ISOEFFECT CALCULATION IN HDR BRACHYTHERAPY(BASIC CLINICAL RADIOBIOLOGY)

Alfredo Polo MD, PhD

Division of Human Health

International Atomic Energy Agency

Dose

rate

(Gy/

h)

0,0

2,5

5,0

7,5

10,0

Time (min)0 60 120 180 240 300 360

LDRPDRHDR

TYPES OF BRACHYTHERAPY PROCEDURES(ICRU REPORT 38)

Clinical work of Brachytherapy since 1950 was to optimise the therapeutic ratio by exploiting the differential response of

healthly and malignant tissue to the delivery of the maximal tumoricidal dose in as short time as possible.

B. Pierquin 1992

BASIC RADIATION DAMAGE

Valu

e (%

)

0

20

40

60

80

100

Fraction time (%)0 20 40 60 80 100

DOSELinear.(DOSE)DAMAGELog.(DAMAGE)REPAIRExpon.(REPAIR)

INSIDE A FRACTION

LINEAR QUADRATIC MODEL

NSD: Nominal standard dose (Ellis, 1969)

TDF: time-dose-fractionation (Orton & Ellis, 1973)

ERD: extrapolated response dose (Barendsen, 1982)

LQ: linear-quadratic (Orton & Cohen, 1988)

Modelo LinealModelo Lineal--QuadrQuadrááticotico•• αααααααα:: Parámetro que expresa la muerte

celular por impacto único/daño letal (parte lineal). Valor en Gy-1

•• ββββββββ: : Parámetro que expresa la muerte celular por impacto doble/daño subletal (parte cuadrática). Valor en Gy-2

•• αααααααα//ββββββββ: : proporción entre el daño letal respecto al subletal de un tejido. Valor en Gy.

♦♦αααααααα//ββββββββ alto: alto: Tejidos en los que predomina el componente α, la muerte por daño letal, en los que, por lo tanto, predomina el efecto de la dosis total. Dosis por fracción de 1-2 Gy (y dosis total altas, > 60 Gy) son adecuadas para esterilizar sus células (a estas dosis predomina la muerte por impacto único). Corresponde a tejidos de respuesta rápida, con valores de α/β entre 6-20 en su mayoría.

♦♦αααααααα//ββββββββ bajo: bajo: Tejidos en los que predomina el componente β, la muerte por daño subletal, en los que, por lo tanto, predomina el efecto de la dosis por fracción. Dosis por fracción altas (>3-4) y dosis totales reducidas (< 50-60 Gy) son adecuadas. Corresponde a tejidos de respuesta lenta, con valores de α/β < 6 en su mayoría.

* *Conventional hypofractionation

Extreme hypofractionation

Grey zone

Rapid proliferative tissues are less sensitive to changes in fractionation (large doses per fraction or higher dose rate)

Slow proliferative tissues are more sensitive to changes in fractionation (large doses per fraction or lower dose rate)

Fuks Z, Kolesnick R. Engaging the vascular component of the tumor response. Cancer Cell. 2005;8:89-91.

ENDOTELIAL MEDIATED CELL DAMAGE

The much smaller proportion at 2 Gy than 8 Gy per pulse is showed

!Only the red proportion is altered by α/β, T1/2 and dose per pulse

!Keeping low the dose per pulse guarantees minimal risk of excess damage in late tissues

INSIDE A FRACTION

Adapted from Fowler 1999

FRACTION FRACTION FRACTIONGAP GAP

Creation of SLD

Repair of SLD

Δ no repair of SLD

Time

Dose

rate

per

pul

se

BETWEEN FRACTIONS

1. Conventional EBRT/HDR daily fractions (>24h) permit enought time between fractions for full repair to occur.

2. If interfraction time is reduced to less than aprox 8h, repair between fraction may be incomplete and cell survival decreased.

3. A potential for therapeutic gain exists when the fractionation sensitivity α/β for the host dose limiting late reacting normal tissues is greater than a tumor lying within such tissue.

Thames HD et al. Incomplete repair model for survival after fractionated and continuous irradiation. IJRO 1985; 47: 319 !Dale RG et al. The application of the LQ formula dose-effect equation to fractionated and protracted radiotherapy. B J Radiol 1985; 58: 515

SUBLETHAL DAMAGE REPAIR: incomplete repair

BASIC MODEL FORISOEFFECT CALCULATION

PII S0360-3016(99)00330-2

PHYSICS CONTRIBUTION

A SIMPLE METHOD OF OBTAINING EQUIVALENT DOSES FOR USE INHDR BRACHYTHERAPY

SUBIR NAG, M.D., AND NILENDU GUPTA, PH.D.Division of Radiation Oncology, Arthur G. James Cancer Hospital and Research Institute, Ohio State University, Columbus, OH

Purpose: To develop a simple program that can be easily used by clinicians to calculate the tumor and late tissueequivalent doses (as if given in 2 Gy/day fractions) for different high-dose-rate (HDR) brachytherapy regimens.The program should take into account the normal tissue sparing effect of brachytherapy.Methods and Materials: Using Microsoft Excel, a program was developed incorporating the linear-quadratic(LQ) formula to calculate the biologically equivalent dose (BED). To express the BED in terms more familiar toall clinicians, it was reconverted to equivalent doses as if given as fractionated irradiