s e e F i g . 5 ) . F u r th e rm o re , th e v e r y s im p le m o d e l u n d e r ly in g S p e n c e r - A t t ix t h e o r y d oes n o t j u s t i f y a n y e la b o r a t e scheme f o r c o m p u tin g a v a lu e o f Дс f o r a p a r t i c u l a r - s i z e and shape o f

c a v i t y . H o w eve r, a i r ( дс ^ ' f o r med = H2° and med = A-*- h asb een e v a lu a te d f o r v a r io u s Дс fro m 10 k e v up t o 200 k e v f o r 20 M ev e le c t r o n s i n w a t e r and a lu m in iu m r e s p e c t iv e l y . The v a lu e s o b ta in e d a r e g iv e n in T a b le V I . As e x p e c te d , th e v a r i a t i o nСДf o r med = Нг 0 i s v e r y s lo w , b u t f o r med = A l , s in c r e a s e s b y m ore th a n 0 .5 % a s дс in c r e a s e s fro m 10 t o o n ly 20 k e v ,

g r a d u a l ly a p p ro a c h in g t h e sBG - v a lu e o f 0 .8 3 7 a s ^ f u r t h e r in c r e a s e s .

3 . 4 . 2 . V a r i a t i o n w i t h E0 an d d e p th

4 . MODELLING THE RATIO OF RESPONSES OF A LUM IN IUM - AND GRAPHITE-WALLED CHAMBERS

4 . 1 E x c h a n g in g w a l l m a t e r ia ls

The e f f e c t on th e re s p o n s e o f a 0 .6 cm3 F a rm e r cham ber o f e x c h a n g in g t h e g r a p h i t e t h im b le f o r one made o f a lu m in iu m a t th e d e p th o f maximum d ose i n a 20 MeV (n o m in a l e n e r g y ) e le c t r o n beam h a s b e e n m easured b y Nahum e t a l . [ 1 4 ] . The g r a p h i t e

106 NAHUM

t h im b le had a w a l l th ic k n e s s o f 0 .3 5 mm o r 0 .0 6 0 g > cm- 2 ; th e c o rre s p o n d in g f ig u r e s f o r th e a lu m in iu m th im b le w ere 0 .0 9 mm and 0 . 0 2 4 g • cm- 2 . T he a i r vo lu m es w i t h t h e tw o th im b le s w e re c a r e f u l l y d e te rm in e d b y m e c h a n ic a l m eans, th u s e n a b l in g th e

A l Сr a t i o o f mass i o n i s a t i o n , Jg /Jg t o b e d e te r m in e d .

4 . 1 . 1 . The a lu m in iu m -g r a p h ite re s p o n s e r a t i o : e x p e r im e n t

The cham ber w i t h i t s tw o d i f f e r e n t th im b le s was i r r a d i a t e d i n t u r n b y 20 MeV e le c t r o n s a t i d e n t i c a l d e p th s c lo s e t o th e d o s e maximum i n a PMMA ( l u c i t e , p e rs p e x e t c . ) p h a n to m . The f o l lo w in g v a lu e was o b ta in e d in [ 1 4 ] :

4 . 1 . 2 . The a lu m in iu m -g r a p h ite re s p o n s e r a t i o : th e o r y

The mass i o n i s a t i o n r a t i o above can b e e x p re s s e d as

j A l D A1 g „ a i r

Jg Da i r

assu m in g t h a t W /e i s th e same i n e a c h с а з е . F o r i d e n t i c a l D ^ j , t h i s ca n b e w r i t t e n as

„SA3_ a m e d .c .a i r ( 18 )

„SA3sm e d , A l , a i r

u s in g th e s to p p in g -p o w e r r a t i o f o r th e 3 -m e d ia s i t u a t i o n d e f in e d i n s e c t io n 2 . 4 .

W iese s ^ ^ - r a t i o s w i l l now b e e v a lu a t e d . F i r s t l y i t w i l l b e assumed t h a t th e m a t e r ia l o f t h e phantom i s w a t e r ; w a t e r h a s I = 7 5 .0 eV com pared t o PMMA's I - v a l u e o f 7 4 .0 eV ( T a b le I I I ) . Thus th e s e m e d ia « ire v i r t u a l l y e q u iv a le n t f o r e le c t r o n d o s im e tr y p u rp o s e s . C o n s e q u e n tly , th e s - r a t i o s d e r iv e d fro m t h e 20 MeV w a t e r FLURZ ru n can b e d i r e c t l y em p lo ye d .

The e x p r e s s io n f o r JgA1/JgC i n E q u . ( 1 8 ) can b e w r i t t e n u s in g E q u .( 1 4 ) as

A1

-BGaw a t e r . a i r

sw a t e r , a i r ^ дс )

,SAS ç . a i r ^ *

s c ? a i r+ < !-« « >

( 1 9 )

A l

-BG

sw a t e r , a i r ^ ^ c )-BGs A l , a i r

+ < 1 -«A 1>

IAEA-SM-298/81 107

едзa . s to p p in g -p o w e r r a t i o s r e q u ir e d t o e v a lu a t e s k a t e r A 1 a i r

and s r o t e r . C . a i r * f o =20M eV' ^ ro - 0 . 4 - 0 . 5 .

TABLE V I I

^ c( k e V )

S S \ < A c > ù w a t e r , a i r 1- s £ A < Л С > *üc , a x r c„SA ( A „ )

A l , ал. I e

-BGsw a t e r , a i r s B Gs c , a i r

-BGs A l , a i r

10 1 .0 0 2 0 1 .0 0 0 .9 6 7 4

20 1 .0 0 1 1 .9 9 9 .9 7 3 3

30 1 .0 0 0 4 . 99 8 s .9 7 6 1

* E s t im a te b a s e d on v a lu e s a t E 0 = 10 MeV and th e chan g e f o r w a t e r , a i r fro m lOM eV t o 20MeV.

b . V a lu e s o f as a f u n c t io n o f med=C andmed = A1 ; 20 MeV e l e c t r o n s , Ac = l0 k e V ( á a t a ta k e n fro m F ig u r e 4 ) ; s t a t e d t o n e a r e s t 5%.

^ w a l l(M eV ) eC еА1

0 .1 0 .6 0 0 .6 50 . 2 0 .7 0 0 .7 50 .3 0 .7 5 0 .8 0

n ie tw o p a ra m e te rs t h a t depend on t h e g e o m e try o f t h e io n cham ber a r e A y ^ l and Ac . The a i r c a v i t y h a s a d ia m e te r o fa b o u t 6 mm w h ic h i s t h e c s d a ra n g e i n a i r o f a n 18 k e v

Д1 re l e c t r o n . C o n s e q u e n t ly , t h e ab o ve e x p r e s s io n f o r J g/Jg w i l l

b e e v a lu a te d f o r « 1 0 , 20 and 30 k e V . The t h ic k n e s s o ft h e a lu m in iu m t h im b le , 0 .0 2 4 g -c m ~ z, i s t h e c s d a ra n g e i n a lu m in iu m o f a 0 .1 2 5 MeV e l e c t r o n . T a k in g i n t o a c c o u n t o b l iq u e in c id e n c e and t h e e f f e c t o f e le c t r o n s c a t t e r i n g , t h e v a lu e Дцдт i - 0 . 2 MeV seems r e a s o n a b le . H o w e v e r, E q u (1 9 ) w i l l b e e v a lu a te d f o r c o r re s p o n d in g t o “ 0 . 1 , 0 . 2 and 0 . 3

108 NAHUM

*-4

°<?

икaiГ0 4->4 « W i

«C0>

F/G. 7. Theoretical prediction of the response ratio, for three different £ ^ rvalues and three

different A,.-values; 20 M e V electrons in water, depth No. 7. Also shown is the experimental value from Ref. [14] — position along Дc-axis has no significance.

•s r

DAG T H IC K N È S S /m g . c m " 2

FIG. 8. Variation of mass ionization ratio, j f¥dag/j , with thickness of dag layer. Experiment (*)

from Ref. [14]. Theory, Eq. (20), evaluated with A^aU = 0.2 M e V and A^aU = 0.3 MeV; ( o) is for b-eff corresponding to r0 = 1.0 x tcav; (o) is for A eg corresponding to r0 = 1.5 x tmv(tcav is the diameter of the dag-air-dag cavity).

IAEA-SM-298/81 109

M eV. The t h ic k n e s s o f th e g r a p h i t e t h im b le , 0 .0 6 0 g<an- 2 , i s th e c s d a ra n g e i n c a rb o n o f a 0 .2 3 MeV e l e t ro n ; a f i x e d v a lu e o f Л — п = 0 . 3 M e V w as ch o sen a s th e v a lu e o f h a r d ly a f f e c t s th e f i n a l r e s u l t .

T a b le V i l a c o n ta in s t h e v a lu e s o f th e SA/BG r a t i o s in E q u (1 9 ) f o r Aq = 1 0 , 20 and 30 k e V f o r 2 0 MeV e le c t r o n s an d z / r Q = 0 . 4 - 0 . 5 ( t h e e x a c t d e p th i s n o t a c r i t i c a l q u a n t i t y a s was shown i n s e c t io n 3 . 3 ) . T a b le V I l b c o n ta in s v a lu e s o f ec and «Д2 » ta k e n fro m th e c u rv e s in F ig u r e 4 a t EQ = 20 MeV f o r w a te r

and A l r e s p e c t iv e l y . The r e s u l t i n g JgA1/ J gc - r a t i o , a c c o rd in g

t o E q u (1 9 ) , i s p l o t t e d i n F ig u r e 7 , w h ic h i l l u s t r a t e s t h a t th e c h o ic e o f Дс i s p a r t i c u l a r l y c r i t i c a l . T h is v a r i a t i o n i s

e n t i r e l y due t o a _r> th e v a lu e s o f s ^ ^ ^sh o w in g n e g l i g i b l e d ep en dence on Aq o r A ^ ^ i * T h is was t o be e x p e c te d a s w a t e r and g r a p h i t e h a v e v e r y s i m i l a r I - v a l u e s .

The e x p e r im e n ta l r e s u l t i s a ls o in d ic a t e d i n th e f i g u r e . A

c h o ic e o f Aq « 1 0 k e V and л - 0 . 3 MeV w o u ld p ro d u c e p e r f e c t

a g re e m e n t b e tw e e n t h e o r y and e x p e r im e n t . M a k in g re a s o n a b le c h o ic e s o f A ^^aii ж 0 . 2 MeV and Aq * 20 k e V r e s u l t s i n a t h e o r e t i c a l re s p o n s e r a t i o o f 1 .0 2 0 , w h ic h s t i l l a c c o u n ts f o r 2 .0 % o f t h e m easured 2 . 7 ± 0 .1 % d e v ia t io n o f th e r a t i o fro m u n i t y .

4 . 2 T he e f f e c t o f a d ag l a y e r on th e a lu m in iu m th im b le re s p o n s e

4 . 2 . 1 E x p e r im e n t

Nahum e t a l . [ 1 4 ] a ls o d e te rm in e d th e e f f e c t on cham ber re s p o n s e i n t h e 20 MeV e le c t r o n beam o f a d d in g s u c c e s s iv e ly t h i c k e r c o a ts o f dag ( g r a p h i t e e q u iv a l e n t ) t o th e in s id e o f th e a lu m in iu m t h im b le . The ch an g e i n t h e a i r vo lum e was d e te rm in e d f o r ea ch c o a t e n a b l in g J g ^ ^ / J g ^ t o b e d e te rm in e d as a f u n c t io n o f t h e a v e ra g e t h ic k n e s s o f th e d ag l a y e r . The e x p e r im e n ta l v a lu e s f o r [ 1 4 ] a r e shown i n F ig u r e 8 ; a v e r y t h in l a y e r o f dag h a s a d r a m a t ic e f f e c t on th e cham ber re s p o n s e .

4 . 2 . 2 T h e o ry

H ie p r e s e n t t h e o r y c a n n o t s t r i c t l y b e a p p l ie d t o t h i s 4 -m e d ia s i t u a t i o n . H o w e v e r, i t w i l l b e assumed t h a t g r a p h i t e i s a i r - e q u i v a l e n t , w h ic h F ig u r e 5 in d ic a t e s t o b e a re a s o n a b le a s s u m p tio n . Then th e s i t u a t i o n i s re d u c e d t o o n ly 3 m e d ia , w it h t h e th ic k n e s s o f t h e d ag l a y e r b e in g r e f l e c t e d i n th e v a lu e o f Aq . S t r i c t l y , t h e t h e o r y i s t o be i n t e r p r e t e d as p r e d i c t i n g t h e r a t i o o f t o D c w h e re D c i s th e a v e ra g ev a lu e o f th e a b s o rb e d d o s e o v e r t h e w h o le o f th e c a v i t y . The e x p e r im e n ta l m e as u rem e n ts / h o w e v e r , a r e p r o p o r t io n a l t o th e

110 NAHUM

a b s o rb e d d ose fro m o n ly t h e c e n t r e o f th e a i r - e q u i v a l e n t c a v i t y , w h ere t h e r e i s a c t u a l a i r . A g r a d ie n t i n d ose a c ro s s t h e c a v i t y c o u ld im p ly a d i f f e r e n c e b e tw e e n D c and 0 a ^r . T h is s h o u ld b e b o rn e i n m in d when c o m p a rin g th e m easurem ents shown i n F ig u r e 7 w i t h th e p r e d i c t i o n s o f th e t h e o r y .

H ie t h e o r e t i c a l e x p r e s s io n f o r th e r a t i o o f th e mass i o n i s a t i o n f o r th e a lu m in iu m t h im b le w i t h th e d ag l a y e r , assum ed a i r e q u iv a l e n t , t o t h a t o f t h e g r a p h i t e th im b le

jA l-t-d a g

,BG» w a t e r . a i r

sw a t e r , a i r ( »S?aix+ U -« c >

A l

SBGù_KâÎÊXU5UJC

s w a t e r , a i r ^ ^eff )

^ . a i r ^ ^ e f f )_BG

A l , cLLT

( 2 0 )

+ d - « A l )

i s a s f o r E q u (1 9 ) e x c e p t t h a t i s t h e c u t o f f a p p r o p r ia t e t ot h e e f f e c t i v e a i r c a v i t y . E q u (2 0 ) h a s b e e n e v a lu a te d f o r c o rre s p o n d in g t o (А ц а П )& i “ 0 . 2 HeV f o r v a r y in g A g f f / «с = 0 .7 5 c o rre s p o n d in g t o ( Aw a i l )c « 0 . 3 HeV and Дс - 1 0 k e V , and f o r Де ££ v a r y in g fro m 10 k e V t o 2 0 0 k e V ; th e v a lu e s f o r Ae f f - 10 t o 30 k e V c o rre s p o n d c l o s e ly t o t h e ( Awa1 )a1 = 0 . 2 MeV c u rv e i n F ig u r e 7 .

In o r d e r t o com pare t h e o r y w i t h e x p e r im e n t , Agf f - v a lu e s m ust b e a s s ig n e d t o v a lu e s o f t h e dag t h ic k n e s s . T h is h a s b e e n d on e a c c o rd in g t o tw o d i f f e r e n t schem es: Ae f f h a s b e e n s e t e q u a l t o th e e n e rg y o f an e le c t r o n w i t h a c s d a ra n g e i n c a rb o n e q u a l t o

i ) 1 . 0 x t o t a l t h ic k n e s s ( i n g-cm- * ) o f th e d a g - a i r - d a g "s a n d w ic h " a c ro s s a d ia m e te r

i i ) 1 .5 x t h i s th ic k n e s s .

T h e s e schem es r e s u l t i n A g f f “ 22 and 28 k e V r e s p e c t iv e l y f o r z e r o d ag th ic k n e s s , in c r e a s in g t o 11 0 an d 140 k e v r e s p e c t iv e l y f o r a th ic k n e s s o f 9 mg•cm- 2 .

T he v a lu e s o b ta in e d c o r re s p o n d in g t o t h e ab o ve tw o schem es h a v e b e e n added t o th e e x p e r im e n ta l v a lu e s i n F ig u r e 8 . I t w i l l b e seen t h a t i n n e i t h e r c a s e do t h e t h e o r e t i c a l v a lu e s p r e d i c t t h e v e r y r a p id ch an g e i n J„ - r a t i o fo u n d e x p e r im e n t a l ly b e tw e e n th e b a r e A l t h im b le and t n e f i r s t d ag c o a t in g o f 0 .7 5 mg-cm- 2 . H o w eve r, th e v e r y g r a d u a l ch an g e f o r d ag t h ic k n e s s

IAEA-SM-298/81 111

in c r e a s in g b eyo n d 3 m g . сш—2 i s not. in c o n s is t e n t w i t h th e t h e o r y . I n g e n e r a l , th e a s s u m p tio n t h a t d ag ( i . e . c a r b o n ) i s a i r - e q u i v a l e n t w o u ld b e e x p e c te d t o u n d e r e s t im a te t h e e f f e c t o f th e d ag c o a t in g as c a rb o n ( I *» 78 e V ) i s m ore d i s s i m i l a r t o a lu m in iu m ( I «* 166 e V ) th a n a i r i s ( I - 8 5 .7 e V ) .

5 . APPLICATIO N TO "PROTOCOL" ELECTRON DOSIMETRY

5 . 1 C u r r e n t p r a c t ic e

None o f t h e v a r io u s n a t i o n a l and i n t e r n a t i o n a l p r o t o c o lsf o r th e d e t e r m in a t io n o f ab so rb e d d ose i n w a t e r i n m e g a v o lta g ee le c t r o n beams ( se e s e c t io n 1 ) ta k e i n t o a c c o u n t th e e f f e c t o f a non-m edium e q u iv a le n t w a l l . H o w ever, i o n i s a t i o n cham bers a v a i l a b le c o m m e r c ia l ly h a v e w a l l m a t e r ia ls ra n g in g fro m A -1 5 0 p l a s t i c w i t h I = 6 5 .1 e V t o C -5 5 2 a i r - e q u i v a l e n t p l a s t i c w i t h I = 8 6 .8 eV w h ic h ca n b e com pared t o th e w a t e r I - v a l u e o f 7 5 .0 eV ( T a b l e I I I ) . T he t h e o r y p re s e n te d h e re w i l l b e u sed t o e s t im a te th e m a g n itu d e o f th e c o n n e c t io n f a c t o r a p p l ic a b le t o such c h a m b e rs .

5 .2 T h e o r e t i c a l e s t i jn a t e o f c o r r e c t io n f a c t o r

The c o r r e c t io n f a c t o r t h a t m u l t i p l i e s th e c o n v e n t io n a lS A

smed a ir - t o t a k e a c c o u n t o f th e w a l l m a t e r ia l h a s b e e n d e f in e d b y E q u (1 4 ) . T h is ham b e e n e v a lu a te d f o r med = w a t e r , с = a i r , w a l l - A -1 5 0 and w a l l « C -5 5 2 f o r = 10 k e V , f o r v a lu e s o f « c o rre s p o n d in g t o - v a lu e s fro m 0 .0 1 t o 1 . 0 M ev f o r 10 MeVe le c t r o n s a t d e p th z / r Q = 0 . 4 - 0 . 5 . The - r a t i o sa p p e a r in g i n E q u (1 4 ) h a v e b een ta k e n fro m T a b le I V and v a lu e s o f e fro m th e c u rv e f o r w a te r i n F ig u r e 4 . T he r e s u l t i n gедэ едc o r r e c t io n f a c t o r s , sS a te r ,A 1 5 0 ,a ir< ¿ w a l l ) / sw a t e r , a i r

с д д S As w a te r ,C 5 5 2 , a i r ^ Aw a l l ^ w a te r , a i r • P i t t e d a s a f u n c t io no f in F ig u r e 9 .

The maximum d e v ia t io n fro m u n i t y , c o r re s p o n d in g t o =Eç/Z i . e . e = 1 . 0 , was 0 .5 2% f o r A -1 5 0 and 0 .5 8 % f o r c -5 5 2 ¿ t h i s can b e r e a d i l y e s t im a te d b y lo c a t in g th e v a lu e s o f s s a / s f o r w a t e r , A -1 5 0 and C -5 5 2 i n T a b le I V o r F ig u r e 5 . V a lu e s o f0 .3 9 % and 0 .4 8 % r e s u l t i f Aç ■ 20 ke V in s t e a d o f 10 k e V . T h is w i l l now b e a p p l ie d t o tw o c o m m e rc ia l io n ch am b ers .

The E x r a d in " t i s s u e - e q u iv a le n t " cham ber h as an A -1 5 0 w a l l

o f th ic k n e s s 0 .1 1 3 g*cm- i , [ 9 ] , f o r w h ic h A v a i l '“0 ,4 5 MeV i s a p p r o p r ia t e , le a d in g t o a c o r r e c t io n f a c t o r o f 1 .0 0 5 . The c o rre s p o n d in g f ig u r e s f o r th e C a p in te c P R -06C cham ber w h ic h h a s a C -5 5 2 w a l l , a r e 0 .0 5 0 g .cm - * [ 9 ] , 0 .2 5 MeV and 0 .9 9 5 . The may-imnm d e v ia t io n fro m u n i t y o f th e c o r r e c t io n f a c t o r f o r a g r a p h i t e w a l l i s o n ly 0 .2 4 % , w h ic h s u g g e s ts t h a t t h e e f f e c t o f t h i s v e r y common w a l l m a t e r ia l can b e ig n o re d when m aking

112 NAHUM

û„all/MeV

FIG. 9. Theoretical correction factor, ^ aKr wdt шг(^ц}^у>ш,.тг’ for д с = 10 keV, wall = A-150plastic (------ ); wall = C-552 plastic (-------- ); 10 M e V electrons in water; depth No. 7 (the maximumpossible deviation from unity, corresponding to A wall = E q/2, is indicated by an arrow on the

ordinate).

m easurem ents i n w a t e r . S i m i l a r l y th e e f f e c t o f th e commonly a p p l ie d c o n d u c tin g l a y e r o f dag on t h e in s id e o f a w a t e r - l i k e w a l l such as PMMA i s p r e d ic t e d t o b e n e g l i g i b l e .

6 . D is c u s s io n and C o n c lu s io n s

The a p p ro x im a te t h e o r y d e v e lo p e d i n t h i s w o rk h a s b een shown t o b e c o n s is t e n t w i t h m easurem ents made o f th e e f f e c t o f e x c h a n g in g a g r a p h i t e th im b le f o r an a lu m in iu m o n e , th o u g h th e a g re e m e n t i s n o t e x a c t . The e x p r e s s io n ( E q u .1 4 ) f o r t h e new q u a n t i t y w a l l с s h o u ld b e s e e n a s in d i c a t i n g th e o r d e r o fm a g n itu d e o f th e c o r r e c t io n t o th e c o n v e n t io n a l q u a n t i t y cr a t h e r th a n a s an e x a c t p r e d i c t i o n . I n p a r t i c u l a r , t h e th e o r y m akes th e a s s u m p tio n t h a t th e p r im a r y e le c t r o n f lu e n c e i n th e u n d is tu rb e d m edium , [4 ^ r l ] roe<j / i s n o t p e r tu r b e d b y th e p re s e n c e o f th e n o n -m e d iu m -e q u iv a le n t w a l l . T h is w o u ld c l e a r l y n o t b e re a s o n a b le f o r a w a l l o f a th ic k n e s s e q u a l t o th e maximum 6 - r a y r a n g e , e . g . ~ 2 g -c m г f o r E0 *» 10 MeV, when d i f f e r e n c e s i n e le c t r o n s c a t t e r i n g b e tw e e n th e w a l l m a t e r ia l and t h e m edium , w h e th e r due t o d e n s i t y o r a to m ic num ber d i f f e r e n c e s , c o u ld n o t

IAEA-SM-298/81 113

b e ig n o r e d . H o w eve r, due t o th e p re d o m in a n c e o f v e r y lo w -e n e r g y 6 - r a y s , a w a l l o f o n ly - 0 .0 5 /g -c m - 2 t h i c k i s s u f f i c i e n t t o g e n e r a te 6 - r a y s t h a t c o n t r ib u t e - 80% o f th e t o t a l 6 - r a y c a v i t y d ose f o r a i r c a v i t i e s o f c o n v e n t io n a l d im e n s io n s , i . e . Дд » 10 - 20 k e V . A w a l l o f t h i s t h ic k n e s s can b e assumed t o h a v e a n e g l i g i b l e in f lu e n c e on th e p r im a r y e le c t r o n f lu e n c e w h i le h a v in g c o n s id e r a b le in f lu e n c e o n th e 6 - r a y f lu e n c e i n th e c a v i t y .

The c u r r e n t t h e o r y , l i k e t h e S p e n c e r - A t t ix t h e o r y w h ic h i s i t s s t a r t i n g p o i n t , d oes n o t t a k e a n y a c c o u n t o f 6 - r a y s c a t t e r i n g e f f e c t s d ue t o a to m ic num ber d i f f e r e n c e s b e tw e e n th e w a l l , o r m edium , and th e c a v i t y m a t e r i a l , u s u a l ly a i r . Such e f f e c t s f o r t h e " s e c o n d a ry " e le c t r o n s g e n e ra te d b y p h o to n beams h a v e b e e n shown t o b e im p o r ta n t i n g e n e r a l c a v i t y t h e o r y [ 3 4 ] . I t i s e x p e c te d t h a t s i m i l a r c o r r e c t io n s , e s p e c i a l l y f o r 6 - r a y s w it h reuiges o f t h e o r d e r o f th e c a v i t y s i z e , w i l l b e n e c e s s a ry i n a m ore e x a c t t r e a t m e n t .

I t s h o u ld b e p o s s ib le t o in c o r p o r a t e e le m e n ts o f th e p r e s e n t t h e o r y i n t o t h e e x p r e s s io n f o r t h e e f f e c t o f a n o n -m e d iu m -e q u iv a le n t w a l l i n t h e c a s e o f an i n c id e n t p h o to n beam . M easu rem en ts w i t h ал a lu m in iu m t h im b le ( + A l b u i ld - u p c a p ) c o a te d w i t h d i f f e r e n t dag th ic k n e s s e s h a v e a ls o b e e n made i n a C o -6 0 beam [ 14 ] . The A lm o n d -S v en ss o n e x p r e s s io n f o r a c o m p o s ite A l /C w a l l f a i l e d t o p r e d i c t th e v e r y m arked chan g e in re s p o n s e o b s e rv e d [ 1 4 ] , s i m i l a r t o t h a t fo u n d i n th e e le c t r o n beam c a s e , w h ic h can b e a t t r i b u t e d t o 8 - r a y g e n e r a t io n i n th e d a g , r a t h e r th a n p h o to n i n t e r a c t i o n s i n t h i s t h i n l a y e r .

M o n te -C a r lo s im u la t io n o f 3 -m e d ia d e t e c t o r g e o m e tr ie s ax e d e s i r a b le as a c o m p lim e n t t o e x p e r im e n t , i n f u r t h e r i n g o u r u n d e r s ta n d in g o f 6 - r a y e f f e c t s . I n p a r t i c u l a r , l i g h t c o u ld be shed on th e im p o r t ал ее o f 6 - r a y s c a t t e r i n g e f f e c t s m e n tio n e d a b o v e , and on how and h e n c e « s h o u ld b e c h o s e n . Af u r t h e r v e r y im p o r ta n t t a s k f o r M o n te -C a r lo i s t o in v e s t ig a t e th e a c c u ra c y , f o r d i s s i m i l a r m a t e r ia ls , o f th e b a s ic S p e n c e r - A t t ix t h e o r y o f w h ic h t h e p r e s e n t w o rk i s an e x t e n s io n .

R E F E R E N C E S

[ 1 ] S P E N C E R ,L .V ., A T T IX ,F .H . , R a d .R e s .3 ( 1 9 5 5 ) 2 3 9 .[ 2 ] INTERNATIONAL COMMISSION ON RADIATION UNITS AND

MEASUREMEIfTS, R a d ia t io n D o s im e try i E le c t r o n Beams w it hE n e rg ie s b etw een 1 and 50MeV, ICRU R e p o rt 3 5 , I CRU,B e thesd a,M D 20814 ( 1 9 8 4 ) .

[ 3 ] NACP (N o r d ic A s s o c ia t io n o f C l i n i c a l P h y s ic s ) , P ro c e d u re s i n E x t e r n a l R a d ia t io n T h e ra p y b e tw e e n 1 and 50 MeV, A c ta R a d io l .O n e .19 ( 1 9 8 0 ) 5 5 .

[ 4 ] S u pp lem ent t o NACP ( 1 9 8 0 ) , E le c t r o n Beams w it h MeanE n e rg ie s a t th e P hantom S u r fa c e b e lo w 15 MeV, A c taR a d io l .O n e .20 ( 1 9 8 1 ) 4 0 2 .

[ 5 ] AAPM (A m e ric a n A s s o c ia t io n o f P h y s ic is t s in M e d ic in e ) , AP r o to c o l f o r th e D e te r m in a t io n o f A b so rb ed Dose fro mH ig h -E n e rg y P hoton and E le c t r o n Beams, M e d .P h y s .1 0 ( 1 9 8 3 ) 7 4 1 .

[ 6 ] HPA ( H o s p i t a l P h y s ic is t s ' A s s o c ia t io n ) , R e v is e d Code o f P r a c t ic e f o r th e D o s im e try o f 2 t o 25 KV X - r a y , and o f C a es iu m -1 37 and C o b a l t - 6 0 G an m a-ray Beams, P h y s .M e d .B io l .28 ( 1 9 8 3 ) 1 0 9 7 .

[ 7 ] SEFM (S o c ie d a d E sp a rtó la de P i s i c a M e d ic a ) , P ro c e d im ie n to s recom endados p a ra l a d o s im e t r ía d e fo to n e s y e le c t r o n e s de e n e r g ía s co m p re n d id a s e n t r e 1 MeV y 50 MeV en r a d io t e r a p ia de h ace s e x te r n o s . P u b l ic a t io n K o .1 -1 9 8 4 , M a d r id , S p a in .

[ 8 ] HPA, Code o f P r a c t ic e f o r E le c t r o n Beam D o s im e try in R a d io th e ra p y , P h y s .M e d .B io l .Э0 ( 1 9 8 5 ) 1 1 6 9 .

[ 9 ] M IJNHEER,B . J . , A A L B E R S ,A .H .L ., V IS S E R ,A .G . , WITTKAMPER, C o n s is te n c y and s i m p l i c i t y i n th e d e te r m in a t io n o f ab so rb e d dose in h ig h -e n e r g y p h o to n beams i A new co d e o f p r a c t ic e , R a d io t h e r .O n c o l .7 ( 1 9 8 6 ) 3 7 1 .

[ 1 0 ] S w iss S o c ie ty o f R a d ia t io n B io lo g y and R a d ia t io n P h y s ic s , D o s im e try o f h ig h -e n e r g y p h o to n and e le c t r o n beams ¡ Recccm endatiorus ( 1 9 8 6 ) .

[ 1 1 ] CFMRI (C o m ité F r a n ç a is d e M es u res d e e Rayonnem ents I o n i s a n t e ) , R ecom nendations p o u r l a m esure de l a d ose ab s o rb e « dans le s fa is c e a u x d ' e le c t r o n s e t d é p h o to n s d 'e n e r g ie co m p ris e e n t r e 1 e t 50 MeV, R a p p o rt 2 , P a r i s , ( 1 9 8 7 ) .

[ 1 2 ] IAEA ( I n t e r n a t i o n a l A to m ic E n e rg y A g e n c y ) , A b so rb ed d ose d e te r m in a t io n i n p h o to n and e le c t r o n beams ia n i n t e r n a t i o n a l Code o f P r a c t i c e , T e c h n ic a l R e p o r t S e r ie s N o .2 7 7 , IA E A , V ie n n a , ( 1 9 8 7 ) .

[ 1 3 ] A IH 0 N D ,P .R ., SVENSSON,H . , A c ta R a d io l .T h e r .P h y s .B io l . 16 ( 1 9 7 7 ) 1 7 7 .

[ 1 4 ] NAHUM, A. E . , HENRY,W .H ., R O S S ,C .K ., M e d ic a l and B io lo g iC & l E n g in e e r in g and C o m p u tin g ,23 ( 1 9 8 5 ) S u p p l .P a r t 1 , p . 6 1 2 . (P ro c e e d in g s o f th e V I I ICM P, E sp o o , 1 9 8 5 ) .

[ 1 5 ] N A H U M ,A .E ., P h y s .M e d .B io l .23 ( 1 9 7 8 ) 2 4 .

[ 1 6 ] NAHUM,A .E . , Calculations of E le c t r o n F lu x S p e c tr a in W a te r I r r a d i a t e d w it h M e g a v o lta g e E le c t r o n and P hoton Beams w it h A p p l ic a t io n s t o D o s im e try , T h e s is , U n iv .o f E d in b u rg h , 1976 ( U n i v e r s i t y M ic r o f i lm s I n t e r n a t i o n a l , o r d e r N o .7 7 - 7 0 ,0 0 6 ) .

[ 1 7 ] B E R G E R ,M .J., S E L T Z E R ,S .M ., C a lc u la t io n o f e n e rg y and c h a rg e d e p o s it io n and o f th e e le c t r o n f l u x in a w a te r medium bom barded w ith 20 MeV e le c t r o n s , A n n .N .T . A c a d .S e i . 161 ( 1 9 6 9 ) 8 .

114 NAHUM

IAEA-SM-298/81 115

[ 1 8 ]

[ 1 9 ]

[2 0 ]

[2 1 ]

[2 2 ]

[ 2 3 ][ 2 4 ][ 2 5 ]

[ 2 6 ][ 2 7 ][ 2 8 ]

[ 2 9 ]

[ 3 0 ] [ 3 0 ] [ 3 2 ]

[ 3 3 ]

[ 3 4 ]

ANDREO,P. , A p l ic a c ió n d e l m étodo de M o nte c a r l o a l a p e n e t r a c ió n y d o s im e t r ía de h a c e s de e le c t r o n e s , T h e s is , U n i v e r s i t y o f Z a ra g o z a , (1 9 8 1 ) .ROGERS,D .W .O . , B IELAJEW ,A. P . , NAHUM,A . E . , P h y s .M e d .B io l . 30 ( 1 9 8 5 ) 4 2 9 ..N A H U M ,A .E ., BRAHM E,A., E le c t r o n D e p th -D o s e D i s t r ib u t io n s i n U n ifo rm and N o n -U n ifo rm M e d ia , p . 9 8 -1 2 7 i n TheC o m p u ta tio n o f Dose D i s t r ib u t io n s in E le c t r o n Bean R a d io th e ra p y (N A H U M ,A .E . , E d . ), ttneâ U n iv e r s i t y ( 1 9 8 5 ) . S E L T Z E R ,S .M ., H U B B E L L ,J .H ., B E R G E R ,M .J ., Some T h e o r e t ic a l A s p e c ts o f E le c t r o n s and P h oto n D o s im e try , IA E A -S M -2 2 2 /0 5 ,p .3 -4 3 in N a t io n a l and I n t e r n a t i o n a l S t a n d a r d iz a t io n o f R a d ia t io n D o s i in e t r y ,V o l . I I , IA E A p u b l ic a t io n S T I/P U B /4 7 1 ( 1 9 7 8 ) .SVENSSON,H. , NAHUM,A . E . , P re s e n t K now ledge o f S to p p in g - P o v e r R a t io s f o r I o n i z a t i o n C ham bers, i n v i t e d p a p e r a t V I ICMP, Hamburg ( 1 9 8 2 ) .B IE L A J E W ,A .P ., P h y s .M e d .B io l .3 1 ( 1 9 8 6 ) 1 6 1 .AN DREO ,P ., NAHUM,A . E . , P h ys .M ed , B i o l .3 0 ( 1 9 8 5 ) 1 0 5 5 . NELSON,W .R . , H IR A Y A M A ,A ., ROGERS,D .W .0 . , T he EGS4 C b d e-S ys tem , S ta n fo r d L in e a r A c c e le r a t o r C e n te r R e p o rt S L A C -265 , S t a n f o r d , CA 94305 ( 1 9 8 5 ) .ROGERS,D .W .0 . , B IE L A J E W ,A .F ., P r i v a t e c o m m u n ic a tio n . ROGERS,D .W .O ., N u c l . In s tru m .M e th o d s A 227 ( 1 9 8 4 ) 5 3 5 . ROGERS,D .W .0 . , B IE L A JE W ,A .P . , The Use o f EGS f o r M onte C a r lo C a lc u la t io n s i n M e d ic a l P h y s ic s , N a t io n a l R e se arc h C o u n c il R e p o r t P X N R -2692 , NRC, O tta w a ( 1 9 8 4 ) .B IE L A J E W ,A .P ., ROGERS,D .W .0 . , N u c l . In s t r u m .M eth o ds B IB ( 1 9 8 7 ) 1 6 5 .B IE L A J E W ,A .P ., p r i v a t e c o o m u n ic a t io n .ROGERS,D .W .O ., B IE L A JE W ,A .K ., M e d .P h y s .1 3 ( 1 9 8 6 ) 6 8 7 . INTERNATIONAL COMCISSION ON RADIATION UN ITS AND MEASUREMENTS, S to p p in g Pow ers f o r E le c t r o n s and P o s i t r o n s , ICRU R e p o rt 3 7 , ICRU , B e th e e d a , MD 20814 ( 1 9 8 4 ) .S TER N H EIM ER ,R .M ., BERGER,M. J . , SELTZER ,S .M . , A to m ic D a ta and N u c le a r D a ta T a b le s 3 0 ( 1 9 8 4 ) 2 6 1 .KEARSLEY E . , P h y s . M ed . B i o l . 2 9 ( 1 9 8 4 ) 1 1 7 9 .

IAEA-SM-298/8

D E P E N D E N C E O F S O M E D O S I M E T R I C P A R A M E T E R S O N B E A M S I Z E I N A N I R R A D I A T E D P H A N T O M

J.R. CUNNINGHAM, M. WOO Physics Division,Ontario Cancer Institute,Toronto, Ontario,Canada

Abstract

DEPENDENCE OF SOME DOSIMETRIC PARAMETERS ON BEAM SIZE IN AN IRRADIATED PHANTOM.

When an ionization chamber is used for the purpose of determining absorbed dose, the reading obtained from the electrometer must be multiplied by a number of factors. There are at least four kinds of these factors and all of them are difficult to determine cleanly and with precision. The kinds are: ratios of averaged stopping powers, ratios of averaged mass energy absorption coefficients, perturbation factors and empirical factors related specifically to the chamber. The values of all these factors must depend on the spectrum of photons existing at the point of measurement. The spectrum is in fact rarely known in detail and approximation methods must be used to determine the values to be used. To examine the way in which these parameters might change with field size and depth within a phantom a number of photon spectra were selected from the literature and from these the spectra at points within an irradiated phantom were calculated using Monte Carlo methods. The results indicate that, in producing a variation in these parameters, only field size and low energy photons are important and that the parameter most strongly affected is the ratio of mass energy absorption coefficients.

INTRODUCTION

The equation relating dosimeter reading to absorbed dose in a

high energy photon beam is[l]

Dw = Mu " Nd * Sw/Blr * Pu (1)

where D„ is the absorbed dose in water at the effective point of

measurement of an ionization chamber and Mu is the reading taken from

the electrometer that is attached to the ionization chamber. ND is

the absorbed dose to air calibration factor which must be obtained

from a calibration procedure carried out at a standardization

laboratory. Sw ,.ir is the ratio of averaged stopping powers for the

117

spectrum for water to that of air and Pu is the perturbation factor.

Pu is in turn composed of a number of factors;-

p _ a * SwclI 1 . air * f l i q n / P)w.wall ^ (l~0t) * Sw.alr (2)Sw ,air

Again there are stopping power ratios and (íi.n/р)w.waii is the

ratio of averaged mass energy absorption coefficients for water to

that of the wall material, also evaluated for the users beam, a is

the fraction of the ionization observed that results from electrons

that arise from photon interactions that take place in the walls of

the chamber, and (1-a) is the fraction, if any, of the ionization

that results from electrons coming from the water of the phantom that

is beyond the ion chamber walls. Each of these quantities would be

expected to depend on the energy spectrum of photons present at the

point of measurement.

Methods for obtaining values for S „ , n . alr

(n.n/p)w,waii are given in dosimetry protocols[1,2], by Cunningham

and Schulz[3] and by Johns and Cunningham[4].

Cunningham et al[5] have shown that the ratio of averaged mass

energy absorption coefficients, n , is affected by the

change in spectrum that results from changes in beam size and depth,

changes that have very rarely been allowed for in dose calculations.

In this paper we further examine this quantity and also explore the

influence of these conditions on stopping power ratios, and

perturbation factors.

The irradiation conditions are shown in Figure 1 where a beam

of finite size is irradiating a phantom made of water. A dosimeter,

118 CUNNINGHAM and WOO

IAEA-SM-298/8 119

FIG. 1. Diagram showing the irradiation conditions simulated by Monte Carlo calculations for

generating photon spectra in a phantom. The incident spectrum, d4>0(hv)/dhv, is known and the

spectrum, d<t>(hp)/dhv, at P is calculated. (From Ref. [5].)

FIG. 2. Monte Carlo calculated spectra for a water phantom irradiated with 6 M V linac radiation as

shown by the curve labelled ‘incident spectrum ’. Only a very slight change of spectrum shape can be

seen as the depth is changed. (From Ref. [5].)

cylindrical in shape, with walls made of a different material,

designated as m is located at point P as shown. The photon radiation

seen at the detector will be the result of the attenuation of the

primary radiation that is incident on the surface of the phantom and

the photons that are scattered from within the irradiated volume. The

resultant energy fluence spectrum at point P would be expected to be

dependent on depth, through attenuation of primary, and on field size

and depth through the radiation scattered from the irradiated volume.

The spectrum at point P has been studied using the Monte Carlo

computer code EGS4[6] for a wide range of incident spectra as depth

and field size is changed. An example, from Cunningham et al[5] is

shown in Figure 2, This shows an experimentally determined beam

spectrum for a 6 MV linear accelerator and four spectra derived from

it by Monte Carlo calculations from it. These are intended to

simulate the spectra at the surface in a 10 cm by 10 cm beam and at

depths of 5, 10 and 20 cm in the same beam. There appears to be no

marked change in spectrum as depth increases. The attenuation of low

energy components of the primary is balanced by the buildup of low

energy scattered photons. It is somewhat surprising that the

spectrum at the surface is nearly the same as the input, in air

spectrum. The differences cannot be seen on this diagram. From

these data one would not expect to see changes in any of the

spectrally dependent parameters as depth is changed.

The situation is quite different with respect to field size.

Figure 3, also from Cunningham et al[5], shows the photon spectra at

a depth of 10 cm for four beam sizes, having field areas of 25, 100,


IAEA-SM-298/8 121

FIG. 3. Monte Carlo calculated spectra for a water phantom irradiated with 6 M V linac radiation. The

spectra are for different field sizes and show a buildup of low energy, multiply scattered photons.

400 and approximately 10“ square centimeters. Now the change is

quite marked in that the spectrum has many more low energy components

when the beam, and hence the scattering volume, is large than when it

is small. There is of course no hardening of the primary part of the

beam since the depth is constant. It has been determined from the

Monte Carlo calculations that this accumulation of scattered photons

is the result of multiple scatter processes. A note of interest is

the rather sharp peak which can be seen at an energy of about 0.5

MeV. It is due to annihilation photons.

In the aforementioned paper[5] we examined the effect of this

spectral change on (д.„/р)m2,mlf the ratio of averaged mass energy


absorption coefficients. The ratio was calculated by evaluating the

following expression

where are the components of the energy fluence spectrum

calculated for a point in a phantom made of material mi and

and are the mass energy absorption

coefficients for the same energy components, hpi., for materials m2

and mi respectively^ the summations are over all the energy

components in the spectrum.

The method is straightforward. The spectrum ♦(h»»i.) was generated

for the various beam configurations by Monte Carlo calculations for a

water phantom (m2) and stored so that a library of photon spectra was

accumulated and the simple numerical integration procedure indicated

in Equation (3) was performed. Values for the mass energy absorption

coefficients are obtained from a library of photon interaction

coefficients by table lookup and interpolation. The results, for 6

MV, show that this ratio, for materials used in dosimetry procedures,

changes only slightly even for the large range of field sizes shown.

The material showing the largest variation compared to water is

graphite, which shows for these 6 MV spectra, an extreme variation of

about one-half of one percent. Although this might be of some

relevance for precise dosimetry it is certainly not important for

clinical procedures.

These calculations were repeated for other spectra and the

results can be summarized by saying that the variation of

( 3 )

IAEA-SM-298/8 123

T a b l e 1 . R a t i o s o f a v e r a g e d m a s s e n e r g y a b s o r p t i o n c o e f f i c i e n t s

= ° C o r a d i a t i o n

w a t e r / g r a p h i t e b o n e / a i r

d 2.8

f i e l d r a d i u s

5 . 6 1 1 . 3 5 0 . 0 2.8

f i e l d

5 . 6

r a d i u s

1 1 . 3 5 0 . 0

0 1.11 1.112 1 . 1 1 3 1 . 1 1 5 1 . 0 0 6 1 . 0 6 9 1 . 0 7 6 1 . 0 9 3

5 1.112 1 . 1 1 3 1 . 1 1 5 1.122 1 . 0 6 9 1 . 0 7 7 1 . 0 9 6 1 . 1 4 6

10 1.112 1 . 1 1 3 1 . 1 1 7 1 . 1 2 7 1 . 0 7 0 1 . 0 8 1 1 . 1 0 8 1 . 1 8 5

20 1.112 1 . 1 1 4 1 . 1 1 9 1 . 1 3 5 1 . 0 7 2 1 . 0 8 8 1 . 1 2 6 1 . 2 4 6

2 6 M V l i n a c r a d i a t i o n

w a t e r / g r a p h i t e b o n e / a i r

d 2.8

f i e l d r a d i u s

5 . 6 1 1 . 3 5 0 . 0 2.8

f i e l d

5 . 6

r a d i u s

1 1 . 3 5 0 . 0

0 1 . 1 2 6 1 . 1 2 7 1 . 1 2 7 1 . 1 2 8 1 . 0 8 6 1 . 0 8 7 1 . 0 9 0 1 . 0 9 7

5 1 . 1 2 7 1 . 1 2 8 1 . 1 2 8 1 . 1 3 0 1 . 0 8 8 1 . 0 9 0 1 . 0 9 6 1 . 1 1 4

10 1 . 1 2 8 1 . 1 2 8 1 . 1 2 8 1 . 1 3 1 1 . 0 9 0 1 . 0 9 2 1 . 0 9 9 1 . 1 2 7

20 1 . 1 2 9 1 . 1 2 9 1 . 1 3 0 1 . 1 3 3 1 . 0 9 3 1 . 0 9 6 1 . 1 0 6 1 . 1 4 6

(tf»n/p)w«t«.ir,„гарте, is small for all energies equal to or greater

than that of cobalt. Some results are shown in Table 1 for

water-to-graphite and bone-to-air. For water-to-graphite the value

for an extremely large field size is a little more than 2% higher

than it is for a small field. This might be important for total body

treatments but is not for calibration procedures.

As can be seen, the variation in this quantity when bone is

involved is much greater, being almost 20%, and this might be

important in some biological experiments. The situation is similar,

but the changes somewhat less at much higher energies, as can be

seen.

At conventional energy X-rays, say 270 kVp, this ratio for water

to graphite appears to be almost 15% greater for a 20 cm by 20 cm

beam than it is for a small beam. This clearly has implications for

dosimetry and since relative biological effectiveness (RBE) data is

referred to radiation of this energy, it calls into question much of

the data in the literature on this subject.

NEW CALCULATIONS

Ratios of averaged stopping powers were calculated from the

expression

2>< E3)mj. • S lon(E 3)m2 Sm2,mx = - (4)

* Sion(E j)m x

This is very similar to Equation (3) in appearance but is much

more complicated because 0(E3)mi is the spectrum of electron energies


IAEA-SM-298/8 125

Table 2. Ratios of averaged restricted mass stopping powers for water/graphite

4 MV linac radiation

field radius

d 2.8 5.6 11.3 50.0

0 1.135 1.135 1.135 1.135

5 1.135 1.135 1.134 1.134

10 1.135 1.135 1.134 1.133

20 1.136 1.135 1.134 1.132

seen at the point for which the calculation is made. This spectrum

was calculated as the slowing down spectrum for each component, hPi,

of the photon spectrum by methods that are described elsewhere[4,3].

SioniEj)™, and Sion(E3)mi are the restricted mass ionization

stopping powers for materials ma and mi,respectively.

This ratio was evaluated for 20 MeV, 4 MV, cobalt and 270 kVp

photon spectra. The in air spectra were kindly supplied by

Andreo[7]. The results obtained for a 4 MV bremsstrahlung spectrum

are shown in Table 2. It can be seen that for water compared to

graphite the difference in the stopping power ratio for a small beam

compared to a very large beam is very small indeed, less than one

half of a percent in the extreme and less than 0.2% over a range

reasonable for dosimetry.


Table 3. Ratios of averaged restricted mass stopping powers for water/graphite

20 MV linac radiation 270 kVp X-radiation

d 2.8

field radius

5.6 11.3 50.0 2.8

field

5.6

radius

11.3 50.0.

0 1.143 1.143 1.143 1.143 1.120 1.120 1.120 1.120

5 1.143 1.143 1.142 1.142 1.120 1.120 1.120 1.120

10 1.143 1.143 1.142 1.142 1.120 1.120 1.120 1.120

20 1.143 1.143 1.142 1.141 1.120 1.120 1.120 1.120

For both high, 20 MV radiation and low, 270 kVp radiation, the/

results were similar, again showing less than 0.2% variation in the

stopping power ratios for water to graphite. The calculated values

are shown in Table 3 and it would seem that, in general, the

variation in the photon spectrum as a function of field size is not

reflected in a variation in stopping power ratio.

Calculations for the attenuation part of the perturbation factor,

pu, by a method described by Cunningham and Sontag[8] for the same

range of beam energies also failed to show an appreciable variation

with field size.

CONCLUSIONS

The parametersj ratio of averaged mass energy absorption

coefficients, ratio of averaged stopping powers and perturbation

factors, have been examined with respect to their dependence on field

size and depth. The important variation is field size and only the

absorption coefficients ratio shows an appreciable effect for

materials and beam configurations relevant to photon beam dosimetry

and then only for low energy X-rays.

REFERENCES

[1] IAEA, Absorbed dose determination in Photon and Electron Beams,

"An International Code of Practice”, Authors, P. Andreo, J.R.

Cunninghajn, K. Hohfeld, H. Svensson (International Atomic Energy

Agency, Vienna, 1987).

[2] TASK GROUP 21, Radiation Therapy Committee, AAPM, Med. Phys. 10,

(1983), 741.

[3] CUNNINGHAM, J.R., SCHULZ, J.; Med. Phys. 11, (1984), 618.

[4] JOHNS, H.E., CUNNINGHAM, J.R., "The Physics of Radiology", 4th

Ed. (Charles C. Thomas, Springfield 111. 1983).

[5] CUNNINGHAM, J.R., WOO, M., ROGERS, D.W.O., BIELAJEW, A.F., Med.

Phys. 13, (1986), 496.

[6] NELSON, W.R., HIRAYAMA, A., ROGERS, D.W.O., "The EGS4 Code

System", Stanford Linear Accelerator Report 265, (1985).

[7] ANDREO, P. (personal communication).

[8] CUNNINGHAM, J.R. and SONTAG, M.R., Med. Phys. 1*. (1980), 672.

IAEA-SM-298/8 127

IAEA-SM-298/78

D O S I M E T R Y O F O R T H O V O L T A G E X - R A Y B E A M S

B.J. MIJNHEER Radiotherapy Department,The Netherlands Cancer Institute

(Antoni van Leeuwenhoekhuis),Amsterdam,The Netherlands

L.M. CHINJoint Center for Radiation Therapy

and Department of Radiation Therapy,Harvard Medical School,Boston, Massachusetts,United States of America

Abstract

DOSIMETRY OF ORTHOVOLTAGE X-RAY BEAMS.The absorbed dose to a medium irradiated by orthovoltage X-ray beam s (10 0 -3 0 0 kV) is

usually determ ined according to the form alism recom m ended by the ICRU. The absorbed dose to water can be calculated from the reading of an ionization cham ber, the exposure calibration facto r and the facto r F , which converts exposure to absorbed dose to w ater for the specified radiation quality . In a review of published data o f dose m easurem ents in orthovoltage X-ray beams and using this form alism , large differences can be observed. In a proposed new formalism, the calibration facto r for 60Co gamma rays is also applied for m easurem ents in orthovoltage beams. Experim ents using different types o f ionization cham bers and analysed according to b o th the new and the ICRU formalisms are described. The results have been com pared with those recently obtained by o ther groups using different calibration or m easurement procedures.

1. INTRODUCTION

The determination of absorbed dose to a medium

irradiated by orthovoltage X-ray beams ОСЮ-300 kV) is

usually based on the procedure described in ICRU Report 23

[1]. An ionization chamber calibrated in air, in terms of

exp'osure, is used to measure exposure at a specified point in

a standard (water) phantom. The exposure is then related to

129

130 MIJNHEER and CHIN

absorbed dose to the medium by means of a composite

coefficient. By using published depth dose tables and isodose

charts or performing relative measurements using the same or

another ionization chamber, the absorbed dose at any point of

interest is determined. A similar approach is applied for

megavoltage photon beams. Recently, protocols for the

dosimetry of high-energy photon beams have been revised

since the concept of in-phantom measurement of exposure was

subject to question (e.g. see [2]). In addition, dimensions

and composition of the ionization chamber wall are taken into

account in these protocols for accurate determinations of

absorbed dose. It is the purpose of this paper to quantify

the limitations of the ICRU procedure. By applying the

concepts used in the dosimetry of high-energy photon beams in

the orthovoltage range, estimates of absorbed dose can be

made [3 ]. The resulting absorbed dose values will be compared

with those determined using the ICRU formalism and those

observed by other groups using different methods [^,5,6,7].

2 . ICRU FORMALISM

The equation given in ICRU Report 23 for the

determination of absorbed dose to the undisturbed medium,

D ., from an ionization chamber measurement at the reference med

depth in the medium can be represented by:

where M is the ionization chamber reading normalized to a

standard temperature and pressure, N°V is the exposureÀcalibration factor, which gives the exposure at the location

of the centre of the chamber in the absence of the chamber,

IAEA-SM-298/78 131

at a stated quality of orthovoltage radiation under stated conditions of temperature and pressure. The conversion

coefficient F is appropriate for calculating the absorbed

dose from the exposure under conditions of electron

equilibrium. Values of F tabulated in ICRU Report 23 are

based on the expression:

F = (W . /e).(u /p)m ®d (2)air en air

in which W . /e is the quotient of the average energy air

expended to produce an ion pair in dry air by the electronic

charge, and (y /p)m?d is the ratio of the mass energy- en air

absorption coefficients for the medium and air for the photon

energy spectrum at the position of the centre of the

ionization chamber. The values were obtained for a field size

of 10 cm x 10 cm for a recommended depth of 5 cm in a water

phantom. Owing to the displacement of phantom material by the

different materials of the chamber system, a perturbation

correction factor will be necessary. The magnitude of this

correction is, however, less than for the recommended type

of ionization chamber according to ICRU Report 23 and can

therefore be ignored.

3. EXPERIMENTAL VERIFICATION OF THE ICRU FORMALISM

In order to verify the procedure recommended in the ICRU

Report, experimental comparisons can be made between chambers

of different design. In an extensive study using 14 different

ionization chambers Will and Rakow [8 ] compared absorbed dose

values for four different orthovoltage radiation qualities.

Their results showed that differences up to 29? (in one

situation even of 40% not shown in the figure) between

132 MUNHEER and CHIN

Deviation (%)

FIG. 1. Percentage deviation of relative absorbed dose values from values tabulated in Br. J.

Radiol., Suppl. 10 [12], determined with different types of ionization chambers. The data are

normalized to the value measured free in air at 200 kV, 2.0 m m Си half-value layer, for a field

size of 205 c m 2 at 50 c m focus-surface distance (adapted from Will and R a k o w [8]J.

absorbed dose values determined with different ionization

chambers can be observed (see Fig. 1). Even different

chambers of the same type would produce rather large

deviations. From their results Will and Rakow concluded that

the differences increased with increasing depth in the

phantom and that there was no systematic dependence of the

difference as a function of chamber volume.

IAEA-SM-298/78 133

• OMH K-2 (reference ch.) O NPL 2561- 084 □ PTW Normal ch.- 23331

FIG. 2. Absorbed dose values measured in water at 5 c m depth for a 10 cm X 10 c m field determined with different ionization chambers and analysed according to the ICR U formalism.

The data are normalized to the value of the reference chamber (from Zsdànszky et al. [1 0 ] /

Some of the chambers employed by Will and Rakow had

dimensions much larger than recommended in the ICRU Report:

internal diameter of about 5 mm and a length of about 15 mm.

If, however, the results of these chambers are omitted,

rather large differences can still be observed. This was/•

confirmed by more recent measurements of Zsdanszky and

co-workers [9,10]. These authors measured the absorbed dose

to water for four orthovoltage qualities using five

commercially available ionization chambers and a Secondary

Standard Chamber, after calibration in air. Differences of

about 3% were observed (see Fig. 2) while one of the chambers

gave a deviation of 7.5? during another investigation [9].

A number of factors might be responsible for the

observed discrepancies. Basically these are related to the


angular and spectral changes of the photons with depth in the

phantom compared to the in-air situation and the limitations

of in-phantom measurement of exposure. In addition, the

chamber will displace a certain volume of phantom material

which might not be adequately taken into account during the

calibration procedure. This difference in perturbation effect

during the in-air calibration and in-phantom measurement has

* r -1been discussed theoretically by Liden [11]. According to his

calculations the effect of the volume displaced by an

ionization chamber is due to three phenomena: the increase of

the fluence of the primary radiation, the decreased

filtration of the scattered radiation and the elimination of

scattering from the displaced volume. According to him the

overall effect would be an overestimate of absorbed dose

values determined with an ionization chamber. These results

are confirmed by more recent calculations of Kristensen and

colleagues [7].

It should be noted that in the ICRU formalism the

difference in composition between the wall material and air

OVis included in and not in F. It is assumed that the

effect of such a difference on the charge produced remains

constant regardless of possible changes in electron and

photon energy spectrum, i.e. the depth and field size

employed for the in-phantom measurement. According to ICRU

Report 23 errors of only less than 2% will be introduced if a

particular value of F is applied for field sizes other than

10 cm x 10 cm.

4 . NEW FORMALISM

In a new formalism [3], which is identical in concept to

that used in recent protocols for the dosimetry of high-

IAEA-SM-298/78 135

energy photon beams, Dmgd is related to the ionization

chamber reading M by the equation:

D = M.N .(L/p)wall.(p /p)me^ . P . .P , (3)med gas air en wall, ion repl

where N is the cavity-gas calibration factor for cobalt-60 gas

gamma rays as defined, for instance, in the AAPM protocol

[2], (L/p)'" 11 is the ratio of the mean restricted collision air

mass stopping powers for the wall material and air, P lQn is

the ion recombination factor and prepl is the replacement

correction factor. Note that in this formalism the dimensions

and composition of the ionization chamber wall are taken into

account during the in-phantom measurement. Equation (3) can

be derived either by using first principles or directly from

the equation for Dmgd given in the AAPM protocol for high-

energy photon beams and assuming that the total ionization

is produced by electrons arising in the chamber wall.

Owing to electron and photon energy spectral changes as

a function of field size and depth, the new formalism applies

best with "air equivalent" ionization chambers, i.e. chambers

with wall materials having (L/p)'"^11 unity. Graphite-walled,Э 1 Г

aluminium central electrode chambers need additional

information on the proportion of ionization produced by

electrons arising in each material as well as a very accurate

knowledge of the photon energy spectrum at the position of

the chamber. These chambers are, therefore, impractical to

use in combination with the new formalism.

5 . EXPERIMENTAL VERIFICATION OF THE NEW FORMALISM

Experiments using three different types of ionization

chambers were performed to compare the ICRU and the new


TABLE I. COMPARISON OF ABSORBED DOSE VALUES DETERMINED WITH

THREE DIFFERENT IONIZATION CHAMBERS, APPLYING THE NEW AND THE

ICRU FORMALISM

EXRADIN А1а EXRADIN T2b NE 2505/3A0

Radiationi Quality New ICRU New ICRU ICRU

100 kV / 4.0 mm Al 1.000 0.913 0.977 0.924 0.904

140 kV / 0.5 mm Cu 1.000 0.926 0.979 0.921 0.925

200 kV / 1.0 mm Cu 1.000 0.968 0.996 0.958 0.955

250 kV / Thoreaus-I 1 .000 0.984 1 .011 0.981 0.977

Оосо kV / Thoreaus-II 1 .000 0.998 1.014 1.000 0.992

Note :

Wall and central electrode made from C-552 plastic.13 Wall and central electrode made from A-150 plástic.Q

Graphite wall and aluminium central electrode.

Field size: 7 cm x 7 cm; depth: 1 cm in a water phantom.

The data have been normalized to the value for the C-552

chamber analysed according to the new formalism.

formalism for five different qualities in the orthovoltage

range. The results are presented in Table I. The data have

been normalized to the absorbed dose value obtained with the

air equivalent .(C-552) plastic chamber, analysed according to

the new formalism, at that particular radiation quality. For

this chamber (L/p) ^ 11 is unity. L/p and u /p values have air en

been estimated while P. was assumed to be unity. P , ision J repl

assumed to be unity in the present calculation, as in the

IAEA-SM-298/78 137

ICRU formalism. Details of the numerical values for the

physical quantities required for the analysis of the

measurements, can be found elsewhere [3]-

The results presented in Table I show that at lower

photon energies all chambers give a lower absorbed dose

value using the ICRU formalism compared with the new

formalism for the C-552 chamber. The difference is

increasing with decreasing photon energy and amounts to 9% at 100 kV.

6 . COMPARISON WITH OTHER RECENT ABSORBED DOSE MEASUREMENTS

Absorbed dose values to water determined by the ICRU

formalism are systematically lower than those derived

according to the new formalism. Our findings can be compared

with those of Kubo [4] and Mattsson [5] obtained with a water

calorimeter. The ratio of absorbed dose values determined

with a graphite ionization chamber and applying the ICRU

formalism, p S ^ P h i t e relative to those determined with a w CcL 1

water calorimeter, Dw , are presented in Table II. For

c'obalt-60 gamma rays the difference is attributed to the heat

defect of water. If the same correction would have been

applied for the orthovoltage beams, the difference between

the calorimeter results and ionization chamber data would

vary between about 2 and 5%. Although this difference is

smaller than the differences presented in Table I, the

calorimetric findings support qualitatively the C-552 plastic

ionization chamber results analysed according to the new

formalism, i.e. the ICRU formalism underestimates the dose.

A similar conclusion can be drawn from the data

presented by Schneider et al. [6]. They compared the ICRU

formalism with absorbed dose to water determinations using

ionization chambers calibrated against a graphite-walled


GRAPHITE IONIZATION CHAMBER AND APPLYING THE ICRU FORMALISM,

^graphite AND д WATER CALORIMETER, DCal, FOR DIFFERENT w w

RADIATION QUALITIES

TABLE I I . RATIO BETWEEN ABSORBED DOSE VALUES OBTAINED USING A

Reference Radiation quality

(HVL mm Cu)

Dgraphite/Dcal w w

Mattsson [5] 0.15 0.930

Kubo [4] 0.57 0.925

Kubo [4] 0.695 0.928

Mattsson [5] 1.2 0.947

Kubo [4] 1.76 0.937

Kubo [4] Co-60 0.962

Mattsson [5] Co-60 0.966

Note :

The Co-60 ionization chamber data were analysed using recent

protocols for the dosimetry of high-energy photons.

extrapolation chamber in a graphite phantom. The differences

between both methods of absorbed dose determination,

expressed as a perturbation factor, are of the same order of

magnitude as those presented in Table I, although applied to

a somewhat different type of ionization chamber. Their

perturbation factor includes effects of the wall material and

the size of the chamber both during the in-air calibration

and the in-phantom measurement.

On the other hand, Kristensen et al. [7] did not observe

a considerable deviation between absorbed dose values using a

IAEA-SM-298/78 139

Farmer type chamber and applying the ICRU formalism and those

obtained using LiF and alanine detectors.

7 . CONCLUSIONS

It has been observed by a number of authors that

different ionization chambers give differences in absorbed

dose values using the ICRU formalism. There are now also

three independent methods which indicate that the values of

the absorbed dose to water determined by the ICRU formalism

are systematically too low while, on the other hand,in one

investigation no significant deviation was observed for a

Farmer type chamber. These discrepancies might be caused by

photon and electron spectral changes in the phantom compared

to the in-air situation, which is not adequately taken into

account in the ICRU formalism. The concept of in-phantom

measurement of exposure as applied in the ICRU formalism

might, in addition, be responsible for part of these

differences. More work will be necessary to explain

quantitatively the differences observed in absorbed dose

values and to develop better formalisms to obtain absorbed

dose values in phantoms irradiated by orthovoltage X-ray

beams. These new procedures should be applicable for dose

determinations at a reference point in a reference field and

also yield absorbed dose values at other points in the

irradiated volume.

REFERENCES

[1] INTERNATIONAL COMMISSION ON RADIATION UNITS AND

MEASUREMENTS, Measurement of Absorbed Dose in a

Phantom Irradiated by a Single Beam of X or Gamma

Rays, ICRU Report 23, ICRU, Bethesda, Maryland (1973).


[2] AAPM Task Group 21, Med. Phys. 1£ (1983) 741.

[3] MIJNHEER, B.J., CHIN, L.M., Phys. Med. Biol. (1987),

(Submitted for publication).

[4] KUBO, H., Radiother. Oncol. 4 (1985) 275.

[5] MATTSS0N,0., Report CCEMRI (I) 185-15, Offilib, Paris

(1985).

[6] SCHNEIDER, U., GROSSWENDT, B . , KRAMER, H.M., IAEA-SM-

298/34, These proceedings.

[7] KRISTENSEN, M., HJORTENBERG, P., HANSEN, J.W., WILLE,

M., IAEA-SM-298/45, These Proceedings.

[8] WILL, W., RAKOW, A., Strahlentherapie J28 (1965) 532.

[9] HIZcf, J., ZSDANSZKY, K., NIKL, I., Isotopenpraxis 1_7

( 1 9 8 0 ) 1 0 6 .

[10] ZSDANSZKY, K., HIZO, J., NICKL, I., "Some remarks on the

calibration of clinical dose meters in terms of absorbed

dose in water", Biomedical Dosimetry: Physical Aspects,

Instrumentation, Calibration (Proc. Symp. Paris, 1980),

IAEA, Vienna (1981) 355.

[11] LIDEN, K.V.H., "Errors introduced by finite size of

ion chambers in depth-dose measurements", Selected

Topics in Radiation Dosimetry (Proc. Int. Conf. Vienna,

1961), IAEA, Vienna (1961) 161.

[12] HPA (Hospital Physicists' Association), Depth Dose

Tables for Use in Radiotherapy, Br. J. Radiol., Suppl.

10, British Institute of Radiology, London (1961).

IAEA-SM-298/34

PERTURBATION CORRECTION FACTOR FOR X-RAYS BETWEEN 70 AND 280 kV

U. SCHNEIDER, B. GROSSWENDT, H.M. KRAMER Physikalisch-Technische Bundesanstalt,Braunschweig,Federal Republic of Germany

Abstract

P ER TU R BA TIO N CO R R ECTIO N FA C TO R FO R X -R A Y S BETW EEN 70 AN D 280 kV.IC R U Report 23 describes a method of determining absorbed dose to water in a water phantom

with an ionization chamber calibrated in free air with respect to air kerma or exposure. For the energy region of conventional X-rays it is shown that this method neglects a chamber type dependent perturbation correction factor, pu. This correction factor takes into account the modification of the radiation field inside the phantom owing to the presence o f the chamber and differences in the ambient material under calibration conditions and in the phantom. Values for pu are presented for graphite and water as phantom material for radiation qualities used in conventional radiation therapy.

1 . INTRODUCTION

ICRU Report 23 describes a method of determining the absorbed dose, D , in a water phantom with an ionization chamber calibrated in free air with respect to the quantity exposure. Under

the reference conditions

Dw = M" V ^ ^ e n W ^ e n ^ a U )

is the reading of the calibrated ionization chamber,is the calibration factor with respect to the quant i ty exposure,is the average energy necessary to produce an ion pair in air divided by the elementary charge, e, is the mass energy absorption coefficient of water (w) and air (a), respectively (averaged over the photon energy fluence spectrum at the point of measurement inside the water phantom).

Using the air kerma as the calibration quantity one obtains

V *” ■ v < i ? f W f > . U a )

where is the calibration factor with respect to the air

kermaand (ц /о) is the mass energy transfer coefficient of air. t r i Э.

wwhere M

NX

(W/e)

and U - / ? )

141

142 SCHNEIDER et al.

HVL (Си)

FIG. I. Ratio o f the values for the absorbed dose in graphite (D — N-M, N calibration factor, M reading) determined with two different types o f ionization chambers A and В corresponding to the method described in ICRU Report 23 dependent on the radiation quality. The latter is characterized by the mean energy, E , o f the photon fluence spectrum at the point o f measurement x ~ 3 cm in the graphite phantom or, alternatively, by the Си half-value layer o f the primary radiation. (Chamber A: PTW M2333I, chamber B: PTW M23332).

Using Eqs. (1) or (la) in the energy region of conventional X-rays for different types of ionization chambers, values for the absorbed dose in water are obtained which differ by up to several per cent [l]. Similar results have been found in other phantom materials. Figure 1 shows the ratio of absorbed doses in graphite determined with two different ionization chambers as a function of the mean radiation energy for the radiation qualities used by the Physikalisch-Technische Bundesanstalt (PTB) for the calibration of therapy dosimeters.

One explanation for the differences is the neglecting of a chamber type dependent perturbation correction factor, p , which takes into account the modification of the radiation field inside the phantom owing to the presence of the chamber and the change of the reference conditions with respect to the ambient material (free air during the calibration, water during the measurement). Thus Eq. (la) has to be modified to

Dw = M" ( lb )

This conclusion is also supported by preliminary results of absorbed dose measurement with a water calorimeter £2 ], which disagree with ionization chamber measurements by several per cent.

IAEA-SM-298/34 143

If it were possible to determine the absorbed dose in the water phantom directly (for instance by caloric measurements) one could obtain also a calibration factor, N^, independent of the calibration in free air for each ionization chamber. In this case a second relation would be obtained

D = MW • (2)w D

and the correction factor, p , could be determined by means of Eqs. (lb) and (2) as U

P u - f M V W . (3)

2 . METHODS OF DETERMINING THE PERTURBATION CORRECTION

The perturbation factor, p , could not be evaluated in the water phantom so far since Nß is not available. However, as the absorbed dose to graphite in a graphite phantom can be obtained by means of an extrapolation chamber [з], a perturbation factor, p * , in a graphite phantom can be experimentally determined. This extrapolation chamber forms part of the standard for absorbed dose in water developed in the PTB to over

come the shortcomings of using ionization chambers calibrated in free air. The perturbation factors, p and py , will presumably be of similar magnitude, because they are mainly caused by differences in the density of air and the materials water and

graphite, respectively. So,

pu - T T - ^ V ^ c (3 a )К

with the index с for graphite instead of w for water and with Nq referring now to the absorbed dose in the graphite phantom.

Monte Carlo calculations were used to obtain the even more

important perturbation factor for water. Since it is much easier to calculate kerma values than absorbed dose values,

relation (lb) can be rewritten as

Kw = MW* N • (ц /p) -p (4)w K tr X w,a u

or, still more simplified, as

( 4 a )


are the water kerma and the air kerma inside the water phantom, respectively is the ratio of the mass energy transfer coefficients of water and air, again averaged over the photon energy fluence spectrum at the point of measurement inside the water phantom.

К = N . M (5)3. 14.

where К is the air kerma in free air,Эand M is the reading of the ionization chamber with the

calibration factor, N^, with respect to the air kerma in free air.

From Eqs. (4a) and (5) one obtains

K»/K = p • MW/M (6)a a u

The ratio Kw /K can be calculated by the Monte Carlo techni- a a w

que while the ratio M /М is easy to measure. So p can bedetermined by a combination of calculations and measurements.In analogy to relation (6) the following relation for a graphite phantom is obtained

K°/K = p / • MC/M (6a)a a u

3 . TESTING OF THE MONTE CARLO CALCULATION

The reliability of the Monte Carlo program was tested in a comparison with experimental data. At the point of measurement the experimentally determined absorbed dose, D , in the graphite phantom was compared with the graphite kerma, Kc , in the graphite phantom as obtained from the calculation. In thisQcomparison differences between the values of D and Kc were neglected since in the energy region of conventional X-rays the

bremsstrahlung is negligible. For the purposes of comparability both values were normalized to air kerma in free air.

Figure 2 shows the results of the test. The ratios of the graphite kerma in the graphite phantom to the air kerma in free air, both calculated and experimentally determined, are given as a function of the mean energy of the primary radiation. Experimentally is determined using the extrapolation chamber, whereas К is determined with a calibrated ionization chamber. Part (a) of Fig. 2 compares the data for a depth of

where Kw and Kw w a

In free air

IAEA-SM-298/34 145

н т cu)

HVL (Cu)

FIG. 2. Comparison o f the calculated ratio o f graphite kerma K ‘c in the graphite phantom and air kerma Ka in free air (crosses connected by a fu ll line) with the experimentally determined ratio (open circles connected by a dashed line) as a function o f the radiation quality characterized by the mean energy, Ep, o f the primary radiation (and, in addition, the half-value layer in Си) (a) fo r a depth o f 1.2 cm in the graphite phantom, (b) fo r a depth o f nearly 3 cm. The uncertainty o f the calculated values is presented by error bars, the uncertainty o f the experimental values is about the same (somewhat smaller fo r higher energies and somewhat higher fo r lower energies).

1.2 cm in the graphite phantom (corresponding to a mass per area value of 2 g-cm ) agd part (b) for a depth of about 3 cm (corresponding to 5 g«cm ). With the exception of the point at the lowest energy, the agreement between the calculated and experimentally determined values is very good in part (a). In part (b) the agreement is only satisfactory for energies above 60 keV, whereas for smaller energies the discrepancy increases with decreasing energy. In summary, Fig. 2 indicates that the Monte Carlo calculations are consistent with experimental data at least for small phantom depths. However, precautions may-be required in interpreting data for greater depths, especially for small energies.


m (cu)

agl__LJ__LJ__I__I I I I I20 40 _60 80 100 keV 120

m (Cu)------ ►

FIG. 3. Perturbation factor, p ', fo r the ionization chamber A placed (a) in a depth o f 1.2 cm, and (b j in a depth o f nearly 3 cm inside a graphite phantom, dependent on the radiation quality characterized by the mean energy,E, o f the photon fluence spectrum at the point o f measurement (and, alternatively, by the Cu half-value layer o f the primary radiation). The crosses represent experimental data derived from the calibration factors due to Eq. (3a) (the uncertainties are indicated by the fu ll lines), the open circles represent data derived from Eq. (6a) (the uncertainties are indicated by error bars).

4 . RESULTS FOR THE DETERMINATION OF PERTURBATION CORRECTIONS

Figure 3 presents results for the determination of the perturbation correction, p * , in a graphite phantom applying relations (3a) and (6a). Again part (a) shows data for a depth of1.2 cm and part (b) for a depth of about 3 cm as a function of energy. As already shown in Fig. 2, the extent of the agreement between the results of the two methods deteriorates for small energies at the greater depth in Fig. 3(b).

Figure 4 presents results for the determination of the perturbation correction factor, p , in a water phantom, now exclusively based on relation (6). Part (a) shows data for a

IAEA-SM-298/34 147

Н Ш Cu)

Г

НЩ Си)

FIG. 4. Perturbation factor, p u, fo r the ionization chamber A placed (a) in a depth o f 2 cm and (b) in a depth o f 5 cm inside a water phantom dependent on the radiation quality characterized by the mean energy, E, o f the photon fluence spectrum at the point o f measurement (and, alternatively, by the Си half-value layer o f the primary radiation).

depth of 2 cm in the water phantom and part (b) data for a depth of 5 cm. The values of p in part (a) agree with the values of p* in Figure 3(a) witHin the limits of uncertainty whereas the values of p in part (b) seem to be slightly smaller than the values of p ; in Figure 3(b) evaluated with relation (6). u

5 . DISCUSSION

The paper demonstrates the necessity to add a correction factor, p , to the formula given in ICRU Report 23 to evaluate the absorBed dose to water in a water phantom with an ionization chamber calibrated in free air. Furthermore, it appears


that this ionization chamber type dependent perturbation factor, p , has a value greater than one in general in the energy region of conventional X-rays. Beyond that, Fig. 3 leaves the question unanswered why the method based on Monte Carlo calculations yields p values which tend to be in increasing disagreement for increasing phantom depths and decreasing energy in comparison with p values yielded by the method based on cali

bration factors.

This behaviour seems to indicate that the photoeffect is not treated entirely correctly in the Monte Carlo calculations.

However, a check referring to the input photoeffect cross-section data has not produced any inconsistency. Moreover, it must be stated that both the Monte Carlo procedure and the experimental method are based on the assumption that the published

(ц n / >) or ( ) values are correct at least within the indicated uncertainty of about 2% for the photon energies of conventional X-rays. Any systematic deviations of these values from the true value, especially for low energies where the photoeffect is dominant, would produce incorrect p values. As seen from Eqs. (3) or (3a), p is also directly proportional to the (u /p) or (ц, /p) values in the method based on calibra-, . -, 6П I ЬГ )tion factors.

The two methods used in the present study could be brought into better agreement if the photoeffect cross-section in the low energy region were smaller them that actually used. Therefore, from the dosimetric point of view, a re-evaluation of these data for low photon energies would be very valuable.

REFERENCES

|l| HIZO, J., ZSDANSKY, K., NIKL, I., Erfahrungen bei der Kalibrierung von Ionisationskammern im Wasserphantom, Isotopen- praxis 17 (1980) 106_.

ZSDANSKY, K., HIZÓ, J., NICKL, I., Some Remarks on the Calibration of Clinical Dose Meters in Terms of Absorbed Dose in Water, Biomedical Dosimetry; Physical Aspects, Instrumentation,.Calibration (Proc. Int. Symp. Paris, 1980), IAEA, Vienna (1981) 355.

12 1 KUBO, H., Water Calorimetric Determination of Absorbed Dose

by 280 kV Orthovoltage X-Rays, Radiother. and Oncol. 4 (1985) 2 7 § .

13 1 SCHNEIDER, U . , "A new method for deriving the absorbed dose

in phantom material from measured ion dose for X-rays generated at voltages up to 300 kV", Biomedical Dosimetry: Physical Aspects, Instrumentation, Calibration (Proc. Int. Symp. Paris, 1980), IAEA, Vienna (1981) 223.

IAEA-SM-298/45

DETERMINATION OF IONIZATION CHAMBER KERMA CORRECTION FACTORS FOR MEASUREMENTS IN MEDIA EXPOSED TO ORTHO VOLTAGE X-RAYS

M. KRISTENSEN, P. HJORTENBERG Department of Radiation Physics,The Finsen Institute,The University Hospital,Copenhagen

J.W . HANSEN, M. WILLE Ris0 National Laboratory,Roskilde

Denmark

Abstract

D E T E R M IN A T IO N O F IO N IZ A T IO N C H A M B E R K E R M A C O R R E C T IO N F A C T O R S F O R

M E A S U R E M E N T S IN M E D IA E X P O S E D T O O R T H O V O L T A G E X -R A Y S .

K e rm a c o r r e c t io n f a c to r s , a « , w e re d e te rm in e d f o r a c y lin d r ic a l F a r m e r c h a m b e r a n d

f o r tw o s p h e r ic a l c h a m b e r s , h a v in g a ir -e q u iv a le n t w a lls a n d d ia m e te r s o f 19 a n d 10 m m , re s p e c tiv e ly . T h e c h a m b e rs w e re i r r a d ia te d a t a d e p th o f 2 c m in w a te r w ith tw o X -ra y b e am s,

h av in g a H V T o f 2 .3 m m A1 a n d 4 .6 m m A l, re s p e c tiv e ly , а к is d e f in e d a c c o rd in g to

aii-Кц = M u -N k -Q !K. <*k is c a lc u la te d f o r th e s p h e r ic a l c h a m b e r s a s su m in g t h a t th e c h a m b e r

signal is p r o p o r t io n a l to th e m e a n v a lu e o f k e r m a a v erag ed o v e r a s p h e r ic a l s u rfa c e c o n c e n tr ic w ith th e w a ll. T h re e e x p e r im e n ta l d e te r m in a t io n s o f « к w e re m a d e u s in g th r e e d i f f e r e n t ty p e s o f d e te c to r s : (a ) a n io n iz a t io n c h a m b e r , (b ) L iF , a n d (c ) a la n in e . T h e d e te c to r s h a d v o lu m e s

less th a n 15 m m 3. E x p e r im e n ta l v a lu e s o f f r o m 0 .9 to 1 .0 w e re o b ta in e d . C a lc u la te d a n d

e x p e r im e n ta l va lu e s s h o w a g re e m e n t w i th in 4% . In a g re e m e n t w i th th e r e c o m m e n d a t io n o f

IC R U o v e r th e p a s t 25 y e a rs v a lu e s c lo se to u n i ty w e re o b ta in e d f o r t h e F a r m e r c h a m b e r .

R e c e n tly i t h a s b e e n r e c o m m e n d e d t h a t a b s o r b e d d o s e to w a te r b e d e r iv e d f r o m a b s o r b e d d o s e to g ra p h i te . U sin g th is m e th o d , c h a m b e r s s im ila r to th o s e in v e s t ig a te d h e re h a v e b e e n c a l ib ra te d

a t s im ila r X -ra y q u a li t ie s . V a lu e s o f a K th u s o b ta in e d w e re a p p r o x im a te ly 15% h ig h e r th a n

th o s e o b ta in e d b y th e a u th o r s . I t is su g g es te d th a t th is d is c r e p a n c y c o u ld b e c a u s e d b y e r ro rs

in th e th e o r e t ic a l v a lu e s o f (Д е л /Р )carbon-

149

150 KRISTENSEN et al.

According to the recommendation of I.C.R.U., ref. [1], kerma

to air, . К in homoqeneous media similar to tissue, irradiated ’ air u y

with medium energy X-rays, can be obtained from the reading, Mu

of small ionisation chambers (like the Farmer thimble chamber),

embedded in the media using

. К = M • N.. • ct,, (1)air u u К К

where is the air-kerma calibration factor for the chamber ex

posed in free air. A value of unity for is recommended provi

ded the point of reference is chosen at the centre of the chamb

er. Absorbed dose to a small mass of material, Z at the reference-

point can be obtained from eq. (1 ) using

D-, =: (u /p)^. * • К givingZ иеп K air air u 4 4

DZ “ V NK ' • “ K ( 2 >

1. INTRODUCTION

where a, = 1 .

Theoretical values of (u /p)^- were confirmed in ref. [2]Hen K air L J

for muscle tissue and "average tissue". Recently, however, the

validity of eq. (2), using = 1, was questioned by U. Schnei

der, ref. [3]. Instead,it is recommended that absorbed dose to

material, h^O be derived from absorbed dose to carbon using

IAEA-SM-298/45 151

FIG. 1. ocK for chamber, С in Ref. [ 4 ]• : 2 cm depth.O ; 5 cm depth.

According to ref. [4] this method gives values of for small

chambers which deviate significantly from unity as can be seen

in fig. 1 .

In order to examine and possibly to confirm these values of

a^, the present investigation is confined to determination of

in 100 kV X-ray beams filtered by 1.7 mm A1 and 1.7 mm A1 +

0.1 mm Cu,respectively, giving effective photon energies ,Ее }

of 31 keV and 41 keV, respectively.

2. THEORY FOR THE RESPONSE OF SPHERICAL CHAMBERS

The chambers are filled with air and have air-equivalent

walls. They are irradiated with 100 kV X-rays. In order to


, 0.2

0.1 ■

FIG. 2. vs (r) fo r chamber A at 35 ke V. A: 5% from central electrode. B: 67% from spherical wall

clarify the calculation of a^, defined by eq. (l);this factor

is divided into two

aK " KNK( 4 )

where is the kerma calibration factor for the chamber

placed in a medium, assuming that the kerma is constant in a

cavity replacing the chamber. corrects the kerma calibra

tion factor for a non-linear variation of the kerma in the ca

vity mentioned above and does also relate the kerma at the re

ference point (the centre) to the kerma in the same point in

the homogeneous medium. The calculations, referred to below,

indicate that the fluence-change in a point in a spherical ca

vity caused by the cavity being filled up with medium material

is a function of the distance, r, from the centre to the point.

Consequently,the distribution of the sensitive material must

Table 1. Relative calibration factors and effective

radii of sensitivity , Re f f .

IAEA-SM-298/45 153

D e t e c t o r I d . A t С D 1 D 3

N K N K -R

e f f .

c m

■ N K R e f f .

e r a

N KN K

m i / d h 2 o

R a d i a t i o n

E e f f . , k e V

1 0 0 0 , ( 6 0 C o ) 1 0 . 9 7 1 1 1 1

1 4 0 0 . 9 5 0 . 9 9

8 0 0 . 9 6 0 . 9 4

6 0 1 . 0 0

4 1 , [ Q 2 ] 0 . 9 5 0 . 9 5 0 . 8 8 0 . 9 2 0 . 3 4 1 . 0 1 0 . 9 0 1 . 0 2

3 1 , [ Q } ] 0 . 9 7 0 . 9 5 0 . 8 8 0 . 9 5 0 . 3 4 1 . 0 2 1 . 0 1 0 . 9 8

2 4 0 . 9 6 0 . 9 3 0 . 8 2

1 5 1 . 0 5 0 . 9 3 0 . 7 7

9 1 . 3 4 0 . 8 3 0 . 7 7

be taken into account in order to predict the response. Fig. 2

shows, as an example, such a distribution, v (r) weighted

by the fractional contribution to the air ionisation. The ra

dius, R ¿..of an "effective surface of measurement" is obtain- ’ eff ’

ed from

RX(RefF /R)= / v (r) • X(r/R) dr (5)err 0 s

where R is the cavity radius and^((r/R)is proportional to the

TABLE 2. Details of ionisation chambers


C h a m b e r

I d .

G e o m e t r y D i m e n s i o n s

o u t e r m e a s ,

m m

W a l l

t h i c k n e s s

m g - c m - 2

T y p e

A S p h . D i a m . 1 9 3 5 S h o n k a , N o . 1 6 1

В S p h . D i a m . 1 0 1 3 0O w n c o n s t r u c t i o n , u s i n g a k o n d i o -

m e t e r c h a m b e r ( P T W ) . C e n t r . e l e c

t r o d e , 1 3 m m d i a m . , s u r r o u n d e d b y

A l - f o i l , 0 . 0 1 m m t h i c k .

С C y l i n d . L e n g t h 2 7

D i a m . 7

6 0 0 . 6 c m 3 F a r m e r t y p e 2 5 0 5 - 3

D 1 C y l i n d . L e n g t h 3 . 3

D i a m . 2 . 0

2 0 O w n c o n s t r u c t i o n .

T h e r e f e r e n c e p o i n t i s i n t h e c e n t r e o f t h e c h a m b e r .

fluence-change distribution. So far it has been assumed that

secondary electrons are emitted isotropically. This is known

to be incorrect. Ionisation measurements on the emission

from a thin Al-foil; placed on the inside wall of chamber В (see

table 2) and irradiated at different angles, indicate a small

change in the sensitivity distribution. This corresponds to a

displacement of an "effective point of measurement" of less

than approx. 0.07 • R. (where 2 R is the diameter of the inner

wall) causing a negligible change of the response. The response

of a spherical chamber is then calculated assuming that the sig

nal is proportional to the mean kerma on the spherical surface

of radius Rgff Estimated values of Re^^ for the two spherical

chambers used here are given in table 1 .

3. APPROXIMATE CALCULATIONS OF THE RELATIONS BETWEEN THE KERMA

IAEA-SM-298/45 155

IN A SMALL SPHERICAL BODY AND KERMA IN THE CAVITY CREATED

WHEN THE SPHERICAL BODY IS REMOVED

3.1. FLUENCE CALCULATIONS

It is generally experienced that the transmission of photons

in broad beam geometries is only slightly affected by the scat

tering. (An attenuation factor of e ^tr * d } where el is the di

stanceras been recommended). For 30-40 keV photons equals

approx. T, the photo-attenuation coefficient.

3.1.1 CONDITIONS AND ASSUMPTIONS

A) The radius of the sphere, R,is less than 1 cm.

B) The spherical body of radius R is inside a homogeneous me

dium of the same material as the body.

C) The fluence in the cavity, tQfis monochromatic with energy,

D) фо is constant within the cavity and is having a constant

angular distribution.

<5E) Coherent scattering in the body is neglected.

3.1.2 RESULTS OF CALCULATION OF $ (R ) AND^ (R )____T p______Ts p

(Rp) denotes the average value of the fluence in the sphere

when filled by medium material, averaged over the surface of a

sphere with radius, R ,concentric with the cavity-sphere.


X

l IX y Ч-l

FIG. 3. x (X ) = 0.5 (1/Х) / y i n ------------dy.о Ь - Л

ф (R ) is the contribution to 6 (R ) created inside the ys p v p

spherical body by scattering of ro

R • X(R /R) = RX _________ e_____I__

For Rp<R, RXepuals the mean distance from a point, P, to

the surface of a sphere with radius R, averaged over all di

rections. P has a distance, R .from the centre.P

For Rp >R, RX is the chord-length-mean value ofchords going

through P also averaged over 4'^solid angles. X(Rp/R) can

be found analytically. A graph of X(Rp/R) is shown in fig. 3.

is the Compton attenuation coefficient, - 0.16 cm

The following approximate results are obtained

1 %, for 0 < x < 0 . 1. ~/?*X(Rp/ R)‘ Tф(кр) = Ф0 *e ± ( 6 )

3 %, for 0 < t < 0.4

?s(Rp> - Ф0 • м0 • R ‘ X(Rp/R) - е ~ 1 л R 'r (7)

IAEA-SM-298/45 1 57

In order to arrive at eq. (6) <|>(Rp) was calculated in the

centre considering up to two times scattering and at the peri-

Г\ . Vphery, one time scattering. Ф5 'р' was calculated consider

ing one time scattering.

It is further estimated that a first order expansion of

<b(R ) , ф ( R ) = ф ( L - T • R • X (R /R)j is accurate within ±0.5 P Y P °\ P /

for tR « 1 and for RyQ <0.16.

3.2 KERMA CALCULATION

Using К = (ф-ф5 )(иеп/рЦ • E2 + Ф8(уеп/р)е а -2 • Ё2

we obtain the following approx.

е- т • R • X Í R / R ) + • R • X(Rp/R) • ']

( 8 )

- 1 4R t ^ "*where e L is omitted in фз and ДЕ = Е2 - Е is the average

energy change of a Compton-scattered photon and Д(р /p) is

the corresponding change of (yen/p)* The conditions are those

valid in sect. 3.1.1.

3.2.1 REVIEW OF CONDITION D IN SECT. 3.1.1.

(Non-linear variation of К )о

The results of the previous investigation show that the kerma

is non-linear and not constant in the homogeneous medium assum

ing a constant kerma in the cavity.

This situation does not occur with the irradiation conditi

ons used here. It may be assumed instead that the final kerma

is constant, resulting in an non-linear variation of K- A

calculation shows however, that eq. (8) is valid within 0.5 %

if К is substitued by K (R R) and if R • т <0.2.o o p,


3.2.2 LINEAR VARIATION OF К _о

It is obvious that eq. (8) is valid if Kq has a linear vari

ation provided Kq is substituted by*K^(R R) giving as before

1<(Rp,R) = 1<o(Rp-v R) | V T ' R ' ^ (Rp/R)

/af A(''Jen//p _

+

(9)

3.2.3 EXAMINATION OF CONDITION С IN SECT. 3.1.1.

(Application to X-ray spectra)

Let (KQ)|r be the spectral distribution of Kq and we obtain

f „ | с к Д - e_T • R * < £ * v R -X ■ ( f dE

Due to the small variation in

ГДЕ A(^en/P)p^RX- + —-— —J max. 0.01(for 20 keV <E <60 keV

and for R <1 clothe second integral can be approximated by

IAEA-SM-298/45 159

evaluated at the effective energy, E-efpdetermined from the

l'st HVT. The important term is

tively^and Д (0) = 0, Д (0.1) = 0.008, Д (0.2) = 0.023.

т was estimated experimentally as follows. Chamber D was plac

ed in the centre of a spherical shell of A1 having a wall thick-

- 2ness of 0.15 g-cm and an outer diameter of 1 cm. Irradiati

ons were performed "in-air" and "in-phantom" at 2 cm depth

with and without the Al-absorber.

As the ratio, a of т for any two low-z materials is expected

to be independent of energy in the energy range considered here

we obtain g - а-тд

The following results were obtained

dE

The spectrum is approximated by

ï К • 8 • (E - E) • E 3 , 0.2 E <E <E N о O 0 00 , E <0.2 E , and E > E o ’ o

giving

where т and Kq are the spectrum mean values of т and Kq,respec

to^, (100 kV, 1.7 mm Al)

"in-air" = (0.19 +0.03) cmо- 1

Hin-phantom" : = (0 .12 5 ±0.0 1) cm 1


[ Q2 ] , (100 kV, 0 . 1 mm Cu + 0 . 1 7 mm Al)

"in-air" = (0.09 ±0.03) cm- 1О

fl in-phantom" : = (0.07 ±0.01) cnf1о

The uncertainties are 2 STD estimated from the experiments.

The uncertainties of the theoretical values of т for Al and

H2O are not included. As can be seen,a "beam hardening" takes

place "in-phantom" as expected. This is especially pronounced

at [Q^] giving rise to an additional uncertainty of т for the

chamber A with a diameter of 19 mm.

Finally we obtain for water-media

P =(airK)"in-phantom" = A + В ( 1 0 )

u (airKQ) in the air cavity "in-phantom"

where

4. CALCULATION OF P AND KMI/ FOR SPHERICAL IONISATION CHAMBERSu NK

IAEA-SM-298/4S 161

4.1 P u

According to the analysis given in sect. 2 P^ can be obtained

from eq. 10 using R^ = Rg^ and assuming that (air 1?) in phantom

= (air R) in the centre of the filled cavity.

4,2 KNK AND Pu’ wall

Assuming the chamber to have air-equivalent walls then

NK = <w /e )a l r • (V ■ p ) “ 1 • (PUj ^ Г 1

where V • p is the mass of dry air in the chamber and Pu ac

counts for the attenuation in the wall. It is assumed in eq.

10 that the spherical body is surrounded by medium. However,

the calculations have shown that this restriction is unneces

sary at the level of 1 % accuracy assuming R < 1 cm. Applying

eq. 10, (using wall material parameters) for R = Rq and R = R^

where 2 Rq is the outer diameter and 2 R¿ is the inner dia

meter of the wall, gives

P n n - P (R R f-f) ' [P (R-.R i-J] '*"• A more accurateu, wall u oj eff L u H eff J

approximation is probably obtained using

T a b l e 3. E x p e r i m e n t a l a nd c a l c u l a t e d v a l u e s ofC*^. a n d k'К NK

X-ray [Qj] [Q2]

Chamber A

Value l^s %

В

Value s %

С

Value s %

A

Value s %

В

Value s %

С

Value s %

KNKExperiment

0.983 0.8 0.997 0.8 0.985 0.8 0.981 0.8

KNKCalc.

0.993 0.5 0.990 1 0.998 0.5 0.996 2

“KExperiment Detec. D 1

0.914 2.4 0.960 2.2 0.992 2.4 0.937 2.0 0.963 1.7 0.973 2.0


0.895 3.5 0.941 3.4 0.972 3.5 0.966 2.4 0.993 2.2 1.003 2.4


0.908 3.1 0.954 3.0 0.985 3.1 0.963 3.6 0.990 3.5 1.000 3.6

aKCalc.

0.942 1.6 0.953 1.8 0.974 1.6 0.979 2.5

s = (2 • STD of value) • 100 value

D = (у„/т) * (ß„- )• I— + -( /¿J^on ^ о i

IAEA-SM-298/45 163

ДЕ , A [4 n / p ) a i r ]>

o - 6 . = Ï ft. X(ReffyRo) - R.- X(Reff/Ri>

Values of N,, = N,, • P n1 for chamber A are qiven in table 1.К К u, wall y

\It is seen that almost constant values of N^ are obtained for 15 keV

<E<40 keV, confirming the air-equivalence of the chamber wall.

Now K.M/ can be obtained for chamber A using NK y

(P ),/ u,wall "in-air"

^ ^u,wall) "in-phantom"

The values are given in table 3.

Also K ^ for chamber В is calculated. However, some reser

vation concerning the accuracy of these values must be made due

to the Al-compensation used in this chamber.

4 . 3 a ,

aK is given by aK = Ру • KNj<

Values of a,/ are given in table 3. К

5. EXPERIMENTS

5.1. DETAILS OF DETECTORS

5.1.1 IONISATION CHAMBERS

Constructional details are given in table 2 and air-kerma

calibration factors are given in table 1 .

5.1.2 D 2, (LiF-DOSIMETER)

Solid cylindrical rods of LiF, (Harshaw TLD 100) of 7 mm

length and diameter, 1 mm were cut into rods 1 - 1.5 mm long

in order to achieve angular independent response.

5.1.3 D 3, (ALANINE-DOSIMETER)

Each dosimeter consists of approx. 5 mg alanine with 2.5 %

sulphur added in order to make it water-equivalent. The pow

der is contained in a polyethylene cylinder having an outer

diam. of 2 mm and a length of approx. 5 mm and is sealed with

paraffin wax. The radiation-induced number of free radicals

were measured, (see ref. [5]), by electron spin resonance

(ESR), measurements conducted by the Riso National Labora

tory. Response factors for the dosimeters irradiated in air

are given in table 1 as g where M- is the dosimeter

indication per unit of mass and g is the corresponding

mean dose to the dosimeter calculated as if it was made of

water. Du n was determined from air-kerma measurements. n^U

5.2 IRRADIATION CONDITIONS

X-ray generator: Müller RT 100

Nominal voltage: 100 kV

Quality, Q 1 : Filter, 1.7 Al; HVT, 2.3 mm A1

Quality, Q 2 : Filter, 0.1 mm Cu + 1.7 mm Al; HVT,


4.6 mm A1

IAEA-SM-298/45 165

A В

FIG.4. Irradiation geometry.A: Irradiation o f dosimeter, D$.B: Irradiation o f all other detectors.

Field size at chamber location: 12 cm diameter

Focus distance: See fig, 4

Monitor of exposure: See fig. 4

5.2.1 "In-air" irradiation

The detectors were placed on a 45 cm high block of polysty-_3

rene (mass density approx. 0.025 g«cm ).

5.2.2 "In-air-in-phantom" irradiation

The detectors were placed in the centre of a cubical cavity,

6 x 6 x 6 cm3, placed with its centre at a depth of 5 cm in a

PMMA phantom. The aim was to establish a homogeneous kerma

distribution which simulates the angular- and energy distribut

ion of the kerma in the homogeneous phantom at 2 cm depth.

5.2.3 "In-phantom" irradiation

A. Phantom material, Mix-D.

Signals from chamber В were compared to signals from detector

D 1, D 2 and D 3.

Chamber В was placed in a spherical cavity of diameter 1 cm

at a depth of 2.2 cm.

D I was placed in the same cavity filled up with shells of

Mix-D having outer diameter of 10 mm and different inner dia

meters, the smallest being 3 mm.

D 2 and D 3 were placed in 4 cylindrical cavities of 5 mm

length and of diameter 2 mm at a distance of 10 mm from the

centre of chamber B.

B. Phantom material, water

Chamber A, В and С were placed in the same position at a

depth of 2 cm.

5.3 EXPERIMENTAL PROCEDURES

5.3.!

K|^ was determined for chamber В, С and D 1 by reference to

for chamber A using

166 KRÏSTENSEN et al.

(V ) - "in-air" • ^NK^chamber ANK detector, X “ (Му/Мл)„. . . .

X A "in-air-in-phantom"

where and Мд are the signals from chamber X and chamber A,

respectively.

IAEA-SM-298/4S 167

5.3.2 DETERMINATION OF aK

5.3.2.1 for chamber В

"Method 1", Detector D 1 was used

Pu was determined for chamber В by comparisons to chamber

D 1, "in-phantom" and "in-air-in-phantom". The signals from

D 1 for different cavity diameters were extrapolated to a value,

(Mni) at zero diameter. As P at zero diameter equals 1 we DI о u ^

obtain

С ) r / ^ R] "i i(P..)

DI о BJ"in-phantom"u chamber В (Mr.,/Mn).,- . , , ,DI В "m-air-in-phantom1

using from 5.3.1 we get = Ру •

The results are given in table 3.

"Method 2", Detector D 2 (LiF) was used

1) 8 detectors, D 2 were intercalibrated, "in-air" giving sig

nals, --- Rg.

2) The 8 detectors were divided into two groups, i and j.

Group i was irr. with chamber B, "in-phantom" and group j


was irr. with chamber В, "in-air" giving corresponding

signals:

M. for D 2, and (MD)„. , , „ for Вi ’ В "m-phantom"

M. for D 2, and (MD)„. . „ for Вj ’ В "in-air"

Assuming that the signals from the D 2 detectors are proport

ional to air-kerma we obtain

âir^ "in-phantom" _ iî^"in-phantom" .( • K)„. . „ " (M./R.)„. . „ aK, LiFair "in-air j j "in-air"

The small deviation from unity of a,, . -r was estimated, giv-К j L 1 Г

ing

0.991 ±0.01, [Qj]î/ i ■; r - {

’ L1 0.993 ±0.01, [Q2]

From the signals from chamber В we obtain

âir^"in-phantom" _ "in-phantom"

âir^ "in-air" "in-air" ^

Values of determined by these equations are given in table 3

"Method 2", Detector D 3 (alanine) was used

The procedure was similar to that used with the LiF-detectors

A group of 8 dosimeters was divided into two groups which were

irradiated "in-phantom" and "in-air", respectively, giving sig

nals, M^ "in-phantom" and Mj "inâir". After X-ray-irradiation

and read-out the 8 dosimeters were intercalibrated, using ^Co-

radiation, giving signals, R ^ --- Rg. The parts of the sig

nals due to the reference irradiation are obtained as (R^-M^),

---- (Rg-Mg). Doses of approx. 200 Gy and 2000 Gy were deliv

ered by the X-rays and by the ^Co-radiation;respectively.

Assuming linearity we obtain

âir^"in-phantom" „ n n<airK> - = A ■ В - С

where

M./R- - M.л - 1 1_____ i.

M./R ■ - M .J J J

g _ ^ên'^bÔ^'in-phantom"

^ e n ^ H ^ "in-air"

CP )r _ u "in-phantom", alanine

(P )u "in-air", alanine

According to ref. [4], В - 1 and due to the close water-equi-

valence of alanine (also concerning mass density)

(P )u "in-phantom" = 1. The small deviation from unity of (P . . ’ u "m-air1

was estimated to be {+q 'q q i’ [Q^]

Using the signals from chamber В we obtain

âir^"in-phantom" _ # ^B^"in-phantom"

(airK)"in-air" ^ "in-air"

a,, derived from these equations is given in table 3.К

IAEA-SM-298/4S 169

5.3.2.2 for chamber A and chamber C


was determined by comparison "in-air" and "in-phantom"

to chamber В using

(M /MB) „ ., ч _ x В "in-air_____ / \К chamber X " (M /Mn)„. . . „ K Bx В "in-phantom"

where (ct )ß is anyone of the previous results for chamber B.

The values of are given in table 3.

6. DISCUSSION

The experimental values of were measured with reference

to calculated values for chamber A. This procedure is justi

fied by the thin wall of A and the fair constancy of the kerma-

calibration factor, corrected for wall-attenuation, observed

for E __ < 40 keV. eff

As can be seen, all the coresponding experimental values of

for chamber В are in mutual agreement and in agreement with

the calculated values. This confirms that the kerma-to-air-

determinations were consistently transferred from a point in

free air to a point at 2 cm depth in water, within an uncer

tainty of approx. 2 %.

A significant deviation between measured and calculated valu

es of is perhaps seen for chamber A at [Q^]. The deviation

may be caused by a softening of the photon spectrum at shallower

depths, resulting in an increased value of x- The value of

T used in the calculation was determined experimentally in a

cavity of diam. 10 mm and might need a correction in order to be

applied to the cavity of 19 mm diam. associated with chamber A.

for chamber С is close to unity in agreement with the re

commendations of I.C.R.U., [1].

For the spherical chambers, the calculations made here indi

cate that will be close to unity at X-rays generated by some

what higher potentials than used here. This is in agreement

with the experimental results reported in ref. [6].

We conclude that the results of reported in ref. [4] dif

fer at all medium X-ray qualities, from the results referred to

above including those of the present investigation. As des

cribed in sect. 1 the values of reported in ref. [4] are de

rived from determinations of absorbed dose to graphite. Ab

sorbed dose to graphite was determined from air-ionisation in

a graphite-wall-extrapolation chamber. From the results of 01,

thus derived, combined with the results of for similar

chambers found in this investigation, it is deduced that ab

sorbed dose to graphite determined from air-ionisation in

this particular graphite chamber deviates by 15 % ±8 % from

absorbed dose to carbon derived from air-kerma at

E __ = 30 -40 keV. eff

IAEA-SM-298/45 171


FIG. 5. Comparison o f different procedures used to determine absorbed dose to carbon. 0: A tt ix e ta l. [ 8 ] o ; Greening, Randle [ 7 ]Д ; Combined experiments, Schneider [ 3 ] and present work * v Point o f normalization.

Similar deviations were obtained by other investigators [7],

[8]. The deviations may be expressed as a factor (D)j equal to

D.the ratio 7 -, where D.. is the dose to graphite derived from air-

K K

kerma and D. is dose to graphite derived by independent means.J

In ref. [7] J.R. Greening and K.J. Randle related the charge

emitted from graphite in a vacuum chamber (assumed proportio

nal to absorbed dose to graphite) to absorbed dose derived

from air-kerma. In ref. [8] F.H. Attix et coll. investigated

air ionisation in an extrapolation chamber having graphite

walls. From both experiments we have derived values of (D)j .

These are given in fig. 5 normalised to a value of unity at

E ^ = 120 keV. This procedure is justified by the result of

an experiment reported by G.P. Barnard'et coll. in ref. [9].

They found that = 1 ±0.01 at this X-ray quality. Also

in fig. 5 are given values of (D)j based on values of

from ref. [4] and from the present work. Should the graphite

walls be of pure carbon the results would indicate that the

theoretical value of (уег/Р-)аг is in error by approximately

16 % at a photon energy of about 35 keV.

IAEA-SM-298/45 173

REFERENCES

[1] Clinical Dosimetry, I.C.R.U. Report 10 d, 1962.

[2] GROSS, W., et coll., Experimental determination of the

absorbed dose from X-Rays in tissue, Rad. Res. 18,

1963.

[3] SCHNEIDER, U., "A new method for deriving the absorbed

dose in phantom material from measured ion dose for X-

rays generated at voltages up to 300 kV^" IAEA-SM-249/59.

[4] Draft of an I.A.E.A.-protocol, dated 21. November 1985.

Not yet published.

[5] HANSEN, J.W., et coll., "Detection of low- and high- let

radiation with alanine". Accepted for publication in

Radiation Protection Dosimetry.

[6] ZOETELIEF, J., et coll., "Displacement corrections for

spherical ion chambers in phantoms irradiated with neu

tron and photon beams," IAEA-SM-249/38.

KRISTENSEN et al.

GREENING, J.R., RANDLE, K.J., A vacuum chamber investi

gation of low energy electrons liberated by X-rays,

Br. J. Radiol., Vol. 41, 1968.

ATTIX, F.H., et coll., Cavity ionisation as function

of wall material. Journal of Research of the National

Bureau of Standards, Vol. 60, Nr. 3, March, 1958.

BARNARD, G.P., et coll., On the congruity of N.P.L.

exposure standards, Phys. Med. Biol., Vol. 9, 1964.

IAEA-SM-298/69

PERTURBATION CORRECTION FACTORS IN IONIZATION CHAMBER DOSIMETRY

B. NILSSON*, A. MONTELIUS*,P. ANDREO**, B. SORCINI** Department of Radiation Physics,

The Karolinska Institute and University o f Stockholm,

Stockholm,Sweden

** Sección de Física,Departamento de Radiológica,Hospital Clínico Universitario,Zaragoza,Spain

Abstract

P ER TU R BA TIO N C O R R ECTIO N FA C TO R S IN IO N IZA TIO N CH A M BER D O SIM ETR Y.The perturbation of the electron fluence in parallel-plate ionization chambers has been studied

using an extrapolation chamber in which it is possible to change the material of the front wall, side wall and back wall separately. With this chamber it is possible to investigate the effect of both the wall material and the chamber geometry. A graphite chamber has a very small fluence perturbation. Using this chamber as a reference, measurements were made with either the chamber front wall, side wall or back wall replaced, by aluminium or A-150 (tissue-equivalent plastic). Measurements were made in beams of “ Co 7 -rays, 6 and 21 M V X-rays and 9 and 22 MeV electrons. Furthermore, some preliminary comparable calculations with the EGS4 Monte Carlo code have been performed. The experimental results for photons show that with a homogeneous chamber of graphite a specific ionization nearly independent of plate separation is obtained. This is what is expected from Fano’s theorem. When changing the different walls from graphite to, for example, aluminium, large differences in the specific ionization are obtained. An aluminium front wall causes a decrease as large as 10 per cent in the specific ionization and an aluminium side wall or back wall gives an increase of up to 2 0 per cent in the specific ionization. In electron beams also large perturbation effects are obtained that vary with chamber geometry and wall material. This supports earlier results obtained by others with commercial parallel- plate chambers that indicate large perturbation effects, especially for low electron energies. The present results show that in order to reduce the perturbation it is important to have all chamber walls made of the same material and to use a large guard in contrast to most commercial parallel-plate and extrapolation chambers used today.

1. INTRODUCTION

Most d o s im e t r y p r o t o c o l s propose i o n i z a t i o n chambers as the d o s i m e t r i c d e t e c t o r f o r de te rm in in g the absorbed dose to wate r i n r a d i a t i o n th e rap y beams [ 1 - 6 ] . For photons and h igh

175

176 NILSSON et al.

energy e l e c t r o n s a t h im b le chamber i s o f t e n recommended bu t f o r l ow energy e l e c t r o n s a ,pa ra l l e i - p l a t e chamber shou ld be used. To o b t a i n the absorbed dose to wa te r f rom the s p e c i f i c i o n i z a t i o n i n the chamber d i f f e r e n t c o r r e c t i o n f a c t o r s have t o be a p p l i e d . An im p o r ta n t c o r r e c t i o n f a c t o r i s due to the p e r t u r b a t i o n o f the e l e c t r o n f l u e n c e i n the phantom owing t o th e presence o f the i o n i z a t i o n chamber. Th is p e r t u r b a t i o n i s dependent on the m a t e r i a l and the t h i c k n e s s o f the chamber w a l l , the s i z e and shape o f the chamber c a v i t y and the energy and type o f r a d i a t i o n ( e l e c t r o n s o r p h o to n s ) . Recommendations o f the p e r t u r b a t i o n c o r r e c t i o n f a c t o r s are g iven i n the d i f f e r e n t d os im e t r y p r o t o c o l s . However, t h e re are s t i l l u n c e r t a i n t i e s and d i f f e r e n c e s in the response between p a r a l l e l - p l a t e chambers and t h im b le chambers have been observed [ 7 - 1 0 ] . An energy dependence i n the response o f p a r a l l e l - p l a t e chambers i n e l e c t r o n beams has been r e p o r te d [ 7 , 1 1 , 1 2 ] . Th is i n d i c a t e s t h a t p e r t u r b a t i o n e f f e c t s are p resen t i n c o n t r a d i c t i o n to the s ta tements i n the AAPM d os im e t r y p r o t o c o l [3 ]. To de te rm ine these p e r t u r b a t i o n c o r r e c t i o n s accur a t e l y and t o be ab le to e x p l a i n the r e s u l t s ob ta ined w i t h the d i f f e r e n t commercial p a r a l l e l - p l a t e chambers, measurements w i t h an e x t r a p o l a t i o n chamber were made. In t h i s chamber the m a t e r i a l i n the f r o n t , s i d e and back w a l l can be exchanged s e p a r a t e l y [13]. In t h i s way, th e v a r i a t i o n w i t h both the chamber geometry and th e w a l l m a t e r i a l can be i n v e s t i g a t e d . A ls o the c o n t r i b u t i o n s to the p e r t u r b a t i o n e f f e c t f rom the d i f f e r e n t w a l l s e c t i o n s may be se pa ra te d . Th is expe r imen ta l method i s s i m i l a r t o the one used by A t t i x e t a l . [ 1 4 ] . However, they changed a l l waI I s i n the chamber and d i d not measure a t h ig h e r ene rg ie s than Co Y - ra y s .

To e x p e r i m e n t a l l y i n v e s t i g a t e a l l i n t e r e s t i n g comb ina t ions o f w a l l m a t e r i a l , chamber geometry and typ e o f r a d i a t i o n i s a f o rm id a b le t a s k . Wi th Monte Ca r lo c a l c u l a t i o n s i t i s p o s s i b l e to s im u la t e d i f f e r e n t co mb in a t i ons . Th is te chn iq ue can be ve ry usef u l f o r de te rm in in g p e r t u r b a t i o n c o r r e c t i o n s f o r a s p e c i f i c chamber o r when d es ign ing new chambers. The expe r im en ta l r e s u l t s o b ta ine d i n t h i s i n v e s t i g a t i o n cou ld be used as a benchmark f o r the Monte Car lo code. Some p r e l i m i n a r y r e s u l t s o f Monte Car lo c a l c u l a t i o n s w i t h th e EGS4 code [1 5 -17 ] a re presented i n t h i s r e p o r t .

2. EXPERIMENTS

The measurements were made w i t h an e x t r a p o l a t i o n chamber i n which the f r o n t w a l l and the back w a l l ( c o l l e c t o r and guard) co u ld be exchanged. Side w a l l r i n g s w i t h d i f f e r e n t th i ckne sses cou ld be i n s e r t e d i n th e chamber ( F i g . l ) . A g r a p h i t e chamber has a ve ry smal l f l u e n c e p e r t u r b a t i o n . Using t h i s chamber as a r e f e r e n c e , measurements were made w i t h e i t h e r th e chamber f r o n t w a l l , s i de w a l l o r back w a l l r ep laced by a lumin ium o r A - 150 ( t i s s u e - e q u i v a l e n t p l a s t i c ) . The p l a t e s e p a ra t i o n was v a r i e d between 1.4 and 11.4 mm.

IAEA-SM-298/69 177

V 7 \ 7

POLYSTYRENE REXOLITE PHANTOM A-150 EXCHANGEABLE

WALL MATERIAL

FIG. I. Experimental geometry with the extrapolation chamber (right) and simplified calculational geometry (left).

The c o l l e c t i n g volume o f the chamber was determined from ca pac i t ance measurements. P o l a r i t y e f f e c t s and leakage c u r r e n t swere i n v e s t i g a t e d and found to be s m a l l . The p r e c i s i o n o f themeasurements was v e ry good and had a s tanda rd d e v i a t i o n o f less than 0 .5 per c e n t . The accuracy i n c l u d i n g a l s o the d e t e r m i n a t i o n o f the chamber volume v a r i e d w i t h p l a t e s e p a ra t i o n but f rom repeated measurements an es t i m a te d s ta nd ard d e v i a t i o n o f less than 1 per cant was o b ta i n e d . The measurements were per formed i n beams o f Co 1.25 MeV y - r a y s , 6 and 21 MV X- rays and 9 and22 MeV e le c t r o n s f rom a M ic r o t r o n .

Most commercial p a r a l l e l - p l a t e chambers have as f r o n t w a l l a t h i n f o i l coated w i t h a c onduc t i ng l a y e r . In t h i s inhomogene- ous s i t u a t i o n th e e l e c t r o n s reach ing the chamber are produced in the co nd uc t i n g l a y e r , the f o i l and i n the phantom m a t e r i a l . In the p re sen t exper imen ts we have endeavoured a more homogeneous s i t u a t i o n where the w a l l s a re t h i c k enough t o p ro v id e a l l the e le c t r o n s reach in g th e chamber. Thus, the f r o n t w a l l had a th i ckne ss equal t o th e depth o f dose maximum f o r photons. The i n s e r t e d s id e w a l l r i n g had a th i c k n e s s o f 3 mm,-and the exchangeable back w a l l 2 mm. Th is i s enough f o r the Co measurements but somewhat too smal l f o r h ig h e r ene rg ie s c o n s i d e r i n g the e l e c t r o n ranges. However, measurements w i t h t h i n n e r and t h i c k e r s ide w a l l s i n d i c a t e t h a t 3 mm i s s u f f i c i e n t f o r a l l ene rg ies .

178 NILSSON et al.

This can be unders tood f rom the more fo rw a rd d i r e c t e d emiss ion and lower s c a t t e r i n g power o f the secondary e l e c t r o n s g i v i n g a smal l incr ease i n l a t e r a l e l e c t r o n range w i t h i n c r e a s i n g energy[ 1 8 ] .

For e l e c t r o n s the f r o n t w a l l t h i c k n e s s f o r the d i f f e r e n t m a t e r i a l s was chosen t o be a t dose maximum in wa te r (16 mm f o r 9 MeV and 30 mm f o r 22 MeV). Sca l in g t o the d i f f e r e n t f r o n t w a l l m a t e r i a l s was done by us ing th e range r e l a t i o n suggested by Markus [1 9 ] and recommended by NACP [ 1 ] . Even us ing t h i s r e l a t i o n t h e r e w i l l , owing t o th e d i f f e r e n t e l e c t r o n s c a t t e r i n g p r o p e r t i e s o f the m a t e r i a l s , be d i f f e r e n c e s i n the e l e c t r o n f l u e n c e a t the chamber s u r f a c e . This must be remembered when compar ing the r e s u l t s f o r the d i f f e r e n t f r o n t w a l l s .

The e x t r a p o l a t i o n chamber was p laced i n a p o l y s t y r e n e phantom i n o rd e r t o ge t f u l l s c a t t e r c o n t r i b u t i o n . A c o ns ta n t SSD o f 100 cm t o the back s ide o f the f r o n t w a l l was always used. The f i e l d s i z e used was 20 cm x 20 cm.

3. CALCULATIONS

The Monte Car lo method has been used to compare w i t h some o f our expe r imen ta l measurements. Th i s has been done i n o rd e r to t e s t a f l e x i b l e t o o l which i s ab le t o s im u la te v a r i o u s se t -ups t h a t would o th e rw is e r e q u i r e the c o n s t r u c t i o n o f d i f f e r e n t i o n i z a t i o n chambers.

The EGS4 Monte Ca r lo system as m o d i f i e d a t NRCC has been employed i n our c a l c u l a t i o n s . A use r code i n c l u d i n g th e PRESTA a l g o r i t h m [20] has been developed t h a t u t i l i z e s the NRCC c y l i n d r i c a l geometry package t o reproduce the expe r imen ta l s e t -u p and compute the absorbed dose a t any r eg io n o f i n t e r e s t when d i f f e r en t m a t e r i a l s are used as b u i l d u p l a y e rs and w a l l s i n our chamb e r . As i n d i c a t e d i n F ig . l , a s i m p l i f i e d geometry has been used i n the c a l c u l a t i o n s . An energy o f 10 keV has been used f o r the Monte Ca r l o c u t - o f f f o r e l e c t r o n t r a n s p o r t , w h e r e a s a c u t - o f f o f1 keV has been used f o r the p ro d u c t i o n o f d e l t a rays (AE) , photon t r a n s p o r t and bremss t rah lung p r o d u c t i o n . The maximum s tep s i z e was always chosen to be equal t o th e s m a l l e r d imension o f each s im u la te d geometry. No va r ian c e r e d u c t i o n method has been used but our c a l c u l a t i o n s i n c l u d e f o r photon beams a r e j e c t i o n c r i t e r i o n t h a t d is re g a rd s e l e c t r o n t r a n s p o r t i n reg io ns where t h e i r csda ( c on t i nuous -s low in g -dow n a p p ro x im a t ion ) range i s s m a l l e r than the d i s t a n c e t o the c o l l e c t i n g volume. In o rd e r to save CPU-time a f i e l d s i z e e q u i v a l e n t t o 10 cm x 10 cm has been used in th e c a l c u l a t i o n s . I t i s assumed t h a t the s m a l l e r f i e l d s i z e does no t i n f l u e n c e th e r e s u l t s . A p a r a l l e l beam was used f o r the c a l c u l a t i o n s .

IAEA-SM-298/69 179

PLATE SEPARATION (mm)

FIG. 2. Relative specific ionization at dose maximum as a function o f plate separation for different wall material combinations in a 60Co beam. Front, side and back walls are denoted F, S and B, respectively. The wall materials were graphite (C), aluminium (Al) and tissue-equivalent plastic (TE).

4. RESULTS AND DISCUSSION

4 . 1 . Measurements

The r e s u l t s o f the measurements are presented i n Figs 2-6 which show the r e l a t i v e s p e c i f i c i o n i z a t i o n ( i o n i z a t i o n per u n i t mass) as a f u n c t i o n o f p l a t e s e p a r a t i o n . A l l va lues are norma l ized to the s i t u a t i o n w i t h a l l w a l l s made o f g r a p h i t e and a p l a t e s e p a ra t i o n o f 3 .0 mm. Th is va lue i s chosen as a compromise between a smal l p e r t u r b a t i o n and a h i g l v ^ c c u r a c y .

F igu re 2 shows the r e s u l t f o r Co Y - r a y s . The chamber w i t h g r a p h i t e on a l l s i de s does not show any s i g n i f i c a n t v a r i a t i o n w i t h p l a t e s e p a ra t i o n i n d i c a t i n g t h a t F an o ' s theorem i s v a l i d a t dose maximum.

When exchang ing one o f the w a l l s w i t h a lu min ium, la rge e f f e c t s o ccu r . Wi th a lumin ium as a f r o n t w a l l t h e r e i s no o r a ve ry smal l v a r i a t i o n w i t h p l a t e s e p a ra t i o n b u t the s p e c i f i c i o n i z a t i o n i s decreased by 10 per c e n t . Th is can be unders tood f rom the h ig h e r e l e c t r o n s c a t t e r i n g power i n a lumin ium g i v i n g a h ig he r b a c k - s c a t t e r o f th e e l e c t r o n s produced i n the a lumin ium f r o n t w a l l and thus a low er emiss ion o f e l e c t r o n s i n th e fo rward

180 NILSSON et al.


FIG. 3. Relative specific ionization at dose maximum as a function o f plate separation for different wall material combinations for 6 MV X-rays. For abbreviations see Fig. 2.


FIG. 4. Relative specific ionization at dose maximum as a function o f plate separation for different wall material combinations for 21 MV X-rays. For abbreviations see Fig. 2.

IAEA-SM-298/69 181


FIG. 5. Relative specific ionization at dose maximum as a function o f plate separation for different wall material combinations for 9 MeV electrons. For abbreviations see Fig. 2.

d i r e c t i o n . This r e s u l t i s conf i rmed by measurements and c a l c u l a t i o n s made o f the e l e c t r o n f l u e n c e beh ind s lab s o f d i f f e r e n t m a t e r i a l s i r r a d i a t e d w i t h photons [ 2 1 ] .

Wi th a lumin ium as back w a l l m a t e r i a l an in c rea s e o f 14-17 per cent i n th e s p e c i f i c i o n i z a t i o n i s o b t a i n e d . Th is i s an e f f e c t o f th e l a r g e r e l e c t r o n b a c k - s c a t t e r i n g c o e f f i c i e n t f o r a lumin ium. For e ne rg ies below 1 MeV the b a c k - s c a t t e r c o e f f i c i e n t f o r e l e c t r o n s i s about t h re e t imes l a r g e r f o r a lumin ium than f o r g ra p h i t e [ 2 2 ] . Wi th i n c r e a s i n g p l a t e s e p a ra t i o n the s p e c i f i c i o n i z a t i o n w i l l decrease because the r e l a t i v e c o n t r i b u t i o n o f e le c t r o n s f rom the back w a l l w i l l decrease.

Aluminium as s id e w a l l m a t e r i a l g ives an i n c r e a s i n g s p e c i f i c i o n i z a t i o n w i t h i n c r e a s i n g p l a t e s e p a r a t i o n . Th is i s caused by the h ig h e r s c a t t e r i n g power in a lumin ium g i v i n g a h ig he r emiss ion o f o u t s c a t t e r e d e l e c t r o n s a t l a r g e ang les and more photon i n t e r a c t i o n s i n the s id e w a l l owing t o the h ig h e r d e n s i t y i n a lumin ium.

T i s s u e - e q u i v a l e n t p l a s t i c (A-150) i s s i m i l a r i n atomic number t o g r a p h i t e g i v i n g a mass s c a t t e r i n g power ve ry c los e to g r a p h i t e . However, the d e n s i t y i s les s than t h a t o f g r a p h i t e . This im p l i e s fewer photon i n t e r a c t i o n s i n the A-150 s id e w a l l . This i s a ls o e v id e n t f rom F ig . 2, showing a smal l bu t s i g n i f i cant decrease in the s p e c i f i c i o n i z a t i o n w i t h i n c r e a s i n g p l a t e

182 NILSSON et al.


FIG. 6. Relative specific ionization at dose maximum as a function o f plate separation for different wall material combinations for 22 MeV electrons. For abbreviations see Fig. 2.

s e p a r a t i o n . Exchanging the f r o n t w a l l o r back w a l l by A-150 d id not g iv e any s i g n i f i c a n t change compared to g r a p h i t e .

The r e s u l t s f o r 6 and 21 MV X- rays are p r e s e n t e d . i n Figs 3 arid 4. The r e s u l t s f o r 6 MV X- rays are s i m i l a r to the r e s u l t s o b ta ine d f o r ^ C o . There i s , however, a somewhat l a r g e r v a r i a t i o n w i t h p l a t e s e p a ra t i o n when us ing a lumin ium as f r o n t o r back w a l l .

For 21 MV X- rays some d i f f e r e n c e s shou ld be noted. Wi th a g r a p h i t e w a l l chamber t h e re i s now a decrease o f 2 per ce nt in the s p e c i f i c i o n i z a t i o n w i t h p l a t e s e p a ra t i o n . This may be exp la i n e d by two d i f f e r e n t e f f e c t s . One e f f e c t i s the i nve rs e square law e f f e c t [23 ] which may have l a r g e r i n f l u e n c e a t h igh ene rg ies where most o f the e l e c t r o n s are fo rw a rd d i r e c t e d a long the photon d i r e c t i o n . The o th e r p o s s i b l e e f f e c t . i s th e v a r i a t i o n i n the r e s t r i c t e d mass s to pp ing power r a t i o (s .. . ) w i t hchamber s i z e and co r respon d ing Д- v a l u e . g r a p h i t e , a i r

Another d i f f e r e n c e compared w i t h the low er e ne rg ies i s t h a t w i t h a lumin ium as f r o n t w a l l m a t e r i a l a h ig h e r s p e c i f i c i o n i z a t i o n i s o b ta i n e d . Th is depends on the increased p a i r p r o d u c t i o n w i t h a tomic number as was shown in p re v io us c a l c u l a t i o n s o f the e l e c t r o n f l u e n c e beh ind s la bs o f d i f f e r e n t m a t e r i a l s [21] .

Resu l t s f o r e l e c t r o n beams are shown i n Figs 5 and 6. F ig .5 shows the r e s u l t f o r an e l e c t r o n beam w i t h an energy o f 9 MeV

IAEA-SM-298/69 183

a t phantom s u r fa c e g i v i n g a mean energy o f 5.7 MeV a t 16 mm depth i n w a t e r . A homogeneous chamber w i t h a l l w a l l s made o f g r a p h i t e g ives a s l i g h t decrease i n the s p e c i f i c i o n i z a t i o n w i t h i n c r e a s i n g p l a t e s e p a ra t i o n . This can be e x p la in e d as f o r 21 MV X-rays w i t h the square law e f f e c t and change in s to pp ing power r a t i o w i t h i n c r e a s i n g chamber s i z e .

The h ig h e r s p e c i f i c i o n i z a t i o n behind a f r o n t w a l l o f • a lumin ium i s o b ta ine d because the h ig h e r s c a t t e r i n g power o f a luminium w i l l g iv e a h ig h e r p r i m a ry e l e c t r o n f l u e n c e a t dose maximum. The va lue 1.14 o f the r a t i o between the maximum doses i n a luminium and g r a p h i t e was ob ta ine d us ing the s c a l i n g law presented by Harder [ 2 4 ] . The va lu e i s in f a i r agreement w i t h the expe r im en ta l r e s u l t a t minimum p l a t e s e p a ra t i o n ( F i g . 5 ) . In c re as in g p l a t e s e p a ra t i o n w i l l decrease the i n f l u e n c e o f the a lumin ium f r o n t w a l l because o f the h igh mean s c a t t e r i n g angle o f the e l e c t r o n s beh ind a lumin ium. The h ig h e r s c a t t e r i n g power o f a lumin ium e x p la i n s the h ig h e r s p e c i f i c i o n i z a t i o n when the back o r s id e w a l l i s changed f rom carbon t o a lumin ium.

The t h re e curves w i t h A-150 in the f r o n t , s i d e o r back w a l l s do not d i f f e r v e ry much f rom the curve measured w i t h the g r a p h i t e w a l l e d chamber. The l a r g e s t d i f f e r e n c e i s ob ta ined w i th the A-150 back w a l l , where the s p e c i f i c i o n i z a t i o n i s lower by about 2 per c e n t . Th is can be e x p la in ed by the somewhat lower b a c k - s c a t t e r f rom A-150 compared w i t h g r a p h i t e .

S i m i l a r r e s u l t s a re ob ta ined f o r an e l e c t r o n beam w i t h an energy o f 22 MeV a t phantom s u r fa c e g i v i n g .a mean energy o f 14.8 MeV a t 30 mm depth i n w a te r . The i o n i z a t i o n in c rea s e a t 1.4 mm p l a t e s e p a ra t i o n w i t h a lumin ium f r o n t w a l l i s s m a l l e r than t h a t f o r 9 MeV. A lso the s c a l i n g law [2 4 ] g ives a s m a l l e r value(1 .10) o f the dose maximum r a t i o a lumin ium t o g r a p h i t e . Thee f f e c t s o f exchanging the back or s id e w a l l s a re s m a l l e r than f o r 9 MeV because the c o n t r i b u t i o n f rom back and s ide s c a t t e re d e le c t r o n s i s smal l a t these e ne rg ies .

4 .2 . C a l c u la t i o n s

The p r e l i m i n a r y r e s u l t s f o r a g r a p h i t e chamber and a chamber w i t h a lumin iunig-wa l ls o f the c a l c u l a t i o n s us ing the Monte Car lo method f o r Co y r a y s are i n c lu de d in F ig . 2. A l l r e s u l t s a re norma l ized i n the same way as the e xpe r i m en ta l ones. The i n d i c a t e d e r r o r bars are the ones g iven by the EGS4 program. The agreement between c a l c u l a t i o n s and expe r im ent i s a t t h i s s tage not good, bu t the main tendenc ies i n th e expe r imen ta lcurves are r e f l e c t e d i n the c a l c u l a t e d p o i n t s .

F i r s t o f a l l the e r r o r s are s t i l l too l a r g e f o r any def i n i t e co nc lus io ns and we are c o n t i n u i n g our c a l c u l a t i o n s . But we have a l s o i n d i c a t i o n s t h a t the va lues o f some o f the bas ic parameters such as AE and ESTEPE as w e l l as the random number g en e ra to r may i n f l u e n c e the r e s u l t s . So f a r we have not had t ime (CPU-t ime) t o i n v e s t i g a t e these problems i n d e t a i l bu t we bel i e v e t h a t i t i s v e ry im p o r t a n t t o t e s t a l l r e l e v a n t parameters i n a Monte Ca r lo code f o r th e s p e c i f i c s i t u a t i o n cons ide red .

184 NILSSON et al.

The r e s u l t s o f our measurements s t r o n g l y su ppor t the r e commendations o f us ing homogeneous chambers w i t h a l l w a l l s made o f the same m a t e r i a l [ 7 ] . The chamber d ia me te r and guard w id th should be l a r g e and the p l a t e s e p a ra t i o n s m a l l . The minimum p e r t u r b a t i o n i s ob ta ined w i t h g r a p h i t e w a l l s . Most commercial chambers do not f u l f i l l these recommendat ions. They o f t e n have t h i n f r o n t w a l l s o f g r a p h i t e d o r a lu m in i zed m y la r f o i l s and the o t h e r w a l l s made o f e . g . r e x o l i t e , t i s s u e - e q u i v a l e n t p l a s t i c o r p o l y m e th y lm e th a c r y la te , and one e x t r a p o l a t i o n chamber has s ide w a l l s made o f a lumin ium. The degree o f p e r t u r b a t i o n i s m a in l y r e l a t e d to the geometry o f the chamber showing a h igh p e r t u r b a t i o n f o r chambers w i t h l a r g e h e i g h t - t o - d i a m e t e r r a t i o s . In o rd e r t o compare d i f f e r e n t chambers a l i n e a r s c a l i n g o f the dimensions may be made. By s c a l i n g the d iame te rs o f commercial chambers to the d iame ter 44 mm, used i n our chamber, p l a t e s e pa ra t i on s between 3 and 18 mm are o b ta in e d . Our measurements have shown cons i d e r a b l e p e r t u r b a t i o n e f f e c t s a t these p l a t e se pa ra t i on s even w i t h a guard r i n g w id t h o f 8 mm. E a r l i e r i t bgs been conc luded t h a t p e r t u r b a t i o n e f f e c t s are n e g l i g i b l e f o r Co and t h a t o n l y a smal l guard o r no guard a t a l l i s needed [ 7 ] . A lso f o r h ig he r photon energ ies l a r g e p e r t u r b a t i o n e f f e c t s may be ob ta ined i n p a r a l l e l - p l a t e chambers.

Several papers r e p o r t p e r t u r b a t i o n e f f e c t s f o r e l e c t r o n beams w i th ene rg ies below 10 MeV [ 7 , 1 1 , 1 2 ] . The r e s u l t s o f Kubo e t a l . [ И ] show t h a t the p e r t u r b a t i o n i s l a r g e s t in chambers w i t h l a r g e h e i g h t - t o - d i a m e t e r r a t i o and our measurements f o r 9 MeV e le c t r o n s su ppor t t h e i r r e s u l t s .

5. CONCLUSIONS

ACKNOWLEDGEMENT

This work has been suppor ted by a g r a n t f rom Konung Gus ta f V's Jub i l eums fond , Stockholm.

REFERENCES

[ 1 ] NORDIC ASSOCIATION OF CLINICAL PHYSICS, Acta R ad io l .Oncol . 20 (1980) 55.

[2 ] NORDIC ASSOCIATION OF CLINICAL PHYSICS, Acta R ad io l .Oncol . 20 (1981) 85.

[3 ] AMERICAN ASSOCIATION OF PHYSICISTS IN MEDICINE, Med. Phys. 10 (1983) 741.

[ 4 ] HOSPITAL PHYSICISTS' ASSOCIATION, Phys. Med. B i o l . 28(1983) 1097.

[ 5 ] HOSPITAL PHYSICISTS' ASSOCIATION, Phys. Med. B i o l . 30(1985) 1169.

IAEA-SM-298/69 185

[ 6 ] INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, R a d ia t i o n Dos im et r y : E le c t r o n Beams w i t h Energ ies between 1 and 50 MeV, ICRU Repor t 35, Bethesda, MD (1984) .

[ 7 ] MATTSSON, L . O . , JOHANSSON, K . A . , SVENSSON, H . , Acta R a d io l . Oncol . 20 (1981) 385.

[ 8 ] JONES, D . , Med. Phys. 8 (1981) 239.[9 ] KWIATKWOSKI, T . , e t a l . , Med. Phys. 12 (1985) 518 (ab

s t r a c t ) .[1 0 ] ROGERS, D.W.O., BIELAJEW, A . F . , NAHUM, A . E . , Phys. Med.

ß i o l . 30 (1985) 429.[11 ] KUBO, H . , KENT, L . J . , KRITHIVAS, G. , Med. Phys. 13 (1986)

908.[1 2 ] CASSON, H . , KILEY, J . P . , Med. Phys. U (1987) 216.[1 3 ] NILSSON, В . , MONTELIUS, A . , Med. Phys. _13. (1986) 191.[1 4 ] ATTIX, F . H . , De La VERGNE, L . , RITZ, V .H . , J . Res. N a t l .

Bur. Stand. 60 (1958) 235.[15 ] NELSON, W.R., HIRAYAMA, H . , ROGERS, D.W.O., S tan fo rd

L in e a r A c c e l e r a t o r Cen te r , Repor t SLAC-265, C a l i f o r n i a (1985) .

[16 ] ROGERS, D.W.O., Nuc l . I ns t r um . Methods 227 (1984) 535.[1 7 ] ROGERS, D.W.O., BIELAJEW, A . F . , The use o f EGS f o r Monte

Car lo c a l c u l a t i o n s i n Medical Phys i cs , N a t io na l Research Counc i l o f Canada, Repor t PXNR-2692, Ottawa (1984) .

[1 8 ] NILSSON, В . , A n a l y s i s o f Q u a l i t y C h a r a c t e r i s t i c s o f Rad io- t h e r a p e u t i c Photon Beams, Thes is S t oc k h o lm ,1985.

[19 ] MARKUS, В . , S t r a h l e n t h e r a p i e _124 (1964) 33.[20 ] BIELAJEW, A . F . , ROGERS, D.W.O., PRESTA, The "Parameter

Reduced E l e c t r o n - S t e p T ra n s p o r t A l g o r i t h m " f o r E le c t r o n Monte Car lo T r a n s p o r t , N a t io na l Research Counci l o f Canada, Repor t PIRS-042, Ottawa (1986) .

[21 ] NILSSON, B . , Phys. Med. B i o l . 30 (1985) 139.[22] TABATA, T . , ITO, R . , OKABE, S . , Nuc l . I n s t r um . Methods 94

(1971) 509.[2 3 ] WINGATE, C . L . , GROSS, W., FAILLA, G . , Rad io l ogy 79 (1962)

984.[24 ] HARDER, D . , Proceedings o f the Second Symposium on M ic r o

d o s im e t r y , Repor t No. 4452 (EBERT, H.G. , Ed ) , Commission o f th e European Communities, B russe ls (1970) 567.

IAEA-SM-298/82

PERTURBATION CORRECTION FACTORS FOR THE PLANE-PARALLEL CHAMBER NE 2534

R. GAJEWSKI, J. IZEWSKACancer Centre of the Maria Sklodowska-Curie Institute,Warsaw,Poland

Abstract

PER TU RBA TIO N C O R R ECTIO N FA C TO R S FO R TH E P L A N E -P A R A LLE L CH A M BER N E 2534.

The perturbation correction factor (pu) was determined as a function of electron energy for the plane-parallel chamber type 2534 manufactured by Nuclear Enterprises (PTW/Markus model R23343). For this purpose both an experimental and a numerical method were used. The experimental method was based on the comparison of the meter readings for the N E 2534 chamber and the standard chamber. The numerical method was based on the Ferm i-Eyges theory, namely on the algorithm developed by Storchi and Huizenga concerning the calculation of the spatial distribution of an electron beam in a low -Z medium. Storchi and Huizenga’s approach was modified by eliminating the electrons scattered at large angles from the beam. The dependence of the scattering power factor on the mean electron energy at a given depth in the medium was also taken into account.

1. INTRODUCTION

The NE 2534 electron beam chamber is a flat, cylindrical, thin window unsealed air ionization chamber suitable for the dosimetry of therapy level electron beams. Its air gap is 6 mm in diameter and 2 mm high. The entrance window (also6 mm in diameter) and cylindrical side wall together make a polarizing electrode. A collecting electrode (5.4 mm in diameter) is surrounded by a veiy narrow guard ring (outer diameter 6 mm, inner diameter 5.8 mm).

The potential distribution in the air gap of the chamber was calculated by a relaxation method. Tracks of ions generated at some points of an air volume were determined by using the computed values of the potential distribution. It appeared that only the ions that were generated close to the guard ring were not collected by the collecting electrode.

Owing to the construction o f the chamber (very narrow guard ring), the values of the perturbation factor for low electron energies were expected to differ substantially from the values recommended by Nuclear Enterprises [1].

For the purpose of determining the perturbation factor values both an experimental and a numerical method were used.

187

188 GAJEWSKI and IZEWSKA

2. EXPERIMENTAL METHOD

This method is based on a comparison of the meter readings for both the Nuclear Enterprises 2534 chamber examined and a standard chamber with known parameters. Both chambers were irradiated under the same conditions. The perturbation correction factor for the plane-parallel chamber type 2534, pu pp, is related to the corresponding perturbation factor for the standard chamber, pu std by

Pu,,pp Pu,stdNp,std * Mu,sl

'll.pp * Mu,iPPd )

where Mu std and Mupp are the meter readings for the same absorbed dose to the phantom, corrected for the recombination losses, for the standard and examined chambers, respectively. NDjStd and NDpp are the absorbed dose to air ionization chamber factors for the standard and examined chambers, respectively. NDstd was measured at the National Standard Laboratory. NDpp was determined according to the method described by Mattsson et al. [2]. For this purpose an electron beam of energy E0 = 19.3 MeV was used. For this beam the effect of in-scattering from the side walls is negligible, which was checked by a film technique. Two standard chambers were used, the thimble chamber NPL/2561 and the plane-parallel KRT03P chamber developed at the Institute of Nuclear Studies at Swierk, Poland. The values of the perturbation factor for the thimble chamber NPL/2561 were taken from experimental data of Johansson et al. [3]. The plane-parallel chamber KRT03P has a guard ring wide enough to equal (1 .0 0 0 ) the perturbation correction factor for electron energies of concern.

3. NUMERICAL METHOD

The perturbation correction factor, pU) is defined as the quotient of the nondisturbed electron fluence in the phantom at a depth of the effective point of measurer ment and the mean electron fluence in a sensitive volume of the chamber at the same depth in the phantom. To determine the perturbation factor, the algorithm for calculating the electron fluence distribution in a composed medium must be developed. In such a case values of the linear scattering power should depend both on the depth in the medium and on the lateral position. An adequate iterative method has been proposed by Storchi and Huizenga [4]. They calculated the spatial distribution of the electrons in a plane perpendicular to the central axis, from the angular distribution of the electrons in each pixel of the plane just above it. The transport of electrons through a thin slab of material is described by the following equation

F(z+ô,r,w ) = F(z,r-<5w,co') p s (« ' — «) dw'J Q

(2)

IAEA-SM-298/82 189

where F is the distribution of the electrons as a function of depth z, lateral position r = (x,y) and direction со = {вх,ву). Öx and ву are the projected angles and ß denotes the space of all values of co. p 6 (со' — со) is the scattering function that describes the multiple scattering in a slab of thickness ô. pb depends on the kind of material and on the electron energy.

Storchi and Huizenga used in this equation the explicit form of p5

p6 (со' — со) =1

xkôexp

>\2(со — со')кУ (3)

where (со - со') = (0 Х - # ' ) 2 + (ву - ву) , and к is the linear scattering power. Furthermore, Storchi and Huizenga assumed that the shape of the angular distribution can be approximated by a Gaussian function at each point.

F(z,r,co) = Fo2 тr0 2 eXP

(co — со)

2 0 2(4)

where F0(z,r) is the planar fluence, w(z,r) is the mean direction and ö 2(z,r) is the mean square angular spread.

After substituting Eqs (2) and (3) into Eq. (1) they obtained the Gaussian function which gives the values of the distribution in direction co at each point r at depth z + 6 .

F(z+ô,r,co) = F0

7t(20 2 + kô)exp -

(co - co) 2

2 0 2 + kÔ(5)

To be consistent with the general assumption made in Eq. (4) Storchi and Huizenga approximated the distribution at z + ô by a Gaussian function in co. This was achieved by computing the first three moments of F (i = 0, 1, 2).

The present authors modified Eq. (2) as follows

F(z + ô,r) = <p( z,co)_ 7t(20 2 + kô)

exp -(co — co) 2

2 0 2 + kôdco (6 )

where <p(z,co) is a function that describes the elimination of the electrons scattered at large angles from the beam. <p(z,co) may be written in the following form

and

1 for Rp - s > 0 0 for Rp - s < 0

1 for co < cog 0 for со > со,,

for z < R.5 0

for z > R5 0

(7.1)

(7.2)

where Rp is the practical range, R50 is the half-value depth, s is the electron track length and cog is the cut-off angle.


z/r0

FIG. 1. Dependence of the mean square scattering angle on the depth in graphite phantom fo r 10 MeV electron beams1 — our calculation;2 — experimental data o f Roos [5].

It was assumed that the track length, s, of electrons which reach a point at adepth, z, in a phantom is greater than depth z. Track length, s, depends on the angle,w, and depth, z, and can be estimated by the relation

s = (1 + w2)c-z for < R50 (8 )

where 0.5 < с < 0.6

, Pi tbm

Pm 0i

where z, is the thickness of i-material, is the density of i-material, roi is the continuous slowing down range o f i-material, r0m, pm are as above, for the main material (for which Rp is taken). It means that the electron energy and, consequently, the maximum depth that electrons can reach depend on the scattering angle. The electrons for which the track length calculated according to Eq. (8 ) equals a

IAEA-SM-298/82 191

z/ro

FIG. 2. Primary electron fluence distribution along the beam axis, broad beam o f monoenergetic 20 MeV electrons1 — our calculation;2 — calculated by Andreo [6].

value of the practical range, Rp, are eliminated from subsequent calculation steps (Eq. (7.1)).

For depths, z, greater than Rso (Eq. (7.2)) the electrons scattered at angle, со, greater than the cut-off angle, ojg, are eliminated from further calculation.

The choice of the proper values of the linear scattering power, k(z), is an important factor. According to the experimental data of Roos [5], the mean square scattering angle, в 2, increases almost linearly at the point of interest. This suggests that the linear scattering power, k(z), is constant with depth, z, in phantom. On the other hand, assuming the constant value of linear scattering power, e.g. k(z) = const = k(E0), leads to results inconsistent with Roos’ data. For this reason it was assumed that the linear scattering power, k(z), equals the value k(Ez) for each depth, z, and relevant mean electron energy, Ez. This assumption was examined as follows:

(1) The mean square scattering angle as a function of depth in a graphite phantom was computed and compared with Roos’ results (Fig. 1);

(2) The primary electron fluence distribution along the central axis under broad beam conditions was computed and compared with results obtained by Andreo [6 ] (Fig. 2).


TABLE I. PERTURBATION CORRECTION FACTOR (pu) VALUES

E z (MeV) 2 . 2 4.8 5.5 9.7 12.7 14.5

Pu.pp exper. 0.973 0.978 0.981 0.989 0.995 1

Pu.pp numer. 0.977 0.983 0.986 0.995 0.998 1 . 0 0 0

Electron fluence distributions in the chamber cavity and in homogeneous medium were computed according to the iterative procedure presented in two- dimensional geometry. The one pixel size in the x-y plane was 0.05 x 0.05 mm. The perturbation correction factor, pu, was computed for six different electron energies, E0, in PMMA phantom at the depth of the maximum percentage depth dose.

4. RESULTS

The values of perturbation correction factor, pu, obtained by both experimental and numerical methods are given in Table I.

Some differences between the experimental and the numerical values of the perturbation factor were found.

Errors encountered in the experimental method are caused by:

(1) limited accuracy in the determination of the relevant factors such as ND std,Nd.pp* Pu.std)

(2 ) the assumption that the position of an effective point of measurement is constant for all electron energies for the thimble standard chamber;

(3) the choice of the values of restricted stopping power with only one cut-off energy for all chambers applied in spite of different dimensions of their air volumes.

In our numerical model the secondary electrons have been neglected in the computation. Assumption k(z) = k(Ez) is not precise and provides some errors because changes in electron energy distribution with depth are not taken into account. Consequently, the perturbation effect seems to be more important than that derived from the numerical method.

REFERENCES

[1] Electron Beam Chamber 2534, Manual, Nuclear Enterprises Ltd (1984).[2] M ATTSSO N , L .O ., JO H AN SSO N , K .-A ., SVEN SSO N , H ., Acta Radiol., Oncol. 20 (1981) 6 .

IAEA-SM-298/82 193

[3] JO H AN SSO N , K .-A ., M ATTSSO N , L .O ., LIN D B O R G , L ., SVEN SSO N , H ., “ Absorbeddose determination with ionization chambers in electron and photon beams having energies between 1 and 50 M eV” , National and International Standardization of Radiation Dosimetry (Proc. Symp. Atlanta, 1977), Vol. 2, IA E A , Vienna (1978) 243-270.

[4] STO R C H I, P .R .M ., H U IZEN G A , H „ Phys. Med. Biol. 30 5 (1985) 467-473.[5] RO OS, H ., D R EPPER, P ., H A R D ER , D ., Proceedings of the Fourth Symposium on

Microdosimetry (1973).[6 ] A N D REO , P ., from IC R U Report 35 (1984).

DOSIMETRY IN BRACHYTHERAPY

(Session III)

Chairman

J.S. LAUGHLINUnited States of America

Poster Rapporteur

A. DUTREIXFrance

IAEA-SM-298/99

Invited Paper

MODERN DEVELOPMENTS IN BRACHYTHERAPY DOSIMETRY

A. DUTREIX Unité de radiophysique,Institut Gustave-Roussy,Villejuif,France

Abstract

MODERN DEVELOPMENTS IN BRACHYTHERAPY DOSIMETRY.Since the 1960s, radium and radon have been progressively replaced by artificial radionuclides.

The mass of radium as a reference for source strength specification should be replaced by a more modern quantity; the reference air-kerma-rate has been recommended by ICRU since 1985. Very few data have been published on the dosimetric parameters of iridium-192 sources which are needed for dose calculations. Data on platinum filtration and tissue attenuation for iridium-192 wires are presented. In modern computer programs, isodose surfaces may be displayed in perspective view. Dose distributions may also be displayed superimposed on anatomical structures in any plane recomputed from CT transverse scans.

1 . INTRODUCTION

The history of braehytherapy began three years only

after the discovery of radium by Pierre and Marie Curie in 1898.

Two years before, Henri Beequerel had described "non visible

radiations emitted by uranium". Five years after the first

physical experiment, the first medical use of radium had been

proposed by Danlos in Paris and, four years later, an American

surgeon, Robert Abbe, used radium to treat cancer [ 1 ]. In

contrast, about twenty years have passed between the discovery of

artificial radioactivity by Irene and Frederic Joliot in 193^ and

the replacement of radon and radium by artificial radionuclides in

brachytherapy. Myers [ 2 ] introduced cobalt needles in 19^8,

Henschke joined him later on and proposed gold seeds in 1953 [ 3 ]

and iridium seeds a few years later.

Radiation safety problems provided much of the initial

rationale for the introduction of artificial radionuclides for two

197

198 DUTREIX

main reasons : the high risk of contamination by the daughter

products of radium and the large thickness of lead needed for

adequate mobile barriers or containers because of the high energy

of the Y-rays emitted. The physical flexibility and the source

miniaturization of the radium substitutes, both necessary in the

modern afterloading techniques must also be regarded as advantages

of prime importance. The most important gamma emitters for

temporary implants (interstitial or intracavitary) are iridium-192

and caesium-137 and, to a lesser extent, cobalt-60. For permanent

implants, iodine-125 is progressively replacing gold-198.

2 . SPECIFICATION OF SOORCE STRENGTH

2 . 1 . C o n ven tio n a l methods o f s p e c i f ic a t io n

When only radium sources were used in brachytherapy, the

strength of sources was specified in terms of the mass of radium

contained in the source. The total added filtration was also

indicated in millimetres of platinum, usually 0.5 mm Pt for radium

needles and 1 to 2 mm Pt for radium tubes.

When artificial radionuclides became available, their

strength was first specified in terms of the activity contained in

the source. It quickly appeared that this specification method was

of little practical interest for two reasons: first, the

comparison with radium tubes was not straightforward because the

absorbed dose at a given distance depended largely on the auto

absorption and filtration of the emitted Y-rays by the source

itself and its sheath; secondly, accurate determination of the

contained activity is a laborious and complex procedure.

In order to compare radium substitutes with radium

itself, it has been proposed to specify sources in mg-radium

equivalent, the mass of radium, filtered by 0.5 mm of platinum

which leads to the same exposure rate as that from the radioactive

source of interest at the same .distance. It is no longer

convenient to use radium sources as a reference because the use of

radium has widely decreased throughout the world and because of

IAEA-SM-298/99 199

th e la rg e d if fe r e n c e s in shape and s iz e o f modern sources as

compared to radium n eed les and tu b e s . A nother d i f f i c u l t y l i e s in

th e s ta n d a rd iz a t io n to 0 .5 mm p la tin u m : th e dose r a te a t a g iv e n

d is ta n c e from a s tan d ard 10 mg radium tu be f i l t e r e d by 1 mm o f

p la tin u m o r more, is le s s th an th e dose r a te d e l iv e r e d a t th e same

d is ta n c e by a 10 mg R a -e q u iv a le n t so u rce . F o r in s ta n c e , a 10 mg

radium tube f i l t e r e d by 2 mm o f p la tin u m d e l iv e r s a dose in

t is s u e s eq u a l to 83% o f th e dose d e liv e r e d by a 10 mg radium

e q u iv a le n t caesium tu b e .

on, in term s o f a p p a re n t a c t i v i t y im p lie s th e measurement o f th e

exposure r a t e (o r th e kerma r a t e ) a t a g iv e n d is ta n c e . T h e re fo re ,

i t q u ic k ly became e v id e n t th a t th e c a lc u la t io n o f th e e q u iv a le n t

mass o f radium o r th e ap p are n t a c t i v i t y was a u s e le s s s tep le a d in g

to an in c re a s e d r is k o f e r r o r in th e use o f co n ve rs io n f a c to r s .

2 . 2 . Modern developm ents in so urce s p e c i f ic a t io n

R e c e n tly , s e v e ra l o rg a n iz a tio n s (C F M R I [ M] , ICRU [ 5 ] and

AAPM [ 6 ] ) have recommended s p e c i f ic a t io n o f source s tre n g th s in

term s o f k e rm a -ra te in f r e e space a t a re fe re n c e d is tà n c e , K^.

ICRU recommends th e use o f th e " re fe re n c e a i r k e rm a -ra te " -1 2e x p r e s s e d i n y G y . h . m .

sources o f 1 mg R a -e q u iv a le n t o r o f ap p are n t a c t i v i t y eq u a l to

1 mCl o r 1 MBq.

source o f re fe re n c e a i r k e rm a -ra te is e a s i ly c a lc u la te d as

fo llo w s :

The s p e c i f ic a t io n in term s o f mg Ra e q u iv a le n t o r , l a t e r

- 1 2 - 1 2 - 1 21 yG y.h .m = 1 cG y.h .cm = 1 ra d .h .cm .

T a b le I shows th e re fe re n c e a i r k e rm a -ra te o f v a r io u s

The absorbed dose in w a te r a t a d is ta n c e R from a p o in t

a i r

where ф ( R ) i s a f a c to r ac co u n tin g f o r t is s u e a t te n u a t io n

( s e c t io n 3 . 2 ) .

2 0 0 DUTREIX

* *yTABLE I . R e fere n ce a i r kerma r a te in y G y .h .m fo r

sources o f ap p are n t a c t i v i t y 1 MBq, 1 mCi o r 1 mg Ra equ.

R a d io n u c lid e

1 2R e feren ce a i r k e rm a -ra te (u G y .h - .m )

1 MBq 1 mCi 1 mg Ra equ

60¿y Co О.ЗО9 11 .4 7 .2 0

125

53 10 .0 3 4 2 1.27 7 .2 0

137

55 Cs O.O791 2 .9 3 7 .2 0

192

77 I r 0 .1 1 6 4 .2 8 7 .2 0

198

79 Au0 .0 5 4 8 2 .0 3 7 .2 0

226

88 Ra 0 .1 9 7 7 .2 8 7 .2 0

M en

L Pi s th e r a t i o o f th e mean mass energy a b s o rp tio n

a i r

c o e f f ic ie n t s in w a te r and in a i r . T h is r a t io is a lm ost ind ependent

o f energy f o r th e e n e rg ie s o f X - and y - r a y s e m itte d by th e

ra d io n u c lid e s used in b rac h y th e ra p y excep t f o r io d in e - 125 : i t s

v a lu e is eq u a l to 1.1 f o r most o f th e ra d io n u c lid e s [ 4 ] .

IAEA-SM-298/99 201

The w idespread use o f com puters in ra d io th e ra p y has made

p o s s ib le th e d e te rm in a tio n o f com plete dose d is t r ib u t io n f o r

i n t e r s t i t i a l o r in t r a c a v i t a r y ra d io th e ra p y . B e fo re the com puter

e r a , r a d io th e r a p is ts and p h y s ic is ts co u ld o n ly e v a lu a te th e

absorbed dose a t a re fe re n c e p o in t from s ta n d ard ta b le s assuming

an id e a l source arran g em en t. The in t r o d u c t io n o f com puters has

re s u lte d in a new approach in b ra c h y th e ra p y d o s im e try w ith th e

c a lc u la t io n o f dose d is t r ib u t io n s around a r ra y s o f sources f o r

a c tu a l im p la n ts in in d iv id u a l p a t ie n t s .

The developm ent o f a dose co m p u tation system in v o lv e s

th e d e f in i t io n o f a m a th e m a tic a l model and th e developm ent o f a

co n ve n ien t a lg o r ith m . A dose co m p u tation model i s n e c e s s a r ily

ap p ro xim ate and has to be re v is e d from tim e to tim e in o rd e r to

im prove th e a p p ro x im a tio n s . The m a th e m a tic a l model uses param eters

e i t h e r measured o r c a lc u la te d and we have r e c e n t ly re v is e d some o f

th e p aram eters used f o r i r id iu m -1 9 2 so u rce s .

W hile ir id iu m -1 9 2 has been used f o r many ye a rs fo r

i n t e r s t i t i a l o r in t r a c a v i t a r y b ra c h y th e ra p y , i t i s in t e r e s t in g to

n o te how few measurements have been made on fu nd am en ta l d o s im e tr ic

p ro p e r t ie s o f t h is r a d io n u c lid e . I t can be p a r t l y e x p la in e d by th e

d i f f i c u l t y l in k e d to th e complex spectrum , from a few keV X -ra y s

to 612 keV Y -ra y s , and e s p e c ia l ly to th e low en ergy component. Any

measurement should th en be c o rre c te d f o r energy dependence o f th e

d e te c to r in c re a s in g th e u s u a l d i f f i c u l t i e s en countered when

m easuring low dose ra te s a t s h o rt d is ta n c e s o f ra d io a c t iv e

so u rces . U n fo r tu n a te ly , th e same reasons make th e o r e t ic a l

c a lc u la t io n s d o u b tfu l .

3.1. X- and у -ray attenuation in platinum

The d e te rm in a tio n o f k e rm a -ra te in f r e e space has to be

made a t a d is ta n c e from th e so u rce , la rg e enough as compared to

th e source le n g th , f o r th e source to be co n s id e re d as a p o in t

so u rce . The g e o m e tr ic a l c o n d it io n s o f th e measurement im p ly th a t

3. DETERMINATION OF ABSORBED DOSE IN PATIENTS

2 0 2 DUTREIX

th e X - o r Y -ra y s measured by th e d o s im ete r have passed th rough th e

source m a te r ia l and th e f i l t e r in an o rth o g o n a l d i r e c t io n . The

re fe re n c e a i r k e rm a -ra te th en accounts f o r th e a u to -a b s o rp tio n and

f i l t r a t i o n o f th e source in a d ir e c t io n p e rp e n d ic u la r to th e

source a x is . However, a t a p o in t a t a s h o rt d is ta n c e from an

a c tu a l so u rce , some o f th e e m itte d X - and Y -ra y s d e l iv e r in g th e

dose a t th a t p o in t pass o b liq u e ly th rough th e source and th e

f i l t e r , r e s u l t in g in a d ecrease in th e dose. The necessary

c o r r e c t io n , known as o b liq u e f i l t r a t i o n c o r r e c t io n , im p lie s th e

knowledge o f th e mass a t te n u a t io n c o e f f ic ie n t o f th e f i l t e r and

source m a te r ia ls f o r e n e rg ie s o f th e e m itte d Y -ra y s .

I r id iu m w ire s a re made o f an a l lo y o f i r id iu m and

p la tin u m and embedded in an in a c t iv e sheath o f p la tin u m . Auto

a b s o rp tio n and f i l t r a t i o n a re governed by th e t o t a l d ia m e te r o f

th e w ire and th e mass a t te n u a t io n c o e f f i c ie n t o f th e e m itte d

photons in i r id iu m and p la tin u m . The a tom ic number o f i r id iu m and

p la tin u m a re v e ry c lo s e and th e whole source can be co n s id e re d as

made o f p la tin u m o n ly .

As we have n o t found in th e l i t e r a t u r e e x p e rim e n ta l d a ta

on p la tin u m f i l t r a t i o n o f ir id iu m w ir e s , our own e x p e rim e n ta l

r e s u l ts [ 7 ] a re p resen ted h e re .

S im u lta n e o u s ly , t h e o r e t ic a l c a lc u la t io n s based on th e

Monte C a rlo method [ 8 ] have been a c h ie v e d . A la y e r o f p la tin u m

f i l t e r s X - and Y -ra ys o f th e lo w es t energy m o d ify in g th e e m itte d

spectrum and, th e r e fo r e , th e spectrum o f s c a tte re d photons in a

complex way. F ig u re 1 shows th e v a r ia t io n o f th e mass a t te n u a t io n

c o e f f ic ie n t in p la tin u m as a fu n c t io n o f p la tin u m th ic k n e s s

e s tim a te d from measurements and c a lc u la t io n . T ab le I I shows th e

v a r ia t io n o f th e mean energy o f th e spectrum em erging from th e

source computed f o r v a r io u s p la tin u m f i l t r a t i o n s by Monte C a rlo

c a lc u la t io n s . The v a r ia t io n in th e mean spectrum energy e x p la in s

th e v a r ia t io n observed in th e mass a t te n u a t io n c o e f f i c ie n t .

3 . 2 . A tte n u a tio n in w a te r

S c a t te r in g and a t te n u a t io n o f photons in w a te r has been• •

o fte n expressed as th e r a t io Xw/Xa o f th e exposure r a te in w a te r

IAEA-SM-298/99 203

(1 /100 m m Pt)

FIG. 1. Variation o f the mass attenuation coefficient in platinum, o f X- and y -rays emitted by an iridium-192 source, versus the added platinum filtration e in 1/100 mm. e = 0 corresponds to an iridium wire 0.3 mm in diameter. Circles stand for experimental data and black dots for data calculated by the Monte Carlo method.

• •Xw to th e e x p o s u re -ra te in a i r Xa measured a t th e same d is ta n c e R

from th e so u rce . In modern d o s im e tr ic q u a n t i t ie s i t can be• •

expressed as th e r a t io cp(R) = Kw/Ka o f th e k e rm a -ra te to a i r in . •

w a te r Kw, to th e k e rm a -ra te to a i r in a i r Ka.

O nly two s e ts o f measurement o f cp (R) f o r ir id iu m -1 9 2

have appeared in th e l i t e r a t u r e [ 9 , 1 0 ] showing some d is c re p a n c ie s

w ith c a lc u la te d d a ta as shown by M e is b e rg e r [1 0 ] and by Glasgow

[1 1 ] in a re v ie w o f th e l i t e r a t u r e . The la rg e d if fe r e n c e s observed

between th e two s e ts o f measured d a ta on th e one hand and between

c a lc u la t io n s and measurements on th e o th e r hand a re w e l l e x p la in e d

by th e complex spectrum and th e e f f e c t s o f f i l t r a t i o n shown in

s e c tio n 3 .1 .

F ig u re 2 shows th e v a r ia t io n o f cp (R ) as a fu n c t io n o f

f i l t e r th ic k n e s s . The curves a re n o rm a lized f o r a source 0 .3 mm in

204 DUTREIX

TABLE I I . Mean energy E o f th e photon spectrum f o r I r i d i u m - 192

w ire s w ith d i f f e r e n t p la tin u m f i l t e r th ic k n e s s e s

F i l t e r

th ic k n e s s

(mm P t)

W ire

d ia m e te r

(mm)

Ë

(keV )

0 0 348

0 0 .1 352

0 .1 0 .3 363

0 .2 0 .5 369

0 .3 0 .7 374

0 .4 0 .9 376

0 .9 5 2 .0 388

FIG. 2. Variation o f the normalized transmission factor in water versus the added platinum filtration e in 1/100 mm. For each distance R, the transmission factor <p(R) is normalized to the value measured for an iridium wire 0.3 mm in diameter without added filtration. The transmission factor is measured at three different distances R, 2, 5 and 10 cm.

IAEA-SM-298/99 205

1.05

1.00

cc»

0.95

0.90

0.85

6 = 0 .3 mm

■-------Ф = 0 .7 mm

10R (cm)

FIG. 3. Variation o f the transmission factor <p(R) in water for two typical iridium-192 wires 0.1 mm in diameter filtered respectively by 0.1 and 0.3 mm ofplantinum (external diameters 0.3 and 0.7 mm). The dashed curve corresponds to a zero diameter. Crosses correspond to the polynomial fit by Meisberger.

d ia m e te r w ith no added f i l t r a t i o n . F ig u re 3 shows th e measured

v a r ia t io n o f cp(R) f o r two t y p ic a l p la tin u m f i l t e r s compared to

th e M e isb e rg er p o lyn o m ia l f i t o f p u b lis h e d d a ta . Curves show

c le a r ly th e v a r ia t io n o f t is s u e a t te n u a t io n w ith f i l t e r th ic k n e s s .

The la rg e v a r ia t io n observed e x p la in s th e d if fe r e n c e s between

measured o r computed curves found in th e l i t e r a t u r e . They a re

o b v io u s ly due to d if fe r e n c e s e i t h e r i n th e f i l t r a t i o n o f th e

sources used f o r exp erim en ts o r i n th e spectrum co n s id e re d in

c a lc u la t io n .

4 . DISPLAY OF DOSE DISTRIBUTIONS

4 . 1 . C o n v e n tio n a l d is p la y o f dose d is t r ib u t io n s

Dose co m putation in b rac h y th e ra p y i s most o f te n based on

o rth o g o n a l ra d io g ra p h s , o f f e r in g a good v is u a l i z a t io n o f m e t a l l ic

MES

Sagittal Oblique TOS PLAN i .0

ISODOSES2000 1200 830 530

1500 1000 660 420

12 06 87 I.G.R LE 12 6 87

AQ - 1.00

cGy

8 6

PLAN

ISODOSES

M E S

Reperes Oblique POS. PLAN - .0

12 06 87 LGR LE 12 6 87

A ü - 1.00

DOSE DE REF.170 100 70 20 EN % DE

120 85 50 10 1164.0

FIG. 4. Dose distribution fo r an implant in the mobile tongue with three iridium-192 hairpins. Dose distributions are shown in two orthogonal planes, parallel (4a) and perpendicular (4b) to the hairpin branches. 1 and 2 are respectively the midanterior outline o f the chin and o f the jaw , 3 and 4 the left and right angles o f the jaw , 5 and 6 submaxillary nodes, 7 the spinal chord. Doses are given in cGy per day. (Original computer printout.)

IAEA-SM-298/99 207

FIG. 5. Perspective view o f the 60 Gy reference surface isodose fo r an intracavitary therapy in gynecology with caesium-137 sources. The pear shape o f the isodose is shown and the exact volume (139.6 cm3) is automatically calculated. (Original computer printout.)

sources in s o f t t is s u e s . The r e s u l t in g dose d is t r ib u t io n s a re

p res en ted as s e ts o f curves in chosen p la n e s . Some anatom ic

landm arks may be in d ic a te d on th e p lanes o f in t e r e s t such as bones

o r organs a t r i s k (F ig u re ^ ) .

D is p la y o f a s u rfa c e isodose in a p e rs p e c tiv e v iew is

u s e fu l in some c irc u m s ta n c e s . The volume o f t is s u e s enclosed in

th e s u rfa c e isodose can be a u to m a t ic a l ly e v a lu a te d . F ig u re 5 shows

th e example o f th e 60 Gy re fe re n c e isodose in a c e r v ix cancer

t re a tm e n t.

208 DUTREIX

4 . 2 . CT and b ra c h y th e ra p y tre a tm e n t p la n n in g

CT scans a re w id e ly used as b a s ic p a t ie n t d a ta f o r

e x te r n a l th e ra p y , b u t i t i s o n ly r e c e n t ly th a t th ey have been used

in b ra c h y th e ra p y . Two main d i f f i c u l t i e s a re encountered when u s ing

CT im ages: f i r s t , th e re c o n s tru c t io n o f th e source p o s it io n in

space from a l im ite d number o f tra n s v e rs e s l ic e s is in a c c u ra te ;

se c o n d ly , in c o n tra s t to e x te r n a l th e ra p y , tra n s v e rs e p la n e s a re

n ot alw ays s u ita b le f o r th e r a d io th e r a p is t to judge on th e q u a l i t y

o f th e im p la n t and to p re s c r ib e th e tre a tm e n t.

4 . 2 . 1 . R e c o n s tru c tio n o f so urce p o s it io n s

To overcome th e d i f f i c u l t y o f source lo c a l iz a t io n

through CT im ages, we use th e two o rth o g o n a l scout v iew s o f th e

p a t ie n t , s e t-u p on th e CT couch, w ith dummy sources p o s it io n e d in

th e a p p l ic a t o r . The use o f dummy sources has been made p o s s ib le by

th e a f te r lo a d in g methods. The a c tu a l p o s it io n o f th e sources in

space is computed w ith re s p e c t to CT s l ic e s . The 3D dose

d is t r ib u t io n is then computed u s ing th e c o n v e n tio n a l a lg o r ith m s .

4 . 2 . 2 . 3D d is p la y o f dose d is t r ib u t io n s

In our com puter system dose d is t r ib u t io n s a re d is p la y e d

as co lo u re d areas superim posed to anatom ic s t r u c tu r e s . In each

co lo u red a re a , co rrespo n d ing to a g iv e n dose ra n g e , th e c o lo u r

v a r ie s from b la c k f o r a i r c a v i t ie s to th e l ig h t e r c o lo u r f o r bony

s tr u c tu r e s as shown in F ig u re 6 f o r in t r a c a v i t a r y th e ra p y .

Dose d is t r ib u t io n com putation in tra n s v e rs e p lan es is

e s s e n t ia l f o r e x te r n a l th e ra p y where beam axes a re o fte n c o p la n a r

o r p laced in p a r a l l e l p la n e s . In c o n t ra s t , in b ra c h y th e ra p y dose

d is t r ib u t io n u s u a lly needs to be computed in p lanes r e la te d to th e

main d ir e c t io n o f th e im p lan ted sources and not in tra n s v e rs e

p la n e s . For in s ta n c e , in i n t e r s t i t i a l im p la n ts r a d io th e r a p is ts

u s u a lly base t h e i r judgem ent f o r dose s p e c i f ic a t io n on p la n e s

e i t h e r o rth o g o n a l o r p a r a l l e l to th e main d ir e c t io n o f th e

IAEA-SM-298/99 209

FIG. 6. Dose distribution superimposed on anatomical structures, in an intracavitary therapy fo r cervix cancer. The oblique frontal plane (a) and oblique sagittal plane (b) both containing the intra-uterine source, are computed from CT transverse sections.

ra d io a c t iv e so u rce s . The e x a c t p o s it io n o f th e p la n e s o f in t e r e s t

is d eterm ined as fo llo w s . The o rth o g o n a l p r o je c t io n o f th e sources

on two p la n e s , s a g i t t a l and f r o n t a l , a re computed from source

p ro je c t io n s in th e scout v iew s and a re d is p la y e d on th e computer

te r m in a l . The r a d io th e r a p is t o r th e p h y s ic is t may th en choose in

an in t e r a c t iv e way th e o r ie n t a t io n o f th e p la n e s o f in t e r e s t .

S ec tio n s o f anatom ic s tr u c tu r e s in those p la n e s a re recomputed

from th e CT images and th e dose d is t r ib u t io n s a re superim posed as

f o r tra n s v e rs e s e c t io n s . F o r in t r a c a v i t a r y a p p lic a t io n s a t le a s t

two p lanes a re recomputed as recommended by ICRU [ 5 ] : th e o b liq u e

2 1 0 DUTREIX

f r o n t a l p la n e and th e o b liq u e s a g i t t a l p la n e , both c o n ta in in g th e

i n t r a - u t e r in e source ( F ig . 6 ) . T ran sv erse p la n e s a re u s e fu l

w henever e x te r n a l th e ra p y is combined w ith b ra c h y th e ra p y .

5 . CONCLUSION

The advent o f a r t i f i c i a l ra d io n u c lid e s c o in c id e n t w ith

te c h n o lo g ic a l p ro gress in source m a n u fac tu rin g as w e l l as in

m edica l e le c tro n ic s and com puters, has d r a s t ic a l l y tra n s fo rm ed th e

p ra c t ic e o f b ra c h y th e ra p y . I t e x p la in s th e renew al o f in t e r e s t fo r

b rac h y th e ra p y tec h n iq u es among r a d io th e r a p is ts . I t i s , th e r e fo r e ,

th e ta s k o f p h y s ic is ts to b r in g t h e i r e f f o r t s on th e d o s im e tr ic

asp ects o f b ra c h y th e ra p y , to encourage th e use o f modern

q u a n t i t ie s and to im prove th e accuracy o f d o s im e tr ic p a ra m e te rs .

W ith th e a v a i l a b i l i t y o f CT scanners and s o p h is t ic a te d

com puter program s, one can im prove th e accùracy in dose

d is t r ib u t io n c a lc u la t io n and a tte m p t to be more c o n s is te n t in dose

s p e c i f ic a t io n . T h is endeavour would r e s u l t in a b e t t e r c l i n i c a l

e v a lu a t io n o f th e b rac h y th e ra p y te c h n iq u e s .

REFERENCES

[ 1 ] DEL REGATO, J .A . , " B ra c h y th e ra p y " in :F ro n tie rs o f R a d ia t io nTherapy and Oncology (V a e th , J .M . , E d . ) , K arg er ( N . Y . ) , _12(1 9 7 8 ) 5 .

[ 2 ] MYERS, W .G ., A p p lic a t io n o f a r t i f i c i a l r a d io a c t iv e is o to p e s in th e ra p y : C o b a lt 6 0 , Am. J . R o en tg en o l. 6£ (1 9 4 8 ) 81 5 .

[ 3 ] HENSCHKE, U . K . , JAMES, A . G. , MYERS, W. G. , Radiogold seeds incancer th e ra p y , N u c leo n ics 2 1 ( 1953) 46.

[ 4 ] CFMRI (C om ité F ra n ç a is pour la Mesure des Rayonnements I o n i s a n ts ) , Recommandations pour l a d é te rm in a tio n des dosesabsorbées en c u r ie th é r a p ie . Rapport n° 1, Bureau N a t io n a l de M é tro lo g ie , P a r is ( 1 9 8 3 ) .

[ 5 ] ICRU ( In t e r n a t io n a l Commission on R a d ia tio n U n its and Measure m e n ts ), Dose and volume s p e c i f ic a t io n f o r re p o r t in g i n t r a c a v ita r y th e ra p y in g yn eco log y, ICRU R epo rt 3 8 , In t e r n a t io n a l Commission on R a d ia t io n U n its and M easurem ents, B ethesda, M aryland ( 1 9 8 5 ) .

IAEA-SM-298/99 211

[ 6 ] AAPM (A m erican A s s o c ia tio n o f P h y s ic is ts in M e d ic in e ) , S p e c if i c a t io n o f b rac h y th e ra p y source s tre n g th , AAPM Task Group R eport 3 2 , Am erican I n s t i t u t e o f P h y s ic s , New Y o rk , NY (1986).

[ 7 ] DIEMERT, M ., A tte n u a tio n e t d if fu s io n des rayons X e t y émis p ar Ie s sources d 'i r id iu m 192 u t i l i s é e s en c u r ie th é r a p ie , T h e s is , C o n s e rv a to ire N a t io n a l des A r ts e t M é t ie r s , P a r is( 1 9 8 2 ) .

[ 8 ] CAZES, C . , E tude d o s im é triq u e de l ' i r i d i u m 192 p ar la méthode de M o n te -C a r lo , T h e s is , F a c u lté des S c ie n c e s , Toulouse (1981).

[ 9 ] MEREDITH, W . J . , GREENE, D . , KAWASHIMA, K . , The a t te n u a t io n and s c a t te r in g in a phantom o f gamma-rays from some ra d io n u c lid e s used in mould and i n t e r s t i t i a l gamma-rays th e ra p y , B r . J . R a d io l. 39 (1965) 280.

[10] MEISBERGEH, L . L . , KELLER, R . J . , SHALEK, R . J . , The e f f e c t iv e a t te n u a t io n in w a te r o f th e gamma-rays o f g o ld - 198, i r id iu m - 192, ce s iu m -13 7 , rad iu m -226 and c o b a l t -6 0 , R ad io lo g y 90 ( 1968) 953.

[ 1 1 ] GLASGOW, G . P . , The r a t io o f th e dose in w a te r to exposure in a i r f o r a p o in t source o f ir id iu m -1 9 2 : a re v ie w , in Recent Advances in B rach y th erap y P hys ics (S h e a re r D . R . , E d . ) , AAPM, M ed ica l P h ys ics Monograph 7 ( 1981) 104.

IAEA-SM-298/23

COMPARAISON DES DISTRIBUTIONS DE DOSE EN CURIETHERAPIE INTERSTITIELLE AUTOUR DE SOURCES CONTINUES ET DISCONTINUES

A. BRIDIER, H. KAFROUNI,J.-P. HOULARD, A. DUTREIX Unité de radiophysique,Institut Gustave-Roussy,Villejuif, France

A bstract-R ésum é

COMPARISON OF DOSE DISTRIBUTIONS AROUND CONTINUOUS AND DISCRETE SOURCES IN INTERSTITIAL RADIOTHERAPY.

Radioactive implants in interstitial radiotherapy using the Paris system were initially to be for lines which were radioactive along the whole of their lengths. The use of ‘source trains’ made up of a set of individual sources a given interval apart led to study being made of the conditions for which discrete sources could replace continuous sources in the Paris system. A systematic study of the dose distributions around both types of source was carried out. The distributions were calculated, on a VAX 8600 computer using a program developed by the Gustave-Roussy Institute, taking into account oblique filtration and attenuation by the tissues. The program makes it possible to calculate volumes within an isodose of a chosen value on the basis of a dose matrix with a basic grid size of 2 mm. The geometrical conditions for which the dose distributions round continuous sources and discrete series of individual sources are not significantly different, were calculated beforehand; this gave a simple equivalence rule between a continuous source of length L and total activity KN and n individual sources of activity KNs with a spacing of s between them: L = n-s and KN = n-KNs. On this basis, a more thorough study was made of the dose distributions using the volume-dose distributions for the main volumes used in the Paris system to describe radioactive implantation. The study made it possible to compare continuous sources with series of individual sources of equivalent length for some source devices of similar configurations to those used in clinical practice according to the rules of the Paris system.

COMPARAISON DES DISTRIBUTIONS DE DOSE EN CURIETHERAPIE INTERSTITIELLE AUTOUR DE SOURCES CONTINUES ET DISCONTINUES.

Les implantations radioactives réalisées en curiethérapie interstitielle conformément au système de Paris étaient prévues initialement pour des lignes continuement radioactives sur toute leur longueur. L’emploi de «trains de sources» composés d’un ensemble de sources élémentaires séparées par un intervalle donné a conduit à étudier les conditions pour lesquelles les sources discontinues pouvaient remplacer les sources continues dans le système de Paris. Une étude systématique de répartition des doses autour de ces deux types de sources a été réalisée. Les distributions de dose sont obtenues à partir d ’un programme de calcul mis au point à l’Institut Gustave-Roussy, sur un ordinateur VAX 8600, tenant compte de la filtration oblique et de l’atténuation par les tissus. Ce programme permet le calcul des volumes délimités par une isodose de valeur choisie à partir de matrice de dose dont les mailles élémentaires ont une taille de 2 mm. Préalablement, on a établi les conditions géométriques pour lesquelles les distributions de dose autour des sources continues et des trains de sources élémentaires ne présentent

213

214 BRIDIER et al.

pas de différence significative. Cette étude a conduit à une règle d’équivalence simple entre une source continue de longueur L et d’activité totale KN et n sources élémentaires d’activité KNs dont les centres sont espacés de s avec L = n-s et KN = n-KNs. Sur ces bases, une étude plus approfondie de la répartition des doses a été effectuée au moyen des distributions volume-dose et en se référant aux principaux volumes utilisés dans le système de Paris pour décrire l’implantation radioactive. Cette étude a permis de comparer les sources continues avec les trains de sources élémentaires de longueurs équivalentes pour un certain nombre de dispositifs de sources de configuration proche de ceux utilisés en pratique clinique d’après les règles du système de Paris.

1. INTRODUCTION

L ’emploi, en curiethérapie interstitielle, de sources discontinues composées d ’un ensemble de sources élémentaires séparées par un intervalle donné a conduit plusieurs auteurs à analyser l ’uniformité des distributions de dose résultant de leur utilisation dans un système de dosimétrie par comparaison avec des sources continues [1, 2].

La comparaison des distributions de dose autour des sources continues et discontinues a été reprise dans ce travail dans le but d ’étudier les conditions pour lesquelles, dans le système de Paris [3, 4], les «trains de sources» pouvaient remplacer les sources continues ayant servi de référence pour l ’établissement des règles de ce système.

La comparaison repose sur une étude systématique par ordinateur et se réfère à la forme des isodoses, à la distribution volume-dose et aux volumes plus spécifiquement considérés dans le système de Paris pour décrire l ’implantation radioactive [3]. Elle porte sur divers dispositifs d ’implantation concernant des géométries simples de deux à quatre lignes ainsi que quelques exemples de configurations géométriques proches de celles utilisées en pratique clinique.

2. MATERIEL ET METHODES

2.1. Règles d ’équivalence et program m e de calcul

La comparaison des distributions de dose autour de trains de sources élémentaires et de sources continuement et uniformément radioactives sur toute leur longueur a été faite pour des sources d ’iridium 192 de diamètre 0,1 mm entourées d ’une gaine de platine d ’épaisseur 0,1 mm.

Les trains de sources sont composés de n sources élémentaires de longueur égale ls, et d ’écartement s entre les centres de deux sources voisines.

Dans le cas d ’implantations comportant deux lignes ou plus, les sources élémentaires ont toujours été considérées comme alignées exactement les unes en face des autres et caractérisées par des activités identiques.

IAEA-SM-298/23 215

'Is

L = n ' s 1 Kn _ Kns

KN = n .k Ns I L s

FIG. 1. Règles d ’équivalence entre une source continue de longueur L et d ’activité totale exprimée en termes de débit de kerma normal KN (ptGy-h'1 -m2) et une source discontinue composée de n sources élémentaires de longueur ls, dont les centres sont espacés de s et dont le débit de kerma normal de chaque source est KNs.

Dans le cadre de cette comparaison avec les sources radioactives continues de longueur L et de débit de kerma normal Kñ (exprimé en /xGy-hf1 -m 2), différents arrangements des sources ont été envisagés tant en nombre de sources (4 à 24) qu’en longueur de chaque source (ponctuelle à 8 mm) et en distance entre les centres dedeux sources voisines (5 à 15 mm) mais en respectant toujours les règlesd’équivalence suivantes (fig. 1):

— même longueur active équivalente des sources continues et des trains de sources (L = n-s);

— même activité totale pour les deux types de sources, soit en termes de débit de kerma normal KN = n-K Ns (KN et KNs représentant respectivement les débits de kerma normal pour les sources continues et pour les trains de sources).

Les divers exemples d ’implantation considérés dans cette étude diffèrent par le nombre, la longueur et la disposition géométrique des lignes radioactives: ils ont tous été définis géométriquement selon les règles du système de Paris [3, 4]. Chaque comparaison a été faite en prenant un débit de kerma normal linéique de 8,72 ¡/.Gy- h '1 •m2'c m '1 pour les sources continues et un temps d ’application de un jour.

La comparaison des distributions de dose a reposé conjointement sur l ’examen des répartitions de dose dans les plans principaux de l’implantation radioactive et sur l’étude des volumes isodoses, exprimées en cm3. Les répartitions de dose et les volumes ont été calculés sur un ordinateur VAX 8600 sur le base d ’un programme de calcul mis au point à l ’Institut Gustave-Roussy par Rosenwald et Dutreix [5] et adapté pour les besoins de la présente étude à la simulation de diverses configurations de trains de sources. Ce programme de calcul tient compte de l ’atténuation par les tissus et de la filtration oblique du rayonnement dans la source et sa gaine.

La correction due à la filtration oblique, surtout importante en bout de source, n ’a pas été prise en compte dans ce travail. Cette hypothèse ne devrait pas, toutefois, modifier fondamentalement les conclusions déduites de cette étude qui concerne

216 BRIDIER et al.

spécifiquement une comparaison des distributions de dose autour de sources continues et discontinues.

Les volumes isodoses sont calculés par sommation de toutes les mailles élémentaires cubiques caractérisées par une dose supérieure ou égale à la valeur de l ’isodose considérée. La dimension de chaque maille a été choisie suffisamment petite ( 2 x 2 x 2 mm3) afin d ’atteindre une précision suffisante en particulier sur les valeurs des volumes des isodoses de forte valeur. L ’emploi d ’une dimension de maille supérieure à cette valeur ne peut que conduire à des résultats inexploitables pour ce type d ’étude.

2.2. C ritères de com paraison

En raison du caractère très hétérogène de la dose à l ’intérieur du volume cible où doit être délivrée la dose prescrite, et de la forme très différente des isodoses, la comparaison des distributions de dose autour des sources discontinues et des sources continues peut difficilement être traduite de manière simple.

Paul et al. [1] ont proposé comme critère de comparaison un index d ’uniformité (U.I.).

Marinello et al. [2] ont basé la comparaison sur l’étude de la variation de la dose à l ’intérieur de l ’application et sur les dimensions des isodoses.

Dans le cadre de cette comparaison, plusieurs critères de comparaison ont été introduits. Ils se réfèrent, d ’une part, à la distribution dose-volume pour traduire spatialement l ’hétérogénéité de la distribution de la dose dans l ’implantation radioactive et, d ’autre part, aux principaux volumes définis dans le système de Paris [3].

Ces volumes sont le volume traité (VT), le volume de surdosage (Vs) et le volume irradié (V^.

Le volume traité est le volume limité par la surface isodose de référence dont la valeur est égale à 85% de la dose de base. La dose de base représente la moyenne arithmétique des doses minimales à l’intérieur du volume de référence.

Le volume de surdosage est le volume englobant tous les points recevant une dose supérieure où égale à deux fois la valeur de la dose de référence. Il donne une évaluation de l’importance de la zone surdosée existant autour des lignes radioactives à l ’intérieur des manchons de surdosage.

A l’extérieur du volume traité, le volume irradié est utilisé pour définir le volume de tissus qui reçoit une dose considérée comme significative pour la tolérance des tissus. La valeur de cette dose est choisie égale à 50% de la dose de référence.

Les critères que nous avons choisis pour la comparaison sont les suivants:— pour chaque dispositif géométrique considéré, le rapport VT/VTcont des

volumes traités avec des sources discontinues et avec des sources continues équivalentes doit être le plus proche de 1. En addition, un «rapport d ’élongation» (lT/eT) qui est le rapport de la longueur à l’épaisseur traitée correspondant aux dimensions minimales de l ’isodose de référence dans les deux plans principaux de

IAEA-SM-298/23 217

PLAN CENTRAL PLAN PP'

м Х Э - р'

p.

I Vc --Sc.h|

h

!><

FIG. 2. Représentation de quelques volumes cibles considérés dans l ’étude.

symétrie de l ’application, a été introduit pour traduire la forme du volume de référence;

— le volume traité doit entourer au plus près le volume cible (Vc), c ’est-à-dire que leur rapport VC/VT doit être le plus proche de 1 ;

— les manchons de surdosage doivent représenter la plus petite fraction du volume traité (VS/VT le plus petit) afin de réaliser la distribution de dose la plus homogène possible à l’intérieur du volume traité;

— et, enfin, le rapport volume irradié sur volume traité (V¡/VT) doit également être le plus proche de 1 afin d’obtenir une irradiation limitée des tissus sains avoisinants le volume cible.

Dans cette étude, le volume cible a été assimilé à une figure géométrique simple dont les côtés sont limités spatialement par la partie la plus rentrante de la surface isodose de valeur égale à la dose de référence. Pour les lignes continues, les dimensions de ce volume géométrique ont été définies, pour chacun des modèles géométriques d ’application considérés, dans deux plans qui sont le plan central principal transverse coupant les lignes radioactives par leur milieu et le plan de symétrie de l ’application perpendiculaire au précédent (fig. 2).

Pour les trains de sources qui présentent des isodoses sinueuses, la section droite du volume cible a été définie comme la moyenne des sections droites, au niveau de la région centrale de l’application, passant respectivement par le milieu des sources élémentaires et à une distance égale à s/2 de ces sources. La hauteur du volume cible a été définie comme pour les sources continues.

3. ETUDE COMPARATIVE DES DISTRIBUTIONS DE DOSE

3.1. Cas d ’une ligne radioactive

Contrairement aux isodoses caractéristiques d’un fil uniformément radioactif qui reste pratiquement parallèle à la source sur les trois quarts de sa longueur, les

218 BRIDIER et al.

2E '£

О

2

s=7,5fi

s =1

d (mm)

5 10 15

FIG. 3. Déviation, dans le plan central, de la position (±e) des isodoses autour d ’un arrangement de sources ponctuelles par rapport aux mêmes isodoses autour d ’une source continue équivalente en longueur active L et en activité totale. La variation de e est représentée en fonction de la valeur des isodoses, identifiées par leur distance d à la source, pour différents écartements s des sources élémentaires et différentes longueurs actives équivalentes des trains de sources.

isodoses autour des trains de sources, caractérisées par une activité totale et une longueur active équivalentes, présentent une sinuosité d ’autant plus marquée qu’elles sont proches des sources avec des maxima et des minima situés respectivement en vis-à-vis des sources et entre celles-ci.

L ’importance des écarts e de position des isodoses entre trains de sources et sources continues a été déterminée pour différentes valeurs d ’isodoses repérées par leur distance d à la ligne continue. Cette détermination a été faite dans le plan transverse central du fil et pour différents arrangements de sources élémentaires. Les isodoses autour des trains de sources sont d ’autant plus sinueuses (e plus grand) que, pour un écartement s donné entre les centres des sources élémentaires, la longueur active des sources élémentaires ls diminue et que les isodoses concernées se trouvent à proximité des sources (d petit). Pour les sources ponctuelles, les écarts e obtenus peuvent atteindre de l ’ordre de 2 mm ou plus à proximité des sources (d voisin de3 à 5 mm) lorsque leur écartement s est supérieur à 10 mm mais, à écartement fixé, la valeur de ces écarts e ne dépend pratiquement pas de la longueur active équivalente L, donc de la longueur des trains de sources (fig. 3).

Au-delà d ’une certaine distance d des sources, égale à l’écartement s des sources, la sinuosité des isodoses disparaît (e tend vers 0) et les isodoses deviennent superposables aux isodoses de même valeur rencontrées autour d ’une ligne radioactive continue.

IAEA-SM-298/23 219

_________ _ _ _ _Jkm ;-------------®------------ f-Z

! ! Icmi ;!, 1 t 6 г m „

FIG. 4. Variation de la dose, seh n l'axe médian d'une implantation de deux lignes parallèles de longueur 6 cm écartées de 1 cm, pour des sources continues et des arrangements de six sources élémentaires de différentes longueurs espacées de 10 mm. Les doses sont normalisées par rapport à la dose de base de l'implantation des sources continues. Les sources continues et les sources discontinues sont équivalentes en longueur active (6 cm) et ont la même activité totale.

3.2. Cas de dispositifs im plantés conform ém ent au système de Paris

3.2.1. Spécification de la dose et arrangements de sources élémentaires utilisables dans le système de ParisL ’implantation de plusieurs trains de sources disposés selon les règles du

système de Paris conduit à une variation de dose hétérogène sur toute la hauteur du volume cible due à l’écartement des sources élémentaires.

L ’importance de cette variation selon l ’axe parallèle aux lignes et équidistant de celles-ci est d ’autant plus marquée que, pour un écartement s des sources élémentaires fixé, leur longueur ls est plus petite (fig. 4).

Il ressort également de la comparaison de la figure 4 , faite en normalisant les doses par rapport à la dose de base de l ’implantation avec des sources continues que,

TABLEAU I. COMPARAISON DES PRINCIPAUX VOLUMES POUR DES SOURCES CONTINUES (cont.) ET POUR DIFFERENTS ARRANGEMENTS DE SOURCES DISCONTINUES (n, ls, s) EQUIVALENTS. CAS D ’UNE IMPLANTATION DE DEUX LIGNES PARALLELES DE LONGUEUR 6 cm ECARTEES DE 1 cm

n s(mm) (mm)

(s - y (mm) DBM

DBm

DBa V T i l Vc ет V t

Vs

vT

V i

V Tn D®cont. VT.com.

4 15 1 3,5 1,80 1,04 0,85 isodose référence 0,22 4,12discontinue

4 15 4 2,75 1,68 1,02 0,89 isodose référence 0,21 3,95discontinue

6 10 1 1,5 1,25 1,015 1,03 11,5 0,84 0,20 3,53

6 10 4 1,0 1,17 1,00 0,98 11,1 0,86 0,20 3,56

6 10 6 0,67 1,10 0,995 1,02 10,3 0,86 0,18 3,62

12 5 1 0,33 1,01 1,00 1,01 9,6 0,84 0,14 3,58

12 5 4 0,08 1,00 1,00 1,01 9,5 0,83 0,18 3,61

Source continue (KN = 52,32 /iGy-h ‘‘ •m2) 1,00 1,00 9,5 0,84 0,19 3,65

a Pour les sources discontinues, DB = (DBm + DBM)/2 (voir texte).

IAEA-SM-298/23 221

pour un arrangement choisi de sources élémentaires, la variation, parallèlement aux lignes, tant des doses maximales DM en vis-à-vis des sources que des doses minimales Dm calculées à la distance s/2 des précédentes, se fait similairement à la variation de dose relative aux sources continues équivalentes et presque symétriquement par rapport à celle-ci. La symétrie est d ’autant mieux réalisée que les sources élémentaires ont une longueur plus grande. En conséquence, la moyenne arithmétique des doses DM et Dm calculées dans la région centrale de l ’application correspond à la dose de base DB des sources continues équivalentes.

Ce résultat, confirmé pour des configurations géométriques plus complexes, justifie la proposition faite par G. Marinello et al. [2] de spécifier les doses pour des sources discontinues à partir de la moyenne arithmétique des doses de base maximale et minimale (DBM + DBm)/2 calculées dans les plans de la région centrale passant respectivement par les sources et à une distance s/2 de celles-ci.

Le remplacement des sources continues par des sources discontinues dans le système de Paris ne peut conduire à des distributions de dose comparables que si les règles d ’équivalence définies au paragraphe 2.1.1 sont respectées. Mais, même si ces critères d ’équivalence sont respectés, l ’arrangement des sources élémentaires, en nombre, longueur et écartement doit être tel que le rapport (s - ls) soit suffisamment petit et inférieur à des valeurs voisines de 5 mm. Par exemple, des sources discontinues comportant un trop petit nombre de sources (n = 4) trop espacées (s = 15 mm) conduisent à une isodose de référence discontinue et donc à un traitement incorrect du volume cible (tableau I).

3.2.2. Cas des dispositifs géométriques simples

L ’étude comparative des distributions de dose entre des sources continues et des sources discontinues a été faite sur plusieurs dispositifs simples comportant deux lignes parallèles, trois lignes en triangle et quatre lignes en carré (tableaux I et II; fig. 5).

A l ’exclusion des arrangements de sources ne répondant pas aux conditions géométriques définies précédemment (cas des arrangements n = 4, s = 15 mm pour 1, = 1 ou 4 mm et n = 6, s = 10 mm pour ls = 1 mm), les différents arrangements choisis conduisent, par rapport aux sources continues équivalentes, à une dose de base identique, à un volume traité (en cm 3) et à un volume irradié ( V [ / V T

analogues) très similaires. D ’autre part, les répartitions des doses relatives aux doses inférieures à la dose de référence sont pratiquement confondues (distributions volume-dose identiques) (fig. 5). Il apparaît toutefois que, pour une géométrie donnée (plan, carré, etc.), les plus petites longueurs actives ls entraînent, à s constant, pour la plupart des arrangements de sources considérés, une irradiation du volume cible plus homogène puisque tous les volumes englobés par une isodose de valeur donnée supérieure à la dose de référence sont plus petits que ceux correspondants pour les sources continues. Ce résultat est quantifié par une valeur plus petite du rapport V S/ V T .

TABLEAU II. COMPARAISON DES PRINCIPAUX VOLUMES POUR DES SOURCES CONTINUES (cont.) ET POUR DES SOURCES DISCONTINUES EQUIVALENTES COMPOSEES DE 6 SOURCES ELEMENTAIRES ESPACEES DE 10 mm ET DE DIFFERENTES LONGUEURS ls. CAS D ’IMPLANTATIONS EN CARRE ET EN TRIANGLE

Dispositif lsDBMDBm

DBa

DBCOM.

VT

Vt.COIU.i leT

VçVT

v s

VT

V.

VT

Carré 1 1,07 1,01 0,95 3,00 0,82 0,11 2,75(4 lignes) 4 1,04 1,00 0,97 2,90 0,80 0,13 2,71

6 1,03 1,01 0,99 2,85 0,80 0,15 2,66

cont.b - 1,00 1,00 2,75 0,79 0,20 2,65

Triangle l 1,15 1,00 0,92 3,70 0,79 0,14 2,99(3 lignes) 4 1,12 1,00 0,99 3,50 0,79 0,13 3,03

6 1,08 1,00 0,98 3,45 0,78 0,15 3,01

cont.b — 1,00 1,00 3,25 ' 0,77 0,18 3,23

a Pour les sources discontinues, DB = (DBm + DBM)/2 (voir texte). b Source continue.

BRIDIER et al.

IAEA-SM-298/23 223

FIG. 5. Comparaison des distributions volume-dose pour une implantation en carré conforme au système de Paris (4 lignes de longueur 6 cm écartées de 1 cm) entre des sources continues et des sources discontinues composées de 6 sources élémentaires espacées de 10 mm de longueur respective 1 mm et 4 mm. Les sources continues et discontinues sont équivalentes en longueur active (6 cm) et ont la même activité totale. Les doses sont exprimées en fonction de la dose de référence relative à chaque dispositif.

De même, pour un dispositif donné, bien que le volume cible représente pratiquement la même fraction du volume traité (VC/VT constant) quel que soit l’arrangement de sources considéré, les arrangements composés, à s constant, de sources de plus petites longueurs ls, donnent un volume traité plus allongé dans la direction parallèle aux sources (valeur plus grande du rapport lT/er). La différence de hauteur traitée entre des sources de 1 mm et des sources continues représente, pour l’ensemble des dispositifs, en moyenne 4 mm (tableaux I, II et fig. 4). Pour les mêmes conditions, bien que l’épaisseur traitée ait en moyenne une valeur identique à 1 mm près, la périphérie latérale du volume cible est irradiée à une dose moins uniforme avec les petites longueurs de sources ls en raison de la sinuosité des isodoses (fig. 5).

TABLEAU III. COMPARAISON DES PRINCIPAUX VOLUMES POUR DES SOURCES CONTINUES (cont.) ET POUR DES SOURCES DISCONTINUES COMPOSEES DE SOURCES ELEMENTAIRES DE LONGUEUR 4 mm ESPACEES DE 10 mm EQUIVALENTES EN LONGUEUR ACTIVE ET EN ACTIVITE TOTALE2. CAS DE DIVERS DISPOSITIFS PROCHES DE CEUX UTILISES EN PRATIQUE CLINIQUE

Dispositif Type de sourceVT lx

ejVçVT

Vs

vT

V.VT

vTb

VTУт,сот.

4 lignes en plan 6 sources/ligne .... 0,99 8,50 0,83 0,12 3,67 1,00(L = 6 cm; E = 1 cm) continue ............... 1,00 8,10 0,85 0,13 3,67 0,99

4 lignes en losange 7 sources/ligne .... 1,00 3,10 0,77 0,10 2,91 1,02(L = 7 cm; R = 1,2 cm) continue ............... 1,00 3,05 0,78 0,08 2,93 1,02

5 lignes en triangle 5 sources/ligne .... 1,00 2,75 0,84 0,09 2,80 1,02(L = 5 cm; E = 1,2 cm) continue ............... 1,00 2,50 0,85 0,09 2,83 1,02

6 lignes en carré 5 sources/ligne .... 1,00 1,75 0,77 0,09 2,66 1,02(L = 5 cm; E = 1,2 cm) continue ............... 1,00 1,80 0,76 0,09 2,68 1,02

7 lignes en hexagone 4 sources/ligne .... 1,02 1,30 0,83 0,06 2,56 0,98(L = 4 cm; E = 1,2 cm) continue ............... 1,00 1,20 0,80 0,07 2,63 1,01

* 52,32 /iG y h - '-m 2.b VT est le volume traité donné par la relation empirique (voir texte au paragraphe 3).

224 BRIDIER

et al.

IAEA-SM-298/23 225

L ’utilisation de petites longueurs de sources peut, pour certains écartements s, conduire à sous-doser une partie du volume cible située en regard des extrémités des lignes radioactives. A titre d ’exemple, deux lignes radioactives parallèles de 6 cm de longueur, espacées de 1 cm et formées chacune de six sources élémentaires de 1 mm espacées de 10 mm conduisent à sous-doser de 3% un volume représentant environ 1% du volume traité (fig. 4).

3.2.3. Cas des configurations géométriques proches de celles utilisées en pratique clinique

Divers dispositifs géométriques (plan, triangle, carré, hexagone et losange) conformes aux règles du système de Paris ont été utilisés pour cette comparaison (tableau III). Dans tous ces dispositifs, les sources discontinues fournissent une distribution des doses et une répartition volume-dose très similaires de celles relatives à des sources continues équivalentes (tableau III et fig. 6). La quasi égalité des rapports VT/VT,con„ VC/VT, V]/VT et Vs/Vx confirme ce résultat. En effet, le gain sur l ’uniformité de la dose produit à l ’intérieur du volume cible par l ’emploi de sources discontinues se réduit lorsque le dispositif géométrique devient plus complexe et, en particulier, lorsque le nombre de lignes radioactives augmente.

4. RELATION EMPIRIQUE DONNANT LE VOLUME TRAITE ENFONCTION DES PARAMETRES GEOMETRIQUES DEL ’IMPLANTATION. APPLICATION AUX SOURCES DISCONTINUES

La surface isodose de référence, entourant le volume traité VT, peut être assimilée schématiquement à la juxtaposition de «cigares» allongés centrés sur les lignes radioactives et pratiquement cylindriques sur les trois quarts de la longueur des lignes.

Sur cette base et en assimilant chaque «cigare» à un cylindre de hauteur égale à la longueur du fil radioactif et de diamètre proportionnel à l’écartement des lignes (E), le volume traité peut être, en première approximation, exprimé proportionnellement au nombre de lignes (N), à la longueur des lignes (L) et au carré de leur écartement (E):

V t (cm3) = k - N - E 2-L (1)

Les valeurs proposées pour le coefficient de proportionnalité k ont été déduitesd ’une évaluation systématique, par ordinateur, des volumes traités. Elles résultent,d ’une part, des résultats d ’une étude précédente sur 59 dispositifs géométriques [6] et, d ’autre part, de la présente étude.

Les valeurs de k sont:— 0,47 pour les dispositifs en plans et triangles;— 0,57 pour les dispositifs en carrés.

226 BRIDIER et al.

FIG. 6. Comparaison des distributions volume-dose pour deux exemples d'implantation (6 lignes en carré et 7 lignes en hexagone) conformes au système de Paris, entre des sources continues et des sources discontinues composées de n sources élémentaires de longueur 4 mm et écartées de 10 mm. Les sources continues et discontinues sont équivalentes en longueur active et ont la même activité totale. Les doses sont exprimées en fonction de la dose de référence relative à chaque dispositif.

Compte tenu des conclusions de l ’étude comparative des distributions de doses, la relation précédente, établie pour des sources continues, peut s’appliquer avec un bon accord aux dispositifs formés de sources discontinues sous réserve^ toutefois, que ces dernières respectent les conditions se rapportant à leur application dans le système de Paris et définies précédemment (tableau III).

L ’étude quantitative des volumes montre également que le volume irradié (VO correspond pour l’ensemble des dispositifs étudiés à environ trois fois le volume traité (VT) et que son importance par rapport au volume traité dépend plus précisé

IAEA-SM-298/23 227

ment de la disposition géométrique des lignes. Le rapport Vi/VT est en moyenne égal à 3,6 pour les dispositifs en plans, à 2,9 pour les dispositifs en triangles et tend vers 2,7 pour les dispositifs en carré et ceux comportant un grand nombre de lignes.

5. CONCLUSION

Lorsque les sources discontinues composées de n sources élémentaires, de longueur ls et d ’écartement s entre leurs centres respectent les règles d ’équivalence en longueur active et en activité totale et ont un arrangement de sources élémentaires caractérisé par (s - ls) inférieur à une valeur voisine de 5 mm, leurs distributions de dose sont comparables, pour des implantations conformes au système de Paris, à celles produites par des sources continues équivalentes et implantées selon la même disposition géométrique.

La superposition des distributions volume-dose et des distributions de dose est d ’autant meilleure que, à dispositif géométrique fixé, le nombre de sources élémentaires et leur longueur sont plus grands et leur écartement plus petit et que, à arrangement donné des sources, le nombre de lignes radioactives est plus grand.

Sous respect des conditions précédentes, et pour un dispositif donné, la dose de base définie par la moyenne arithmétique des doses de base minimale et maximale ainsi que les volumes traité, irradié et de surdosage sont pratiquement égaux à ceux relatifs au même dispositif formé de sources continues équivalentes. Les sources discontinues répondant à ces conditions peuvent être utilisées dans le système de Paris et avoir leurs distributions de dose décrites selon les mêmes relations que pour les sources continues.

L ’emploi de sources élémentaires de petite longueur par rapport à leur écartement (par exemple sources de 1 mm espacées de 10 mm) conduit, comparativement aux sources continues équivalentes, à une distribution de dose identique à l’extérieur du volume traité, mais généralement à une irradiation plus homogène à l’intérieur de celui-ci (VS/VT plus petit). Avec ce modèle d ’arrangement de sources, le volume traité est légèrement plus petit avec, toutefois, une irradiation plus homogène de la région située entre les extrémités des lignes et une uniformité de la dose relativement moins bonne en périphérie du volume cible selon une direction parallèle aux lignes.

REFERENCES

[1] PAUL, J.M., KOCH, R.F., PHILIP, P.C., KHAN, F.R., Comparison between continuous and discrete sources in interstitial brachytherapy, Session on Brachytherapy, American Association of Physicists in Medicine, Med. Phys. 11 (1985).

[2] MARINELLO, G., VALERO, M., LEUNG, S., PIERQUIN, B., Comparative dosimetry between iridium wires and seed ribbons, Int. J. Rad. Oncol., Biol. Phys. 11 (1985) 1733.

[3] DUTREIX, A., MARINELLO, G., WAMBERSIE, A., Dosimétrie en curiethérapie, Collection Bases de la radiothérapie, de la radiobiologie et de la radioprotection, Masson, Paris (1982).

BRIDIER et al.

DUTREIX, A., MARINELLO, G., «The Paris System», Modem Brachytherapy (PIERQU1N, B., WILSON, J.F., CHASSAGNE, D., dir. publ.), Masson Publishing, New York (1987) 25.ROSENWALD, J.C., DUTREIX, A., Etude d’un programme sur ordinateur pour le calcul des doses en curiethérapie gynécologique, J. Radiol. Electrol. 51 (1970) 651.BRIDIER, A ., et al., «Etude quantitative des volumes isodoses caractéristiques des implantations radioactives réalisées en curiethérapie interstitielle: Application à la recherche de l’optimisation de la géométrie de l’implantation», Actes XXIIe Congrès de la Société française des physiciens d’hôpital, Versailles (1983) 165.

IAEA-SM-298/26

D O S IM E T R IE DES SOURCES SO LID ES D ’IO D E 125 M O D E LE 6711

J.R. ISTURIZ PINEDA Centre G .-F.-Ledere,Dijon

A. DUTREIX Unité de radiophysique,Institut Gustave-Roussy,Villejuif

France

Abstract-Résumé

DOSIMETRY FOR MODEL 6711IODINE-125 SOLID SOURCES.The physical specifications of model 6711 I2SI sources manufactured by the 3M company

are given and an algorithm is then described for the dosimetric calculation in the surrounding water. The function <Ï>(R) for absorption and scattering in the water is determined by thermoluminescence using an original method which makes it possible to approximate the mean energy in the water at the same time. The constant kerma rate in air is calculated using spectrometric data and taking into account silver and titanium fluorescence lines. The isodoses calculated by computer using the algorithm are compared to those obtained using photo densitometry and to published data. The isodoses for three sources and for different source distances are given, as are the coefficients needed to use the table of results.

DOSIMETRIE DES SOURCES SOLIDES D’IODE 125 MODELE 6711.Après présentation des spécifications physiques des sources d’iode 125 modèle 6711

fabriquées par la société 3M, on décrit un algorithme perm ettant le calcul dosimétrique dans l’eau autour de celles-ci. La fonction d’absorption et de diffusion dans l’eau, appelée fonction 4>(R), est déterminée par thermoluminescence selon une méthode originale perm ettant en même temps une approche de l’énergie moyenne dans l’eau. La constante de débit de kerma dans l’air est calculée à partir des données spectrométriques en tenant compte de la présence des raies de fluorescence de l’argent et du titane. Les isodoses calculées par ordinateur à partir de notre algorithme sont comparées aux résultats obtenus par photodensitométrie et aux données publiées. On donne les isodoses obtenues pour trois sources pour des écartements divers ainsi que les coefficients nécessaires à l’utilisation du tableau de résultats.

1. CARACTERISTIQUES PHYSIQUES DES SOURCES

Les sources solides d’iode 125 modèle 6711 sont constituées d ’un cylindre d’argent massif sur lequel est déposée une résine d ’iode 125 (fig. 1 ). L’ensemble est contenu dans un cylindre creux de titane de 0,05 mm d ’épaisseur et de 1,6 mm de diamètre extérieur.

229

230 ISTURIZ PINEDA et DUTREIX

C y lin d re d ’ A g0 ,0 5 m m T i

0,8 mm (ш ш5 m m

,O m m __ 4 ,5 m m _

1

FIG. 1. Source d ’iode 125 modèle 6711.

FIG. 2. Vue d 'une source d ’iode 125 (6711).T: épaisseur de titane; T ': diam ètre du cylindre d ’argent; L: longueur active de la source.

S 1

FIG. 3. Coupe axiale d ’une source d ’iode 125.S 3: couronne d ’iode 125 déposée sur le cylindre d ’argent m assif (constante); S \ + S i : partie de la couronne d ’iode 125 vue par le po in t P (S \: constante; S 2 : variable fo n c tio n de x);S 2 = 2 -n ■ c o s '1 (ro/(rt + x )}-(r i2 - ro2), avec: ro: rayon du cylindre d ’argent; rs: rayon m oyen du cylindre d ’iode; ri: rayon interne de la paroi de Ti; rt: rayon de la source.

IAEA-SM-298/26 231

Le cylindre d ’argent massif perm et le repérage radiographique des sources dans l’espace et, en conséquence, une meilleure précision dans le calcul de la dose autour de celles-ci.

2. ALGORITHME MATHEMATIQUE

Nous avons étudié un algorithme qui tient com pte de la présence du cylindre d’argent et de la gaine de titane. Le débit de dose dans l’air en un point P (fig. 2 et 3) à une distance x de la surface d ’une source d ’activité At et de longueur active L est donné par:

D = À + B = 1,03 À (1)

ou:

À est le débit de dose dû à l’iode 125 vu par P, tel que

N 02

À = r V b N ’ E XF(T) ’ / e "MT/COS0d0 i = 1 0 i

B est le débit de dose au même point dû à l’iode 125 derrière le cylindre d ’argent, tel que

M 04

ô = r v r ^ I x ( 1 - F ( 7 ) ) ‘ / е "/Л7со50dei = l 03

F(7 ) est la fonction qui perm et de calculer la fraction d’iode vue par le point P, (1 - F (7 )) est la fonction qui perm et de calculer la fraction d ’iode cachée derrière le cylindre d’argent.N et M sont le nom bre de sources élémentaires.

On a

F (7) = (S, + S2)/S 3

et

( 1 - F ( 7 ) ) = ( S 3 - ( S 1 + S 2 ) ) / S 3

Sj et S3 étant constantes et S2 fonction de x.

232 ISTURIZ PINEDA et DUTREIX

On aura ainsi:

F (7 ) = 0,464 pour x = 0 et F (7 ) = 0,671 pour x = 10 mm.

Après calcul par ordinateur, on dém ontre que le rapport des débits de dose À/В est pratiquem ent constant et égal à 1,03. Ceci perm et la simplification des calculs m ontrée en (1).

3. DETERMINATION DE LA FONCTION D’ABSORPTION ET DIFFUSIONDANS L’EAU Ф(Ю

La fonction d ’absorption et diffusion dans l’eau <ï>(R) a été déterm inée par thermoluminescence à l’aide du borate de lithium en poudre étalonné au préalable entre 7 et 34 keV. Les mesures ont été réalisées dans l’air et dans l ’eau avec un dispositif perm ettant la reproductibilité du positionnem ent des cylindres de borate et de la source aussi bien dans l’air que dans l’eau. On a fait tourner la source et les cylindres de borate pendant toutes les mesures, perm ettant ainsi de s’affranchir des problèmes d ’hétérogénéité liés à la source d’une part et à l’irradiation hétérogène des cylindres de borate d ’autre part.

La meilleure approche de <£>(R) est donnée par un polynôme du 5e degré:

$ (R ) = 1,15 - 0,3316 R + 0,05 R2 - 0,0021 R3 - 0,00013 R4 + 0,00001 R 5

4. VALEURS UTILISEES POUR NOS CALCULS

L’activité contenue dans une source d’iode 125 modèle 6711 à été calculée à partir de notre algorithme de calcul. Elle est égale à 1,70 fois l’activité apparente mesurée dans une chambre puits.

FIG. 4. Courbes d ’isodose en unités arbitraires obtenues par ordinateur superposées au film dosimétrique.

IAEA-SM-298/26 233

FIG. 5. Dosimétrie de trois sources coplanaires e t parallèles pour des écartem ents allant de 6â 20 mm. Isovaleurs: 100, 80, 50, 30, 20, 15, 10, 8, 5, 3, 1, 0,5.

La valeur utilisée pour la constante de débit de kerma dans l’air (Г 5) est0,041 jiG y-m 2/M Bq-h (constante de débit d ’exposition: (Г5 ) = 1,75 R- c m2/mCi-h).

L’énergie m oyenne mesurée par spectrom étrie est de 27,2 keV com pte tenu de la présence des raies de fluorescence de l’argent et du titane.

TABLEAU I. DOSES EN cG y/h DANS L’EAU AUTOUR D ’UNE SOURCE D ’IODE 125 MODELE 6711 DE 37 MBq (1 mCi) D’ACTIVITE APPARENTE

U>-P*

Distance au long de l’axe (cm)

Distance transverse au centre de la source

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

0,0 — 5,992 1,321 0,514 0,255 0,146 0,092 0,062 0,045 0,033 0,026

0,5 0,548 2,703 1,001 0,448 0,235 0,138 0,088 0,060 0,044 0,033 0,026

1,0 0,015 0,827 0,546 0,316 0,188 0,119 0,079 0,056 0,041 0,031 0,025

1,5 0,001 0,313 0,284 0,203 0,138 0,095 0,067 0,049 0,037 0,029 0,024

2,0 0,000 0,140 0,155 0,128 0,098 0,073 0,055 0,042 0,033 0,027 0,022

2,5 0,000 0,071 0,090 0,083 0,069 0,056 0,044 0,036 0,029 0,024 0,020

3,0 0,000 0,039 0,056 0,055 0,050 0,042 0,036 0,030 0,025 0,021 0,018

3,5 0,000 0,023 0,036 0,039 0,036 0,033 0,029 0,025 0,021 0,019 0,016

4,0 0,000 0,014 0,025 0,028 0,027 0,026 0,023 0,021 0,018 0,016 0,015

4,5 0,000 0,009 0,018 0,021 0,021 0,020 0,019 0,017 0,016 0,014 0,013

5,0 0,000 0,006 0,013 0,016 0,017 0,017 0,016 0,015 0,014 0,013 0,012

PINEDA et D

UTREIX

IAEA-SM-298/26 235

Les courbes d’isodoses obtenues par ordinateur sont comparées aux courbes obtenues par photodensitom étrie par film (fig. 4).

Nos calculs sont comparés à ceux fournis dans la littérature par Scallon [1 ], Bassil [2] et Krishnaswamy [3 ,4].

Nous m ontrons (fig. 5) la dosimétrie en unités arbitraires de trois sources coplanaires et parallèles pour des écartements de 6 à 20 mm.

Sur le tableau I, nous m ontrons les résultats en cGy/h dans l’eau obtenues pour une source de 37 MBq (1 mCi) d ’activité apparente.

5. RESULTATS

REFERENCES

[1] SCALLON, J.E., et al., Am. J. Roentgenol. 105 (1969) 157-164.[2] BASSIL, S., et al., The Use of 125I for Interstitial Implants, U.S. Department of Health,

Education and Welfare, Public Health Service, New York (1975).[3] KRISHNASWAMY, V., Dose distribution around an 12SI seed source in tissue,

Radiology 126 2 (1978).[4] KRISHNASWAMY, V., Dose tables for 125I seed implants, Radiology 1 3 2 3 (1979).

IAEA-SM-298/41

C H A R A C T E R IZ A T IO N O F 137Cs LO W DOSE R A TE SOURCES FO R B R A C H Y TH E R A P Y AN D DOSE A L G O R IT H M V E R IF IC A T IO N

A.M . DI NALLO, L. BEGNOZZI, V. PANICHELLI,M. BENASSIMedical Physics and Expert Systems Laboratory,Regina Elena Institute,Rome

G.A. LO VISOLODivision of Physics and Biomedical Sciences,CRE Casaccia,ENEA,Rome

Italy

A bstract

CHARACTERIZATION OF 137Cs LOW DOSE RATE SOURCES FOR BRACHYTHERAPY AND DOSE ALGORITHM VERIFICATION.

To achieve brachythrapy efficiency in the clinical routine, some quality assurance procedures have been developed to control the dose distribution algorithm and the nominal parameters of 137Cs low dose rate sources. Experimental methods, based on the dose measurements in air, in water and in perspex phantom by means of TLDs 100 LiF and an ionization chamber, are described. The source characterization is obtained by means of an optimization process to evaluate a physical parameter involved in the theoretical algorithm, and the dose measurement in a well defined point.

1. INTRODUCTION

Radiotherapy efficiency can be improved by introducing quality assurance measures into the daily clinical practice. This efficiency is reduced by the fact that many procedures proposed for this purpose often are too time consuming to be routinely applied.

Therefore, to achieve a good accuracy in evaluating the dose distribution in patients, the most important aim is to provide procedures which are practical, unsophisticated and easy to apply under clinical routine conditions.

The dose calculations are usually made using semi- empirical algorithms and nominal parameters of the

237

238 Di NALLO et al.

sources; these may significantly vary from the real ones.

In the present report, we have described the procedures adopted to achieve the following aims:(a) To performe quality assurance control of the

algorithm of dose calculation by means of dose measurements in air, in water and in a water- equivalent perspex phantom, using two different methods,TLD and ionization chamber, and by means of mathematical optimisation of the physical parameter involved in the calculation.

(b) To perform characterisation of the source by verifying the source nominal activity by means of dose measurement with the ionisation chamber in a well defined point.

(c) To provide the dose measured to characterize the sources used in brachytherapy, as recommended in the literature.

(d) To provide good localization of the source within a patient and good knowledge of the critical organ locations, using radiographic technique and spatial reconstruction software.

2. MATERIAL AND METHODS

Verification of the coherence of the doses calculated and measured was made using a Cs 137 source with a total activity of 112 mCi (4.1 GBq> and a total nominal length of 56 mm. The source was made up of seven active elements; each of which having a length of 1 . 6 mm and diameter of 0 . 8 mm, was closed by an inactive ball and had three inactive steel balls 1.54 mm in diameter,all contained in a flexible steel wire.

The dosimetric systems employed were the following:(1) Thermoluminescent dosimeters LiF(TLD-100) and aHarshaw 2000A, 2000B reader for measurements inair and in perspex phantom.(2) A PR05 ionization chamber with a sensitive volume of 0.07 ml and with walls of 220 mg/cif? thickness, and an exposure rate meter Capiritec for measurements in air and in water.

The TLDs and the ionization chamber were calibrated on the same known Co 60 beam. The dosimetric measurements were made in a direction orthogonal to the longitudinal axis of the source, passing through its centre, at distances of 2, 4, ó, 8 and 10 cm using TLDs and at distances of only 2 and

IAEA-SM-298/41 239

active length

- a .................- . . a ---------------- -a Off S e tА В С

I----- 1i cm

FIG. 1. Measurement points scheme.

FIG. 2. Experimental device fo r measurements in air with thermoluminescent dosimeters.

4 cm using the chamber, because of the low exposure rate at greater distances.

Further measurements were made in air, in points А, В, С of Fig.l, in a direction parallel to the orthogonal axis of the source at a distance of 2 cm from the source within the bounds of the active length, that is the region of clinical interest, as considered in the literature [lj .

The TLDs were exposed in air, closed within a small perspex container of 1 mm thickness and to

240 Di NALLO et al.

reduce the scatter ta a minimum (Fig, 2) were placed an a mylar plane of approximately 0 , 1 mm thickness supported by a thin perspex frame.

In phantom, the TLDs were placed at the same distances, from the centre of the source as used in the measurements in air, but with a perspex thickness which was equivalent to that in water, analogously to the techniques used for the calibration of external beams in different phantom materials [2] . Thethickness of the perspex, equivalent to that of water, was established by means of the following formula [3,4]:

Д wdp = ------ ==----- * dw

/ J p

where dp, JU p and dw,yUw are the thickness and the coefficient of the average linear attenuation of perspex and water, respectively.

The two theoretical algorithms are performed by software in FORTRAN IV language which work, on a PDF 11/34- computer. The first one reconstructs the spatial coordinates of the source from two orthogonal radiograph projections.

From randomly digitised points from the two images, firstly, the software reconstructs a spatial distribution of points.

Then, it performes a spatial fitting, providing the source position with 1 mm accuracy, The second algorithm of dose calculation is based on the following hypotheses:

(1) The active elements are point-like sources;

(2) The self-absorption of the source itself and the absorption in the steel wire which contains the source are negligible;

(3) The attenuation of the steel capsule which contains the radioactive element, and the attenuation of the alternated inactive steel spheres are : evaluated for each position.

With these assumptions, the dose of the small mass of water ¿1 m around point "P", is obtained by the expression:

Dose <Jm,P ) = Г* f *2? ~ * e x p (-¿Lds, >*g(dt.) w i =l r i s 1 - 1

while the dose in the same mass m around point "P" in air is obtained by the equation:

IAEA-SM-298/41 241

Dose ( jm,P) ~Г* f *2 ^ 1 * e xp ( - /J c ds. ) (1 )air i=1 t ? s 1

where

Г= 3.32 L R * h V m C i 1 «cm2 3 :

is the gamma specific constant for the Cs 137 source f = 0.966 is the rad/roentgen factor for water;ft(i) is the activity of the "i" point source ; r^ is the distance of the "i" point source from point "P"; ;AJs is the coefficient of linear , attenuation ofthe steel ;dsi is the sum of the radiation paths in thesteel capsule and in the alternated spheres;dti = rj- ds^ is the actual path in water;g(dtj ) = ft + Bdtj + C + D d t . 3 is thepolynomial of Meisberger M ,with ft = 1.0091 к 10° , В = -9.015 x 10

С = -3.459 x 104 , D = -2.817 x 105ft software written in Fortran IV was purposely

designed to estimate the value ofAJs which produces the best fitting of the values of measured doses in air and the values calculated with E q . (1),respectively, normalised to the value at a point at a distance of 2 cm from the centre of the source.

The fitting is obtained by applying mathematical methods of non-linear optimization .

3. RESULTS ;I

Figures 3 and 4 are graphs showing the experimental data of dose rates.; The data are normalised at the value obtained at 2 cm on the axis passing through the centre of the source, with the TLDs in air and in perspex, respectively,and the curve of the theoretical dose rate in air and in water. The experimental standard deviation values are less than + 2 .8%.

The good agreement between the measured and the calculated values, in air and in phantom, was reached utilising the value^Js= 0.047 mm 1 for the coefficient of linear attenuation of the steel , obtained by the fitting of the experimental data in a i r . I

Table I shows the values measured at 2 and 4 cm from the centre of the source with TLDs and the

242 Di NALLO et al.

• / -KD ( c G y • h )

FIG. 3. Graph o f the dose rate D (cGy h ') in a i r ---------- : theoretical and я , + ; experimental;norm alized to the value a t 2 cm from the source centre .

ionization chamber, respectively, in air and in water or water-equivalent phantom.

The values measured in air with the ionization chamber are higher than the corresponding values measured with TLDs, even though these differences are in the range of the estimated exper¿mental errors. The overestimation of the measurements w¿th the ionization chamber ¿n air, as compared with those c a n n e d out with TLDs, can probably be attributed to the finite dimensions of the chamber and to the strong field gradient existing around the source, which crosses the chamber monodirectionally. The wall of the chamber, close to the source, is therefore closer than the TLD, so that it may be hypothesized that the effective point of measurement is closer to the source than the geometrical one establ¿shed by the centre of the chamber ¿tself.

At 4 cm this effect is less evident than at 2 cm, because the gradient is lower. The phenomenon cannot

IAEA-SM-298/41 243

D ( c G y • h ' 1 )

FIG. 4. Graph o f the dose rate D (cGy-h ') in water equivalent perspex --------------- : theoretical and■ : experimental; normalized to the value at 2 cm from the source centre.

T a b l e I . D o s e r a t e m e a s u r e d i n a i r a n d i n

w a t e r o r p e r s p e x w i t h i o n i z a t i o n

c h a m b e r a n d w i t h T L D .

D O S E R A T E ( c G y • h - 1 )

A I R W A T E R P E R S P E X

c m C h a m b e r T L D C h a m b e r T L D

2 5 7 . 4 1 Í 1.996 5 6 . 3 4 Í 1 . 7 9 6 5 5 . 7 7 Í 1. 1 96 5 6 . 0 4 Í 2 . 6 %

4 1 8 . 6 9 i 1 . 7 9 6 1 8 . 1 8 i 2 . 3 9 6 1 7 . 9 + 2 . 8 % 1 8 . 0 0 + 2 . 6 %

244 Di NALLO et al.

be observed in water, because the effect caused by the strong gradient could be masked by the presence of the scattered radiation.

4. DISCUSSION

The method of dose measurement in air with TLDs combined with mathematical procedures of optimization permits evaluating the value of /J s. The value of this parameter, as revealed in the literature [3,7] , varies between 0.022 mm and 0.057 mm

The utilization in our software of the extreme values, would have introduced a dose evaluationuncertainty that, relative to the position, varies from 1 to 4%.

Our evaluation of Д1 s permits to achieve therequired accuracy in dose calculation. The use ofnormalized values in the process of optimization, eliminates the uncertainty on sources activity,

Being confident of the algorithm accuracy, the comparison of the theoretical dose value with the measured dose value at a well defined point, allows a characterization of the source eliminating the uncertainty on the activity.

The value of the parameter may also beestablished from the data of the measurements carried out in phantom, using in the optimization software the algorithm which expresses the theoretical dose in water. '

In this case, however, the algorithm contains the polynomial of Meisberger whose coefficients are already the result of an optimization .

The use of the ionization chamber is suitable for measuring doses in air and in water for brachytherapeutic sources with a great activity and in points that are not close to the source itself,

Therefore, the procedures illustrated, together with the accurate reconstruction of the source position, are suitable to achieve a good control of treatments in brachytherapy.

REFERENCES

[l] JAYARAMftN S . , LANZL L.H., AGARWAL S.K., An overview of errors in line source dosimetry for gamma-ray brachytherapy,Med. Phys. 10 6(1983) 871.

IAEA-SM-298/41 245

ALMOND P. R., Й comparison of X-ray dose calibration using different phantom materials, Radiother. Oncol. (1985) 319.

HUBBELL -J. H. Photon Cross Sections,Attenuation Coefficients and EnergyAbsorption Coefficients from 10 keV to 100 GeV, NBS report N. 8681. (1966).

MEREDITH W. .J., GREEN D., and KAWA5MIMA K.,The attenuation and scattering in a phantom of gamma rays from some radionuclides used in mould and interstitial gamma ray therapy, Br.J. Radiol.39 (1966) 280.

MEISBERGER L. L., KELLER R. J., and SHALEl< R. .J, , The effective attenuation in water of the gamma rays of goId-198, iridium-192, cesium-137,radium-226 and cobalt-60, Radiology 90 (1968) 953.

MARQUARDT D., An algorithm of least-squares estimation of nonlinear parameters, J . Soc. Industr, Appl. Math 11, (1963) 431.

CASSEL К. J . A fundamental approach to the design of a dose_rate calculation program for use in brachytherapy planning , B r . -J. Radiol. 56 (1983) 113.

IAEA-SM-298/37

C L IN IC A L D O S IM E TR Y O F B R A C H Y TH E R A P Y SOURCES IN TISSU E E Q U IV A LE N T P H A N TO M

G. ARCOVITO, A. PIERMATTEI, F. ANDREASI BASSI Institute of Physics,Catholic University Medical School,Rome

C. BACCIDepartment of Physics,“ La Sapienza” University,Rome

Italy

A bstract

CLINICAL DOSIMETRY OF BRACHYTHERAPY SOURCES IN TISSUE EQUIVALENT PHANTOM.

The dosimetry of 125I seeds (mod. 6711, supplied by 3M) used in interstitial brachytherapy treatments is discussed. Measurement results show that the dose rate per unit activity at 1 cm from the source centre in muscle equivalent tissue (0.89 ± 0.04 Gy-m2-s4 -Bq"1 x 10'17) differs by about 14% from the value (1.02 ± 0.05 G y-m ^s-1 -Bq'1 x 10“17) obtained from lucite measurements currently used. Dose distributions were measured around each seed in perspex and equations fitting experimental data as a function of both the angle around and the distance from the source centre were determined. The responses of four different cylindrical ionization chambers placed at distances ranging between 1 cm and 10 cm from the centre of an l92Ir high activity (740 GBq maximum activity) point source (2 mm in diameter and 1 mm in height), used in intracavitary treatments, were also studied. As expected, the experimental results differ from dose rate measurements made by means of TLDs at distances shorter than 3 cm from the source centre. These differences can reach values of about 15% at 1 cm distance. A modification of the cavity Bragg-Gray formulation is analysed in order to use ionization chambers in high dose gradients. Experimental results of both l25I seed dosimetry and the study of ionization chamber responses used in proximity of a high activity brachytherapy source show a great number of specific dosimetric problems arising in brachytherapy dosimetry, emphasizing the necessity of protocols like that used in absorbed dose determination from high energy photon beams in radiotherapy.

1. INTRODUCTION

I n th e l a s t decade , r a d i a t i o n s o u r c e s c o n s t i t u t e d by d i f f e r e n t a r t i f i c i a l r a d i o i s o t o p e s u b s t i t u t e s o f ee6,Ra have been used more and more i n b r a c h y t h e r a p y t r e a t m e n t s . As an exam p le : low e n e rg y and low a c t i v i t y

247

248 ARCOVITO et al.

i d = 1 seec|s used i n permanent i n t e r s t i t i a l b r a c h y t h e r a py i m p l a n t s , as w e l l as h i g h m i n i a t u r e c u r i e - s i z e d 1<st2I r , i a '7Cs and fc°Co s o u rc e s i n re m o te a f t e r l o a d i n g r a d i o t h e r a p y .

M o re o v e r , some re m o te a - f t e r l o a d in g s y s te m s , ejq. t h e D u c h le r s y s te m , use -few h ig h a c t i v i t y s o u r c e s ( o n l y one a t t im e s ) such as l i ,ei ] r and i a 7 Cs.

D e s p i t e t h i s l a r g e v a r i e t y o f r a d i o a c t i v e s o u r c e s and b r a c h y t h e r a p y a p p l i c a t i o n s , d o s i m e t r y p r o t o c o l s , as p r o t o c o l s f o r the d e t e r m i n a t i o n o f abso rbed dose f rom h ig h e n e rg y p ho ton and e l e c t r o n beams i n r a d i o t h e r a py , do not e x i s t .

R e c e n t l y , some a u t h o r s [ ID r e p o r t e d on t h e im p o r ta n c e o f s p e c i f y i n g t h e s t r e n g t h o f b r a c h y t h e r a p y s o u r c e s by th e e xp o su re r a t e (o r Kerma r a t e ) , measured a t a c e r t a i n d i s t a n c e f rom th e s o u r c e s ' c e n t r e s , r a t h e r tha n by a c t u a l o r ‘ app a re n t * a c t i v i t y v a l u e s .

In t h i s way , e r r o r s a r i s i n g f rom b o th d i s c r e p a n c i e s i n d e t e r m i n i n g t h e s p e c i f i c c o n s t a n t Г o r e x p o s u re r a t e c o n s t a n t , as used by v a r i o u s s u p p l i e r s , and d i f f e r e n c e s i n e s t i m a t i n g f i l t r a t i o n c o r r e c t i o n s f o r each s h i e l d e d s o u r c e , c o u l d be a v o i d e d .

However, i n b r a c h y t h e r a p y d o s i m e t r y , when compared w i t h h i g h e n e rg y p h o to n beam r a d i o t h e r a p y d o s i m e t r y , s p e c i f i c p ro b le m s a r i s e as a r e s u l t o f two main f a c t o r s : (a) t h e n e c e s s i t y t o make dose r a t emeasurements i n v e r y c l o s e p r o x i m i t y t o t h e s o u r c e s and (b) t h e s t r o n g dependence o f dose d i s t r i b u t i o n s a round low e n e rg y s o u r c e s on d i f f e r e n t t i s s u e s , so t h a t a p p r o p r i a t e d o s i m e t r y phantoms have t o be used .

We a re r e p o r t i n g an e x p e r i m e n t a l d o s i m e t r i c p r o c e d u r e made i n a t i s s u e e q u i v a l e n t s o l i d phantom p r e v i o u s l y used , as r e p o r t e d [ 2 3 , -for dose r a t e measurements o-f low a c t i v i t y i-aEI r and 1чЭВАи s o u r c e s , used i n b r a c h y t h e r a p y i n t e r s t i t i a l t r e a t m e n t s . The r e s u l t s o b t a i n e d ag reed w i t h th o s e r e p o r t e d i n t h e l i t e r a t u r e . I n t h i s p a p e r , t h e r e s u l t s o f e x p e r i m e n t a l d o s i m e t r y o f low a c t i v i t y i e = I seeds a r e r e p o r t e d . TLDs were used f o r dose r a t e measurements o f a l l t h e s e s o u r c e s . At

IAEA-SM-298/37 249

p r e s e n t , t h e y seem t o be t h e most s u i t a b l e d o s i m e t e r s , ow ing t o t h e i r s m a l l s i z e and h i g h s e n s i t i v i t y .

However, t h e y must be c a l i b r a t e d a g a i n s t an i o n i z a t i o n chamber, by means o í b road X - r a y beams o f e f f e c t i v e ene rgy a p p r o x i m a t e l y e q u a l t o t h e a v e ra g e e n e rg y o-f each s o u r c e . M o re o v e r , s o u r c e r a d i a t i o n s p e c t r a o f maximum e n e rg y h i g h e r t h a n 100 keV, change when beams pass t h r o u g h a medium, so t h a t o n l y manganese doped l i t h i u m b o r a t e TLDs, w i t h a re s p o n s e p r a c t i c a l l y i n dependen t o f e n e r g y , s h o u ld be used .

The i o n i z a t i o n chambers c o u l d be used f o r dose r a t e measurements o f h i g h a c t i v i t y b r a c h y t h e r a p y s o u r c e s . I n d e e d , t h e y a re t h e most u s e f u l d o s i m e t e r s f o r t h e i r im m ed ia te r a d i a t i o n e n e rg y ind ependen t r e s p o n s e , a l s o f o r i n v i v o d o s i m e t r y and q u a l i t y a s s u ra n c e p r o b le m s . As i t i s e x p e c t e d , i n d e t e r m i n i n g t h e dose r a t e i n t h e medium, t h e h ig h dose g r a d i e n t s near t h e r a d i a t i o n s o u r c e s s t r o n g l y a f f e c t t h e i o n i z a t i o n chambers re s p o n s e s , as a consequence o f t h e i r f i n i t e vo lum e .

I n o r d e r t o a n a l y z e th e p o s s i b i l i t y o f u s i n g i o n i z a t i o n chambers f o r dose measurements near h i g h a c t i v i t y b r a c h y t h e r a p y s o u r c e s , we a r e r e p o r t i n g dose r a t e measurements made by f o u r d i f f e r e n t i o n i z a t i o n chambers a lo n g t h e t r a n s v e r s e a x i s o f a l i t t l e c y l i n d r i c a l 1<?,eI r s o u r c e between 1 cm and 10 cm f rom i t s c e n t e r .

I t i s our o p i n i o n t h a t f ro m th e s e e x p e r i m e n t a l r e s u l t s o b t a i n e d b o th i n i a = I seeds d o s i m e t r y and i n dosemeasurements by i o n i z a t i o n chambers c l o s e t o ab r a c h y t h e r a p y s o u r c e , t h e n e c e s s i t y t o e s t a b l i s hg e n e r a l e x p e r i m e n t a l p r o c e d u r e s i n b r a c h y t h e r a p y d o s i m e t r y s h o u ld be e v i d e n t .

8 . MATERIALS AND METHODS

2 . 1 . i a = I seeds

As p r e v i o u s l y r e p o r t e d [£?], we d e s ig n e d and b u i l t a 30 x 30 x 30 cm p e rs p e x phan tom, s c h e m a t i c a l l y shown i n F i g . l . I t i s c o n s t i t u t e d by t h r e e d i f f e r e n t s e c t i o n s ,

250 ARCOVITO et al.

ЛП . ......

4 À p Ж -

V /Ж л i .... — С [ / D A

mШ Ш Ш Ё 7 / ^ /

<a)

¿ Ж

FIG. I. Schematic drawing o f the perspex phantom sections for measurements with (a) photographic film, (b) ionization chamber and (c) TLDs.

i n wh ich TLDs, i o n i z a t i o n chambers and p h o t o g r a p h i c f i l m s can be used -for dose measurements o f any k i n d o f a v a i l a b l e b r a c h y t h e r a p y s o u r c e s , f o r d i s t a n c e s up t o H cm from t h e i r c e n t r e s .

M o re o v e r , f o l l o w i n g t h e i n d i c a t i o n s r e p o r t e d by W h i te e t a l . [ 3 3 , we p re p a re d a p p r o p r i a t e phantom s e c t i o n s c o n s t i t u t e d by m a t e r i a l s u b s t i t u t e s o f m usc le (MS1 1 ) , a d ip o s e (AP6) and b r e a s t (BRIE) t i s s u e .

1£2SI seeds ( mod. 6711 ) , 21 .1 ±1 .1 MBq, s u p p l i e d by3M were used , and dose r a t e measurements a lo n g t h e i r t r a n s v e r s e a x i s were made by means o f TLDs L i F 100.

Dose d i s t r i b u t i o n s a round t h e s e seeds were measured i n p e r s p e x phantom by Kodak X-Omat V and X-0mat TL p h o t o g r a p h i c f i l m s . D e n s i t o m e t r i e r e a d i n g s were made by means o f a P e r k i n - E lmer PDS 1010 m ic r o d e n s i t o m e t e r , wh ich has a g e o m e t r i c a l r e s o l u t i o n up t o 1 m ic r o n and a d e n s i t y p h o t o g r a p h i c a c c u r a c y o f 0 . 0 2 i n th e ra n g e 0 т 4 . 0 . D e n s i t y r e a d i n g s were dose c a l i b r a t e d .

IAEA-SM-298/37 251

An » « I r s o u r c e 1 mm i n h e i g h t and 2 mm i n d i a m e t e r , o f 740 GBq maximum a c t i v i t y , was used f o r dose r a t emeasurements w i t h i o n i z a t i o n cham bers . I n t h e remotea f t e r l o a d i n g B u c h le r Sys tem, t h i s s o u r c e can bem e c h a n i c a l l y moved i n i t s a p p l i c a t o r , so t h a t , t o g e t h e r w i t h two f i x e d l 3 7 Cs s o u r c e s , a l o t o fd i f f e r e n t dose d i s t r i b u t i o n s may be o b t a i n e d . Wep r e v i o u s l y r e p o r t e d C4] on t h e d o s i m e t r y o f t h e remotea f t e r l o a d i n g B u c h le r Sys tem.

In t h i s s t u d y t h e 1<эе1г s o u r c e was used as a p i n p o i n t f i x e d s o u r c e and dose r a t e measurements were made by f o u r d i f f e r e n t i o n i z a t i o n cham bers , namely PRD5 and PR05-P, w i t h a C a p in t e c e l e c t r o m e t e r , PTN-N and PTW- m ic r o w i t h a F r i b u r g e l e c t r o m e t e r .

The w a te r dose r a t e a t 1 cm f rom t h e s o u r c e c e n t r e ,Dw( l ) , was o b t a i n e d f rom p e rs p e x measurements w i t hTLDs 800 ( L i BBoE0 7 : Mn) . Assuming [ 4 ] t h a t t h i s‘ « I r s o u r c e , f o r d i s t a n c e s f rom i t s c e n t r e equ a l t o o r g r e a t e r t h a n 1 cm, can be c o n s i d e r e d as a p o i n t s o u r c e , t h e dose r a t e Dw ( r ) i n w a te r was c a l c u l a t e d by th e f o l l o w i n g e q u a t i o n :

Dw ( 1 ) M ( r )Dw (r) = ----- - --------

r e M(l>

where M ( r ) i s M e i s b e r g e r ' s p o l y n o m ia l f u n c t i o n [ 5 ] , wh ich a c c o u n ts f o r c o n t r i b u t i o n s t o t h e dose due t o a b s o r p t i o n and s c a t t e r i n g e f f e c t s i n w a t e r .

3 . RESULTS

3 . 1 . i e s I seeds d o s i m e t r y

The dose r a t e D ( r ) a lo n g th e t r a n s v e r s e a x i s o f eachl i t t l e * e » i seed my be d e s c r i b e d by t h e f o l l o w i n g e q u a t i o n :

D*D i r ) = A -------- g t ( r )

r s

2 . 2 . Dose measurements by ion izat ion chambers

252 ARCOVITO et al.

where A i s t h e s o u r c e ' a p p a r e n t ' a c t i v i t y , Dt i s t h e s p e c i f i c dose r a t e d e f i n e d as t h e dose r a t e v a l u e a t 1 cm -from a seed c e n t r e o-f u n i t a c t i v i t y , and g t <r) i s a ■ func t ion wh ich a c c o u n ts f o r t h e dose c o n t r i b u t i o n -for a t t e n u a t i o n and s c a t t e r i n g e f f e c t s (e q ua l t o 1 .0 f o r r = 1 c m ) .

T a b le 1 r e p o r t s t h e s p e c i f i c dose r a t e v a l u e s Dt measured i n p e r s p e x , i n w a te r and i n t h r e e d i f f e r e n t t i s s u e s u b s t i t u t e m a t e r i a l s .

F i g u r e g shows t h e e x p e r i m e n t a l d a t a o f g t ( r ) o b t a i n e d i n d i f f e r e n t m ed ia , r e p o r t e d v e r s u s t h e seed d i s t a n c e r , f i t t e d by t h e f o l l o w i n g e q u a t i o n :

g t ( r ) = A0 + A, r + Ae r e + A3 r a

u s in g t h e l e a s t s q u a re s f i t t i n g method [ 6 ] .

T a b le I I r e p o r t s a c o m p a r is o n between t h e s p e c i f i c dose r a t e v a l u e o b t a i n e d f rom m usc le t i s s u e s u b s t i t u t e measurements u s i n g t h i s d o s i m e t r i c p r o c e d u r e and t h e v a l u e as c a l c u l a t e d by Kr i shnaswamy [ 7 ] f rom dose r a t e measurements i n a l u c i t e phan tom, show ing a d i f f e r e n c e o f abou t 14*/. be tween th e s e r e s u l t s .

TABLE I . MEASURED SPECIFIC DOSE RATE Dt IN DIFFERENT

MATERIALS

U n i t s : Gy»mE- s - 1 • Bq~1 ( x 10_1V ) л

Perspex Water MS11 AP6 BRIE

0.60 ±.03 0.89 ±.04 0.89 ±.04 0.57 +.03 0.68 ±.03

“ To c o n v e r t t o rad-cm£a- h " 1>mCi“ 1- m u l t i p l y f i g u r e s i n t a b l e by 1 .332.

TABLE I I . MUSCLE SPECIFIC DOSE RATE Dt MEASURED IN

TISSUE SUBSTITUTE (MS11) COMPARED WITH DATA DERIVED FROM

MEASUREMENTS IN PERSPEX

U n i t s : G y m6-’ 'S -1 *Bq-1 ( x lO - 1 7 )

Muscle s p e c i f i c

dose r a t e Dt

IAEA-SM-298/37 253

0 .89+0.04 Measured i n MS11 (5)

1 .02+0.05 De r ived f rom measurement i n pe rspex (5)

1 .01+0.05 Der ived f rom measurement i n pe rspex (6)

g, i r )

FIG. 2. Measured g, (r) plotted versus distance r from the 1251 seed centre. Solid lines are the g, (r) computed polynomial functions.

254 ARCO VITO et al.

FIG. 3. F(r, в) values measured at 1 cm from ,2SI ( я) , m Au ( a ) and ,92Ir ( o ) source centre ‘versus ’ в angle. Solid lines are the F(r, в) computed functions.

F i g u r e 3 shows th e measured r e l a t i v e t w o - d i m e n s i o n a ldose d i s t r i b u t i o n a t 1 cm -from th e c e n t r e o f * e=!is e e d s , w i t h t h e r e l a t i v e dose d i s t r i b u t i o n s measured a round ‘ * e I r and 1<5,eAu seeds C23.

I t was -found t h a t a l l t h e s e e x p e r i m e n t a l d a ta can bef i t t e d by t h e e q u a t i o n o f t h e f o r m :

D ( r ,6) = D ( r ,90° ) • F ( r ,6)

where

D ( r , 6 )F ( r ,6) = --------------- = F ( r ,0®) + < 8 / * ) e [ l - F ( r , O e) ] 0 ( n - e )

D ( r ,90 ° )

IAEA-SM-298/37 255

and

D ( r , 0 ° )F ( r , 0 ° ) = ---------------- = a + b t l - e x p ( - r / c ) ]

D ( r ,90° )

w i t h a = 0 . 0 , b = 0 . 6 3 , с = 1 .45 cm f o r iESl s e e d s ; a = 0 . 5 7 , b = 0 . 1 9 , с = 3 . 0 cm f o r ^ ^ I r w i r e s ( 8 . 5 mm i n l e n g t h ) , a = 0 . 6 6 , b = 0 . 3 1 , с = 9 . 0 cm f o r i a e Au seed s . The f i t t i n g c u r v e s a r e r e p o r t e d as s o l i d l i n e s .

3 . 8 . Dose measurements by i o n i z a t i o n chambers

Measurements i n p e rs p e x phantom were c a r r i e d o u t a t 10 cm f rom t h e 19EI r s o u r c e c e n t e r by t h e f o u r i o n i z a t i o n chambers d e s c r i b e d a b o v e . I n o r d e r t o re ach th e dose r a t e v a l u e s , Dmeul, f rom th e e l e c t r o m e t e rr e a d i n g s , M, n o r m a l i z e d t o 88°C and one s ta n d a r datm osphere (C o r s c a l e d i v i s i o n s ) , t h e f o l l o w i n g e q u a t i o n , recommended by t h e AAPM p r o t o c o l f o r absorbed dose d e t e r m i n a t i o n f rom h ig h e n e rg y p h o to nbeams, was u s e d :

Dm.* = H N g A lo n ( L / p ) P l or t Pre p PWMll (1)

where

Ne. „ = c a v i t y - gas c a l i b r a t i o n f a c t o r (Gy/C orG y / s c a l e d i v i s i o n s ) ;

Alo n = i o n i z a t i o n c o l l e c t i o n e f f i c i e n c y a t t im e■ o f chamber c a l i b r a t i o n ;

( L / p ) metlget,= mean r e s t r i c t e d c o l l i s i o n mass s t o p p i n g power ;

P lo n = i o n - r e c o m b i n a t i o n f a c t o r ;Ргыр = f a c t o r t h a t c o r r e c t s f o r re p la c e m e n t o f

phantom m a t e r i a l by i o n i z a t i o n chamber;Pw« u = f a c t o r accou n t i g f o r t h e d i f f e r e n c e

between phantom and w a l l m a t e r i a l , d e f i n e d i n E q . (10) o f R e f . C83.

As i s known, Eq. (1) i s t h e m o d i f i c a t i o n o f t h e c a v i t y B ragg -G ra y f o r m u l a t i o n , . w h ich i s in d e p e n d e n t o f t h e

256 ARCOVITO et al.

TABLE I I I . RESULTS OBTAINED

SOURCE BY TLD-800 AND FOUR

Eq. (1)

U n i t s : Gy*s - 1 «Bq-1 ( x 10~1S

TLD-800 PR05 PR05-P

3 .25 3.21 3.31

(±7'/.) (±4*/) (+4X)

AT 10 cm FROM THE » *a l r

IONIZATION CHAMBERS USING

PTW-N PTW-micro

3 .20 3 .29

(+4*/.) (+ 4 ‘/.)

AD*

-5-

— f -♦ A

8

-10-

-15-J

4- t -

r ic m )

Kan} • test) иь

♦ РЯ05Р 0.60 0.40 1.5

□ PR05 1.20 0.40 3.0

рте micro 1.25 0.35 3.6

о PTW N 1.55 0.50 3.1

FIG. 4. Percentage differences, ДD%, between expected and measured dose rate values with ionization chambers in proximity o f a high activity 192Ir point source as a function o f the source distance r.

IAEA-SM-298/37 257

c a v i t y s i z e . I n p r a c t i c e , i o n i z a t i o n chambers a lw a y s p e r t u r b t h e p h o to n and e l e c t r o n f l u e n c e s t h a t must be a ccou n te d f o r by c e r t a i n f a c t o r s as Ри я 1 , and Pr-»p .

T a b le I I I shows t h e r e s u l t s o b t a i n e d a t 10 cm f ro m t h e 19HI r s o u r c e , by each i o n i z a t i o n chamber u s i n g E q . ( l ) , i n wh ich Pw eU was c a l c u l a t e d w i t h a = 1 , t h a t means t h e t o t a l i o n i z a t i o n i n c h am be rs ' vo lumes was p roduced by e l e c t r o n s g e n e r a te d i n t h e chambers* w a l l s С83 . M o re o v e r , t h e e x p e r i m e n t a l v a l u e f o r P lo n was e q u a l t o 1 w i t h i n 0.5*/., and Ргир was assumed e qu a l t o 1.

As T a b le I I I r e p o r t s , a l l t h e i o n i z a t i o n c h am be rs ' dose r a t e measurements ag ree w i t h t h e TLD 800 d a t a , w i t h i n t h e e x p e r i m e n t a l e r r o r s , so t h a t , a t t h i s d i s t a n c e , each i o n i z a t i o n chamber c o u l d be c o n s i d e r e d as a p o i n t p r o b e .

Then, i o n i z a t i o n measurements were made be tween 10 cm and 1 cm f rom th e 1-3eI r s o u r c e c e n t r e , 1 cm a t a t im e a lo n g i t s t r a n s v e r s e a x i s .

F i g u r e 4 shows p e r c e n t a g e d i f f e r e n c e s between measured and e x pe c ted dose r a t e v a l u e s , r e p o r t e d as a f u n c t i o n o f t h e s o u r c e d i s t a n c e r . As can be se e n , th e s e p e r c e n ta g e d i f f e r e n c e s can re a c h v a l u e s o f 15*/. a t d i s t a n c e s o f abou t 1 cm f rom th e s o u r c e .

4 . DISCUSSION AND CONCLUSION

We want t o emphas ize two main r e s u l t s o b t a i n e d i n t h e ie=, I seeds d o s i m e t r y . The f i r s t i s t h e s t r o n g v a r i a t i o n o f b o th t h e s p e c i f i c dose r a t e v a l u e s and t h e dose d i s t r i b u t i o n s measured i n d i f f e r e n t t i s s u e s u b s t i t u t e s a lo n g t h e s e e d s ' t r a n s v e r s e a x i s . The second i s t h e d i f f e r e n c e o f about 15*/. be tween t h e dose r a t e v a l u e a t 1 cm r e p o r t e d by Kr i shnaswamy [ 7 3 , c a l c u l a t e d f rom l u c i t e measurements , and t h e dose r a t e v a l u e measured p u t t i n g TLDs d i r e c t l y i n m usc le s u b s t i t u t e t i s s u e . K r i s h n a s w a m y 's app roach i s based on th e o b s e r v a t i o n t h a t t h e p h o to n f l u e n c e i n l u c i t e and i n w a te r s h o u ld be a lm o s t t h e same, s i n c e t h e l i n e a r a t t e n u a t i o n c o e f f i c i e n t s o f t h e s e two media a r e e q u a l w i t h i n 5*/.. However , as r e p o r t e d i n T a b le I V , t h e

TABLE IV . COMPTON, PHOTOELECTRIC AND TOTAL LINEAR

ATTENUATION COEFFICIENTS (cm "1 ) FOR MUSCLE AND PERSPEX

FOR 30 keV PHOTON ENERGY

(From J . H . H u b e l , NSR DS-NBS-29 1969)

258 ARCOVITO et al.

Compton P h o t o e le c t r i c T o ta l

Muscle 0 .229 0 .144 0 .373

Perspex 0 .257 0.094 0.351

Compton component o f t h e t o t a l l i n e a r a t t e n u a t i o nc o e f f i c i e n t i s h i g h e r i n p e r s p e x th a n i n m u sc le ( w a te r ) , so t h a t t h e 1ESSI seed p h o to n f l u e n c e s h o u ld be h i g h e r i n p e rs pe x t h a n i n m u s c le , i n agreement w i t h t h e r e s u l t o b t a i n e d i n o u r r e s e a r c h [ 7 ] .

R e g a rd in g dose r a t e measurements by i o n i 2 a t i o n cham bers , t h e r e p o r t e d r e s u l t s c l e a r l y show t h a t t h e i r re sp on se s a r e s t r o n g l y a f f e c t e d by h i g h dose r a t e g r a d i e n t s , as a consequence o f t h e i r s i z e s . From E q . ( l ) , t h e m o d i f i e d B ra g g -G ra y e q u a t i o n , i t i s e v i d e n t t h a t t h e i o n i z a t i o n chambers a lw a y s p e r t u r b p h o to n f l u e n c e , as shown i n t h e n e c e s s i t y o f u s i n g c o r r e c t i o n f a c t o r s i n t h i s e q u a t i o n . S in c e Ргир i s t h e o n l y p a ra m e te r d e f i n e d t o a ccou n t f o r dose g r a d i e n t s , we want t o sugges t t h a t E q . ( l ) c o u l d a l s o be used i nh i g h dose g r a d i e n t c o n d i t i o n s , i f an a p p r o p r i a t e newc o r r e c t i o n f a c t o r P“ r «,p i s i n t r o d u c e d . I n d e e d , i tw i l l be dependent no t o n l y on t h e i o n i z a t i o n c h am b e rs ' s i z e s bu t a l s o on t h e s o u r c e d i s t a n c e . However , i t i s o u r o p i n i o n t h a t t h e p o s s i b i l i t y t o use i o n i z a t i o n

IAEA-SM-298/37 259

chambers i n t h e d o s i m e t r y o f h i g h a c t i v i t y s o u r c e s c o u l d improve t h e a c c u r a c y l e v e l o f t h e b r a c h y t h e r a p y t r e a t m e n t s .

As a c o n c l u s i o n , we t h i n k t h a t a l l e x p e r i m e n t a l r e s u l t s r e p o r t e d above b e lo n g t o t h e w id e f i e l d o f s t u d i e s t o e s t a b l i s h common d o s i m e t r i c p r o c e d u r e s , by w h i c h , as i n r a d i o t h e r a p y w i t h h i g h e n e r g y p h o to n beams, t h e a c c u r a c y l e v e l o f b r a c h y t h e r a p y d o s i m e t r y c o u l d be im p ro v e d .

R E F E R E N C E S

[ 1 ] JAYARAMAN, S . , LANZI , L . H . , Med. Phys. 10 (1983)

871. _Í2J ARCOVITO, G . , PIERMATTEI, A . , BACC1, G . , FURETTA, C.

PITTELLA, G . , B rachy the rap y d o s im e t r y by measurements i n r i g i d phantom. In XIV l . C . M . B . E . and V I II .C .M .P . (Espoo, F i n l a n d : August 1985) 1178 -1179.

f 3 J WHITE, D .R . , MARTIN, R . J . , DARLINSON, R . , B r . J .R a d io l . §0 (1977) 814.

[ 4 ] ARC0VIT0, G . , PIERMATTEI, A . , D'ABRAMO, G . , ANDREASI BASSI, F . , B r . J . R a d i o l . 57 (1984) 1119.

C5] MEISBERGER, L . L . , KELLER, R . J . , SHALEK, R . J . , Rad io logy 90 (1968) 953.

[63 PIERMATTEI, A . , ARC0VIT0, G . , ANDREASI BASSI, F . , Dose r a t e and d i s t r i b u t i o n measurements o f lß S I seeds i n t i s s u e . Submi t ted f o r p u b l i c a t i o n i n Med. Phys .

[ 7 ] KRISHNASWAMY, V . , R a d io log y 126 (1978) 489.С 8 ] TASK GROUP 21 , R a d ia t i o n Therapy Commi t te e AAPM.

Med. Phys. 10 (1983) 741.

IAEA-SM-298/79

CLINICAL APPLICATION OF COMPUTER DOSIMETRY IN RADIOTHERAPY OF CARCINOMA OF THE UTERINE CERVIX

A.A. EL-MASRY, A.O. BADIB, M.Y. GOUDA,M.F. NOOMAN, N.M. EL-GHAMRY Radiotherapy and Medical Physics Units,Faculty of Medicine,Alexandria University,Alexandria,Egypt

Abstract

C L IN IC A L A P P L IC A T IO N O F CO M P U TER D O S IM E T R Y IN R A D IO T H E R A P Y O F C A R C IN O M A O F T H E U T E R IN E C E R V IX .

The paper presents the results of computer dosimetry of external beam and intracavitary irradiation in 50 patients with carcinoma of the uterine cervix in Alexandria University Hospitals. The extent of the tumour and the position of critical neighbouring organs were determined for clinical dosimetry. The computed radiation doses to different sites and the summation of external and intracavitary doses were calculated in biological units to be correlated with the treatment results. The treatment protocol consisted of: (a) whole pelvic external cobalt-60 radiotherapy and (b) manual afterloadihg radium application and/or (c) parametrial boost dose of external cobalt-60. Manual and computer dose distribution were made. A ll patients were clinically evaluated at the end of irradiation and at monthly follow-up intervals for 30-42 months. The treatment was well tolerated with immediate complete tumour response in 70% and three year actuarial survival of 68.9%. Computer dosimetry of external beam therapy revealed the optimal distribution in different field arrangements. In brachytherapy, the alpha angle varied between 120 and 180° and the beta angle between 0 and 30°. The dose rates were determined at different pelvic points and organs. Two reference isodose lines were described: a 35 cGy/h reference line for central primary lesions and a 15 cGy/h line for lateral parametrial and oblique lymphatic planes. Using the C R E formalism, the radiation doses of the primary disease and the pelvic nodes by external and intracavitary techniques were added and expressed in reu units. The optimal C R E values with maximal tumour response and minimal complications were: 2800 reu for central lesions and 1700 reu for lateral nodal disease.

1. INTRODUCTION

Radiotherapy plays a major role in the management of patients with carcinoma of the uterine cervix. Brachytherapy is a dominant element in the cure of early stages, while additional external irradiation is necessary in advanced stages [1].

Most of our patients with cancer of the uterine cervix are first seen in relatively advanced stages of the disease with prevailing iocal infection [2]. With this in mind,

261

262 EL-MASRY et al.

the relative contribution of external irradiation to the overall radiotherapy regime has been increased.

Dosimetry of external beam therapy and brachytherapy is facilitated by the use of computers táking into consideration various external field arrangements, different loadings of the uterine and vaginal applicators and anatomic variations[3]. The combination of external beam and continuous low dose rate intracavitary therapy raises the problem of dose addition when combining schedules differing in their dose-time factors. The total biological effectiveness of such complex regimes may be expressed with the help of the cumulative radiation effect (CRE) formalism [4].

In the present study the radiation dose distribution of external and intracavitary therapy in different points and organs were computed in a series of patients with carcinoma of the cervix uteri. The CRE values attained were correlated with the probability of tumour control.

2. MATERIAL AND METHODS

The clinical material included 50 consecutive patients with histologically verified squamous cell carcinoma of the uterine cervix of different clinical stages of the disease. According to the UICC system of clinical staging [5], the material consisted of 10 TIB, 20 TIIA + B, and 20 T ill cases. Positive lymphography signs were seen in 33 cases (66%).

2.1. Radiotherapy protocol

Treatment was planned according to the extent of the disease and consisted of two to three schedules:

External cobalt-60 whole pelvic irradiation: The dose varied with the stage: Stage IB: 30 Gy, Stage II: 40 Gy, and Stage III: 50 Gy in 3-5 weeks, five fractions per week and 200 cGy per fraction. The treatment volume extended 2 cm beyond the lowermost vaginal disease and covered the external and common iliac nodes. Up to a dose of 40 Gy two parallel opposing fields were used and above that dose 3-4 field techniques were selected.

Intracavitary therapy: This consisted of a single insertion using the vaginal mould technique [6] with radium or caesium tubes. The isodose distribution around the sources was obtained by computer [7] and manually [8]. For dose prescription a 35 ± 5 cGy/h isodose line was used as a reference line to enclose the uterus, upper vagina and medial part of the paracervical triangles. The time of the intracavitary application was adjusted such that the combined dose from the first two schedules added up to 75-80 Gy at the reference line.

IAEA-SM-298/79 263

External cobalt-60 parametrial boost dose: In patients with stages IIB and HI, or with radiologic evidence of pelvic nodal métastasés, a boost dose of 10-15 Gy/ 1-2 weeks was given. Two parallel opposing fields covered the whole pelvis but shielded the volume of tissue inside the reference line.

2.2. Calculation of CRE levels

The CRE formalism of Kirk et al. [4] was used to calculate:

(a) The central CRE level at the reference line for the first two schedules.(b) The nodal CRE level at the principal node seen in lymphography for the

three treatment schedules.

2.3. Clinical evaluation and follow-up

The clinical response to treatment was evaluated weekly during treatment and regularly every month after the end of treatment for a minimum of 30 months. Control of the central, pelvic and nodal disease was determined by clinical findings, regular cytological studies of vaginal smears, cervical biopsy when required and follow-up or repeat lymphography.

3. RESULTS

3.1. Dosimetric results

External beam dose distribution was considered optimal in the following techniques:

(a) Two parallel opposed fields when the dose was < 40 Gy and the AP separation was < 20 cm (Fig. 1).

(b) Three-field technique, one anterior and two lateral wedged fields resulting in lower bladder and rectal doses (Fig. 2).

(c) Four-field technique achieving better homogeneity and lower bladder and rectal doses with oblique arrangement (Fig. 3).

Intracavitary dosimetry: The variations in the anatomic angulation between the uterine and vaginal axes are shown in Table I. A standard anatomy of alpha = 120° and beta = 0° was defined for the system. A complete dosimetry calculation was undertaken for every case. Mean dose rates at the different organs and points in the pelvis are given in Table II. High dose rates to the uterine wall, external os and vaginal vault were seen with higher uterine loading. Point A

'nearest to the sources received higher doses with changes in beta angle from 0 to 30°. Bladder and rectal doses were influenced by changes in alpha angle.

HUTCH 1онS 5 D = U « C H .

14 X 14

FIG. 1. Dose distribution fo r tw o opposing open fields.

264 EL-M

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et al.

ПМТЕН1ПН

I S X I S s s d - в и с и .

яигеяюя Z ю

O'

I ’D S l E R l i m Scale

FIG. 3. Dose distribution fo r fo u r open oblique fields.

EL-MA

SRY et

al.

IAEA-SM-298/79 267

TABLE I. VARIATIONS OF ANATOMIC ANGULATION BETWEEN UTERINE AND VAGINAL AXES

Angle No. of cases Per cent

Beta angle0° 32 64

15° 12 2430° 6 12

Alpha angle120° 34 68165° 11 22180° 5 10

TABLE II. MEAN DOSE RATE COMPUTED AT DIFFERENT ANATOMIC POINTS IN OPTIMAL GEOMETRICAL POSITION

Anatomic site Dose rate (cGy/h)

Extérnalos 185.4 ±7.5

Vaginal vault 164.6 ±5.5

Uterine wall 96.5 ±9.3

Point A 43.5 ±6.4

Point В 16.6 ±8.1

Urinary bladder 22.1 ±8.2

Rectum 26.8 ±6.7

The dose rates at point В did not exceed 30-40% of the dose at point A. The mean rectal dose rate was 26.8 ± 6.7 cGy/h.

An atlas of isodose distribution was prepared for various anatomic regulations. All source configurations were included for uterine tubes and vaginal mould. Dose rate distributions were presented in the two major planes of interest on a 1 cm X 1 cm grid (Fig. 4).

EL-MASRY et al.

- 7

00 00 oo oo 0« oo oo 00 00

00 ♦ 1 4?

000000

00 00 00 00 00 00 00 00 00 00 00 00 0000 00 00 00 00 oo 00 00 00 00 00 ос oo00 00 Of 00 00 00 00 00 00 00 00 00 0000 00 00 СО 00 00 00 00 00 00 00 ОС >0000 00 00 00 00 00 00 00 00 00 00 00 -00

00 00 00 00 ОС 00 00 00 00 ОС 00 00 00 00 00 00 00 00 00 00 00 00 «о

«5 «600 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 to 00 00 со 00 оо со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со «О 00 со 00 00 со 00 00 со 00 00 00 00 00 со 00 00 00 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со00 00 (О00 00 со 00 00 со00 00 (О 00 00 СО00 00 со 00 00 с о 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со оо оо ео 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со 00 00 со00 ОQ СО00 00 со 00 00 со 00 00 со

00 00 оо 00 00 00 00 00 оо 00 00 оо 00 00 00 00 00 оо 0 0 00 0 0 00 оо ооОО 00 0000 00 оо 00 00 00 00 00 00 00 <>о 00 00 00 оо 00 00 00 00 00 оо 00 оо оо 00 00 00 00 00 00 00 00 00 00 00 00 00 00 оо 00 00 00 Q0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 оо оо 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 оо 00 00 00 00 оо 00 00 00 00 00 00 00 00 ЪО 0000 оо оо 00 00 00 00 00 00 00 оо оо 00 00 00 00 00 00 00 00 00 00 00 00 00 ОО 00 00 00 00 00 00 00 00 00 00 00 ОО 0000 о о оо 00 00 00 00 0« 0« 00 00 00 00 00 00 00 00 00

FIG. 4. Isodose d istribution (G y/h) (a) in the X -Y plane, (b j in the Y-Z plane.

IAEA-SM-298/79 269

(b)-7 -t -i -• -Î -г » I 00 « I ♦ г О ♦« «S «fc «7

Га;

C R E T u m o u r response C o m p lic a t io n s

(reu) C o m p le te - о R e s idua l = #3100- +

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ЗООО- 00 В

2900- 00BR BR

2800-2700-

, 000000000000

2600- 00000 000000 ••

2500- 0 0 • •

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C o m p lic a t io n s : B : B ladde rR : R e c tu mB R : B la d d e r an d re c tu m

(b)C e n tra l N o d a lC R E C R E(reu ) (re u )

3200- C e n tra l re c .: C - . ¿ 2 0 0P e lv ic re c .: P z

5 ; C e n t .+ p e lv .: CP ; . 2 1 0 0

ЗООО5 1 . 2000

29OO5 5 . I 9OO28005 5.18002700- 5 . I 7OO

26OO5 =.160025005............................................. ----- ------- 5. 15OO2 +0 0 ~ ▼ T « " — ▼ T tjP""^P*?TTTTTTTTTTTTTT’ . 1 1*00

23005---Ç......... .................................................. 5.1300

22005 .................................................. 5.1200

21005 5 . 1 100

19005 -.1000

18005 :• 90°0 0 0 0 - 8 0 0

FIG. 5. Relationship between central CRE levels and tumour response and complications faj and cases with recurrence (bj.

270 EL-M

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et al.

IAEA-SM-298/79 271

C R E (reu)

FIG. 6. Central CRE levels and percentage probability o f primary tum our control.

3.2. Clinical results and CRE values

The three year actuarial survival in this series was 68.9%. Clinically, the optimal CRE value is that value at which the maximum tumour response was gained with minimal complications. This was observed at a central CRE value of 2800 reu. Out of 50 patients, 35 showed complete primary tumour response (70%) and 15 were considered local failures: 9 cases with residual tumours and 6 cases with recurrent disease (Fig. 5 (a) and (b)). All these failures had beta angles of 15 ° or more. The x2 test of independence showed a maximum at the 2800 level, which is statistically highly significant (P < 0.001). The attained CRE levels above 2800 reu were associated with severe rectal and bladder complications in 6 out of 10 cases (60%). This incidence represents 12% of the whole series.Figure 6 shows the relationship (characterized by a steep curve) between the probability of primary tumour control and CRE levels between 2300-2800 reu corresponding to a 30-100% control rate.

Thirty-eight patients were considered having pelvic nodal metastasis based on positive pretreatment lymphograms. Control of the nodal disease was achieved

272 EL-MASRY et al.

FIG. 7. R elationship betw een nodal C RE levels and nodal control.

in 23 cases (60%) as judged by clinical end results after at least 30 months and by post-treatment lymphography. Local failure was seen in 15 cases: 13 with residual disease and 2 with nodal recurrences.

Figure 7 presents the nodal CRE values of controlled and uncontrolled cases. Applying the x2 test, the optimal nodal CRE value was obtained at 1700 reu with P < 0.005. Figure 8 illustrates the probability of control of the nodal disease and local nodal CRE level. The curve is steeper between 1400 and 1900 reu, corresponding to a 0-75% control rate.

4. DISCUSSION

The'rationale for successful radiotherapy for patients with carcinoma of the cervix uteri is to deliver a high radiation dose to the cervix and paracervical region with steep dose gradients anteriorly and posteriorly to keep the bladder and

IAEA-SM-298/79 273

C R E (reu )

FIG. 8. N odal CRE levels and percentage probability o f nodal control.

rectum within the low dose region. To this end, individualization should be permitted aiming at optimizing the dose distribution. To achieve maximum tumour control and to avoid complications, a study of the dose distribution is essential.

The use of computersdn calculating the dose distribution for external and intracavitary radiotherapy is well established [9]. The use of computers improves the precision and considerably reduces the calculation time.

In external beam therapy the simplest method to achieve homogeneous tumour dose distribution in the present study is through anterior and posterior opposing parallel fields. This was seen when the separation of such fields did not exceed 20 cm and the tumour dose was < 40 Gy. Cobalt-60 and particularly higher energies attain such homogeneity without inflicting undue normal tissue damage [10]. When the field separation is more than 20 cm and/or higher doses are needed, the four-field arrangement is recommended. Bentle et al. [11] showed in their material that the box technique can produce a more favourable dose distribution. In the present material the oblique field arrangement resulted in a lower inhomogeneity factor and sparing of the critical organs.

274 EL-MASRY et al.

In brachytherapy, the dose distribution is influenced by variations in the anatomic angulations. The semi-rigid intra-uterine tube used in our series corrected some of the deviations in the cases with mobile uterus. This resulted in less variation in alpha and beta angles when compared with other applicators [12]. This can result in a standard application in which the dose rates at point A right and left are within ±10% and the bladder and rectal doses are within tissue tolerance.

The CRE concept applies to normal tissue tolerance which can be correlated with the local control of moderately sensitive tumours whose control requires doses close to the tolerance level [4]. For the control of the central disease in our series, a CRE level of 2800 reu calculated at the paracervical triangle was optimal. The optimal dose for the control of nodal métastasés was found to be 1700 reu at the principal node. Similar results were reported by Awwad et al. [13], who adjusted the radiation doses to the CRE levels.

Correlation of the central and nodal control showed that, whenever the nodal disease was controlled, the primary tumour was also controlled. The dose level in our protocol seems to be well tolerated since the incidence of high dose effects was within acceptable limits. To reach this dose level, external beam therapy should be a major component in the treatment since the contribution of intracavitary irradiation to the nodal dose is relatively small.

REFERENCES

[ 1 ] F L E T C H E R , G .H . , R U T L E D G E , F . , A m . J . R o e n t g e n o l . I l l ( 1 9 7 1 ) 2 2 5 .

[2 ] IS M A IL , F . A . , R e s u l t s o f R a d i a t i o n T r e a t m e n t o f C a r c i n o m a o f U te r in e C e r v ix , M as te r

T hes is , A l e x a n d r i a U n iv e r s i ty , A l e x a n d r i a ( 1 9 7 6 ) .

[3 ] F R A N K , W .L . , e t al., A m . J. R o e n t g e n o l . 6 8 ( 1 9 6 7 ) 8 7 0 .[4 ] K I R K , J ., e t al., C l in . R ad io l . 2 2 ( 1 9 7 1 ) 145.[5 ] T N M C la ss i f i c a t io n o f M a l i g n a n t T u m o u r s , U IC C , G e n e v a ( 19 7 4 ) .

[6 ] C H A S S A G N E , D., P I E R Q U I N , B., J. R ad io l . E l e c t ro l . 4 7 ( 1 9 6 6 ) 89 .[7 ] R O S E N W A L D , J .C . , D U T R E I X , A . , J. R a d i o l . E l e c t r o l . 51 ( 1 9 7 0 ) 6 7 1 .

[8 ] F L E T C H E R , G .H . , e t al., C a r c i n o m a o f C erv ix , E n d o m e t r i u m a n d O v a ry , Y e a r b o o k

P u b l i sh e r s , In c . , C h ic a g o ( 1 9 6 2 ) 6 9 .

[9 ] O R R , J .S . , “ U se o f c o m p u t e r s in r a d i o t h e r a p y ” , R e c e n t A d v a n c e s in C a n c e r a n d R a d io -

t h e r a p e u t i c s , C h u rc h i l l L iv in g s to n e , L o n d o n ( 1 9 7 1 ) 3 8 7 .[ 1 0 ] F L E T C H E R , G .H . , Br. J. R ad io l . 35 ( 1 9 6 2 ) 5.

[ 1 1 ] B E N T L E , G .C . , e t al., H e a l t h P h y s . 19 ( 1 9 7 0 ) 3 9 1 .

[ 1 2 ] E l - G H A M R A W I , K .A . , M A H F O U Z , M .M ., M O U L D , R . , Z A K I , 0 . , “ C a e s iu m m a n u a l

a f t e r lo a d in g i n t r a c a v i t a r y t r e a t m e n t o f c a r c i n o m a cerv ix : A s im p le m e t h o d o f d o s e

c a l c u l a t i o n ” , R a d i o t h e r a p y in D e v e lo p i n g C o u n t r i e s (P ro c . In t . S y m p . V ie n n a , 1 9 8 6 )

I A E A , V ie n n a ( 1 9 8 7 ) 3 2 5 - 3 3 1 .

[ 1 3 ] A W W A D , H .K . , e t al., C lin . R a d i o l . 3 0 ( 1 9 7 9 ) 2 6 3 .

IAEA-SM-298/58

QUALITY ASSURANCE IN GYNAECOLOGICAL BRACHYTHERAPY

C.H. JONESJoint Department of Physics,Royal Marsden Hospital

and Institute of Cancer Research,London,United Kingdom

Abstract

Q U A LIT Y A SSU R A N C E IN G Y N A E C O LO G IC A L B R A C H Y T H E R A P Y .Quality assurance in brachytherapy is necessary to ensure that radioactive sources are safe to use

and that high standards of dosimetry are achieved and maintained over long periods. The details of a quality assurance programme will depend upon the local facilities available to the user, the construction and activities of the sources to be checked and the clinical techniques being used. Whatever checks are made, it is important that they are convenient and safe to carry out and that they can be repeated regularly. To this end it is useful to have appropriately designed devices which can be used for specific investigations. Some of the devices developed at the Royal Marsden Hospital for swab testing, autoradiography and dosimetry are described.

1 . I N T R O D U C T I O N

Q u a l i t y a s s u r a n c e i n b r a c h y t h e r a p y h a s b e e n d e s c r i b e d i n t h e A A P M R e p o r t N o . 1 3 [ 1 ] . T h e r e p o r t p r o v i d e s b a s i c c r i t e r i a f o r t h e d e s c r i p t i o n a n d c a l i b r a t i o n o f s e a l e d s o u r c e s a n d s u g g e s t s p r o c e d u r a l p o l i c i e s f o r t h e d e v e l o p m e n t o f a c o m p r e h e n s i v e q u a l i t y a s s u r a n c e p r o g r a m m e . T h e f o r m u l a t i o n o f s u c h a p r o g r a m m e w i l l d e p e n d u p o n t h e n u m b e r a n d t y p e o f s o u r c e s u s e d , t h e c l i n i c a l t e c h n i q u e s e m p l o y e d a n d t h e a g e o f t h e s o u r c e s . R a d i a t i o n s o u r c e s a r e m a n u f a c t u r e d a c c o r d i n g t o r i g o r o u s s t a n d a r d s ; t h e c o n t a i n m e n t o f r a d i o a c t i v i t y d e p e n d s u p o n t h e m a n u f a c t u r i n g p r o c e s s a n d t h e p u r p o s e f o r w h i c h t h e y h a v e b e e n d e s i g n e d . A q u a l i t y a s s u r a n c e p r o g r a m m e w i l l i n c l u d e a n u m b e r o f d i f f e r e n t t y p e s o f c h e c k s s o m e o f w h i c h s h o u l d b e c a r r i e d o u t o n r e c e i p t o f s o u r c e s f r o m t h e m a n u f a c t u r e r a n d s u b s e q u e n t l y a t r e g u l a r i n t e r v a l s . M o s t h o s p i t a l s a n d i n s t i t u t i o n s t h a t u s e s e a l e d r a d i o a c t i v e s o u r c e s h a v e e v o l v e d m e t h o d s b y w h i c h t h e y c a n b e a s s e s s e d r e g u l a r l y . T h i s p a p e r d e s c r i b e s d e v i c e s a n d t e c h n i q u e s t h a t h a v e b e e n d e v e l o p e d a t o u r o w n h o s p i t a l t o f a c i l i t a t e t h e c h e c k i n g o f s o u r c e c o n t a i n m e n t , t h e d i s t r i b u t i o n o f r a d i o a c t i v i t y w i t h i n

275

276 JONES

TABLE I.CAESIUM TUBES AND SOUÏCES USED AT RMH (LCNDON) 1972-87

CAESIUM TOBES

Source activity (mg Ra eq)

External source length (inn)

Externalsourcediameter (rnn)

Amershan'.Code

No. of sources

5 12.5 1.9 F4 2C5 20 4.05 G1 4

10 20 4.05 G2 5610 20 2.65 J2 2010 10 3.05 E4 1515 20 4.05 G3 3520 20 4.05 G4 2225 20 4.05 G5 8

AFTEKDQADING SOURCE TRAINS

Vaginal avoids Uterine tubes

Activity (mg Ra eq)

Totalnumber

Activity (mg Ra eq)

Length(cm)

■totalnunber

Manual3 ;Curietrcn 10, 15, 20, 25 14 30-60 5-9 14Selectrcn 15, 22.5, 30, 37.5 16 45-90 4-8 12AutomaticSelectron 30, 45, 60, 75 *“ 90-180

3 Manual flexible source trains are 3 run in diameter.

s e a l e d s o u r c e s a n d a p p l i c a t o r s , a n d t h e m e a s u r e m e n t o f d o s e r a t e s i n a i r a n d t i s s u e e q u i v a l e n t m a t e r i a l . S i n c e 1 9 7 2 w e h a v e u s e d c a e s i u m - 1 3 7 s o u r c e s f o r g y n a e c o l o g i c a l t e c h n i q u e s . T a b l e I d e s c r i b e s t h e s o u r c e s t h a t h a v e b e e n a v a i l a b l e f o r i n t r a c a v i t a r y r a d i o t h e r a p y i n t h e p e r i o d 1 9 7 2 - 8 7 .

A c c u r a c y , p r e c i s i o n , t h e e a s e a n d s a f e t y w i t h w h i c h c h e c k s c a n b e m a d e a r e i m p o r t a n t c o m p o n e n t s o f a n y q u a l i t y a s s u r a n c e p r o g r a m m e : t h e p r o c e d u r e s d e s c r i b e d

IAEA-SM-298/58 277

b e l o w f o r m p a r t o f a m o r e c o m p r e h e n s i v e s y s t e m o f w o r k i n c o r p o r a t i n g t h e s t o r a g e , r e q u i s i t i o n i n g , a n d c l i n i c a l u s e o f s e a l e d r a d i o a c t i v e s o u r c e s .

2 . S WAB T E S T I N G

S o u r c e s m u s t b e t e s t e d f o r l e a k a g e a n d s u r f a c e c o n t a m i n a t i o n a t l e a s t o n c e a y e a r a n d p r e f e r a b l y m o r e f r e q u e n t l y . T h e s o u r c e i s u s u a l l y w i p e d w i t h a s w a b o r t i s s u e m o i s t e n e d w i t h e t h a n o l o r w a t e r : i t i sc o n s i d e r e d t o b e l e a k i n g i f t h e a c t i v i t y r e m o v e d m e a s u r e s m o r e t h a n 0 . 0 0 5 j - t C i . 1 R a d i a t i o n s o u r c e s a r e d e s p a t c h e d f r o m t h e m a n u f a c t u r e r s w i t h a c e r t i f i c a t e w h i c h a d v i s e s t h e p u r c h a s e r o f d e t a i l s o f t h e v a r i o u s t e s t s t h a t h a v e b e e n c a r r i e d o u t b y t h e m a n u f a c t u r e r t o e n s u r e t h a t t h e s o u r c e s a r e n o t l e a k i n g r a d i o a c t i v i t y . I t i s a p p r o p r i a t e f o r t h e u s e r t o c h e c k a l l n e w s o u r c e s b y s w a b t e s t i n g b e f o r e c l i n i c a l u s e t o e n s u r e t h a t t h e o u t s i d e o f t h e s o u r c e i s n o t c o n t a m i n a t e d b y r a d i o a c t i v e d e b r i s t h a t h a s b e e n p i c k e d u p f r o m t h e m e a s u r e m e n t l a b o r a t o r y a t t h e m a n u f a c t u r i n g p l a n t . S o u r c e s s u c h a s G ( g y n a e ) t u b e s t h a t a r e d o u b l y e n c a p s u l a t e d , a r e s o m e t i m e s l e f t w i t h a s m a l l a m o u n t o f r a d i o a c t i v e c o n t a m i n a t i o n o n t h e o u t s i d e o f t h e i n n e r c o n t a i n e r s o t h a t i f t h e o u t e r c o n t a i n e r w e r e t o f r a c t u r e , t h e u s e r w o u l d b e c o m e q u i c k l y a w a r e o f t h e d a m a g e b y t h e d e t e c t i o n o f t h e r e l e a s e o f a s m a l l a n d l i m i t e d q u a n t i t y o f r a d i o a c t i v i t y . W h a t e v e r m e t h o d i s u s e d f o r s w a b t e s t i n g , i t s h o u l d c l e a n t h e o u t s i d e o f t h e s o u r c e c o n t a i n e r w i t h o u t c a u s i n g a b r a s i o n s a n d w i t h o u t e x p o s i n g p e r s o n n e l t o h i g h r a d i a t i o n d o s e s . W e h a v e d e v e l o p e d a s i m p l e d e v i c e w h i c h a l l o w s a l a r g e n u m b e r o f s o u r c e s t o b e t e s t e d q u i c k l y a n d s a f e l y . A c r o s s - s e c t i o n o f t h e d e v i c e i s i l l u s t r a t e d i n F i g u r e 1 . I t c o n s i s t s o f a 2 5 m m t h i c k l e a d p o t , t h e t o p o f w h i c h h a s b e e n d r i l l e d t o t a k e 5 p l a s t i c t u b e s s u p p o r t e d b e n e a t h a c i r c u l a r s p o n g e 1 5 m m t h i c k . T h e s p o n g e a c t s a s a s w a b t h r o u g h w h i c h r a d i o a c t i v e s o u r c e s m a y b e p a s s e d v i a s m a l l c h a n n e l s b o r e d i n l i n e w i t h t h e t u b e s : w e h a v e f o u n d t h a t t h e s i z e , s h a p e a n d t e x t u r eo f t h e ' V u l v a P a c k i n g ' f r o m t h e A m e r s h a m M a n u a l D i s p o s a b l e A f t e r l o a d i n g S y s t e m i s i d e a l f o r t h i s p u r p o s e . T h e d e v i c e i l l u s t r a t e d s h o w s t h i s p a c k i n g i n . p o s i t i o n w i t h a s o u r c e b e i n g p u s h e d t h r o u g h a c h a n n e l s l i g h t l y s m a l l e r t h a n t h e d i a m e t e r o f t h e s o u r c e i t s e l f . T h e p a c k i n g c a n b e t e s t e d f o r c o n t a m i n a t i o n 1 b y r e m o v i n g i t a n d c h e c k i n g w i t h a G e i g e r o r s c i n t i l l a t i o n c o u n t e r . I n p r a c t i c e t h e v u l v a p a c k i n g

1 l Ci = 3.70 x io 10 Bq.

278 JONES

R M H SWAB T E S T D EV IC E

FIG. I. The swab test device has five plastic tubes (only 2 are shown) fo r receiving the radioactive sources.

i s d a m p e n e d w i t h a l i t t l e e t h a n o l w h i c h c a u s e s e x p a n s i o n o f t h e s p o n g e s o t h a t i t v i r t u a l l y e n c a p s u l a t e s a n y s o u r c e t h a t i s p u s h e d t h r o u g h t h e s p o n g e . I t i s a v e r y c o n v e n i e n t m e t h o d o f s w a b t e s t i n g l a r g e n u m b e r s o f s o u r c e s .

3 . A U T O R A D I O G R A P H Y

R a d i a t i o n s o u r c e s p u r c h a s e d f r o m c o m m e r c i a l m a n u f a c t u r e r s s h o u l d b e a u t o r a d i o g r a p h e d p r i o r t o c l i n i c a l u s e t o d e t e r m i n e t h e d i s t r i b u t i o n o f r a d i o a c t i v i t y w i t h i n t h e s o u r c e c o n t a i n e r . S o m e m a n u f a c t u r e r s p r o v i d e t h e u s e r w i t h a u t o r a d i o g r a p h s b u t g e n e r a l l y s p e a k i n g t h e q u a l i t y o f t h e s e i m a g e s i s p o o r . W h e n s o u r c e s a r e t o b e u s e d i n s i d e a p p l i c a t o r s i t i s e q u a l l y i m p o r t a n t t o o b t a i n a u t o r a d i o g r a p h s o f t h e l o a d e d a p p l i c a t o r s f o r p u r p o s e s o f d o s i m e t r y . We h a v e f o u n d i t h e l p f u l t o u s e m o u l d e d w a x d i s c s f o r

IAEA-SM-298/58 279

FIG. 2. (a and d) Wax discs with Selectron applicators showing lead fo il markers.

(b and e) X-ray images o f applicators loaded with radiographic source trains,

(c and f Autoradiographs showing radioactive sources and fo il markers.

p o s i t i o n i n g a n d s u p p o r t i n g t h e r a d i o a c t i v e s o u r c e s a n d t h e a p p l i c a t o r s . L e a d f o i l m a r k e r s e m b e d d e d i n t o t h e s u r f a c e o f t h e w a x p r o v i d e i d e n t i f i c a t i o n m a r k s a n d s c a l e s w h i c h a r e i m a g e d o n f i l m b y r a d i a t i o n e m i t t e d f r o m t h e r a d i o a c t i v e s o u r c e s . O n c e t h e s o u r c e h a s b e e n p o s i t i o n e d i n t h e a p p l i c a t o r o r w a x m o u l d , e n v e l o p e w r a p p e d f i l m s u c h a s K o d a k X - O m a t V f i l m c a n b e p l a c e d o n t o p o f t h e w a x d i s c . S e c o n d a r y e l e c t r o n e m i s s i o n f r o m t h e l e a d f o i l m a r k e r s r e s u l t s i n t h e f o r m a t i o n o f c o r r e s p o n d i n g r a d i o g r a p h i c i m a g e s ( F i g u r e 2 ) . T h i s m e t h o d a l l o w s c o m p a r i s o n s t o b e

280 JONES

m a d e o f d i f f e r e n t a p p l i c a t o r s a n d a l s o p r o v i d e s a r a d i o g r a p h i c r e c o r d o f t h e l o c a t i o n o f t h e r a d i o a c t i v e s o u r c e p e l l e t s i n s i d e l o a d e d a p p l i c a t o r s .

4 . C A L I B R A T I O N O F R A D I A T I O N S O U R C E S

R a d i a t i o n s o u r c e s o b t a i n e d c o m m e r c i a l l y a r e u s u a l l y c a l i b r a t e d i n G y / h a t 1 m e t e r ( a i r k e r m a r a t e ) a n d t h e n o m i n a l ( o r e f f e c t i v e ) a c t i v i t y i s s p e c i f i e d i n B q o r C i . T h e m e t h o d u s e d f o r c a l i b r a t i o n d e p e n d s u p o n t h e c o m m e r c i a l s u p p l i e r . A l t h o u g h a i r k e r m a m e a s u r e m e n t s m a d e a t d i s t a n c e s b e t w e e n 2 5 0 mm a n d 5 0 0 mm c a n b e r e c o r d e d w i t h a p r e c i s i o n o f b e t t e r t h a n ± 1 % , u n c e r t a i n t y a b o u t t h e s c a t t e r c o n t r i b u t i o n , c h a m b e r q u a l i t y f a c t o r a n d t h e e f f e c t s o f s o u r c e g e o m e t r y r e d u c e s t h e a c c u r a c y o f t h e s e m e a s u r e m e n t s s o t h a t s o m e m a n u f a c t u r e r s s p e c i f y i n d i v i d u a l c a l i b r a t e d s o u r c e s w i t h a n o v e r a l l a c c u r a c y o f ± 5 % . I n p r a c t i c e , w h e n a b a t c h o f s o u r c e s o f s i m i l a r d e s i g n a n d s i z e i s m a n u f a c t u r e d , s o u r c e s a r e c o m p a r e d i n a r e - e n t r a n t i o n i s a t i o n c h a m b e r r a t h e r t h a n b y m e a s u r i n g a i r k e r m a r a t e s t i n n o n - s c a t t e r c o n d i t i o n s ) f o r e a c h s o u r c e . I t i s i m p o r t a n t f o r t h e r e g u l a r u s e r o f m u l t i p l e s e a l e d s o u r c e s t o b e a b l e t o m e a s u r e a i r k e r m a r a t e s a n d t o h a v e s o m e c o n v e n i e n t f a c i l i t y f o r c o m p a r i n g s o u r c e a c t i v i t i e s . T o a c h i e v e t h i s , i t i s u s e f u l t o a c q u i r e a ' c a l i b r a t e d ' s o u r c e f r o m t h e c o m m e r c i a l m a n u f a c t u r e r w h i c h w i l l p r o v i d e a k n o w n a i r k e r m a r a t e a t a f i x e d d i s t a n c e a g a i n s t w h i c h o t h e r s o u r c e s c a n b e c o m p a r e d . I d e a l l y , s u c h m e a s u r e m e n t s s h o u l d b e m a d e i n t h e h o s p i t a l l a b o r a t o r y i n n o n s c a t t e r c o n d i t i o n s s i m i l a r t o t h o s e o b t a i n e d a t c a l i b r a t i o n , b u t , i n p r a c t i c e , t h i s i s n o t u s u a l l y p o s s i b l e . S c a t t e r m a y b e r e d u c e d b y s u p p o r t i n g t h e s o u r c e i n s p a c e a t t h e e n d o f a r i g i d p i e c e o f p e r s p e x o r n y l o n s a y 1 5 m m w i d e , 3 m m t h i c k a n d a t l e a s t 3 5 0 mm l o n g : t h e c h a m b e r ' s e e s ' o n l y t h e r a d i o a c t i v e s o u r c e h e l d b y d o u b l e s i d e d s t i c k y t a p e o n t h e 3 m m x 1 5 mm e d g e o f t h e p e r s p e x . We h a v e e m p l o y e d t h i s m e t h o d u s i n g a 3 7 D P i t m a n X - r a y d o s i m e t e r w i t h a 3 5 c m i o n i s a t i o n c h a m b e r a n d a s o u r c e c h a m b e r d i s t a n c e o f 5 0 0 m m . I t i s n e c e s s a r y t o u s e a 1 . 2 m m t h i c k p e r s p e x c a p o v e r t h e i o n i s a t i o n c h a m b e r t o p r o v i d e ' b u i l d - u p ' a n d t o e l i m i n a t e t h e e f f e c t s o f s e c o n d a r y e l e c t r o n e m i s s i o n f r o m t h e r a d i a t i o n s o u r c e b e i n g m e a s u r e d . S e c o n d a r y e l e c t r o n e m i s s i o n f r o m p l a t i n u m s h e a t h e d s o u r c e s i s s i g n i f i c a n t l y g r e a t e r t h a n t h a t f r o m s t a i n l e s s s t e e l s h e a t h e d s o u r c e s . A l t h o u g h i t i s n o t p o s s i b l e t o r e p r o d u c e t h e e x a c t s c a t t e r ( f r e e ) c o n d i t i o n s o b t a i n e d a t t h e m a n u f a c t u r e r s ' c a l i b r a t i o n

IAEA-SM-298/58 281

î.oo-

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О CDC Е 10mg 2mm AL (10mm EL)

• CDC F4 5mg 10mm AL (12.5m m EL) □ CDC G4 20mg 13.5mm AL (20mm EL)

Д CDC G2 10mg 13 .5mm A L (20mm EL)

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Distance from cavity entrance plane to source centre (cm)

FIG. 3. Siel Isotope Calibrator re-entrant ionization chamber sensitivity plot fo r various caesium sources.AL = active length; EL = external length.

TABLE II. COMPARISON OF ACTIVITIES AND AIR KERMA RATES

Source engraving (approx. 20 mg Pa eq)

RelativeactivityAmersham1972

RelativeactivityRMH1987

Relativeair кегли rateRMH1987

CDC4. 4551 1.000 1.000 1.0004446 0.96(6) 0.96(6) 0.96(4)4468 0.99(5) 0.98(0) 0.98(8)4470 0.96(6) 0.96(4) 0.97(2)4553 0.97(0) 0.97(2) 0.97(6)4475 0.98 (4) 0.98(0) 0.98(4)4536 0.96(7) 0.96(6) 0.97(6)4399 0.96(5) 0.96(5) 0.96(8)4475 0.98 (4) 0.98(4) 0.98(3)

282 JONES

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1----1--- 1--- 1----1----1----1----1----1----1--- 1----1----1--- 1----1----1----1----110 20 30 40

Distance O X (mm)

FIG. 4. Dose rate measurements along the lateral axis o f a 20 mg Ra eq. Cs (49.7 mCi) G tube.

l a b o r a t o r y t h e s p e c i f i e d a i r k e r m a r a t e o f t h e c a l i b r a t e d s o u r c e c a n b e u s e d t o d e t e r m i n e t h e s e n s i t i v i t y o f t h e i o n i s a t i o n c h a m b e r w i t h s u f f i c i e n t a c c u r a c y t o a l l o w p r e c i s e c o m p a r a t i v e d o s e r a t e m e a s u r e m e n t s t o b e m a d e o n o t h e r s o u r c e s .

T h e u s e o f a r e - e n t r a n t i o n i s a t i o n c h a m b e r a l s o p r o v i d e s a c o n v e n i e n t w a y o f c o m p a r i n g t h e e f f e c t i v e a c t i v i t i e s o f a b a t c h o f r a d i o a c t i v e s o u r c e s . T h e s o u r c e m u s t b e p o s i t i o n e d w i t h i n t h e c h a m b e r t o m i n i m i s e g e o m e t r i c a l e f f e c t s . F i g u r e 3 s h o w s t h a t t h e m o s t s e n s i t i v e p a r t o f t h e S i e l I s o t o p e C a l i b r a t o r r e e n t r a n t i o n i s a t i o n c h a m b e r i s 1 8 c m f r o m t h e t o p o f t h e c a v i t y . P r o v i d i n g s o u r c e s a r e o f s i m i l a r g e o m e t r i c a l s i z e a n d c o n s t r u c t i o n , s u c h a c h a m b e r c a n b e u s e d t o m e a s u r e a c t i v i t i e s w i t h a p r e c i s i o n o f b e t t e r t h a n 1 % . T a b l e I I s h o w s a g o o d c o r r e l a t i o n b e t w e e n t h e r e l a t i v e a c t i v i t i e s o f a b a t c h o f G t u b e s o u r c e s m e a s u r e d a t A m e r s h a m I n t e r n a t i o n a l a n d a t t h e R o y a l M a r s d e n H o s p i t a l ( R M H ) , L o n d o n . S i n c e a r e e n t r a n t i o n i s a t i o n c h a m b e r a p p r o a c h e s 4 1 7 g e o m e t r y , e f f e c t s d u e t o t h e l e n g t h , , a n d d i a m e t e r o f t h e s o u r c e s a n d t h e i r f i l t r a t i o n w i l l a l l a f f e c t t h e i r a p p a r e n t

IAEA-SM-298/58 283

W IT S OF DISTRIBUTION- (Ш. ЙЯШ/Ш MRGHiriCfiTIOS FRCTOR I .Z.. ) - .100

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F I G . 5 . R a d i a t i o n d o s e d i s t i b u t i o n a r o u n d a 2 0 m g R a e q . C s ( 4 9 . 7 m C i ) G t u b e s h o w i n g g o o d c o r r e l a

t i o n b e t w e e n c o m p u t e r c a l c u l a t i o n s a n d i s o - d e n s i t y p h o t o c o p y p l o t s .

a c t i v i t y . C o n s e q u e n t l y , c o r r e c t i o n f a c t o r s h a v e t o b e a p p l i e d w h e n s o u r c e s o f d i f f e r e n t c o n s t r u c t i o n a r e m e a s u r e d [ 2 ] .

5 . A B S O R B E D D O S E R A T E M E A S U R E M E N T S A R O U N D C A E S I U M G T U B E S O U R C E S

K l e v e n h a g e n [ 3 ] a n d B r e i t m a n [ 4 ] h a v e m e a s u r e d a n d c a l c u l a t e d r e s p e c t i v e l y d o s e r a t e m e a s u r e m e n t s a r o u n d c a e s i u m b r a c h y t h e r a p y s o u r c e s . A l t h o u g h i t i s n o t u s u a l f o r u s e r s t o c h e c k d o s e r a t e d i s t r i b u t i o n s e x p e r i m e n t a l l y a r o u n d a l l s o u r c e s t h a t t h e y u s e

284 JONES

c l i n i c a l l y , i t i s u s e f u l t o b e a b l e t o d o s o f o r o n e o r m o r e s p e c i f i c s o u r c e s w h i c h c a n t h e n b e u s e d a s r e f e r e n c e s o u r c e s . U s i n g T e m e x [ 5 ] s o l i d t i s s u e e q u i v a l e n t m a t e r i a l , w e h a v e c h e c k e d t h e d o s e r a t e a r o u n d a 2 0 m i l l i g r a m r a d i u m e q u i v a l e n t c a e s i u m G t u b e u s i n g P h y s i k a l i s c h - T e c h n i s c h e W e r k s t ä t t e n ( P T W ) c o n d e n s e r i o n i s a t i o n c h a m b e r s a n d a P T W K o n d i o m e t e r e l e c t r o m e t e r s y s t e m . T h e m e t h o d i s , o f c o u r s e , a p p l i c a b l e t o t h e m e a s u r e m e n t o f o t h e r s o u r c e s . T h e s e n s i t i v e v o l u m e o f t h e s e c h a m b e r s i s 2 mm d i a m e t e r x 3 . 2 m m l o n g . T h e c h a m b e r s w e r e c a l i b r a t e d a g a i n s t a s e c o n d a r y s t a n d a r d F a r m e r d o s i m e t e r i n a c a e s i u m t e l e t h e r a p y b e a m i n w a t e r . T h e s o l i d t i s s u e e q u i v a l e n t T e m e x r u b b e r w a s d r i l l e d w i t h v e r t i c a l h o l e s f o r t h e G t u b e a n d i o n i s a t i o n c h a m b e r s . E m p t y h o l e s w e r e p l u g g e d w i t h s o l i d r u b b e r p l u g s o f t h e s a m e d i m e n s i o n s a s t h e c h a m b e r s . T h e t o t a l p h a n t o m i n c l u d i n g t i s s u e e q u i v a l e n t s c a t t e r m a t e r i a l w a s a p p r o x i m a t e l y 2 0 x 2 0 x 2 0 c m . T h e a c c u r a c y o f t h e m e a s u r e m e n t h a s b e e n e s t i m a t e d t o b e - 4 %. F i g u r e 4 s h o w s t h e s e m e a s u r e m e n t s i n r e l a t i o n t o t h o s e o f K l e v e n h a g e n [ 3 ] , B r e i t m a n [ 4 ] a n d t h e I G E NY T a r g e t p r o g r a m [ 6 ] . T h e d i s t r i b u t i o n o f r a d i a t i o n d o s e r a t e s a r o u n d t h e G t u b e w a s m e a s u r e d p h o t o g r a p h i c a l l y b y p l o t t i n g i s o d e n s i t y l i n e s f r o m a u t o r a d i o g r a p h s u s i n g t h e d i f f u s i o n t r a n s f e r p h o t o c o p y t e c h n i q u e [ 7 ] . I t i s i m p o r t a n t t o e n s u r e t h a t a n y c o m p u t e r p r o g r a m t h a t h a s b e e n d e v e l o p e d f o r b r a c h y t h e r a p y d o s i m e t r y p u r p o s e s a g r e e s w e l l w i t h t h e t r u e d o s e r a t e d i s t r i b u t i o n . F i g u r e 5 s h o w s g o o d c o r r e l a t i o n b e t w e e n t h e I G E NY T a r g e t p r o g r a m a n d t h e m e a s u r e d d o s e r a t e d i s t r i b u t i o n s .

6 . C A L I B R A T I O N T E S T O B J E C T

M a n y h o s p i t a l s a r e n o w u s i n g a f t e r l o a d i n g t e c h n i q u e s . T h e s e c a n b e m a n u a l t e c h n i q u e s , a u t o m a t i c l o w d o s e r a t e o r h i g h d o s e r a t e t e c h n i q u e s . I t i s i m p o r t a n t t o b e a b l e t o m e a s u r e a n d c o m p a r e t h e d o s e r a t e s d e l i v e r e d b y t h e s e d i f f e r e n t s y s t e m s a n d w e h a v e d e v e l o p e d a p h a n t o m f o r t h i s p u r p o s e . T h e t e s t o b j e c t i s m a d e f r o m p e r s p e x a n d i s 1 5 0 x 1 5 0 x 1 3 0 m m w i t h a c e n t r a l c y l i n d r i c a l s e c t i o n ( 1 3 0 x 1 1 0 m m d i a m e t e r ) c o n s i s t i n g o f p e r s p e x i n s e r t s . P e r s p e x a n d o t h e r p l a s t i c m a t e r i a l s w h i c h c a n b e d r i l l e d a n d m a n u f a c t u r e d w i t h g r e a t p r e c i s i o n a l l o w r a d i a t i o n s o u r c e s t o b e l o c a t e d v e r y p r e c i s e l y . H o w e v e r , t h e m e a s u r e m e n t o f a b s o l u t e d o s e r a t e s i n n o n - t i s s u e e q u i v a l e n t m a t e r i a l i s l e s s a c c u r a t e b e c a u s e o f s o m e u n c e r t a i n t y a b o u t t h e d o s e s c a l i n g f a c t o r s f o r . p l a s t i c

IAEA-SM-298/S8 285

FIG. 6. Photograph o f RMH perspex dosimetry test object.

m a t e r i a l s . T h e t e s t o b j e c t h a s b e e n d e s i g n e d t o a l l o w f o r t h i s d i f f i c u l t y : m e a s u r e m e n t s c a n b e m a d e i n w a t e r o r p e r s p e x a c c o r d i n g t o t h e r e q u i r e m e n t . F i g u r e 6 s h o w s t h a t t h e c e n t r a l s e c t i o n c a n b e r e m o v e d t o a l l o w v a r i o u s i n s e r t s t o b e u s e d . P e r s p e x i n s e r t s s u c h a s ' A ' a n d ' C ' h a v e b e e n d e s i g n e d t o a l l o w t h e m e a s u r e m e n t o f d o s e r a t e s a t f i x e d d i s t a n c e s f r o m r a d i a t i o n s o u r c e s i n p e r s p e x , s o t h a t t h e d o s e r a t e s f r o m G t u b e s , C u r i e t r o n s o u r c e s , m a n u a l S e l e c t r o n a f t e r l o a d i n g s o u r c e s a s w e l l a s a u t o m a t i c a f t e r l o a d i n g S e l e c t r o n s o u r c e s c a n b e m e a s u r e d a t s p e c i f i c d i s t a n c e s . I n s e r t ' C c o n s i s t s o f 5 t e l e s c o p i c p e r s p e x s e c t i o n s , e a c h t u b e s e c t i o n h a v i n g a w a l l o f t h i c k n e s s o f 1 0 m m . T h e i n n e r m o s t c y l i n d e r i s 4 0 m m i n d i a m e t e r a n d c o n t a i n s c a v i t i e s f o r a r a d i a t i o n s o u r c e a n d a F a r m e r i o n i s a t i o n c h a m b e r t y p e 2 5 8 1 . T h e t e l e s c o p i c s e c t i o n s c o n t a i n c a v i t i e s f o r F a r m e r , P T W , S i m p l e x d o s i m e t e r p r o b e s , V e r t e c VS 1 0 2 s e m i - c o n d u c t o r p r o b e s a n d T L D d o s i m e t e r s a s w e l l a s c a v i t i e s f o r a

286 JONES

FIG. 7. P ho tograph o f te st ob jec t on tab le (sj w ith insert В show ing location o f Se lectron channels 1,

2 , 3 a n d 4. In sert (top right) show s rad iographic a lignm ent o f F arm er dosim eter, Selectron rad iographic

source tra in a n d centre o f p e rsp ex b lo ck (0).

v a r i e t y o f s t a n d a r d t y p e s m a l l s e a l e d b r a c h y t h e r a p y s o u r c e s . P e r s p e x p l u g s m a y b e u s e d f o r f i l l i n g u n w a n t e d c a v i t i e s . I n s e r t ' B ' i s u s e d w i t h a F a r m e r d o s i m e t e r p o s i t i o n e d c e n t r a l l y b e t w e e n 4 r a d i a t i o n s o u r c e t r a i n s . T h e i n s e r t i s d e s i g n e d t o f i t i n t o t h e c a v i t y o f t h e p e r s p e x t e s t p h a n t o m w h i c h c a n t h e n b e f i l l e d w i t h w a t e r . T h e a s s e m b l e d t e s t o b j e c t i s s h o w n i n F i g u r e 7 o n a n a d j u s t a b l e t a b l e t o a l l o w p r e c i s e r a d i o g r a p h i c a l i g n m e n t o f t h e c h a m b e r a n d s o u r c e s : t h e c h a m b e r f a c t o r c a n b e m e a s u r e d a c c u r a t e l y b y m e a n s o f a c a l i b r a t e d t e l e t h e r a p y b e a m . A d d i t i o n a l i n s e r t s c a n b e u s e d t o i n v e s t i g a t e t h e d o s e r a t e s a r o u n d s p a t i a l l y f i x e d c o n f i g u r a t i o n s o f s e a l e d s o u r c e s . F o r e x a m p l e , i n s e r t ' D ' s h o w n i n F i g u r e 6 c o n s i s t s o f a u t e r i n e t u b e a n d 2 o v o i d s o f t h e A m e r s h a m I n t e r n a t i o n a l m a n u a l a f t e r l o a d i n g s y s t e m e m b e d d e d i n w a x t o s i m u l a t e a t y p i c a l i n s e r t i o n . F i g u r e 8 s h o w s 4 C T s c a n s o f t h e t e s t o b j e c t w i t h c o r r e s p o n d i n g i n s e r t s А , В , С a n d D h i g h - l i g h t i n g t h e g e o m e t r i c a l c o n f i g u r a t i o n o f s o m e o f t h e c a v i t i e s

IAEA-SM-298/58 287

a v a i l a b l e . I n s e r t ' E 1 c o n s i s t s o f o n e o f a s e r i e s o f p e r s p e x t u b e s w h i c h c a n b e p u t i n t o t h e w a t e r p h a n t o m t o s i m u l a t e c y l i n d r i c a l a i r c a v i t i e s b e t w e e n a r a d i a t i o n s o u r c e a n d t h e i o n i s a t i o n c h a m b e r ( T a b l e I I I ) .

TABLE III.% INCREASE IN DOSE PATE MEASURED AT 50 MM FROM 80 MM LONG SET.FCTPON SOURCE: CAVITÏ LOCATED BETWEEN SOURCE AND DOSIMETER

Cavity diameter % Dose(90 inn long) increase

32 rim 17.826 14.816 9.213 8.0

I n s e r t В i s p a r t i c u l a r l y u s e f u l f o r c a l i b r a t i n g S e l e c t r o n l o w d o s e r a t e s o u r c e s : a s a l r e a d yi n d i c a t e d , t h e d o s i m e t e r i s s u p p o r t e d c e n t r a l l y a n d t h e S e l e c t r o n t u b e s m a y b e p o s i t i o n e d r a d i a l l y a t d i s t a n c e s o f 5 , 4 , 3 a n d 2 c m f r o m t h e c e n t r e o f t h e p r o b e . T h e s t r a i g h t a p p l i c a t o r t u b e s a r e h e l d i n t h e r e q u i r e d p o s i t i o n b y t h e p e r s p e x t o p a n d b o t t o m p l a t e s a n d a t h i n c i r c u l a r p e r s p e x p l a t e l o c a t e d w i t h i n t h e c a v i t y o f t h e t e s t o b j e c t . T o r e d u c e t h e e f f e c t s o f h i g h d o s e r a t e g r a d i e n t s n e a r t h e i o n i s a t i o n c h a m b e r , a m e t h o d s i m i l a r t o t h a t u s e d b y M e e r t e n s [ 8 ] h a s b e e n e m p l o y e d . E a c h o f t h e 4 l i n e a r s o u r c e a r r a y s u s e d , c o n s i s t s o f 2 x 5 s o u r c e s w i t h 4 0 m m s e p a r a t i o n b e t w e e n e a c h s e t o f 5 s o u r c e s . T h i s s o u r c e c o n f i g u r a t i o n p r o v i d e s a b u t t e r f l y t y p e o f r a d i a t i o n d i s t r i b u t i o n i n w h i c h t h e F a r m e r d o s i m e t e r i s p o s i t i o n e d c e n t r a l l y i n a n a r e a o f l o w - d o s e g r a d i e n t . F i g u r e 9 s h o w s t h e c a l c u l a t e d d o s e d i s t r i b u t i o n f o r t h i s t y p e o f c o n f i g u r a t i o n : i n p r a c t i c e i t h a s b e e nf o u n d p o s s i b l e t o c o n f i r m t h a t t h e c e n t r e l i n e d o s e r a t e i s w i t h i n 2% o f t h a t c a l c u l a t e d u s i n g t h e I G Ë NY T a r g e t p r o g r a m .

FIG . 8. C T sca n s o f te s t o b je c t w ith in ser ts A (a ), B (b ), C(c) a n d D (d ), respectively . Scans (a) a n d (c) sh o w p e rs p e x in serts w ith p e rs p e x p lu g s rem o v e d to illu s tra te

loca tion o f m e a su r in g cavities . S can (b) sh o w s loca tion o f p e rsp ex channels a t 5 0 m m fr o m th e d o sim eter: sca n h a s b een m a d e b e fo re f i l l in g te s t o b je c t w ith w ater. Scan (d) sh o w s sec tio n th rough a vo id s a n d spacers o f A m ersham d isposab le a fte r lo a d in g a p p lic a to r w ith ra d ia lly d is tr ib u ted ca v ities f o r d o sim eters.

JON

ES

IAEA-SM-298/S8 289

UNITS OF DISTRIBUTION WE РйОз-'НР.

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F/G . 9. In terna tiona l G enera l E lecr ic C om pany o f N ew York (target) com pu ter p r in to u t o f dose d is tr ibu tion o f 4 s tra ig h t Se lectron tubes each loaded w ith 2 x 5 pe lle ts w ith 4 0 m m separa tion betw een each

series o f pelle ts. (38 m C i Cs p e lle t.) D o sim e te r ch a m b er is p o s itio n ed a t 0.

7 . S U MMAR Y

Q u a l i t y a s s u r a n c e i n b r a c h y t h e r a p y i n v o l v e s n u m e r o u s r o u t i n e c h e c k s c o v e r i n g s o u r c e i n t e g r i t y a n d t h e c a l i b r a t i o n a n d m e a s u r e m e n t o f r a d i a t i o n d o s e r a t e s . I t i s i m p o r t a n t t h a t c o n t r o l c h e c k s c a n b e c a r r i e d o u t r e g u l a r l y a n d w i t h a m i n i m u m o f i n c o n v e n i e n c e . T h e d e v i c e s d e s c r i b e d i n t h i s p a p e r h a v e b e e n f o u n d u s e f u l f o r t h e s e p u r p o s e s .

290 JONES

[ 1 ] A M E R I C A N A S S O C I A T I O N O F P H Y S I C I S T S I N M E D I C I N E , P h y s i c a l A s p e c t s o f Q u a l i t y A s s u r a n c e i n R a d i a t i o n T h e r a p y ,AAPM R e p . N o . 1 3 ( 1 9 8 4 ) 3 8 .

[ 2 ] W I L L I A M S O N , J . F . , K H A N , F . M . , S H A R M A , S . C . ,F U L L E R T O N , G . D . ,R a d i o l o g y 1 4 2 ( 1 9 8 2 ) 5 1 1 .

[ 3 ] K L E V E N H A G E N , S . C . , B r i t . J . R a d i o l . 4 6 ( 1 9 7 3 )1 0 7 3 .

[ 4 ] B R E I T M A N , K . E . , B r i t . J . R a d i o l . 4 7 ( 1 9 7 4 ) 6 5 7 .

[ 5 ] S T A C E Y , A . J . , B E V A N . A . R . , D I C K E N S ; C . W . , B r i t . J . R a d i o l . 3 4 ( 1 9 6 1 ) 5 1 0 .

[ 6 ] C A S S E L L , K . , B r i t . J . R a d i o l . 5 6 ( 1 9 8 3 ) 1 1 3 .

[ 7 ] L E S C R E N 1 E R , C . , S T A C E Y , A . J . , J o n e s , C . H . ,P h y s . M e d . B i o l . 1 0 ( 1 9 6 5 ) 5 6 7 .

[ 8 ] M E E R T E N S » H . , " A c a l i b r a t i o n m e t h o d f o r S e l e c t r o n L D R s o u r c e s " , B r a c h y t h e r a p y 1 9 8 4 ( P r o c . 3 r d I n t . S e l e c t r o n U s e r s M e e t i n g 1 9 8 4 , M O U L D , R . F . , E d . ) N u c l e t r o n T r a d i n g BV ( 1 9 8 5 ) 5 9 .

REFERENCES

POSTER PRESENTATIONS

Rapporteur: A. DUTREIX (France)

IAEA-SM-298/95P

DOSIMETRY IN 192Ir BRACHYTHERAPY USING PRE-CALCULATED TABLES

G. HORGAS, V. LOKNER, B. PROKRAJAC,S. SPAVENTINuclear Medicine and Oncology Clinic,“ Dr. M. Stojanovié” Clinical Hospital,Zagreb,Yugoslavia

Brachytherapy has become a method of choice in oncotherapy owing to its well known advantages in the treatment of certain tumours. If the application geometry is properly combined with well fixed dose prescription, the results are excellent, both as regards high cure rate and good tolerance of normal tissues. Modern remote afterloading machines and computers permit perfect radioactive source positioning and dose calculations.

Not being in the position to exploit the advantages of these high technology devices for 192Ir brachytherapy we use the manual afterloading technique combined with tabulated dosimetry based on the Paris system.

The dosimetric control after interstitial implantations, considered to be in conformity with the Paris system, is made directly from a series of pre-calculated tables which give the strength of the dose as a function of the distance from the sources. It is necessary to achieve the constructions of equilateral single plane implants, triangles and squares or their summits and to avoid bad implants such as obtuse triangles or rectangles where even the best calculation cannot bring about a satisfactory treatment result.

When the intersections of the radioactive sources with the central plane do not meet the ideal principle of equidistance between the sources, an individual calculation with additional dose rate curves for basal and reference dose readings may easily be applied.

The tables contain the decay correction curve as well as the treatment time correction curves to permit appropriate adjustment of the dose rates according to the disintegration of 192Ir before and during therapy time (Fig. 1).

The intention is to demonstrate the advantages as well as the limitations of this dosimetry method.

291

292 POSTER PRESENTATIONS

(a ) (b )B D c a lc u la tio n p o in t

Effectivelength(cm)

Basal dose, BD(Gy/h)

Reference dose, RD (Gy/h)

1.0 0.298 0.2531.5 0.390 0.3322.0 0.458 0.3892.5 0.510 0.4343.0 0.550 0.4683.5 0.580 0.4934.0 0.608 0.5174.5 0.630 0.5365.0 0.650 0.5535.5 0.664 0.5646.0 0.678 0.5766.5 0.690 0.587

Disintegration corrections

Curve 1

8 9 10 11 12 13 14 15 16 17 18 19 20 Time (weeks)

Time (days)

FIG. 1. (a) H ypoderm ic s ing le p la n e im plan t o f 192Ir w ires in the p a r ie ta l sku ll region co n tro lled by

roen tgenogram ; (b) C entral p la n e sec tion w here reference dose (curved line , 85% o f b a sa l dose)

encloses target volum e. Table f o r R D a n d B D dose ra te reading; (cj l92Ir decay in w eeks; (d) Tim e

(in hours) to be a d d ed to the to ta l tim e o f therapy.

POSTER PRESENTATIONS 293

BIBLIOGRAPHY

BO ISSER IE , G., M A R IN ELLO , G., J. Radiol. (Paris) 60 (1979) 327.

CASEBOW , M .P., Br. J. Radiol. 58 (1985) 549.

D U T R E IX , A ., M A R IN ELLO , G., PIERQ U IN , B., CH A SSAG N E, D ., H O U LA R D , J.P ., J. Radiol. (Paris) 60 (1979) 21.

M A R IN ELLO , G., D U T R E IX , A ., PIERQ UIN, B., CH A SSA G N E, D ., J. Radiol., Electrol. 59 (1978) 621.

PIERQ UIN, B., D U T R E IX , A ., P A IN E, C .H ., CH A SSA G N E, D ., A SH , D ., Acta Radiol., Oncol. 17 (1978) 33.

IAEA-SM-298/18P

ORGAN DOSES FROM RADIOTHERAPYFOR CERVICAL CANCERUSING MONTE CARLO CALCULATIONS

N. PETOUSSI, M. ZANKL, G. WILLIAMS,R. VEIT, G. DREXLER Institut für Strahlenschutz,Gesellschaft für Strahlen- und Umweltforschung mbH,Neuherberg,Federal Republic of Germany

There is evidence that cervical cancer patients treated with radiotherapy had an increased incidence of second primary cancer.

The aim of the present study is to estimate the absorbed dose resulting from radiotherapy treatment of cervical cancer to various organs and tissues in the body. It is part of a large radiation study supported by the World Health Organization and involves the follow-up of 30 000 women treated for primary cervical cancer and the measurement of the incidence of secondary cancers.

In order to calculate the organ and tissue doses a Monte Carlo program was used which simulates the scattering and absorption of photons within a three-dimensional anthropomorphic female phantom, based on a reference woman with ¿11 female organs [1].

Calculations were performed to estimate the absorbed doses to various organs resulting from intracavitary sources such as ovoids arid applicators filled or loaded with radium, “ Co and 137Cs. The intra-utérine applicator was simulated as one or more parallelepiped tubes of dimension 0.2 cm x 0.2 cm X 2.0 cm, situated within the uterus. The ovoids were simulated as 0.2 cm x 1.5 cm x 0.2 cm tubes. '


TABLE I. ORGAN DOSES

Case 1 Case 2 Case 3Organ Brachy Single Ovoids,

therapy ovoid + applicators +only external split

A P + PA A P + PAfields fields

(cGy) (cGy) (cGy)

Bladder 4 515 5 547 8 334

Breast 18 5 21

Kidneys 139 47 160

Liver 80 26 94

Lungs 22 6 25 ■

Ovanes 2 387 . 4 298 5 300

Rectum 1 732 1 767 2 900

Peak dose (skin) 941 8 202 6 700

Point В 4 677 5 268 8 200

RBM (total) 370 333 550

RM pelvis 909 880 1 490

Small intestine 770 314 947

Stomach wall 107 35 122

Thyroid 3 0.8 3.5

Total body 417 370 662

Calculations were made also for external beam therapy. Three beams were used: “ Co, 137Cs and the beam produced by a megavoltage machine. The following fields were involved: anterior pelvis, posterior pelvis, split (parametrium treatment) right and left anterior pelvis, split right and left posterior pelvis and right and left lateral pelvis.

The calculated organ doses were expressed in four different ways: as organ dose per air kerma in the reference field (according to the recommendations of ICRU [2]) ; as organ dose per surface dose, as organ dose per tissue dose at point В and, finally, as dose per fluence in the reference field.

Thirty-six tables were compiled [3] containing the doses for 106 organs and tissues, 12 for internal therapy and 24 for external therapy arrangements. Using these tables, the organ doses for a complete treatment can be easily calculated. As an example, Table I shows some organ doses for three of the cases included in the follow-up study of the WHO.


R EFE R EN C ES

[1] K R A M E R, R ., Z A N K L , M ., W ILLIA M S, G., D R E X L E R , G., The Calculation of Dose from External Photon Exposures Using Reference Human Phantoms and Monte Carlo Methods. Part I: The Male (ADAM ) and Female (EV A ) Adult M athem atical Phantoms, GSF-Bericht S-885, Munich (1982).

[2] IN T E R N A T IO N A L COM M ISSION ON R A D IA T IO N U N ITS A N D M EA SU REM EN TS, Dose and Volume Specifications for Reporting Intracavitary Therapy on Gynecology, IC R U Report 38, IC R U Publications, Bethesda, MD (1985).

[3] PETO USSI, N ., Z A N K L , M., W ILLIA M S, G., V E IT , R ., D R E X L E R , G ., Organ Doses from Radiotherapy for Cervical Cancer, GSF-Bericht 5/87, Munich (1987).

IAEA-SM-298/54P

CONTROL OF OCCUPATIONAL EXPOSURE IN THE USE OF AFTERLOADING SYSTEMS BY MEANS OF CONTROLLED AREAS AND SYSTEMS OF WORK

D. GIFFORD, T.J. GQDDEN, D. KEAR Department of Medical Physics,Bristol General Hospital,Bristol,United. Kingdom

The use of sources of penetrating radiation for the intracavitary and interstitial treatment of patients in radiotherapy and oncology centres has always been a major source of personal radiation dose to the staff in centres nursing these patients. Many methods have been tried in the attempt to minimize personnel doses, such as the use of barriers or shields, the separation of patients undergoing such treatments from other patients, and the rotation of staff. The use of barriers or shields is universally disliked by nursing personnel. While the separation of patients and the rotation of staff may lead to lower individual staff doses, it does not reduce, and may even increase, collective population dose, which is now considered contrary to the ALARA principle.

Whereas in the past, an operational system of procedures for radiation protection could be considered acceptable if individual personnel doses were maintained below the relevant quarterly and annual limits, this is no longer sufficient in the light of ALARA, and positive steps must be taken towards the reduction of personnel doses.


The particular combination of high photon energy sources used for intracavitary and interstitial patients requiring regular and frequently intimate nursing care has always presented a major problem for the health physicist, to which a solution only appeared with the advent of afterloading systems such as the Cathetron and, more recently, Selectron.

In the latter system, the sources are normally contained in a protected housing, which is connected by armoured flexible tubes to a set of appliances or applicators which are inserted into the patient and localized in the operating theatre. The patient is then returned to a specially designated ward and the flexible tubes are connected to the applicators. The patient is then made comfortable, all staff leave the ward, and the sources are then inserted into the applicator under remote control by pneumatic pressure. If it becomes necessary to carry out nursing procedures, or to intervene for any other purpose, the sources are retracted by remote control, so that staff may enter and remain in the room without being irradiated.

This arrangement ideally requires the availability of protected single wards, the ceiling, doors, floor and walls of which are protected to such a degree that the time average dose rate (dose rate averaged over any eight-hour period) is less than 7.5 ¿iSv/h. This, in fact, in the case of sources of high photon energy of activities of 250 mg radium equivalent is quite difficult to achieve, and may require walls of a tickness up to 60 cm of concrete, and doors protected with up to 4 cm of lead. The only way the dose rate can be reduced to the limit set in the UK for a supervised area in the vicinity of the door to the ward is by means of a maze entrance, for which there is often not sufficient room.

An alternative approach to satisfy the requirements of Regulation 6 of the United Kingdom Ionising Radiations Regulations 1985 is by the use of Controlled Areas as laid down in Schedule 6 of the Regulations. Access into controlled areas is only permitted to the patient and persons occupationally exposed to radiation who are designated as classified. Access to other persons who are not classified is allowed only in accordance with Local Rules and Written Systems of Work.

In the case described, four single side wards were originally constructed with walls on one side of 2 feet (60 cm) of concrete, but without protection being provided for.thé entrances. Cost of the protection necessary to reduce time average dose rate in the corridors and adjacent areas to less than 7.5 ¿tSv/h would have been excessive, and the decision was taken to introduce administrative controls based on Local Rules and Systems of Work. .


LOW DOSE RATE BRACHYTHERAPY TECHNIQUES: STAFF EXPOSURE DOSES

C.H. JONES, W. ANDERSON, R. DAVIS,A.M. BIDMEAD, S.H. EVANS Joint Department of Physics,Institute of Cancer Research

and Royal Marsden Hospital,London,United Kingdom

IAEA-SM-298/57P

Statutory regulations focus attention on the safe handling of radioactive brachytherapy sources and the need to record staff exposure doses. The authors report some of the dose measurements on personnel using sealed radiotherapy sources during the period 1956 to 1986. In recent years significant changes have taken place in the availability of high specific activity sources as well as the techniques used to insert these sources into patients. For example, radium has been replaced by caesium-137; rigid needle sources have been replaced by small diameter wire radioactive sources allowing the use of afterloading techniques. In the case of low dose rate gynaecological intracavitary techniques, the traditional manual insertion of radioactive sources has been superseded by manual or automatic afterloading techniques. These changes have resulted in significant reductions in radiation exposure to the several categories of staff involved in brachytherapy.

Exposure dose magnitudes are dependent largely on the clinical technique used, the associated manipulative procedures, and the nursing care of the patient. We have investigated the role of the different types of dosimeter used for measuring staff exposure doses including film monitors, TLD dosimeters and, more recently, PENDIX personal dosimeters. Each type of dosimeter has its merits; film monitors are reliable, and provide a permanent record of staff exposure — they also provide some information about energy discrimination and the direction of the incident radiation field. We have found TLD, to be particularly useful for finger dose measurements. PENDIX miniature GM tube dosimeters provide means of recording doses over a wide range (1 /xSv to 999 mSv) and are useful for rapid assessment of source handling procedures.

Interbed shielding and mobile lead bed shields, remote handling and specially designed workbench facilities have been used to minimize radiation exposure to staff and we have investigated the effectiveness of these factors. Figure 1 shows the gradual decline of collective dose per intracavitary gynaecological treatment for staff responsible for preparing radioactive sources through the period 1965 to 1985.


Years (1965-1985)

F IG . 1. C ollective dose p e r treatm ent fo r radium !caesium handlers.

TABLE I. RADIATION DOSES (MICROSIEVERTS PER INSERTION)

Traditional“ Manualafterloading

Automaticafterloading

Cs handlers 40 10 -

Radiotherapist and assistant 180 20 -

Theatre nurses 80 - -

Ward nurses 225 200 10

Additional staff 50 - 10

Total dose (Microsieverts/80 mg Ra eq Cs-137 insertion)

575 230 20

a Mainly 25 hour insertions.


Table I summarizes our findings for all staff involved in treating and caring for patients receiving gynaecological intracavitary radiotherapy caesium techniques.

Although automatic afterloading systems are expensive they virtually eliminate radiation exposure of staff, provide security for source containment, save space and manpower and also provide the possibility of better nursing care. In the absence of automatic afterloading we have found that the introduction of manual afterloading is the only most effective way of reducing finger and body doses of staff using brachytherapy sources. We have also found that interbed shielding and mobile bed shields are, in relative terms, cost effective methods of reducing radiation exposure to nursing staff [1].

REFERENCE

[1] JO NES, C .H ., B ID M EAD , A .M ., AN D ERSO N , W., EV A N S, S .H., D A V IS , R ., Abstract, 5th Annual Meeting of the European Society for Therapeutic Radiology and Oncology, Baden-Baden (1986) 310.

IAEA-SM-298/74P

PROTECCION RADIOLOGICA EN CURIETERAPIA. ANALISIS DE RIESGOS Y CONTROL DE FUNCIONAMIENTO

V. ANCEÑA, P. LORENZ, G. MARTI, P. ORTIZ Consejo de Seguridad Nuclear,Madrid, España

La diversidad de actuaciones y el movimiento de personas y de material radiactivo que conlleva la práctica de la Curieterapia hacen necesario un análisis de los riesgos asociados a cada una etapas de las de la secuencia de operación:— Preparación del material a implantar.— Colocación del material en el volumen blanco.— Comprobaciones de la calidad del implante. Control inicial y vigilancia

continuada.— Atenciones al enfermo implantado.— Retirada y almacenamiento de las fuentes radiactivas.

De dicho análisis se identifican como riesgos más significativos la posibilidad de pérdida de fuentes en cualquiera de las etapas, y un no despreciable coste


radiológico para el propio paciente, para el personal de la instalación y para miembros del público, originado fundamentalmente por estos dos hechos:— El paciente implantado carece, en la mayoría de los casos, de una formación

radiológica adecuada.— El paciente, por su misma conndición, puede requerir atenciones clínicas no

programadas.Para controlar los riesgos se hace imprescindible disponer de una serie de datos

ordenados cronológicamente en un registro único, orientado a la protección radiológica. En este sentido, y desde la perspectiva y experiencia acumulada por el organismo que controla la seguridad de las instalaciones radiactivas en España, se propone una relación mínima de datos que permita:— Una mejor planificación de las operaciones que se desarrollan en la instalación ante

las situaciones prácticas detectadas.— Determinar con prontitud, ante cualquier situación de incidente, el eslabón de la

secuencia que obligue a adoptar medidas preventivas o correctoras.— Elaborar el contenido del programa de protección radiológica que deberá ser

impartido de forma reciclada al personal profesionalmente expuesto que participe en las operaciones, y la información básica que deberá transmitirse al paciente para que preste una colaboración serena y reflexiva ante las circunstancias que se presenten.

Este control supondría un desarrollo práctico de las recomendaciones hechas por la Comisión Internacional de Protección Radiológica (CIPR) en el capítulo E. “ Radiotherapy” (Publ. 33) y en los capítulos C. “ Brachytherapy” e I. “ Radiation therapy staff education, training and duties” (Publ. 44).

EXTERNAL THERAPY DOSIMETRY

(Session IV)

Chairman

J.E. BURNSUnited Kingdom

Poster Rapporteur

A.E. NAHUMUnited Kingdom

IAEA-SM-298/48

CALCULATION OF ELECTRON CONTAMINATION IN A “ Co THERAPY BEAM

D.W.O. ROGERS, G.M. EWART, A.F. BIELAJEW Physics Division,National Research Council of Canada,Ottawa, Ontario

G. VAN DYKAtomic Energy of Canada Limited,Kanata, Ontario

Canada

Abstract

C A LC U LA T IO N OF E LE C T R O N CO N TAM IN ATIO N IN A “ Co T H E R A P Y BEAM .The EGS Monte Carlo radiation transport system has been used to model the therapy beam from

an A E C L “ Co unit. Photon contamination is shown to be mostly due to the source capsule and to have little effect on the depth-dose curve. The calculations for broad beams show that there are many sources of electron contamination (collimators, air, source capsule) which vary in importance as a function of SSD. The effects of filters and magnets on electron contamination have been studied. The calculations are shown to be in good agreement with experimental results except very close to the surface (< 0 .5 mm) where the calculations underestimate the measurements.

1. Introduction

Electron contamination of broad 60Co therapy beams can increase the maximum dose by up to 15% and can shift the depth of dose maximum from 5 mm to 1 mm. There have been a variety of both theoretical and experimental investigations of this effect (e.g. [1] to [4] and references therein) and it is now well established that electrons are the major contaminant. However, there has been no comprehensive study for 60Co beams which could distinguish the various sources of electron contamination. To investigate the possibilities for reducing this contamination and as a first step in the development of a general Monte Carlo model of an accelerator head, we have modelled a 60Co unit. There has been considerable previous work on modelling the photon contamination in a 60Co therapy unit (see e.g. [5]) but prior to this work ([6]) there has been little study of the effects of the photons on the buildup region. There have been some comparable studies related to electron contamination of accelerator photon beams [7].

303

304 ROGERS et al.

SOURCE

__________________±

S C O R I N G _______________________________

P L A N E S

FIG. 1. The g eo m etry m odelled . There is cylindrica l sym m etry . The source can be a p o in t source , p a ra lle l beam s o r p re-co m p u ted o u tp u t fr o m the 60Co capsu le in Fig. 2.

FIG . 2. M o d e l u sed f o r the en capsu la ted 60Co source.

IAEA-SM-298/48 305

The model uses the EGS Monte Carlo system to simulate the transport of electrons and photons [8]. EGS takes into account photo-electric, Compton and pair production interactions of photons and accounts for the slowing of electrons, the creation of secondary photons and electrons and the multiple scattering of electrons. It was found essential to use a reduced electron step-size to obtain accurate results (see [9]).

Figure 1 presents a schematic of the geometry which was modelled. It was essential to model fully the 60Co source capsule which is shown in figure 2. This was done separately and the phase space parameters of 2 million electrons and photons entering the beam collimation system from the front face of the capsule were stored in a highly compressed format and used repeatedly as input to the rest of the simulation.

The computer code is general but for the purposes of this study a “BASE” case has been defined which represents a broad beam from an AECL therapy unit (Theratron 780, which is rectangular rather than cylindrical as modelled). The inner collimator is solid lead, and fixed to allow an unobstructed beam of up to 39.5 cm diameter at an SSD of 80 cm (equal in area to a 35 x 35 cm2 beam). It is 1.50 cm from the capsule, 6.2 cm thick, with inner and outer radii of 1.4 and 2.68 cm. The outer collimators pivot on a hinge at the inner corner of the inner collimator and are adjusted to define the field size via a line through the center of the capsule face and the outer edge of the outer collimator. The hinge was not modelled and the outer collimator was taken to be solid although in reality it is made of leaves. It was 19.3 cm thick, made of lead, 0.4 cm past the inner collimator and had inner and outer radii of 2.77 and 6.76 cm in the BASE case. The BASE case included no filters or magnets although they could be included either between the collimators or anywhere between the unit and the patient plane by terminating all electron histories entering the magnet region.

To make the calculation tractable required the use of a wide variety of variance reduction techniques, including: i) calculating the effects of the source capsule and repeatedly using the stored results; ii) forcing all photons to interact in the air or the filters before leaving the head and using appropriate weights to account for the extra interactions; iii) terminating the history of any electron unable to reach the patient; iv) forcing all primary photons leaving the head to interact in the air outside the head; v) reusing all particles leaving the head for calculations at each SSD being considered; and vi) calculating depth-dose curves by scoring the planar fluence at the patient surface and folding these with pre-computed depth-dose curves for normally incident mono-energetic particles [10,11]. For low energy photons it was essential to use pre-computed depth-dose curves [11] which included details of the buildup curves. When pre-computed curves were used which did not take into account the buildup in the first 2 mm [10], the low energy photons appeared to contribute significantly to the surface dose.

The variance reduction techniques increase the computing efficiency by up to a factor of 100. To obtain electron depth-dose curves with a few percent statistical

2. Calculations

306 ROGERS et al.

on axis photon spectrum, 100 cm from 60-Co capsule

photon energy / MeV

FIG . 3. On-axis photon spectra, 100 cm fro m the source capsule, w ith and w ithou t the effects o f co llim a to r and a ir scatter.

uncertainty required 5 to 16 hours of VAX/780 CPU time. With the exception of using the pre-computed depth-dose curves, these techniques do not affect the accuracy of the simulation. Using pre-computed depth-dose curves introduces two approximations since they are assumed to be broad and incident normally. These assumptions affect the surface dose somewhat, but have little effect at depths of 1 mm or greater (see [12] and below). One final approximation was that electrons were tracked down to 100 keV and then considered to deposit all their energy on the spot. The range of these electrons is about 14 mg-cm-2 in water and 13 cm in air.

3 . Results

3 .1. Scattered photons

The major source of scattered photons is the source capsule itself, as is shown in Figure 3. The scattered photons contribute 29% of the on-axis fluence or 18% of the maximum dose. The electrons from the capsule have an average energy of 580 keV and represent only 0.5% of the particles leaving the front face. These can still have a large effect on the dose in the buildup region as we shall see below. If we also consider the photons scattered from the collimators, the scatter component goes up to about 32% of the fluence as seen in Figure 3 and Table I.

IAEA-SM-298/48 307

Table I

On-axis photon spectrum from a 60Co unit in the BASE case configuration, including capsule, collimator and air scatter. The values are normalized absolutely per initial 1.25 MeV photon in the source capsule (multiply by 2 to get Bq-1). One standard deviation uncertainties are given in brackets.

Top of bin (MeV)

Photons/sr/MeV / 1.25 MeV photon

Top of bin (MeV)

Photons/sr/MeV / 1.25 MeV photon

0.05 « 0 0.65 0.0176 (2%)0.10 0.0013 (10%) 0.70 0.0168 (3%)0.15 0.0130 (3%) 0.75 0.0181 (3%)0.20 0.0256 (3%) 0.80 0.0183 (4%)0.25 0.0376 (3%) 0.85 0.0197 (2%),0.30 • 0.0355 (2%) 0.90 0.0216 (3%)0.35 0.0297 (3%) 0.95 0.0222 (4%)0.40 0.0245 (4%) 1.00 0.0276 (2%)0.45 0.0203 (4%) 1.05 0.0300 (2%)0.50 0.0212 (2%) 1.10 0.0288 (3%)0.55 0.0229 (3%) 1.15 0.0259 (2%)0.60 0.0188 (3%) 1.20 0.0223 (2%)

1.25 1.094 (<0.5%)

contaminant free Co-60 buildup curve

depth (g e m -2)

FIG . 4. Com parison o f the m easured [1 3 ] and ca lcu la ted bu ildup curves fo r photon beams w ith no electron contam ination.

308 ROGERS et al.

c o m p o n e n ts o f e le c t ro n c o n ta m in a t io n

¿4C0<l>СЦ

09cd

aо ift

«QOО

•в

SSD(cm)

F/G. 5. Components o f electron contam ination as a fu n c tio n o f SSD in the BASE case (39.5 cm diam eter, un filte re d beam).

At dose maximum, about 1% and 4% of the dose comes from photons scattered from the inner and outer collimators, respectively. This result means that our model is incapable of explaining the roughly 10% increase in dose rate observed in clinical photon beams as the beam size increases. At most a 5% increase can be caused by increased collimator scatter. The remainder of the increase must be related to other factors, perhaps a partial blocking of the source with smaller field sizes. Figure 4 presents a comparison of our calculated results with the measurements of Higgins et al. [13] for the buildup region of a beam with no electron contamination. Including scattered photons in the calculations makes a small improvement in the comparison. Scattered photons are found to have only a small effect on the overall depth-dose curve.

3 .2. Electron contamination

3.2.1. BASE case

On account of multiple scattering and creation of knock-on electrons etc, it is quite difficult to define uniquely “where an electron came from”. In figure5, we have separated the electron contamination into several components. The ‘W .O .’ (within outer) component consists of all electrons from electrons or. photons which leave the source capsule in a direction within the outer collimator (i.e. in the beam). This component includes the electrons from the capsule and

IAEA-SM-298/48 309

electron contamination

SSD(cm)

FIG . 6. E lectron contam ination versus SSD fo r a va rie ty o f con figura tions o f filte rs and magnets.

those generated in the air by photons. The ‘I.C.* and ‘O .C .’ components are from those particles which leave the capsule headed for the inner collimator and outer collimator, respectively. Figure 5 presents the components of the electron contamination in the BASE case at 0.05 cm depth as a fraction of the peak dose in a water phantom as a function of SSD. The depth-dose curve resulting from electrons does not vary much at depths from 0.01 cm to 0.15 cm and is roughly the same shape for each component so that figure 5 gives an accurate indication of the overall electron contamination. This figure shows, for example, that at an SSD of 80 cm the contaminant electrons are 45% of the peak photon dose; 22% come from capsule and air generated electrons; 10% and 13% come from particles initially going towards the outer and inner collimators respectively. To get an idea of the electrons generated by the air only, one can look at the “magnet outer” curves in figure 6. We have investigated the effects of changing the collimator material and the collimator geometry somewhat. Electron contamination is virtually independent of material and somewhat dependent on details of the geometry. See reference [6] for a detailed discussion.

3.2.2. Filtered beams

We have investigated the effects of various filters on electron contamination. Figure 6 presents the results as a function of SSD for 0.7 g-cm~2 filters of PMMA or Cu placed at an SSD of 57 cm. These filters are thick enough to stop all contaminant electrons in the beam while only attenuating the photon beam by about 3%. However, they are themselves a source of electrons. Copper makes

310 ROGERS et al.

a better filter because about 40% fewer electrons leave the Cu per transmitted photon. This is because the electrons are much more scattered in the copper and hence have a shorter effective range. This larger scatter also means that those electrons which do escape are less likely to reach the patient. We have investigated the effects of filter position and thickness(see [6]). There is no dramatic dependence on filter thickness. At an SSD of 80 cm the optimum distance for a Cu filter is 27 cm from the source but at SSD=100 cm there is little variation with filter position.

3.2.3. Magnets

Figure 6 also shows the effects of perfect electron sweeping magnets placed either between the collimators (“inner”) or just outside the head ( “outer”). The “outer” case shows the contamination caused by electrons generated in the air outside the therapy head. The “inner” case is almost as good as the “outer” case at typical treatment distances of 80 to 100 cm, but is much easier to implement because of the smaller dimensions of the beam at this point. With the advent of practical high temperature superconducting magnets this option may become more attractive.

3.2.4. Field size

All of the calculations reported above were for large diameter beams. For technical reasons we could only do preliminary runs for small field sizes. However, in agreement with experiment, we find that electron contamination in a 5 x 5 cm2 field is 5 to 15 times less than in the broad beam case.

4. Comparison with experiment

We have compared our results with many of the measurements reported by Attix et al. [3] and in general find very good agreement except at the very surface (<0.5 mm). Figure 7 shows a comparison of the total dose at two depths vs SSD in a broad, unfiltered beam. The agreement at 0.1 g-cm-2 is good at all SSDs, but the calculations underestimate the dose at the surface. To investigate the limitations of using the pre-computed, normally incident depth-dose curves, we have done the much more time consuming “full” calculation at an SSD of 200 cm where only air generated electrons are important. Here the electrons were followed down to 10 keV and full account was taken of their non-normal incidence 011 the phantom. The points marked “full” in figure 7 demonstrate that the approximate methods work well at the greater depths, but they are somewhat inaccurate at the very surface. However, even the full calculation does not agree well with the experimental results for the very surface. In practical terms this is of no consequence because the dose is relatively small there, and these depths are still within the dead layer of the patient’s skin. Nonetheless these discrepancies are unexplained and represent one of the worst cases of disagreement we have found

IAEA-SM-298/48 311

open fíeld - 39.5cm diam 60 Co: caln vs ezpt

■aQiex.

О

33

1CÜ 1UU

SSD (cm)

FIG . 7. Com parison fo r the BASE case between the ca lcu la tions and measurements o fA ttix et a l. [3 ]. The triang les m arked ‘fu ll ' a re calcu la tions fo r w hich the pre-com puted depth-dose curves were no t used and electrons were tracked to 10 keV.

open 39.5cm diam 60 Co beam SSD=72cm caln vs ezpt

depth (cm)

FIG . 8. Com parison o f the calcula ted and m easured [3 ] depth-dose curves a t an SSD o f 72 cm fo r the BASE case. The calcu la ted dose fo r photons on ly is also shown.

312 ROGERS et al.

between Monte Carlo calculations and experimental results. The disagreement may be the result of problems with the experimental results at the very surface; they may be explained by a slight offset in the depth scale; or they may represent theoretical problems in calculating the dose at an interface.

Figure 8 shows a comparison of the complete depth-dose curves as calculated and measured. From figure 7, it can be seen that this is the depth of worst agreement. Yet it is clear that the calculations go a long way towards explaining the electron contamination. Reference [6] presents many comparisons for filtered beams which also show good agreement.

5. Conclusions

The Monte Carlo code described here has been used to demonstrate that electron contamination explains the changes in the buildup region of a broad 60Co therapy beam. Photon contamination is primarily from the source capsule, contributes significantly to the dose, but has little effect on the shape of the depth- dose curve. The electron contamination comes from a wide variety of places but the capsule itself is the major source at close SSDs and air generated electrons dominate at larger distances. Agreement with experiment is excellent except near the surface.

References

(1) Nilsson, B., Brahme, A., Phys.Med.Biol. 24(1979)901.(2) Higgins, P.D., Sibata, C.H., Attix, F.H., Paliwal, B.R., Med.Phys. 10(1983)622.(3) Attix, F.H., Lopez.F., OwaIabi,S., Paliwal.B.R., Med.Phys. 10 (1983) 301.(4) Galbraith,D.M., Rawlinson, J.A., Med.Phys.12 (1985)273-280.(5) ICRU Report 18. “Specification of High Activity Gamma-ray Sources” ICRU, Washington D.C.(1970)(6) Rogers, D.W.O., Bielajew, A.F., Ewart, G.M., van Dyk, G., “Calculation of Contamination of the 60Co Beam from an AECL Therapy Source”, NRC Report PXNR-2710, Jan. 1985 (available from the authors); and Med. Phys.11 (1984) 401 and 12 (1985) 515, abstracts.(7) Petti, P.L., Goodman, M.S., Sisterson, J.M., Biggs, P.J., Gabriel, T.A., Mohan, R., Med. Phys.10 (1983) 856-861.(8) Nelson, W.R., Hiiayama, II., Rogers, D.W.O., “The EGS4 Code System”, Stanford, Calif. (1985) SLAC Report-265.(9) Rogers, D.W.O., Nucl. Instr. Meth. A227 (1984)535-548.(10)Rogers, D.W.O., Health Phys. 46 (1984) 891-914.(11)Rogers, D.W.O., Bielajew, A.F., Med. Phys. 12 (1985) 738-744.(12)Rogers, D.W.O., Bielajew, A.F., “The Use of EGS for Monte Carlo Calculations in Medical Physics”, NRC Report PXNR-2692, (June 1984).(13)Higgins, P.D., Sibata,C.H., Paliwal, B.R., Phys.Med.Biol. 30 (1985) 153-162.

IAEA-SM-298/22

INFLUENCE DE L’OS SUR LA DISTRIBUTION DE DOSE DANS LES FAISCEAUX D’ELECTRONS

F. BIDAULT Service de radiothérapie,Centre hospitalier,Epinal

P. ALETTIUnité de radiophysique,Centre Alexis-Vautrin,Vandœuvre-lès-Nancy

A. DUTREIX Unité de radiophysique,Institut Gustave-Roussy,Villejuif

France

Abstract-Résumé

EFFECT OF BONE ON DOSE DISTRIBUTION IN ELECTRON BEAMS.A method of calculating dose distribution over the beam axis in a heterogeneous medium

(polystyrene, bone-equivalent medium) irradiated with high-energy electrons has-been established from experimental data using the ‘small beam’ model. The method, which uses a decomposition of the dose breakdown due to radiation scattering, has made it possible to account for the overdose in the exposed bone-equivalent medium and the effect of the bone-equivalent medium on the percentage depth dose in the polystyrene downbeam of the heterogeneity. The scattering functions in media made of homogeneous polystyrene, in bone-equivalent materials and in heterogeneous media were established for 9 MeV, 15 MeV and 25 MeV electrons and various circular fields. The scattering functions for heterogeneous media were recalculated by combining the scattering functions for homogeneous polystyrene and bone-equivalent media, and the percentage depth doses over the beam axis derived from them. The uncertainties in the percentage depth doses for the polystyrene downbeam of the heterogeneity were less than 3%,2% and 0.5% for 9 MeV, 15 MeV and 25 MeV electrons, respectively. Uncertainty in the region upbeam of the heterogeneity is cut to under 1% by taking into account the effect of electrons backscattered upbeam by the bone-equivalent medium.

INFLUENCE DE L’OS SUR LA DISTRIBUTION DE DOSE DANS LES FAISCEAUX D’ELECTRONS.

A partir de données expérimentales et en s’inspirant du modèle dit «des petits faisceaux», on a établi une méthode de calcul de la distribution de dose sur l’axe du faisceau, dans un milieu hétérogène (polystyrène-milieu équivalent os) irradié par des électrons de haute énergie. Cette méthode, utilisant la décomposition de la dose due au rayonnement diffusé, a permis de

313

314 BIDAULT et al.

rendre compte du surdosage observé dans le milieu équivalent os traversé ainsi que de l’influence de ce milieu sur le rendement en profondeur dans le polystyrène situé en arrière de l’hétérogénéité. A partir de mesures de rendement en profondeur, on a déterminé les fonctions de diffusion en milieux homogènes polystyrène et matériau équivalent os, ainsi qu’en milieux hétérogènes, pour des électrons d’énergie 9 MeV, 15 MeV et 25 MeV et différents champs circulaires. En combinant les fonctions de diffusion obtenues en milieu homogène polystyrène et en milieu homogène de matériau équivalent os, on a recalculé les fonctions de diffusion en milieu hétérogène. On en a déduit le rendement en profondeur sur l’axe du faisceau. Dans le polystyrène situé en arrière de l’hétérogénéité, l’incertitude commise est inférieure à 3% pour de des électrons de 9 MeV, 2% pour des électrons de 15 MeV et 0,5% pour des électrons de 25 MeV. En tenant compte de l’influence des électrons rétrodiffusés par le milieu équivalent os dans le milieu situé en avant de l’hétérogénéité, l’incertitude commise dans cette région est réduite à une valeur inférieure à 1%.

1. INTRODUCTION

Le problème du calcul de la distribution de dose dans des tissus hétérogènes irradiés par des électrons de haute énergie est complexe à résoudre. En effet, les interactions des électrons avec la matière dépendent du milieu traversé; l’absorption et la diffusion des électrons varient avec le numéro atomique et la densité du milieu.

Depuis quelques années, de nombreux physiciens ont élaboré des théories qui se sont révélées lourdes à utiliser et qui manquaient de vérifications expérimentales. Ces méthodes utilisaient particulièrement la notion de faisceaux élémentaires ou faisceaux pinceaux.

Nous avons réalisé des mesures dans un milieu hétérogène constitué d’un milieu équivalent tissu et d’une plaque de milieu équivalent os, irradié par des faisceaux d’électrons de section circulaire variable. Un essai de modélisation par une méthode appelée modèle «des petits faisceaux» est proposé.

2. RAPPELS THEORIQUES SUR LE MODELE«DES PETITS FAISCEAUX»

Le principe de base de ce modèle de calcul est la décomposition d’un faisceau large en faisceaux élémentaires et de la dose en dose primaire et dose diffusée. On utilise ainsi la notion de fonction de diffusion pour des secteurs des faisceaux circulaires comme dans la méthode de Clarkson pour les faisceaux de photons. Ce modèle a été élaboré à l’Institut Gustave-Roussy [ 1, 2].

2.1. Description du modèle

En un point donné, on calcule la dose par sommation de la dose due au faisceau élémentaire passant par ce point (dose directe) et des doses dues au

FIG. 1. Décomposition du champ d'irradiation en éléments de surface.

316 BIDAULT et al.

rayonnement diffusé par chacun des secteurs angulaires décomposant le champ d’irradiation à partir du point considéré (fig. 1).

On trouvera donc:

Dose au point С = Dose directe au point С + 2 dose diffusée au point С

La dose directe est la dose due aux électrons qui ne sont pas diffusés hors du faisceau élémentaire.

La dose diffusée est la dose due aux électrons diffusés dans le volume élémentaire considéré, par les autres volumes élémentaires.

Dans ce calcul de dose en un point C, on prend en compte la profondeur réelle zC de ce point et on appellera zD la profondeur réelle des différents volumes élémentaires.

Ces volumes élémentaires sont en fait des éléments de surface obtenus par l’interaction des secteurs angulaires et de cercles concentriques (fig. 1). Ainsi nous obtenons la dose au point C, DC:

où:

T(zC,0) est le rendement en profondeur théorique d’un champ de diamètre0 cm obtenu par extrapolation des courbes de rendements en profondeur;FI est la fonction pénombre;SD(zD,r, Дг) représente le diffusé au point C par l’élément de surface entourant le point D, d’aire r Дг Д © à la profondeur zD; et SD(zD, r, Дг) = SD(zD, r + Дг) — SD(zD,r).

Ces fonctions de diffusion sont obtenues à partir des rendements en profondeur mesurés sur l’axe du faisceau:

SC(z, r) = Dose totale (z,r) -T (z , 0)

Ce modèle de calcul à trois dimensions a déjà été testé [2] en milieu homogène, avec différentes obliquités de surface et avec la présence d’une cavité d’air dans le milieu irradié.

3. CONDITIONS DE MESURES (fig. 2)

Nous avons réalisé des mesures par films pour des faisceaux d’électrons d’énergie 9 MeV, 15 MeV (accélérateur Saturne I, CGR MeV) et 25 MeV (accélérateur Sagittaire, CGR MeV).

DC = T(zC,0) X FI + SD (zD, r, Дг)

i— 1 Г = 0

IAEA-SM-298/22 317

FIG. 2. Superposition des deux parties du fantôme (vue de profil).

Des matériaux dits «équivalents» quant à l’atténuation et la diffusion des électrons ont été utilisés:

— matériau équivalent eau: le polystyrène de masse volumique 1,06 g/cm3 en plaques de 30 X 30 cm2 ;

— matériau équivalent os: matériau «SB3» de masse volumique 1,85 g/cm3 en plaques de 30 X 30 cm2 , de 0,5 cm et 1,0 cm d’épaisseur.Le fantôme irradié est constitué de deux parties strictement identiques

avec des plaques de polystyrène et des plaques d’équivalent os. L’hétérogénéité est ainsi considérée comme semi-infinie par rapport aux dimensions du champ d’irradiation.

L’ouverture du collimateur (photons et collimation additionnelle électrons) est constante pour garder un débit de dose constant. Les champs circulaires sont obtenus en intercalant entre le collimateur additionnel et le fantôme une plaque de plomb évidée.

La distance source-fantôme est de 100 cm et la distance plaque de plomb- fantôme est de 5 cm.

318 BIDAULT et al.

FIG.

150,

100

- E L E C T R O N S : 9 M e V

-S S D : 1 0 0 c m

■0 C H A M P

1 2 3 4 5 6

P R O F O N D E U R ( c m )

3. Rendements en profondeur du milieu polystyrène.

% D O S E

IS O .

100

■ E L E C T R O N S : 9 M e V

-S S D : 10 0 cm

■0 C H A M P

( 1) 0 ,0 c m

( 2 ) 0 ,9 5 cm

( 3 ) 1,95 c m

( 4 ) 2 ,9 5 c m

( 5 ) 3 ,7 c m

(6 ) 6 ,8 cm

3 4 5 6

P R O F O N D E U R (c m )

FIG. 4. Rendements en profondeur du milieu hétérogène (polystyrène-os-polystyrène) pour des électrons de 9 MeV.

IAEA-SM-298/22 319

150

100

■E LE C TR O N S :

15 M e V

-S S D : 100 cm -0 CH A M P

(1 ) 0 ,0 cm

(2 ) 0 .9 5 cm

(3 ) 2 ,1 cm

(4 ) 2 ,8 cm

(5 ) 4 ,7 cm

(6 ) 14,7 cm

4 5 6

P R O FO N D E U R (c m )

FIG. 5. Rendements en profondeur du milieu hétérogène (polystyrène-os-polystyrènej pour des électrons de 15 MeV.

4. ETUDE EXPERIMENTALE

L’étude expérimentale est constituée de mesures par films des rendements en profondeur sur l’axe du faisceau d’électrons d’énergie 9 MeV, 15 MeV et 25 MeV.

Les milieux étudiés sont les suivants:

— un milieu homogène polystyrène,— un milieu homogène de matériau équivalent os,— un milieu hétérogène composé d’une plaque d’épaisseur e équivalent os

(e = 0,5 ou 1 cm).

Les champs d’irradiation sont circulaires avec un diamètre ф = 0,95 cm;2,1 cm; 2,8 cm; 4,7 cm; 6,8 cm; 14,7 cm.

Toutes les courbes sont normalisées par rapport à la dose à l’entrée mesurée en milieu homogène polystyrène.

Des travaux précédents [3] ont montré que cette dose à l’entrée est indépendante du diamètre du champ. La figure 3 représente les rendements en profondeur en milieu polystyrène. La figure 4 représente les rendements en profondeur en milieu hétérogène pour des électrons de 9 MeV. La figure 5

320 BIDAULT et al.

représente les rendements en profondeur en milieu hétérogène pour des électrons de 15 MeV.

On constate que la présence d’une plaque de matériau équivalent os dans un fantôme de polystyrène entraîne:1) une augmentation de la dose à l’interface polystyrène-milieu équivalent os;2) un surdosage à l’intérieur du milieu équivalent os;3) un sous-dosage dans le polystyrène situé en arrière du milieu équivalent os.

5. EXPLOITATION DES RESULTATS EXPERIMENTAUX

A partir des courbes de rendements en profondeur et en s’inspirant du modèle des petits faisceaux, nous avons calculé les fonctions de diffusion S(z, r) à une profondeur z et pour un champ circulaire de rayon r.

En partant de la formule générale proposée par J.R. Cunningham [4] pour les faisceaux de photons:

De = DA(z) [f(z, x, y) T(z, 0) + S(z, r)]

où:DA(z) représente la dose dans l’espace libre à la distance SSD + z, f(z, x, y) est la fonction pénombre (à l’axe = 1),S(z, r) est la fonction de diffusion,T(z, 0) est la dose directe (fonction extrapolée du rendement en profondeur pour un champ circulaire de rayon nul).

T (z, 0) est une fonction extrapolée de la forme e_kz, le coefficient k étant obtenu à partir de la partie exponentielle de la courbe de rendement en profondeur du plus petit champ; pour chaque énergie, deux valeurs k! et k2 sont déterminées, l’une pour le milieu homogène polystyrène (ki ) et l’autre pour le milieu homogène os (k2 ).

On considérera

où:DO: dose surfaceSSD: source surface fantôme.

Ainsi

où:D

représente le rendement en profondeur mesuré.

IAEA-SM-298/22 321

% DIFFUSE«•

•\

/ \\ -E L E C T R O N S :

L \ 9 M e V

I -S S D : 100 cm

- 0 CH A M P : 6 .8 cm

— M E S U R E S E T C A L C U L S

- /• M O D E L IS A T IO N

- * O S

• S m m

0 1 2 3 4 5


F IG . 6. F o n c t io n s d e d i f fu s io n p o u r d e s é le c tr o n s d e 9 M e V .

% D IF F U S E

F IG . 7. F o n c t io n s d e d i f fu s io n p o u r d e s é le c tr o n s d e 1 5 M e V .

322 BIDAULT et al.

I

z 1 p o l y ♦ c f

p o l y s t y r è n e <► --j.

T 1 ' os"T"

z1 os

1

p o l y s t y r è n e

F IG . 8. C o u p e d u f a n t ô m e h é té ro g è n e .

A partir de l’expression ci-dessus, on peut donc calculer toutes les fonctions de diffusion, dans tous les milieux et pour toutes les énergies considérées (fig. 6

et 7, courbes en trait plein).

6 . MODELISATION DU CALCUL DE LA DOSE EN MILIEU HETEROGENE

A partir des valeurs des fonctions de diffusion S(z, r) dans le polystyrène et dans le milieu équivalent os, nous proposons un modèle perm ettant de calculer les fonctions de diffusion puis le rendement en profondeur en milieu hétérogène.

6.1. Décomposition du milieu hétérogène

Dans notre étude le milieu irradié est divisé en trois parties (fig. 8 ):1 ) le polystyrène avant le matériau équivalent os;2 ) le matériau équivalent os;3) le polystyrène après le milieu équivalent os.

6.2. Choix des fonctions de diffusion dans les différents milieux

6.2.1. A v a n t l'hétérogénéité

En un point situé à la profondeur z, on choisira la fonction de diffusion Spoly(z, r) de polystyrène à la profondeur z.

IAEA-SM-298/22 323

En un point situé à la profondeur réelle z, on choisit la fonction de diffusion Sos(ze, r) où ze est la profondeur équivalente en milieu homogène équivalent os

_ + Y P e P° lyze Z1 poly zosPe os

^ = 1,65Pe os

où:p e : densité électronique du milieu.

6.2.3. A p r è s l ’h é térogén éité

En un point situé à la profondeur réelle z, on prendra la fonction de diffusion Spoiy (ze , r) avec ze donné pour la relation suivante:

_ Pe polyze — Z1 poly +Z1 os ^ zpoly

“e os

6.3. Résultats 4

Les figures 6 et 7 donnent les fonctions de diffusion modélisées (ronds noirs)pour des électrons de 9 MeV et de 18 MeV respectivement.

Avant l’hétérogénéité, il existe une sous-estimation de la dose due à l’ignorancede l'influence du rétrodiffusé par le matériau équivalent os de densité plus élevée/que le polystyrène.

A l’intérieur de l’hétérogénéité, on observe une surestimation du calcul par rapport à la mesure, car on ne tient pas com pte du manque de diffusé dû au polystyrène.

Après l’hétérogénéité, il y a une sous-estimation du calcul par rapport à la mesure car on ignore l’influence de l’os dans la région d’interface.

6.4. Amélioration du modèle avant l ’hétérogénéité

La sous-estimation de la dose diffusée étant attribuée aux électrons rétro- diffusés par le milieu équivalent os, nous avons utilisé comme facteur correctif au niveau de l’interface la notion d ’EBF décrite par Klevenhagen [5] et reprise par Sordo [6 ]:

6.2.2! Dans l ’hétérogénéité

EBF = A - B exp (~kZ)

324 BIDAULT et al.

où:A, B et k sont des constantes fonctions de l’énergie la plus probable des électrons à la profondeur z: (Ez);Z est le numéro atom ique du matériau diffusant (ici le matériau équivalent os).

De plus, Lambert et Klevenhagen [7] décrivent la notion d ’EBI qui représente l’intensité relative des électrons rétrodiffusés à la distance de l’interface par rapport à l’intensité des électrons rétrodiffusés à l’interface entre les deux milieux (fig. 8 ):

EBI = A ;k 't

avec k ' = 0,61 E “ 0 ’62

A étan t une constante fonction de l’énergie et du matériau situé avant le matériau diffusant.

Ainsi le facteur correctif à apporter aux valeurs des fonctions de diffusion trouvées précédemment:

F (EBF) = 1,00 + (EBF - 1 ) • EBI

Klevenhagen a m ontré qu’il existe une épaisseur de saturation du milieu diffusant à partir de laquelle le coefficient EBF ne varie plus; cette épaisseur est de 0,5 cm pour le milieu équivalent os.

Le facteur correctif F (EBF) a été appliqué pour des valeurs de t comprises entre 0 et 0 , 6 cm.

6.5. Amélioration du modèle après l ’hétérogénéité

On considère que la zone située jusque 2 à 3 cm de profondeur après l’hétérogénéité est une zone de transition qui subit l’influence du milieu diffusant équivalent os, l’épaisseur de cette zone dépendant de l’énergie des électrons sortant de l’os.

Ainsi, le diffusé calculé sera partagé. S(r,z) sera une fonction du diffusé par l’os et du diffusé par le polystyrène et on écrira:

S(r, z) a • Sp0]y (r, zeq) + ß X Sos (r, zeq)

Poszeq — Z1 poly z los " zpoly ' 0i + ß — 1

Ppoly

Les valeurs des coefficients a et ß ont été calculés à partir des valeurs expérimentales des coefficients de diffusion; lorsqu’on s’éloigne de l’interface milieu équivalent os-polystyrène, ß diminue et donc a augmente.

A partir de la profondeur à laquelle on n ’observe plus l’influence de l’os, ß = 0 et a = 1 .

IAEA-SM-298/22 325

ki

0 ,5 .

1,5 2 2 ,5


FIG. 9. Variations des coeffic ien ts a e t ß en fo n c tio n de la pro fondeur dans le fan tôm e.

Pour une énergie et une épaisseur de milieu hétérogène données, on remarque une faible variation des coefficients a et ß en fonction du diamètre du champ d ’irradiation. Nous avons utilisé les valeurs moyennes de ces coefficients.

La figure 9 donne la variation de ces coefficients moyens pour des électrons de 9 MeV.

7. RESULTATS ET DISCUSSION

A partir du modèle considérant la dose en un point donné comme la somme de la dose directe et de la dose diffusée, des données expérimentales précédem m ent citées et des corrections déterminées dans les paragraphes 6.4 et 6.5, on calcule le rendem ent en profondeur sur l’axe du faisceau, R, comme:

Sur les figures 10 et 11 sont représentés les rendem ents en profondeur mesurés et calculés respectivement pour des électrons d’une énergie de 9 MeV et un champ circulaire de 6 , 8 cm de diamètre et pour des électrons d’une énergie de 15 MeV et un champ circulaire de 14,7 cm.

7.1. Résultats avant l ’hétérogénéité

Pour des champs d’irradiation d ’un diamètre supérieur à 1 cm, les écarts relatifs entre les rendem ents mesurés et calculés sont indiqués dans le tableau I.

326 BIDAULT et al.

% DOSE


FIG. 10. R endem en ts en pro fondeur pour des électrons de 9 M eV et un champ de 6,8 cm de diamètre.

7.2. Résultats après l ’hétérogénéité

En utilisant le facteur de correction F (EBF) donné dans le paragraphe 6.4, nous trouvons une incertitude relative inférieure à 1%.

7.3. A l ’intérieur de l’hétérogénéité

Aucune correction n’a pour l’instant été apportée.

8 . CONCLUSION

Ainsi, en s’inspirant du modèle «des petits faisceaux» et à partir de nombreuses données expérimentales, nous avons établi une m éthode de calcul de la distribution de dose sur l’axe du faisceau en milieu hétérogène. Cette m éthode nous perm et de rendre compte du surdosage observé dans le milieu équivalent os traversé ainsi que de l’influence de celui-ci sur le rendem ent en profondeur dans le polystyrène situé en avant et en arrière.

IAEA-SM-298/22 327

% D O S E

FIG. 11. R endem en ts en pro fondeur pour des électrons de 15 M e V et un champ de 14,7 cm de diamètre.

TABLEAU I. ECARTS RELATIFS ENTRE RENDEMENTS MESURES ET CALCULES

Energieélectrons zos: 0,5 cm

(%)zos; 1 cm

(%)

9 MeV < 3 < 2

15 MeV < 2 . < 1

25 MeV < 0 ,5 < 0 ,5

Les résultats obtenus perm ettent de penser que cette m éthode de décomposition de la dose en une somme de dose due au rayonnem ent primaire et de dose due au rayonnem ent diffusé semble être une approche intéressante pour résoudre des cas concrets rencontrés en clinique: petites hétérogénéités d’os, mais de masse volumique inférieure à 1,85 g/cm 3.

BIDAULT et al.

REFERENCES

BRIOT, E., Etude dosimétrique et comparaison des faisceaux d’électrons de 4 à 32 MeV issus de deux types d’accélérateurs linéaires avec balayage et diffuseurs multiples, Thèse doct. n° 2705, Faculté des sciences, Toulouse (1982).DUTREIX, A., BRIOT, E., «The development of a pencil-beam algorithm for clinical use at the Institut Gustave-Roussy», Methods of Computing Dose Distribution in Patients from External Electron Beams (Cours, Hällnös, Suède, 28-31 mars 1984).VILLERET, O., Variations de la distribution des doses dans les faisceaux d’électrons de haute énergie en fonction des paramètres géométriques de l’irradiation, Application au calcul par ordinateur, Thèse doct., Faculté des sciences, Toulouse (1985).CUNNINGHAM, J.R., Photon beam calculation methods, AECL Notice technique TPI 1, Atomic Energy of Canada Ltd (1982).KLEVENHAGEN, S.C., «Physics of electron beam therapy», Medical Physics Handbooks 13, Adam Hilger, Royaume-Uni (1985) 117-134.SORDO, A., Influence de l’os et de la graisse sur la distribution de la dose dans les faisceaux d ’électrons en milieu semi-infini, Thèse doct. n° 2912, Faculté des sciences, Toulouse (1983).LAMBERT, G.D., KLEVENHAGEN, S.C., Penetration of backscattered electrons in polystyrene for energies between 1 and 25 MeV, Phys. Med. Biol. 27 5 (1982) 721-725.

IAEA-SM-298/88

ANALYSIS OF ENERGY DISTRIBUTION BY DEPTH DOSE CURVES AND ITS APPLICATION TO THE DOSIMETRY OF FAST ELECTRONS

G. CHRIST, F. NÜSSLIN Abteilung für Medizinische Physik,Radiologische Universitätsklinik,Tübingen,Federal Republic of Germany

Abstract

ANALYSIS OF ENERGY DISTRIBUTION BY DEPTH DOSE CURVES AND ITS APPLICATION TO THE DOSIMETRY OF FAST ELECTRONS.

The spectral distribution of electrons at any depth in a phantom is of great interest in dosimetry. A method for analysing the spectral distribution has been developed. The energy analysis is made by separating the measured depth dose curve into depth dose curves of monoenergetic electrons. For each monoenergetic beam the energy and the relative yield are determined. As an example, the method is applied to analyse the scatter effect of the applicator on the energy distribution of an electron beam. The energy distribution is found to be a function of the position inside the applicator and of the applicator size. The results of the energy analysis are compared with other well known methods of energy determination. The mean energy derived from the energy analysis is much less than the most probable energy derived from the practical range and much less than the mean energy derived from the 50% range. The application of this method of energy analysis to electron dosimetry is discussed.

1 . IN T R O D U C T IO N

In electron dosimetry a knowledge of the spectral distribution is of great importance. Hence, both the energy distribution at the surface and its variation with depth are of interest. However, it is difficult to determine the spectral distribution of fast electrons. Especially in clinical routine it is not possible to do this in most cases. Therefore other methods have been developed to describe the energy spectrum by a single quantity stating, for example, the most probable energy or the mean energy at the phantom surface, both being determined from range measurements. Various empirical equations have been proposed to approximate these energies [1-5]. Other approaches have been suggested for energy degradation as a function of depth [6-8]. Recently, various other methods have been proposed [9-11] for evaluating the energy spectrum of an electron beam.

329

330 CHRIST and NÜSSLIN

depth in \vater (mm)

FIG. 1. Ionization depth dose curves fo r 5, 10 and 20 M eV m onoenergetic electrons perpendicular incident on a half-infinite water phantom fo llow ing the algorithm o f Tabata and Ito [1 2 \

depth In water (mm)

FIG. 2. Superposition o f three monoenergetic electron beams (5 ,1 0 and 20 Me V) fro m Fig. 1.

2. METHODThe method of energy analysis presented makes

use of the whole information contained in a measured depth dose curve. Each depth dose curve of a clinical electron beam may be considered as the superposition of a number of depth dose curves resulting from monoenergetic electron beams with different primary energies. Fig.l shows three monoenergetic depth dose curves of 5, 10 and 20 MeV initial energies which have been superposed in Fig.2.

IAEA-SM-298/88 331

The weight factor for all three energies was the same. Due to the different ranges of the primary electron energies the three components of the superposition are easily identified. The aim of the analysis is to find out the primary energies and the relative yield of these monoenergetic electron beams contributing to the measured depth dose curve. In this; we can make use of thé fact that the fall-off of the descending part of an electron depth dose curve (without the bremsstrahlung contamination) is mainly determined by the high energy part of the spectral distribution. The relative yield and the energy of each fraction of monoenergetic electrons is obtained from a comparison of measured data with monoenergetic electron depth dose curves calculated according to the model of Tabata and Ito [12]. Subtracting this fraction from the original depth dose curve/ the same method is repeated resulting in a further fraction of monoenergetic electrons. In this way, the clinical electron beam is split up iteratively into several fractions of electrons with different discrete energies and weight factors.

3. MEASUREMENTSThe measurements were carried out at a Philips

linear accelerator SL 75/2o. In a computer assisted water phantom (PTW-Freiburg) central axis depth dose curves and profiles at several depths were measured for all eight nominal energies available between 5 and 20 MeV. The flat Markus chamber [13] was used as ionization chamber. The profile measurements were made along the main axis perpendicular to the direction of electron acceleration. The measurements were performed for three applicators with square field sizes of 60 mm (T 60), 100 mm (T 100) and 200 mm (T 200). All measurements were repeated without the applicators/ however with the same setting of the primary collimator.

4. COMPUTER PROGRAMSAll measured data were processed on a HP 1000

minicomputer. FORTRAN programs were developed for calculating depth dose curves in any direction. The bremsstrahlung contamination was subtracted from the measured depth dose curves. This was made by extrapolation of the contamination from beyond the


maximum range back to the surface taking the build-up effect near the phantom surface into account [14].

Another program allows depth dose curves to be subtracted to obtain, for instance, the difference between the depth dose curves with and without the applicators in order to estimate the scatter induced by the applicator. In the same way the scatter influence of the collimator is obtained.

For the energy analysis an algorithm for energy deposition of fast electrons [12] was used to calculate ionization depth dose curves of a parallel beam of monoenergetic electrons incident normally on a half infinite water phantom. The depth dose curves were corrected for the square law. The computer program fits the monoenergetic data to the measured data within the fall-off region. This is achieved by iterative variation of the energy of the monoenergetic electrons and the corresponding relative yield. The corresponding calculated depth dose curve of the monoenergetic electrons is subtracted from the measured depth dose curve. This method will be continued resulting in further fractions of monoenergetic electrons and their corresponding relative yield. To check the consistency of the energy analysis at least all calculated data are superposed and compared with the measured depth dose curve.

The method described results in the energy distribution of the incident electrons at the phantom surface. To determine the energy distribution as a function of depth in phantom one can calculate the energy loss of the analysed discrete energies separately. Alternatively, the method of energy analysis may be repeated by starting at any depth desired. However, the disadvantage is the missing equilibrium of the secondary electrons in the monoenergetic electron beam near the surface. So, we used separately for each analysed discrete energy the most probable energy according to the Markus formula for energy degradation [8]. On the basis of the spectral distribution it is possible to calculate the mean energy at the phantom surface or at any depth desired. These results have to be compared with the mean energy and with the most probable energy derived from the 50 % range and the practical range, respectively.

IAEA-SM-298/88 333

normalized depth z/Rp

FIG. 3. Scatter contribution o f the applicator as a fu n ctio n o f the norm alized dep th in water fo r the nom inal electron energies 5, 10 and 20 M eV. A pplicator square fie ld size 60 m m (T 60) and 200 m m (T 200).

5. RESULTS5.1. Scattering by applicator

, By subtracting the depth dose curves measured with and without the applicators the scatter contribution of the applicator itself is obtained. Fig. 3 shows the percentage scatter contribution from the T 60 and T 200 applicators for three nominal electron energies as a function of the normalized depth in water in the central axis. The scatter contribution of the applicator decreases with increasing primary energy, increasing applicator size and increasing depth. The last point means a lower energy of the scattered electrons compared with the primary electrons. The same energy would result in a constant amount of scatter contribution independent of the depth. As shown in Fig. 3, scattering from the applicator may contribute up to 70 % of the primary electrons. This means, for example, that for a great part of electrons the source surface distance is much smaller than the scattering foil surface distance.

5.2. Energy of applicator scattered electronsIn the following, the energy quantities will be

given as percentage values normalized to the most


nominal electron energy (MeV)

FIG. 4. Mean energy, E¿, derived fro m the energy analysis as a fu n c tio n o f the primary electron energy fo r the three applicator square fie ld sizes 60 m m (T 60), 100 m m ( T 100) and 200 m m ( T 200).

probable energy of the corresponding nominal energy as determined from a measurement of the practical range without applicator, however with the collimator setting corresponding to the T 60 applicator. This allows all primary energies to be compared directly. The differences in the practical range and, therefore, the differences in the most probable energy using the various applicator sizes are negligible.

Fig. 4 shows the mean energy, Ë (O) , of the applicator scattered electrons for tnree applicator sizes as a function of the nominal energy of the primary electrons. The results were obtained from the measurements in the central axis beam. The mean energy, E^, is calculated from the analysed spectral distribution. The results of Fig. 4 are evaluated assuming the virtual source of the scattered electrons in the centre of the applicator. This was necessary, because the failure analysis showed that the source surface distance strongly influences the energy analysis. As expected from electron scattering theory, Fig. 4 shows the mean energy of scattered electrons decreasing with increasing size of the applicator.

Some results of the energy analysis for off-axis depth dose curves are shown in Fig. 5. At all primary electron energies the size of the applicator

IAEA-SM-298/88 335

off-axie position (%)

FIG. 5. Mean energy, Ed, derived from the energy analysis as a func tio n o f the off-axis position o f the applicator a t 10 Me V nom inal electron energy.

was found to influence strongly the mean energy,Е д (0). For small applicators the mean energy of scattered electrons is highest in the central axis decreasing to the applicator wall, whereas for great applicators it turned out to be vice versa. It should be mentioned that near the edges of the electron field this energy analysis is no more applicable because of electron outscattering.

5.3. Comparison of different methods of energydeterminationFrom all measured and computed depth dose

curves, both the practical range and the 50 % range have been determined. The most probable energy,E p (0), at the phantom surface was obtained using the Markus equation and the mean energy, E(0), at the phantom surface by multiplying the 50 % range of absorbed dose with a constant factor 2.33 MeV/cm [15,16]. Fig. 6 shows a comparison of the results with the mean energy, E¿(0), derived from the analysed discrete energies for the T_200 applicator and all nominal energies. In Fig. 6 E and E<j are normalized to the most probable energy. With increasing primary energy the mean energy, E, approximated by the 50 % range approaches the most probable energy, Ep, while the mean energy, E¿, based


nominal electron energy (MeV)

FIG. 6. The m ost probable energy, E p (0), the mean energy, E(0J, derived from the 50% range and the mean energy, E ¿(0), derived from the energy analysis at the phantom surface as a fu n c tio n o f the nominal electron energy. R esu lts obtained from the central axis measurem en ts w ith the T 200 applicator.

on the spectral distribution results in a nearly constant value of about 80 % of the most probable energy.

6. FAILURE ANALYSISAs mentioned above, the procedure of energy

analysis is easy to test by adding up the various depth dose curves corresponding to the analysed discrete energies and comparing them with the original depth dose curve. Alternatively, the method may be tested by superposing depth dose curves of monoenergetic electrons following the algorithm of Tabata and Ito [12]. The preset values should be consistent with the result of the energy analysis.It turned out that a few preset discrete energies were analysed quite well, while many preset energies resulted in greater discrepancies. However, in both cases the mean energy obtained from the analysed discrete energies and their corresponding relative yield agreed very well with the corresponding preset values.

The results of the energy analysis are strongly influenced by the source surface distance. This was tested by a different source surface distance for the

IAEA-SM-298/88 337

>ф

51

Ф

XmLФС

0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100.

FIG . 7. Degradation o f energy as a fu n c tio n o f dep th in water fo r the m ost probable energy, E p(z), fo r the mean energy, E (z j, derived fro m the 50% range and the mean energy, E d(zJ, derived from the energy analysis. R esults obtained from the central axis measurem ents o f nom inal electron energy 20 M eV w ith the T 60 applicator.

preset depth dose curves and for the theoretical depth dose curves used for energy analysis. A decreasing source surface distance would be expected to be equivalent to a parallel beam of an apparently lower primary electron energy. Therefore, different source surface distances were chosen for the primary electrons originating from the scattering foil and from the applicator walls, respectively.

The main source of error in the analysis of energy distribution is expected to be the calculation of the electron depth dose curves [12]. The algorithm is an empirical adjustment to a number of experimental and theoretical data found by the Monte Carlo method. Nevertheless, it does not basically restrict the method of energy analysis, because the energy analysis can be performed with any algorithm producing monoenergetic electron depth dose curves.

7. APPLICATION TO ELECTRON DOSIMETRYFor electron dosimetry with an ionization

chamber the ionization measurement must be converted to absorbed dose by means of energy dependent factors. These factors include the ratio of electron stopping power from one material to another and from


electron energy under the measurement conditions to those of the calibration. Normally one representative value of energy is used because the spectral electron fluence is not known. If the spectral distribution is known, the analysed discrete energies could be used for computing the stopping power ratios. It is known that greater differences in electron energy result in only small deviations in the stopping power ratios. However, in dosimetry this method may be considered to be more realistic since it refers to the mean energy based on the analysis of the energy spectrum rather than on an empirical equation. Fig. 7 shows the energy degradation of electrons as a function of depth based on different algorithms. While the most probable energy, Ep(z), calculated according to Markus [8] and the mean energy, T!(z), following the Harder equation [4,15] show a linear fall-off, the mean energy,E¿|(z), from the analysis gives a different result due to the limited range of the electrons with lower energies.

REFERENCES[1] ВRAHME, A., SVENSSON, H., Depth absorbed dose

distributions for electrons (Correspondence),Phys.Med.Biol. ^3 4 (1978) 788.

[2] HARDER, D., "Elektronen- und Positronenreichweite im MeV-Bereich", Medizinische Physik, Hrsg. Schmidt, Nürnberg (1984).

[3] HOHLFELD, K., ROOS, M., "Dosismeßverfahren für Ionisationskammern, die zur Anzeige der'Wasser- Energiedosis kalibriert sind", Medizinische Physik, Hrsg. v. Klitzing, Lübeck (1986).

[4] HOSPITAL PHYSICISTS ASSOCIATION, A Practical Guide to Electron Dosimetry 5-35 MeV, HPA Rep. Series No. 4, London (1971).

[5] ROOS, M., TRIER, J.D., "Untersuchungen zur Bestimmung der Energie von Elektronenstrahlen aus der praktischen Reichweite", Medizinische Physik, Hrsg. Schütz, Münster (1983).

[6] ANDREO, P., BRAHME, A., Mean energy in electron beams, Med.Phys. J3 5 (1981) 682.

[7] HARDER, D., "Zur Berechnung des relativen Massenbremsvermögens und der mittleren Elektronenenergie in der Elektronendosimetrie", Medizinische Physik, Hrsg. Schütz, Münster (1983).

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[8] MARKUS, В., Eine einfache Formel zur Bestimmung der mittleren Elektronenenergie in einem mit schnellen Elektronen bestrahlten Körper, Strahlentherapie 154 6 (1978) 388.

[9] KOVAR I., NOVOTNY, J., KOVAR, Z., JIROUSEK, P., VAVRA, S., Calculation of energy spectra for therapeutic electron beams from depth-dose curves, Phys.Med.Biol. 28 12 (1983) 1441.

[10] SCHRÖDER-BABO, P., LEETZ, H.K., HARDER, D.,"Neue Methode zur Messung der mittleren Elektronenenergie", Medizinische Physik,Hrsg. Schmidt, Nürnberg (1984).

[11] DÖRNER, K.J., BURMESTER, U., RUBACH A., HARDER D., "Messung der mittleren Elektronenenergie E0 mit einer Mehrplattenionisationskammer", Medizinische Physik, Hrsg. v. Klitzing, Lübeck (1986).

[12] TABATA, T., ITO, R., An algorithm for the energy deposition by fast electrons, Nucl. Sei. Eng.53 (1974) 226.

[13] MARKUS, В., Eine Parallelplatten-Kleinkammer zur Dosimetrie schneller Elektronen und ihre Anwendung, Strahlentherapie 152 6 (1976) 517.

[14] CHRIST, G., Ein Verfahren zur Energieanalyse schneller Elektronen, Habilitationsschrift, Universität Tübingen (1986).

[15] INTERNATIONAL COMISSION ON RADIATION UNITS AND MEASUREMENTS, Radiation Dosimetry: Electron Beams with Energies Between 1 and 50 MeV, ICRU Rep. 35, ICRU Publications, Bethesda, MD (1984).

[16] WU, A., KALEND, A.M., ZWICKER, R.D.,STERNICK, E.S., Comments on the method of energy determination for electron beams in the TG-21 protocol, .Med. Phys. Y\_ 6 (1984) 871.

IAEA-SM-298/90

COMPUTER ASSISTED FILM ELECTRON DOSIMETRY: 3-D ISODOSE CURVE

M. LAZZERIServizio di Fisica Sanitaria,Istituto di Radiologia,Université di Pisa,Pisa

L. AZZARELLI, S. CESARO, M. CHIMENTI, O. SALVETTI Istituto di Elaborazione dell’Informazione,Consiglio Nazionale delle Ricerche (CNR),Pisa

Italy

Abstract

COMPUTER ASSISTED FILM ELECTRON DOSIMETRY: 3-D ISODOSE CURVE.A method is presented which uses a hardware-software integrated system for the off-line acquisi

tion, processing and restitution of radiographic images in order to obtain a complete set of 3-D isodose curves for high energy electron beams. The image processing system is briefly illustrated and some examples of dose reconstruction are given. The system is automatic and operates in different stages; the most important of these stages are digital image acquisition, data preprocessing and image analysis and graphic and pictorial restitution. The system software structure mainly consists of interactive modules and procedures operating in interconnected environments. The equipment used to acquire the experimental data consists of a linear accelerator and a phantom composed of a number of polystyrene sheets. To detect the electron beams in the planes which are orthogonal with respect to the propagation direction, films were inserted between sheets of this phantom. The films were carefully aligned with respect to the central axis of the beam and were exposed singly. The X-ray films obtained have been digitized and processed. The results so far demonstrate that the method is accurate, quick and offers high resolution. It can thus be considered suitable for use both in the clinical routine and in the experimental testing of models obtained using conformation therapy.

1. INTRODUCTION

In the last few years, two types o-f data processing systems have been of great importance in the optimization of X-ray therapeutic treatment in neoplastic processes: Computerised A:;ial Tomography(CAT) and systems which calculate dose distribution in treatment planning.

Computerized a::ial tomography has permitted a significant step forward in the identification of target volumes and critical organs and, in general,

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342 LAZZERl et al.

in those problems connected with tumour morphology and topology. The acquisition of CAT images and their successive processing using automatic treatment planning systems has made it possible to optimize the choice of radiation technique and the theoretical calculation of dose distribution over target volume.

Treatment planning systems clearly require a considerable number of experimental data as they need to 'know' the distribution curves of real doses for each radiation beam [11. As is known, the quality of the beam, the characteristics of the absorbing body, the parameters chosen for the radiation technique(form and dimensions of the field, the source-surfacedistance, the angulation of the beam, filters, etc.) can considerably modify the real curves of dose distribution. On the other hand, the effects of these factors must be taken into account if a homogeneous radiation of the tumoural focus is to be achieved and, at the same time, in order toprotect the critical organs.

The effectiveness of film dosimetry in thedosimetric study of a beam of radiations, both photons and electrons, produced by a linear accelerator in the treatment of neoplastic processes in oncological radiotherapy has been much discussed. National and international protocols have been established to regulate the methodologies and necessary conditions for measuring techniques which control the beam [2,9]. Film dosimetry appears to have been somewhat isolated from these techniques mainly because of scarce knowledge of the physical and chemical transformation processes in the treatment and development of irradiated X-rays.

In our opinion, the undeniably high resolution and versatility of film dosimetry are factors which encourage more research into its possibilities and into the problems which it undoubtedly raises [6,7,8,12,13]. Wherever possible, and with the help of modern computing technologies, further investigations into possible applications of this technique should be made.

The present study is the result of several years of experience in the automatic analysis of X-ray images [3,4,5,10,11]. Our objective is to present an integrated hardware-software system for off-line image acquisition, processing and restitution.

Using this methodology, film dosimetry has been given new significance, particularly in the applied dosimetric clinical field. Important results have already been obtained in the study of the radiation

IAEA-SM-298/90 343

beam; a study which also constitutes a valid starting point -for an investigation into the dosimetric •features of the radiant beam.

Analyses of X-rays obtained with electrons and/or photons produced by a linear accelerator demonstrate the utility of the method and its accuracy in defining the geometric projection of the size of the penumbra and the uniformity of the dose at different depths and on fields correspondíng to the opening of the collimator, perpendicular to the central ray. Thus, all physical and technical parameters which influence changes in uniformity, such as the scanning of the electron beams or the homogenizing filter, etc.,can be easily detected and measured.

The scope of the paper is to present a two-and three-dimensional reconstruction of electron beams produced by a linear accelerator. The reconstruction has been obtained by analysing X-rays which have been exposed on planes perpendicular to the direction of the beam. The data which can be derived from the analysis can also be used as input in any open system for the calculation of treatment plans.

2. WORKING TECHNIQUES AND TOOLSDosimetric film is digitally processed using a

specialized work-station С4].The main components of the hardware architecture

of the wark-station are:- an x,y scanner for X-ray acquisition;- a video memory to display the images processed

by the system,- a mass memory'to store the data and images;- a personal computer to execute the operations.The scanner is composed of a numerically

controlled mi.crophotometer which, under the guide of resident software, can digitize X-ray film of up to 25x30 c m 1, with a resolution of 2048 paints per line.

Acquisition is performed illuminating the X-ray by a luminous source and measuring the light transmitted using a photodiodes linear array. The X-ray plane is scanned using a translation system run by a step motor.

The video memory is composed of a printed circuit card connected to the computer bus. It can contain an image defined by 1024x1024 pixels, each represented in 8 bits. The card offers a reasonable performance in terms of the data transfer speed and has been given a software library of internal functions.

344 LAZZERI et al.

The card controls a 625 line -frame TV monitor with windows of 512x512 pixels. The display resolution is more than sufficient to view the processed images.

The execution of the procedure implies the activation of software modules which perform the following functions:

- image acquisition: this function, controls thesampling of the image, the A/D conversion of the acquisition values and performs a data correction to eliminate the instrumental errors;

- data preprocessing: this function performsoperati ons 57 spati al filtering to reduce noise present in the X-ray and photometric conversion to obtain dose values of the radiation beam from the optical density measured on X-rays;

- data analysis; this function is used to derive isodose curves in planes oriented in any direction with respect to the source or to reconstruct the beam distribution;

- pictorial and graphic restitution: this function is used to reproduce the images acquired and processed on the video display, and to draw graphic documents on the plotter;

- data management and archiving: the modules ofthis function control system operation flow, local data storage and communication with other computing systems.

In particular, for this last function, communication and information exchange is possible in accordance with certain standard protocols.

The procedure which has been developed consists of two separate phases ( see Fig. 1):

(a) X-ray exposure;(b) data acquisition and processing.In phase.(a) two series of X-ray film are exposed.

The first series (calibration series) is aimed at determining the relationship between the incident dose and consequent blackening of the film, for a given type of film and for given developing conditions. A number of films are exposed with different dose values according to the required precision.

The second series (measurement series) is obtained by exposing the film to detect the distribution of the beam produced by the source. In this case, once the dimensions of the field to be analysed have been

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2D maps 3D reconstructions

FIG. 1. Implemented procedure.

■fixed, the -films are placed in an x-y plane orthogonal to the z axis of the beam, at anincreasing distance from the source. In this way, aseries of measurements are derived for differentsections of the beam and increaseflz can be chosen on the basis of the desired precision.

The X-rays obtained in phase (a) are digitized using the acquisition device.

By an averaging operation, an optical density value OD, associated with the value of dose Dincident on the X-ray, can be derived from each calibration X-ray. From the N X-rays in input, IM pairs of values (optical density, dose) are obtained

346 LAZZERI et al.

and can be used to constitute, by interpolation, the transformation function D=f(OD), which will be used when processing the measurement X-rays.

The measurement X-rays are, in fact, acquired and transformed into numerical matrices of optical density values. From the X-rays exposed in correspondence to the distance z=ze from the source, matrix DD(x,y,ze ) can be derived and, from the set of N measurement X-rays, matrix OD(x,y,z) can be obtai ned.

Using the transformation function D=f(OD), a matrix of absolute dose D describing the trend of the beam is obtained and can be used to perform a long series of measures and evaluations. For example, planar maps of beam distribution in any kind of section, or isodose curves, can be derived from D(x,y,z).3. EXAMPLES

To illustrate the procedure described above, we report a number of examples which refer to a study of electron beams at 6 and 20 MeV.

The calibration curve of the X-ray film used (Kodak X-0mat) has been determined by exposing a series of films, taken from the same pack and developed in the same bath. The X-rays were inserted into a phantom composed of sheets of polystyrene of1.04 g/cm* density and 2 mm thick. They were exposed singly, at the same distance from the source, and the dose was increased each time by a constant value, thus covering the range normally used in radiotherapeutiс applications.

Tab.I. Exposure parameters of calibration radiograms

Electron beam nominal energy (MeV) 6 20Field dimension (cm) 3x3 10x10Exposed radiograms 13 13Exposure step (Gy) 0.1 0. 1Exposure range (Gy) 0. 1-1.3 0.1-1.3Optical density ra n g e 0 . 4 - 2 . 4 0 . 4 -2.4

IAEA-SM-298/90 347

о 0.5

1 2

O ptica l density

FIG. 2. Transfer function D = f (OD).

The X-rays were digitized with a spatialresolution o-f 125 pm and the average value of opticaldensity was obtained from the matrix corresponding to the blackened zone. In this way, the pairs of values <0D,D) used to define the trans-formation functions were also obtained.

Table I summarizes the main features of the; two series. Figure 2 shows the graph of the transformation function for 20 MeV energy.

In a similar way, two series of films were exposed to measure the radiation sources.

The X-rays of each series were exposed singly,keeping the exposure dose constant, increasing thedistance from the source each time by a constantinterval and taking care to align them with respectto the beam axis.

By using the x-y scanner from each X-ray, a matrix of optical density values has been derived. Using the transformation function defined previously, two series of matrices have been derived. Each of these series is composed of dose values in an orthogonal plane to the beam axis, for the X-ray exposuredi stance.

348 LAZZERI et al.

Tab.11.Exposure and acquisition parameters of measurements radiograms

Electron beam nominal energy (MeV) 6 20

Field dimension (cm) 3x 1 Ox 10

Minimum distance (cm) 100 100

Distance step (cm) 0. 25 0. 25

Exposed radiograms 18 18

Sampling resolution (mm) 0. 125 1

As the X-rays were also carefully aligned during the digitizing stage, it is possible to derive the spatial coordinates in the laboratory reference system from the coordinates of the matrices and, in this way, to measure the effective trend of the beams studi e d .

Table II summarizes the main features of the measurement X-rays.

Figures 3-4 show the result of digitizing X-rays exposed to 6 MeV beams. The x,y axes indicate the plane orthogonal to the beam propagation direction z. Source О of the x,y system corresponds to the upper left edge of the X-ray.

The pseudo-colour chromatic scale shows both the optical isodensity values of the X-ray and the isodoses in the exposure plane. In this way, the trend of the beam can be easily observed in various orthogonal sections at different depths.

Figure 5 shows the trend of the 6 MeV beam in the y,z plane parallel to the propagation direction. The z axis is orthogonal to the x,y plane in 0. Figure 5 is the result of the reconstruction obtained processing the data derived from the series of 18 films exposed on planes perpendicular to the beam ax i s .

Figure 6 shows an example of spatial reconstruction: in this case, the image has beenobtained isolating the isodose lines on each input matrix derived from digitized films, and reconstructing their spatial distribution, according to given parameters.

IAEA-SM-298/90 349

FIG. 4. Digital x-y optical density and dose (in cGy) map at 102.0 cm from the source.

LA22ERietal.

w ~ f — y ^ f ^ - - - * ' * --

'« ,* J. . . , ,W« Д /л « к ;. è i i 'г-í' ?>/-' Í - ; '‘ s ;'1.v,i. ;;**■ ' '*>? .'f;,* ' w % f* ¥ * * « v * < »

- Í , - ' - «

4 ’* 3 r * 4' Vu 1 » ч f '■’<• j • :■

^ д -í-.',.,; •■à*- Sy гф* ‘ “ . f i ï ' t «Зъ-з&'Ы. Ш dr-V#-t>í vA. *& 4 á t ¿ ? f.............. í ... ■ 1 ■■■ i. ■• , . , . ■■■ .■■,.•' ■ y V!< y { f1 S~ <

í * V “,ÍS‘

E SjMSíE

f ig . 5. Reco,mStrUc,ed У-Z opticai densUy

anä dosefor а б Mev

source.

IAEA-SM-298/90

FIG. 7. Reconstructed y-z optical density and dose (in cGy) fo r a 20 MeV source.

FIG. 8. Digital y-z optical density and dose (in cGy) fo r a 20 MeV source.

352

LAZZERI et al.

IAEA-SM-298/90 353

Figures 7-10 give examples of electron beams at the nominal energy of 20 MeV.

Figure 7 shows the synthesis in the y,z plane obtained using data derived from 18 films exposed perpendicularly to the beam, whereas Figure 8 gives the results of digitizing an X-ray exposed parallel to the beam.

Figure 9 shows an example of 3D isodose reconstruction for a single predefined value; Figure 10 shows a multiple 3D isodose reconstruction.

4. CONCLUSIONS

We have described a method which can be used in oncological radiotherapy to process X-ray images. The method aims at obtaining a set of two- and three- dimensional isodose curves for electron beams emitted by a linear accelerator.

The method offers two immediate advantages:(a) an efficient approach to film dosimetry, based on the use of the most recent data processing technologies, and high measuring resolution;(b) the possibility of exchanging data between different systems specialized in treatment planning.

We feel that the methodology described here opens up new possibilities in the clinical field of applicative dosimetry.

REFERENCES

С 13 American Association of Physicists in Medicine(AAPM), Electron Dosimetry and Arc Therapy, (Proc. Symp., Wisconsin, 1981).

C2] American Association of Physicists in Medicine (AAPM), Task Group 21, A protocol for the determination of absorbed dose from high-energy photons and electron beams , Med. Phys, vol. 10 no.6 (1983) 741-771.

C3D L. Azzarelli, M. Chimenti, M. Lazzeri, 0. Salvetti "An approach to automatic control in digital radiology",Digital Signal Processing, Firenze,1984

C4D L. Azzarelli, M. Chimenti, M. Lazzeri, 0. Salvetti "Interactive integrated modular system for digital radiology", CAR'85, (Proc. Int. Symp.Berlin, 1985), Springer Verlag, 1985.

С5Э L. Azzarelli, M. Chimenti, M. Lazzeri, 0. Salvetti "Computer assisted electron dosimetry radiotherapy submitted to IEEE Transactions on Circuits and System (Dec. 1986) .

354 LAZZERI et al.

C6] A. Dutreix, Film Dosimetry , AAPM Summer School, Univ. of Vermount, 1976.

[71 J. Dutrei::, A. Dutreix, Film dosimetry of high energy electrons , Annals of New York Academy of Sciences, New York, vol.161 (1969) 33-43.

[83 A. Feldman, C.E. De Almeida, F'.R. Almond,Measurements of electron-beam energy with rapid process film, Med. F'hys. , vol . 1 , no.2, (1974).

[9D International Commision on Radiation Units andMeasurements (ICRU), Rep.no. 10b,14,24,29,33,35,37

C10DM.Lazzeri, L. Azzarelli, S. Cesaro, M. Chimenti,0. Salvetti, "Computer assisted film dosimetry: three dimensional dose planning", C a r '87,(Proc. Int. Symp. Berlin 1987), Springer Verlag, 1987,.

С 11 DM.Lazzeri,S. Cerri,B. Silvano, "Analisi automatica di immagini radiografiche per il contrallo dosimetrico in radioterapia oncologica", in Tecnologie Informatiche in Radioterapia Oncológica (M. Laddaga, M. Lazzeri (Edí)), Pisa (1982).

П12ИА. Niroomand-Rad et al., Film dosimetry of small electron beam for routine radiotherapy planning, Med. Phys., vol.13, no.3 (1986) 416-421.

C133S.C. Sharma, D.L. Wilson and B. Jose,Dosimetry of films for small Therac 20 electron beams, Med. Phys., vol-11 , no.5 (1984) 697-702.

IAEA-SM-298/42

DOSIMETRY OF SMALL X-RAY RADIATION FIELDS

L. BIANCIARDI, L. D ’ANGELO, F.P. GENTILE, M. BENASSI Laboratory of Medical Physics,Regina Elena Institute,Rome

A.S. GUERRADivision of Physics and Biomedical Sciences,CRE Casaccia,ENEA,Rome

Italy

Abstract

DOSIMETRY OF SMALL X-RAY RADIATION FIELDS.The paper describes a procedure which allows a simple and direct experimental determination

of the tissue-maximum ratio (TMR) and the percentage depth dose (PDD) values as well as of the output factor for a 10 MV accelerator and for small square fields of less than 3 cm x 3 cm used in stereotactic radiotherapy. TMR/PDD and output factor data, measured using the above procedure, are reported. On the basis of the results, film dosimetry appears to be a practicable method at field sizes of less than or equal to 1 cm x 1 cm for which it is not always possible to use ion chambers or TLDs.

INTRODUCTION

Methods for stereotactic localization of smallintracranial lesions, as well as techniques for patient head fixation and reproducible positioning on the linear accelerator table, have been extensively reported in the literature |l-5|. Dosimetric procedures for small sizebeams have not yet been well assessed, especially with regard to tissue-maximum ratio (TMR) (or percentage depth dose (PDD)) and output factor determination. Some PDD measurements using TLDs for beam sizes down to 1 cm x 1 cm in a 9 MV accelerator have been reported |6 |- PDD values have been published on the basis of interpolation from calculated zero area PDD values and experimental data from a 3 cm x 3 cm field, for field sizes of 2 cm x 2 cm and1 cm x 1 cm of a 10 MV accelerator |7 |.

355

356 BIANCIARDI et al.

In the present paper, a procedure will be described which allows a simple and direct experimental determination of TMR and PDD values as well as of the output factor for a 10 MV accelerator and for small square fields of less than 3 cm x 3 cm used in stereotactic radiotherapy.

MATERIALS AND METHODS

The X-ray beams were produced by a Siemens Mevatron 74linear accelerator and their size was varied from10 cm x 10 cm to 0.5 cm x 0.5 cm.

Central axis PDD at SSD = 100 cm and TMR measurementswere carried out in a perspex phantom (PTW type 2967,(C H 0 ), Q= 1.18 g-cm ,30 cm x 30 cm x 30 cm). Output 5 8 2measurements at maximum dose depth, d , were made in the same phantom at a source-detector-distance of 100 cm.

Ion chambers, thermoluminescence dosimeters and radiographic films were used as described in Tables I andII.

The reproducibility of the TLD measurements was + 2%, by using selected TLD ribbons that were individually calibrated.

The radiographic films were individually calibratedusing the arrangement schematized in Fig. 1. The films werefixed in the phantom tightly by means of lateral clamps. Anumber of separate areas of the film were irradiated usinga 3 cm x 3 cm square field. Each area was individuallyirradiated with a well-known dose which was varied from onearea to another in the range from 50 to 150 cGy (A inFig. 1). Other areas of the same film were subsequentlyirradiated with a field of the size needed for treatmentand for which the dose had yet to be determined (B inFig. 1). The dose value was subsequently determined usingthe sensitometric curve obtained for the same film with3 cm x 3 cm field size at different doses in the abovementioned range. This procedure was applied at variousphantom depths for TMR/PDD measurements and at d for

m axoutput measurements. Films were then automatically processed and the optical density was initially measured by

IAEA-SM-298/42 357

Table I . Field size ranges and detectors used in TMR/PDD measurements

Field size range 2( cm ) 1 Detector

10 x 10 - 2 x 2 1 p-p ion chamber (PTW Type M23343)10 x 10 - 1 X 1 1 TLD (LiF TLD 100 ribbons)10 x 10 - 0.5 x 0.5 1 radiographic film (Kodak X-0MAT V)

Table II . Field size ranges and detectors used in output factor measurements

Field size range i 2ï ( cm ) Detector

10 x 10 - 3 x 3 cyl. ion chamber (PTW Type M2332)10 x 10 - 1 X 1 TLD (LiF TLD 100 ribbons)10 x 10 - 0.5 x 0.5 radiographic film (Kodak X-0MAT V)

means of an automatic Therados RFA 3 densitometer and thenby a Victoreen 07-424 manual densitometer for the finaloptical density assessment.

The reproducibility of dose measurements usingradiographic film was + 2 % .

The zero area TMR was computed at depths d > d ,maxfrom the relationship:

- ii(d-d )TMR(d,0) = 100 e r max

where d is the depth in perspex and fi is the linear attenuation coefficient that was experimentally determined in good geometry using perspex as an attenuator according to the method described elsewhere |8,9|.


A) B)

FIG. 1. Experimental arrangement o f the radiographie film fo r calibration irradiation at different depths in the plastic phantom. Each area is individually irradiated with a well known dose which is varied from one area to another in the 50-150 cGy range (A). Other areas o f the same film are subsequently irradiated with a field o f the size needed fo r treatment (in this example 1 cm x 1 cm) and fo r which the dose is unknown (B).

RESULTS AND DISCUSSION

Figure 2 shows the central axis PDD in perspex for a 3 cm x 3 cm field obtained by TLD and films in comparison with the plane-parallel ion chamber results (full line).

The maximum deviation among the experimental PDD values, obtained by the different detectors, was within + 2%. The same agreement was. found for irradiation with field sizes of 6 cm x 6 cm and 10 cm x 10 cm.

IAEA-SM-298/42 359

FIG. 2. Measured central axis PDD fo r a 3 cm x 3 cm field. (— ) p-p ion chamber; ( a ) radiographic film; ( o ) TLD.

FIG. 3. Measured central axis PDD fo r a 1 cm x 1 cm field, ( a ) radiographic film; ( o ) TLD.


DEPTH (PERSPEX)FIG. 4. TMR curves fo r various field sizes and detectors:

A — 10 cm X 10 cm, p-p ion chamber В — 3 cm X 3 cm, p-p ion chamber С — 1 cm X 1 cm, radiographic film D — 0.5 cm X 0.5 cm, radiographic filmE — Calculated zero area TMR using a value o f ц = 0.0407 crn1 at d ^ = 1.5 cm.

FIG. 5. Measured output factor.From 10 cm x 10 cm to 3 cm x 3 cm the ion chamber was used; from 3 cm X 3 cm to 0.5 cm X 0.5 cm the radiographic film and TLD were used.

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FIG. 6. B u ild u p reg ion m easurem en ts using rad iograph ic f i lm f o r various f i e ld sizes.

The central axis PDD in perspex for a 1 cm x 1 cm field obtained with TLD and film measurements is shown in Fig. 3. In this case, the maximum deviation between the experimental values referring to these two detectors was within + 2.5%.

The TMR values for the 1 cm x 1 cm and 0.5 cm x 0.5 cm fields, as obtained from radiographic film measurements (curves С and D, respectively), are reported in Fig. 4.

The curves A and В show the TMR values obtained by the plane-parallel ion chamber for 10 cm x 10 cm and 3 cm x 3 cm field sizes, respectively. The zero area TMR values (curve^ E) were calculated using a value ofu =0.0407 cm , at d = 1.5 cm .maxThe dose values at a given depth in the curves A,B,C

and D decrease, as expected, according to the field size irrespective of the dosimetric method used to obtain each of these curves. This would indicate a consistency of the results obtained by radiographic film at a 0.5 cm x 0.5 cm


field size, provided that this film is calibrated according to the procedure described above. The dose values at dmaxin perspex, normalized to the dose value for the 10cmx10.cm field (output factor), are reported in Fig. 5 as a function of the field size. For field sizes equal.to or greater than 3 cm x 3 cm, dose measurements were made by ion chamber, and for field sizes of less than 3 cm x 3 cm, TLD and films were used. The reproducibility of the output factor curve, obtained by films and TLD with field sizes of less than 3 cm x 3 cm, was about + 2.5%.

The results on the buildup region measurementsobtained by radiographic film only are shown in Fig. 6 as afunction of the field size. These results show that, whenthe field size is reduced, d shifts towards the surfacemaxand the entrance dose increases, as is also reported by other authors |6 |. This effect may be due to the increase of the low energy component in the spectral distribution of radiation.

The procedure for radiographic film calibration and dose measurement described above allows for the factors which influence the sensitometric curve (e.g., the dose and the possible variations of the radiation spectrum with depth) ' and seems to be independent of the processing conditions. On the basis of these results, film dosimetry appears to be a practicable method at field sizes of less than or equal to 1 cm x 1 cm for which it is not always possible to use ion chambers and TLD. The reproducibility of the TMR values, obtained by film dosimetry with field sizes of less than 1 cm x 1 cm, was ábout + 3%.

REFERENCES

11 1 GREITZ, T., et al., Acta Radiol., Oncol. 25 (1986) 81. 121 HOUDEK, P.V., et al., Med. Phys. 12 (1985) 333.131 COLOMBO, F., et al., Neurosurgery (1985) 154.14 1 HARTMANN, G.H., et al., Int. J. Radiat. Oncol., Biol.

Phys. 11 (1985) 1185.

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15 1 STURM, V., et al., Int. J. Radiat. Oncol., Biol. Phys.13 (1987) 279.

16 1 ARCOVITO, G., et al., Med. Phys. 12 (1985) 779.171 HOUDEK, P.V., et al., Med. Phys. 10 (1983) 333.181 BAGNE, F., Med. Phys. 6 (1979) 510.I9 I VAN DYK, J., Med. Phys. 4 (1977) 145.

IAEA-SM-298/27

METHODE GENERALE D’OPTIMISATION DE LA DISTRIBUTION DES ISODOSES EN RADIOTHERAPIE PAR FAISCEAUX DE PETITES DIMENSIONS

D. LEFKOPOULOS Services de radiothérapie,Hôpital Tenon,Paris

J.-Y. DEVAUX, J.-C. ROUCAYROL Service d ’exploration fonctionnelle

par les radioisotopes,Hôpital Cochin,Paris

France

Abstract-Résumé

GENERAL METHOD FOR OPTIMIZING ISODOSE DISTRIBUTIONS IN SMALL-BEAM RADIOTHERAPY.

Stereotactic irradiation of small tumours requires dosimetry of high precision and well suited to the shape of the tumour, which is why a method of optimizing the selection of isodoses was developed. The method consists in processing both all the pixels of the isodose matrix and also the largest possible number of convergent beams, and does not simply resolve a system of linear equations in order to find the best solution for the beam weightings. The irradiation problem is analysed in depth by examining its poorness of fit relative to the treatment parameters. The isodose formation process is considered as an integral equation which is transformed after sampling into a matrix equation D = G-P, where D is the isodose matrix, P is the vector of the beam weighting coefficients and G is the transmission matrix, each column of which represents the projection of an individual beam into the isodose matrix space. The form of G is a function of energy, beam dimensions, the angular sampling of the beams, the shape of the contour and the position of the target. The suggested analysis is carried out following decomposition into simple eigenvalues and the creation of two matrix spaces, one for the isodose matrix ŸD and the other for the beam weighting coefficients ФР. The poorness of fit of the problem can be measured by the condition number, which is the ratio of the largest to the smallest of the simple eigenvalues. The decomposition is a very general one, and analogies can be drawn with Fourier frequency analysis. The best solution P for a particular isodose matrix D depends on truncating the simple components while seeking to minimize the error between the isodose prediction and the reconstructed matrices.

METHODE GENERALE D’OPTIMISATION DE LA DISTRIBUTION DES ISODOSES EN RADIOTHERAPIE PAR FAISCEAUX DE PETITES DIMENSIONS.

L’irradiation stéréotaxique des tumeurs de petite taille nécessite une dosimétrie de haute précision, bien adaptée à la forme de la tumeur. C’est dans cet esprit qu’on a développé une méthode d’optimisation du choix des isodoses. Elle consiste à traiter l’ensemble des pixels de la matrice des isodoses et le plus grand nombre possible de faisceaux convergents. Elle ne se borne pas à la simple résolution

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366 LEFKOPOULOS et al.

d’un système d’équations linéaires afin de trouver la meilleure solution de pondération des faisceaux. Elle effectue une analyse approfondie du problème d’irradiation en examinant son mauvais conditionnement en fonction des paramètres de traitement. On considère le processus dé formation des isodoses comme une équation intégrale qui se transforme après échantillonnage en une équation matricielle D = G-P, D étant la matrice des isodoses, P le vecteur des coefficients de pondération des faisceaux et G la matrice de transmission, dont chaque colonne représente la projection d’un faisceau individuel dans l’espace de la matrice des isodoses. La forme de G est fonction de l’énergie, des dimensions du faisceau, de l’échantillonnage angulaire des faisceaux, de la forme du contour et de la position de la cible. L’analyse proposée est réalisée suivant la déconjposition en valeurs singulières de G et la création de deux espaces, celui de la matrice des isodoses et celui du vecteur des coefficients de pondération des faisceaux Чг?. Le mauvais conditionnement du problème peut être mesuré par le nombre de condition qui est le rapport de la plus grande à la plus petite des valeurs singulières. Cette décomposition est très générale et présente des analogies avec l’analyse fréquentielle de Fourier. La meilleure solution P pour une matrice souhaitée des isodoses D est réalisée-en fonction de la troncature des composantes singulières, en cherchant à minimiser l’erreur entre la matrice prédictive des isodoses et la matrice reconstruite.

1. INTRODUCTION

Les problèmes inverses sont fréquemment utilisés dans un large domaine d’applications. Ils consistent à trouver une solution physiquement acceptable à partir d ’un certain nombre de mesures expérimentales. Plusieurs auteurs ont déjà traité le problème inverse dans le domaine médical. Kaplan [1] en médecine nucléaire, Hunt [2] en radiologie, Townsend [3] en imagerie par positrons et Lefkopoulos [4] en tomographie par codage.

Le problème inverse a été également envisagé en radiothérapie avec des faisceaux de grandes dimensions (plus de 3 cm). Les auteurs cherchaient à déterminer la «meilleure dose d ’irradiation possible», en optimisant certains critères sur un petit nombre de points préalablement définis. Parmi ces critères, les plus classiques sont l ’uniformité de la dose à l’intérieur de la tumeur ainsi que la minimisation de la dose aux tissus sains qui entourent la tumeur ou de la dose à certains organes particulièrement vulnérables. Deux démarches ont été tentées. La première consistait à trouver le poids des faisceaux sur une rotation complète [5]. La deuxième recherchait le poids de certains faisceaux prédéfinis, en utilisant des filtres en coin [6 ].

Plus récemment, les irradiations en conditions stéréotaxiques avec des faisceaux de petites dimensions (moins de 3 cm) de cobalt 60 [7, 8 ] ou de rayons X de haute énergie produits par un accélérateur linéaire [9—12] ont été proposées pour le traitement radiochirurgical des malformations vasculaires cérébrales.

Dans le cas des faisceaux de petites dimensions, la radiothérapie par rotation peut être considérée comme un cas particulier de l ’irradiation stéréotaxique 3D. Elle peut même en constituer une solution de remplacement pour un certain nombre d ’applications: par exemple, l ’irradiation de petites tumeurs cérébrales, ou bien les irradiations avec un faisceau fente [13], pour obtenir des distributions de dose comparables à celles des irradiations interstitielles.

IAEA-SM-298/27 367

FIG. 1. Présentation schématique du problème de l ’irradiation par rotation.

Dans cet exposé, nous proposons une méthode générale d ’optimisation. Bien qu’appliquée aux irradiations 2D par rotation avec des faisceaux de petites dimensions, cette méthode peut être également étendue aux irradiations stéréotaxiques 3D. A l’opposé de techniques développées jusqu’à maintenant, la procédure de formation de la distribution de la dose a été considérée dans sa globalité, en tenant compte de l ’ensemble de pixels de la matrice des isodoses et d ’un grand nombre de faisceaux pondérés chacun par un facteur d ’optimisation. Pour cela, nous avons réalisé l’analyse approfondie du problème de l’irradiation par rotation, en examinant le conditionnement du problème en fonction des paramètres d ’irradiation. Cette analyse est fondée sur la décomposition en valeurs singulières d ’un opérateur simulant la procédure physique de formation des isodoses, le but de la méthode étant de trouver une solution du vecteur de pondération physiquement acceptable pour l ’ensemble des faisceaux et pour une configuration donnée.

2. LA FORMULATION MATHEMATIQUE DU PROBLEME DE L ’IRRADIATION PAR ROTATION

La géométrie de l’irradiation par rotation est présentée dans la figure 1. Le contour de la coupe du corps est représenté par S et la surface incluse par R. Le corps est entouré par un ensemble de faisceaux et la position de chaque source de rayons X est définie par le vecteur r, l’isocentre de faisceaux étant commun et situé à l’intérieur du contour S. Ainsi les sources de rayons X sont situées sur la circonférence C d ’un cercle dont le rayon est la distance source-isocentre. Cette description est équivalente à un seul faisceau positionné successivement en différentes incidences. A l’intérieur du corps, la surface R est représentée par un ensemble de K éléments. Soit D¡ la dose du ièmc élément accumulée par la contribution de tous les

faisceaux. Le problème inverse de l’irradiation par rotation peut être énoncé comme suit: étant donné la distribution de la dose D, à l’intérieur du corps, déterminer l ’ensemble des poids des L faisceaux Pj qui satisfont l ’équation:

LD i = X) G Ü'Pj’ pour i=1’ 2’ •••’ K ^

j=l

Ecrite sous forme matricielle, l ’équation (1) devient:

D = G -P (2)

D et P étant des vecteurs respectivement de dimensions K et L et G une matrice de dimensions (K xL ).

Nous appelons la matrice G «matrice de transmission»; elle représente la procédure de détermination de la distribution de la dose à l’intérieur du corps. Chaque colonne de cette matrice représente la contribution de chaque faisceau élémentaire dans le vecteur de dose D. La forme de la matrice G dépend de la géometrie d ’irradiation, de l’énergie des rayons X et des dimensions du faisceau.


3. LE MAUVAIS CONDITIONNEMENT DU PROBLEME D ’IRRADIATIONPAR ROTATION

Nous rappelons le but poursuivi dans notre travail, qui est la détermination du vecteur de pondération P, à partir de la connaissance des éléments de la matrice G et des éléments prédéfinis du vecteur de dose D. Le choix des dimensions des vecteurs D et P est directement lié aux considérations physiques et pratiques de l’irradiation. Pour notre étude, nous avons choisi de prendre K > L . Nous justifions ce choix par deux raisons principales. D ’une part, si nous considérons un pas d ’échantillonnage angulaire de faisceaux trop petit, il n ’y aura pas de différence significative entre deux faisceaux adjacents. L ’augmentation du nombre de faisceaux allongera considérablement le temps de calcul. D ’autre part, le choix du nombre d ’éléments du vecteur D doit se faire avec prudence car si des informations additionnelles peuvent aider à la détermination du vecteur P, le suréchantillonnage du plan des isodoses peut produire une importante dépendance linéaire entre les lignes de la matrice G.

Une solution peut être obtenue en utilisant l ’inverse généralisé de la matrice G[14], donné par:

G ' = (GT-G)-1-GT (3)

si la matrice G (K xL ) est de rang L.

IAEA-SM-298/27 369

Cependant, la présence d’un bruit additif provoque habituellement une grande instabilité dans le processus d’inversion. Dans notre problème, ce bruit additif existe et il est dû à plusieurs phénomènes. Premièrement, le bruit résulte des incertitudes provenant du positionnement de Г isocentre dans le volume cible, de l’énergie de photons et de l ’hétérogénéité du champ suivant la position angulaire. Deuxièmement, une incertitude sur l’existence d ’une solution qui peut satisfaire notre problème résulte du choix d’une matrice G pour un vecteur prévisionnel D donné. Le vecteur D dépend de la forme du volume cible et de sa position à l’intérieur de l’organisme. Une fois les paramètres énergie, dimensions du collimateur et contour définis, la matrice G, qu’elle soit déterminée par modélisation ou de manière expérimentale, dépend du positionnement de l ’axe de rotation par rapport à celui du volume cible.

En utilisant l ’inverse généralisé G ', l ’estimé du vecteur de pondération est égal à un vecteur de pondération idéal plus un vecteur de perturbation ДР = G " e, où e représente le vecteur du bruit.

L ’erreur de perturbation sur l’estimation P:

peut être mesurée comme le rapport de la norme du vecteur de perturbation e à la norme du vecteur D.

Le produit II G" Il • Il G II est appelé nombre de condition R{G} de G et détermine l’erreur relative de l’estimation en termes du rapport de la norme du vecteur du bruit à la norme du vecteur de la dose D. Le nombre de condition peut être présenté directement par le rapport

R{G} = Il G “ Il • Il G II = a,/(jL

de la plus grande ai à la plus petite crL valeur singulière de G. Ainsi, plus le nombre de condition de la matrice G est grand, plus la sensibilité à la perturbation par le bruit sera élevée.

De même, suivant le conditionnement de la matrice de transmission G, des petites fluctuations provenant du bruit additif peuvent provoquer des erreurs importantes dans la solution et même donner des solutions physiquement inacceptables.

Ce type de situation peut être envisagé mathématiquement en utilisant des méthodes de régularisation qui essayent de remplacer le problème mal posé par un problème mieux posé [15-17]. Nous avons décidé de traiter le mauvais conditionnement de notre problème en utilisant l ’analyse de la décomposition en valeurs singulières (SVD) [18]. La méthode SVD est très générale, les autres méthodes de régularisation pouvant être analysées suivant les composantes singulières.


Après avoir présenté la nature du mauvais conditionnement de notre problème, exposons l ’analyse mathématique nous permettant d ’envisager ce dernier.

Pour un système d ’équations linéaires, un système singulier (u„, v„; an) est défini comme suit:

(u„; a l) , n = l , 2, ... est un système caractéristique de G G T

et

(v„; a l) , n = l , 2, ... est un système caractéristique de G T-G.

La courbe des valeurs singulières en fonction de leur indice en ordre monotone décroissant, ou «spectre singulier», caractérise le conditionnement du problème.

Dans notre problème de l’irradiation par rotation, (u„, an) décrit l ’espace de la de dose et (vn, an) l ’espace des facteurs de pondération Ÿp.

Ainsi

l/ff^-G-GT-u„ = un n = l , 2 , ...

et (5)

l/a„2 -GT-G-vn = v„ n = l , 2, ...

Nous supposons sans perte de généralité que > a2 > ... 0. Les a„ sont les valeurs singulières et un et v„ sont les vecteurs singuliers de G. Pour la facilité de présentation nous définissons aussi

= 1 4 i n = l , 2 , ...

Pour représenter schématiquement les dernières équations, nous proposons la figure 2 qui montre la décomposition en valeurs singulières de la matrice G.

La solution du vecteur de pondération cherché est donnée par:

4. LA SOLUTION OPTIMALE DANS L’ESPACE SVD

p n = £ < D ’ u n > (6)

N étant le nombre des composantes singulières utilisées dans l’expansion (6 ) pour obtenir la solution optimale. A ce point, pour faire la liaison entre l’inverse généralisé et l ’analyse SVD, notons que la solution de l ’inverse généralisé est équivalente à celle de l ’expansion SVD correspondant à N = L (c’est-à-dire quand toutes les composantes singulières sont utilisées) [14].

IAEA-SM-298/27 371

M atrice de

tra n sm is s io n G

(KxL)

Composantes, s in g u l iè r e s

de la m a tric e G (KxL)

Tо .u .V n n n

Le s p e c tre des v a le u rs s in g u l iè r e s

FIG. 2. Représentation graphique de la décomposition en valeurs singulières de la matrice de transmission G.

Notre critère d ’optimisation sera le suivant: quand P est approximé par une combinaison de N premières composantes singulières, la solution optimale sera celle qui minimise le paramètre de précision de reconstruction:

= ( E ( - E Gü-pi¡=i ' j=i

2\ 1/2

5. APPLICATION A LA DOSIMETRIE DES RAYONS X AVEC DESFAISCEAUX DE PETITES DIMENSIONS

La méthode d ’optimisation proposée pour des faisceaux de petites dimensions peut être appliquée à de multiples configurations d ’irradiation. Les résultats présentés dans ce mémoire sont fondés sur une configuration d ’irradiation 2D. Nous utiliserons, dans ce chapitre, à la place du terme «vecteur de dose» employé dans l’analyse mathématique, le terme «matrice de dose», plus adapté pour la présentation de nos résultats physiques, ces deux termes étant équivalents.

Pour la formation de la matrice de dose D, nous distinguons deux cas généraux. Dans le premier, la contribution de chaque faisceau élémentaire est basée sur des modèles théoriques, qui utilisent comme données les mesures des facteurs de correction du diffusé du collimateur et du fantôme, le rapport tissu-maximum (RTM), et


le rapport diffusé-maximum (RDM) [19-23]. Dans le second cas, la solution consiste à utiliser directement les données expérimentales pour composer les matrices de dose des faisceaux élémentaires obtenues pour des distances source-surface envisagées en routine. Nous avons utilisé la deuxième méthode, jugée plus fiable, à cette étape de test de notre analyse d ’optimisation. La comparaison des résultats obtenus avec la méthode de Galmarini [21], appartenant à la première catégorie de méthodes, et ceux obtenus avec des films dosimétriques irradiés dans les mêmes conditions, a confirmé la bonne corrélation de ces deux méthodes.

Nous avons testé l ’analyse du mauvais conditionnement du problème d ’irradiation par rotation, dans des conditions contrôlées. Nous nous sommes servis d ’un contour circulaire de 1 0 cm de diamètre, dont le centre coïncide avec l’axe de rotation, et d ’un faisceau cylindrique de 12 mm de diamètre de rayons X de 18 MV. La distance source-isocentre est de 1 0 0 cm.

Pour la formation de la matrice de transmission G, nous avons utilisé une matrice de dose de 30x250 pixels de 1 mm de côté. Elle est obtenue par lecture d ’un film dosimétrique après irradiation par un faisceau unique. Cette matrice nous permet de former les matrices élémentaires de dose correspondant aux différentes incidences. Chaque matrice élémentaire de dose, constituée de 64 x 64 pixels de 1 mm de côté, est positionnée au centre du contour. L ’ensemble de matrices élémentaires de dose forme la matrice de transmission G.

Pour cette étude, la matrice de dose prévisionnelle a été composée de surfaces rectangulaires de même densité de dose de 100%, 80%, 50% et 20%. Nous avons considéré une rotation complète du faisceau autour du contour et nous avons étudié quatre pas d ’échantillonnage angulaire différents: 40°, 20°, 10° et 5° qui correspondent respectivement à 9, 18, 36 et 72 faisceaux. Le mauvais conditionnement du problème d ’irradiation et son influence sur la qualité de la reconstruction de la matrice de dose D ont été étudiés pour ces quatre situations.

En calculant les valeurs singulières de la matrice de transmission G, nous pouvons mesurer quantitativement l ’effet de chaque composante singulière sur l’ensemble de la matricce reconstruite D. Le conditionnement de l ’irradiation, pour chaque pas d ’échantillonnage, est analysé en étudiant le nombre de condition et les vecteurs singuliers de l ’espace de dose ^ D. La précision de la reconstruction de la matrice de dose est basée sur le calcul du paramètre Д.

Les nombres de condition calculés pour les quatre pas d ’échantillonnage Д 0 étudiés: 40°, 20°, 10° et 5°, sont respectivement 5, 39, 126, 295 et montrent que le conditionnement du problème se détériore quand Д 9 diminue.

La figure 3 présente la précision de reconstruction de la matrice de dose en fonction des composantes singulières utilisées dans l ’expansion SVD. Pour Д 9 = 4 0 ° , le problème est bien conditionné et la meilleure solution est celle donnée par l’inverse généralisé. Cela correspond au cas où toutes les composantes singulières sont utilisées. Dans les autres cas, la meilleure solution est obtenue après troncature de certaines des composantes singulières. Quand Д 0 diminue, la solution de l’inverse généralisé devient très imprécise, en opposition avec la solution SVD optimale, qui

IAEA-SM-298/27 373

Nombre de com posantes s in g u l iè r e s u t i l i s é e s N

FIG. 3. Précision de reconstruction de la matrice de dose en fonction du nombre de composantes singulières N, utilisées dans l ’expansion SVD, pour quatre pas d ’échantillonnage:a) Aв = 4 0 ° (L=9), b) A0= 2 0 ° (L=18), c) AQ = 10° (L=36) et d) A0 = 5 ° (L= 72).

s’améliore. Le miminum de Д est relativement insensible à la variation du nombre N de composantes singulières utilisées. Ainsi, bien qu’il soit important d ’obtenir une estimation «précise» du nombre N optimal, le degré de cette précision n ’est pas crucial. Pour des valeurs élevées de N, l ’erreur Д est très grande à cause de l’amplification des perturbations dues aux petites valeurs singulières. Inversement, pour de petites valeurs de N, l ’amplification est due au manque d ’informations fines contenues dans les composantes singulières d ’ordre élevé. Entre ces deux extrêmes se trouve la valeur optimale de N.

Il est important de bien distinguer les notions de solutions mathématiquement et physiquement acceptables. Les solutions mathématiques du vecteur de pondération Pm sont celles pour lesquelles on n’impose pas un critère de positivité. Au contraire, les solutions physiquement acceptables Pp ne peuvent retenir des valeurs de pondération négatives. Dans la figure 3, nous avons présenté les variations de la précision Д en fonction de N en forçant les valeurs négatives à zéro. Dans la figure 4, nous comparons les courbes de précision des solutions mathématiquement et physiquement acceptables pour Д 9 = 10°. Nous observons que la solution mathématique Pm sans troncature (N=L) est la plus précise, le problème dans ce cas étant bien conditionné. Mais cette solution comporte de larges valeurs négatives et n ’est pas

Vec

teur

de

pond

érat

ion


1ЛO

X<

cоÜ<DM

<UT3cо

Nombre de com posantes s in g u l iè r e s u t i l i s é e s N

FIG. 4. Précision de reconstruction pour des solutions mathématiques et des solutions physiquement acceptables, pour Д0=7О°.

xçu

PОтН(0ИЧУ*8a*oи3a)uоa>>*

0 tí 2n

Angle d 'in c id e n c e g Angle d 'in c id e n c e 6

FIG. 5. Vecteurs de pondération P: a) sans troncature (N=36) et b) avec N=13, (àQ = 10°).

IAEA-SM-298/27 375

FIG. 6. Composantes singulières de l ’espace de dose d ’ordre: a) n=2, b) n= 4, c) n=6, d) n=8, pour Д9 = 10°.

physiquement acceptable (fig. 5a). La meilleure solution SVD, physiquement acceptable, est obtenue après troncature des 23 dernières composantes singulières. Dans ce cas, le vecteur de pondération Pp ne comporte ni élément négatif, ni élément positif proche de zéro (fig. 5b).

Pour expliquer plus analytiquement les résultats précédents, nous présentons dans la figure 6 les composantes singulières de l’espace de dose ^ D, pour Д 9 = 10°. Nous pouvons les examiner de deux points de vue, quantitativement et qualitativement. Du point de vue quantitatif, les informations de la matrice de dose sont concentrées dans la première composante singulière, les autres ne retenant qu’une petite partie de l’information globale. Cela n’apparaît pas sur les quatre images car, pour des raisons de présentation, ces images sont normalisées chacune par rapport à leur valeur maximale. Du point de vue qualitatif, nous pouvons observer que les composantes singulières peuvent être caractérisées, par analogie avec le domaine fré- quentiel de l ’espace de Fourier, comme les composantes de l ’espace SVD. Bien que la première composante singulière contienne la plus grande partie de l’information, les autres composantes contiennent les détails fins et contribuent ainsi à une reconstruction plus précise de la matrice de dose prévisionnelle. Cela est montré dans


c d

FIG. 7. a) Matrice prévisionnelle des isodoses. Les reconstructions obtenues, pour AQ = 10°, avecb ) N = l , c) N=13, d) N=36.

la figure 7 où nous présentons les images de reconstructions SVD de la matrice D. Ces images correspondent aux sommes partielles des composantes singulières et montrent l ’effet cumulatif des composantes singulières individuelles sur la reconstruction d ’une matrice de dose prédéfinie. Nous observons qu’un petit nombre de composantes est nécessaire pour obtenir une reconstruction avec des informations significatives (Д0 = 1 0 ° ).

Finalement, nous montrons dans la figure 8 la construction des trois matrices de dose correspondant à des vecteurs de pondération différents. Ces matrices confirment la possibilité d ’obtenir des formes d ’isodoses très variées par l ’utilisation de vecteurs de pondération appropriés.

6 . CONCLUSION

Les méthodes d ’optimisation proposées pour les traitements en radiothérapie ont en commun la détermination d ’une distribution de dose idéale dans le corps du malade. Jusqu’à maintenant, les méthodes mathématiques utilisées étaient basées sur des processus itératifs. Elles se limitaient à l ’optimisation de certains critères sur un

IAEA-SM-298/27 ъ п

с

FIG. 8. Exemples de constructions de matrices de dose, pour AQ = 1CI°, en utilisant les vecteurs de pondération suivants:a) pj=j j = l , 2, 36; b) les éléments 3, 4, 5, 6, 7, 21, 22, 23, 24 et 25 du vecteur P ont la valeur1,0 et les autres la valeur 0,0; c) les éléments 1, 2, 3, 26, 27, 28, 29, 30, 35 et 36 du vecteur P ont la valeur 1,0 et les autres la valeur 0,0.

nombre restreint de points, pour éviter des calculs trop lourds. Ces techniques, bien que suffisantes pour la radiothérapie classique, ne répondent pas aux exigences de haute précision souhaitée pour une irradiation avec des faisceaux de petites dimensions, à cause de la complexité d ’irradiation.

Nous avons étudié le problème des irradiations de haute précision dans sa globalité en tenant compte de l’ensemble de la matrice de dose prévisionnelle. Nous avons effectué une analyse approfondie du processus d ’irradiation dans l’espace vectoriel SVD. Le conditionnement du problème a été étudié en fonction de l’échantillonnage angulaire. Nos résultats montrent que, quand l ’échantillonnage descend au-dessous de 1 0 °, la précision de reconstruction ne s’améliore pas significativement, mais qu’au contraire le temps de calcul augmente considérablement. Ce type d ’étude devrait per-


mettre de choisir un échantillonnage angulaire permettant un bon compromis entre la précision de reconstruction et le temps de calcul.

Bien que nos résultats soient obtenus pour une configuration d ’irradiation simplifiée, ils montrent l ’intérêt de cette méthode d’optimisation pour l ’amélioration de la qualité de traitements en radiothérapie de haute précision. Ils constituent la base d ’un programme interactif pour une détermination dosimétrique prévisionnelle. Ils nous incitent à étudier d ’autres paramètres tels que l ’énergie du faisceau, les dimensions et la forme de faisceaux.

La capacité prévisionnelle de cette méthode ne sera pas réduite par l’utilisation de contours réels ni par les variations de position du volume cible à l ’intérieur du contour. Les applications de la méthode, présentée pour une configuration d ’irradiation 2D peuvent être sans difficulté théorique étendues au domaine des irradiations 3D stéréotaxiques.

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158.[7] SARBY, B., Acta Radiol., Ther., Phys., Biol. 13 (1974) 425.[8] DAHLIN, H., SARBY, B., Acta Radiol., Ther., Phys., Biol. 14 (1975) 209.[9] BETTI, O.O., DERECHINSKY, V.E., Acta Neurochir., Suppl. 33 (1984) 385.

[10] HOUDEK, P.V., VANBUREN, J., FAYOS, J., Med. Phys. 10 3 (1983) 333.t i l l HARTMANN, G.H., et al., Int. J. Radiat. Oncol., Biol. Phys. 11 (1985) 1185.[12] SCHLIENGER, M., Hôpital Tenon, Paris, communication personnnelle.[13] KAMADA, T., TSUJII, H., MIZOE, J.E., WATANABE, Y., IRIE, G., in C.R. 8th Int. Conf.

on the Use of Computers in Radiotherapy, Toronto (1984) 533.[14] PRATT, W.K., in Digital Image Processing, Wiley-Interscience, New York (1978) ch. 10 and

ch.14.[15] TWOMEY, S., J. Franklin Inst. 279 (1965) 95.[16] PHILLIPS, D.L., J. Assoc. Comput. Mach. 9 (1962) 84.[17] TIKHONOV, A.N., Sov. Math. Dokl. 4 (1963) 1035.[18] GOLUB, G., REINSCH, C., Numer. Math. 14 (1970) 403.[19] KHAN, F.M., SEWCHAND, W., LEE, J„ WILLIAMSON, J.F., Med. Phys. 7 (1980) 230.[20] ARCOVITO, G., PIERMATTEI, A., D’ABRAMO, G., ADREASI BASSI, F., Med, Phys. 12

6 (1985) 779.[21] GALMARINI, D., Clinica Antartida, Buenos Aires, communication personnelle.[22] NOUET, P., et al., «Contrôle de qualité dosimétrique des minifaisceaux à l’aide d’un photoden-

sitomètre de très haute précision», C.R. 17e Congrès de la Société française des physiciens d’hôpital, Vittel (France), 1987 (à paraître).

[23] LEFKOPOULOS, D., SCHLIENGER, M., «Dosimétrie 3D pour les irradiations stéréotaxiques», ibid.

POSTER PRESENTATIONS

Rapporteur: A.E. NAHUM (United Kingdom)

IAEA-SM-298/32P

DETERMINATION OF ELECTRON RANGES IN WATER FROM THOSE IN SOLIDS

В. GROSSWENDT, M. ROOS Physikalisch-Technische Bundesanstalt,Braunschweig,Federal Republic of Germany

To determine the absorbed dose of electrons in water it is common practice in radiation therapy to use energy parameters calculated from electron ranges in water. For primary electron energies below about 10 MeV these ranges can be obtained from ranges of electrons in other materials than water by applying appropriate scaling laws. In the energy region below 5 MeV this procedure is unavoidable.

The aim of the present study was, therefore, to analyse the validity of different scaling procedures recommended by national or international associations such as ICRU, NACP, HPA, DIN, NACP and SEFM. The most recently developed phantom material o f Balzer et al. [1] is also included in the investigations.

Hence practical ranges and half-value depths of depth dose distributions for monenergetic electrons were determined from depth dose curves in water, graphite, polymethyl methacrylate (PMMA), a tissue equivalent plastic (A -150), polystyrene and polyethylene in the energy range between 1 and 10 MeV using a Monte Carlo transport model.

The validity of the transport code was tested by comparison of calculated depth dose curves with Monte Carlo results published by other authors [2-4] (see Fig. 1) and, moreover, by comparison with experimental data measured in PMMA and polystyrene using electrons from a microtron (see Fig. 2).

The practical ranges and half-value depths derived from the depth dose curves in the different materials were then converted to those in water using the different scaling laws and compared with the data determined in water directly. It could be shown that the converted practical ranges deviate by up to 7 % and the half-value depths by up to 10% from those in water. A considerable improvement with deviations smaller than 3 % in all cases is achievable if a procedure according to Harder[5] is applied. This method also uses simple scaling relations but takes into account both the energy loss of electrons and their scattering.

379


FIG. I. Energy absorption AE/Az in a depth between z and z + Az fo r 5 MeV electrons in water in dependence o f the depth z normalized to the csda pathlength r0; step function - Monte Carlo results, A - Monte Carlo results o f Nahum [2], + - data o f Seltzer et al. [3], о - results o f Andreo [4].

FIG. 2. Normalized absorbed dose D fo r primary electrons o f energy (a) E0 = 1.049 MeV, (b) E0 = 4.303 MeV in PMMA, and (с) E0 = 1.724 MeV in polystyrol versus depth z; step function - Monte Carlo calculation, о - experimental results.


REFERENCES

[1] BALZER, D, ROBRANDT, B., ROSENOW, U., HARDER, D., “ Optimierung von Polystyrol (ТЮ2) als wasseräquivalentes Phantommaterial für hochenergetische Photonen und Elektronen” , Medizinische Physik ’86 (von KLITZING, L., Ed.), Deutsche Gesellschaft für Medizinische Physik, Lübeck (1986) 247-254.

[2] NAHUM, A.E., Calculations of Electron Flux Spectra in Water Irradiated with Megavoltage Electron and Photon Beams with Applications to Dosimetry, Thesis, University of Edinburgh, 1976.

[3] SELTZER, S.M., HUBBELL, J.H., BERGER, M.J., “ Some theoretical aspects of electron and photon dosimetry” , National and International Standardization of Radiation Dosimetry (Proc. Symp. Atlanta, 1977), Vol. 2, IAEA, Vienna (1978) 3-43.

[4] ANDREO, P., Monte Carlo Simulation of Electron Transport in Water: Absorbed Dose and Fluence Distributions, Report FANZ/80/3, Department of Nucl. Physics, University of Zaragoza (1980).

[5] HARDER, D., “ Some general results from the transport theory of electron absorption” , Microdosimetry (Proc. 2nd Symp. Stresa, 1969), (EBERT, H.G., Ed.), Euratom, Brüssels (1970) 567-594.

IAEA-SM-298/75P

DOSE DISTRIBUTION STUDY OF SOFT X-RAYS AND EXTENSION OF THE APPLICATION OF SHORT DISTANCE RÖNTGEN THERAPY TO ADVANCED SKIN CANCER

Y . SKOROPAD Division of Life Sciences,International Atomic Energy Agency,Vienna

Skin cancer is widespread throughout the world. According to the present tendency advanced cases of skin tumour are expected to prevail in developing countries.

Short distance roentgen therapy (SDR) is one of the cheapest and most accessible treatment techniques of skin cancer and other skin tumours. Several types of machines are used for this purpose. The present study was made using an X-ray machine o f the type RUM-7 (USSR) with X-ray generation up to energies of 50 kV and irradiation field localizers from 10 mm to 50 mm in diameter. Treatment planning techniques of SDR as a rule are based on the information on dose distribution along the beam axis. This creates great difficulties for effective irradiation of relatively advanced tumours, larger than 15-20 mm in diameter. The advanced


tumours can be irradiated with the same X-ray machine using, for instance, the multi- field technique. However, this technique results in ‘hot’ and ‘cold’ areas, which are of great disadvantage and can be the reason for a high rate of recurrences or side effects. Electron beam therapy [1] is thought to be the ideal tool for advanced skin tumours. However, betatrons or linear accelerators are not yet available in developing countries.

Therefore, to find a way of extending the use of SDR, X-ray machines should have great practical significance for developing countries.

A modified tissue equivalent chemical gel dosimeter [2] (p = 1.0, ZT = 7.46, ZT = 6.6, electron density 3.34 X 1023) consisting of K N 03 (0 .1M solution), glucose (0.18%), Grease’s chemical to detect N 0 2-ions (5.0%) and Difco agar (1%) has been developed for a detailed study of the dose distributions of X-rays with halflayer attenuation (HLA) from 0.3 mm A l to 1.6 mm Al. After irradiation the gel dosimeter changes its colour, becomes red and visualizes the shape of the beam. During one hour after irradiation the intensity of the colour increases and then stabilizes for several hours which is sufficient to allow measurement of the optical density. The optical density measured under 600 nm is linearly proportional to the absorbed dose up to 10 Gy and non-linearly proportional from 10 to 80 Gy. Absorbed doses can be estimated from a calibrated curve. The study of the soft X-rays has resulted in a series of dose distributions of the machine of the type RUM-7. Another possibility for the extended use of SDR for more advanced tumours has been found. This has been achieved by using longer skin-source distances (SSDs), a compensator, field shaping shields, etc. As a result, tumours two times larger, with a diameter of up to 8 cm and a thickness of 2 cm, have been effectively irradiated.

The implementation of this approach taking into consideration this specific X-ray machine of low energy will contribute to a better control of superficial cancer in developing countries.

REFERENCES

[1] WACHSMAN, F., Von der Radium-Kontaktbestrahlung über Nahebestrahlung zur Weichstrahlen Therapie und zur Therapie mit schnellen Elektronen, Strahlentherapie 114 (1961) 446-453.

[2] RUDAKOFF, N.P., Nitrate-gel dosimeters, Biological Action of Neutrons, Naukova Dumka, Kiev (1956) 91-93.


DOSIMETRY OF ROTATIONAL TOTAL-SKIN RADIOTHERAPY WITH ELECTRONS

K. MUSKALLA, A. STRATMANN, U. QUAST Abteilung Strahlentherapie,Radiologisches Zentrum,Universitätsklinikum Essen,Essen,Federal Republic of Germany

IAEA-SM-298/6P

The aim in radiotherapy treatment of mycosis fungoides is to irradiate the skin with a sufficiently homogeneous dose distribution up to a few millimetres in depth at each point of the body (uniformity). The target volume is the whole skin of the patient, so that the use of a great number of fixed electron fields would be necessary to cover up the whole skin. The overlapping of many small fields would lead to uncertainties in the dose at the sides of the fields. To avoid this disadvantage, electron fields as large as possible are used. This means treatment at extended distances to cover a large part of the body. To irradiate the whole circumference rotational total skin electron radiotherapy (TSER) is used, giving the highest possible uniformity of the dose distribution.

The physical conditions in rotational TSER are far from known standard situations, partly because of the large distance between the patient and the beàm focus (large field size is required) and because of the permanent rotation of the patient during irradiation. Thus, a special dosimetric procedure is necessary. Systematic measurements of the absolute dose, of the shape and of the range of the distributions were taken depending on various conditions. Beams of various electron energies (5,6, 7 and 9 MeV) were investigated. Furthermore, the angle of the beam incidence relative to the phantom surface was varied and atteniiation- and scatter-screens (acryl-glass) of various thicknesses were used. The dose was measured independently with a parallel-plate ionization chamber (after Markus) and TLDs (LiF-rods) in a tissue-equivalent phantom (polystyrene-white with ТЮ2). The distance between the phantom and the beam focus was varied and the vertical and horizontal uniformity of the beam was examined. The depth dose measurements were carried out with a fixed phantom as .well as with a rotating phantom under treatment conditions.

We have developed an algorithm to calculate the depth dose distribution under rotational irradiation conditions from the experimental fixed field data. The mathematical construction algorithm needs only to sum up the measured doses over the various angles of incidence individually for each measured depth. This construction works well as has been proven by comparison of the calculated and the measured data. Because this mathematical algorithm gives good results in the plane of incidence


(perpendicular to the rotation axis of the detector), it is concluded that the depth dose distribution in tilted surface regions, showing oblique beam incidence, may be derived in the same way from these basic data. This is of great importance for inclined parts of the body (head, shoulders, etc.), where the normal to the surface is not perpendicular to the axis of rotation. Following this procedure, depth dose distributions for any angle of inclined beam incidence may be constructed.

Another important result is that by omission of a certain interval of the integration angle the influence of shadow casting parts of the body on the depth dose distribution may be simulated. Thus, the depth dose distributions may also be calculated for partially shielded parts of the body (i.e. the inner parts of the legs) from the basic data.

The difference between the depth dose distribution at the dose specification point and the dose in any low dose region yields the missing electron depth dose distribution. A corresponding dose distribution has to be added by additional irradiation to obtain a uniform dose distribution in the whole skin. The low dose regions will usually be irradiated with fixed electron fields at normal treatment distances, the dose distributions of which are very similar to the calculated one.

All investigations were carried out with two detector systems with different individual physical characteristics, ionization chambers and TLDs. The calibration factors of both systems depend on the beam energy. However, the sensitivity of the parallel-plate chamber depends on the angle of beam incidence, too. The depth dose distributions and absolute doses are almost the same — within the estimated errors — for both types of detectors.

Finally, it can be summarized that individual physical treatment planning of rotational TSER is enabled by the dosimetric procedure described.

BIBLIOGRAPHY

BJÄRNGARD, B.E., et al., Analysis of dose distributions in whole body superficial electron therapy, Int. J. Radiat. Oncol., Biol. Phys. 2 (1977) 319-324.

KIM, Т.Н., et âl., Clinical aspects of a rotational total skin electron irradiation, Br. J. Radiol. 57 (1984) 501-506.

MUSKALLA, K., QUAST, U. GLAESER, L., “ Einfluß von Strahlrichtung und Energie auf die Dosisverteilung bei der Ganzhaut-Rotationsbestrahlung mit Elektronen” , Medizinische Physik ‘86, (von KLITZING, L., Ed.), Deutsche Gesellschaft für Medizinische Physik, Lübeck (1986) 547-554.

TETENES, P.J., GOODWIN, P.N., Comparative study of superficial whole-body radiotherapeutic techniques using a 4-MeV nonangulated electron beam, Radiology 133 (1977) 219-226.

CHAIRMEN OF SESSIONS

Session I

Session II

Session III

Session IV

H. SVENSSON

A. DUTREIX

J.S. LAUGHLIN

J.E. BURNS

Sweden

France

United States of America

United Kingdom

Session III

Session IV

POSTER RAPPORTEURS

A. DUTREIX

A.E. NAHUM

France

United Kingdom

SECRETARIAT OF THE SYMPOSIUM

ScientificSecretary:

AdministrativeSecretary:

Editor:

M. GUSTAFSSON

H. PROSSER

B. KAUFMANN

Division of Life Sciences, IAEA, Vienna

Division of External Relations, IAEA, Vienna

Division of Publications, IAEA, Vienna

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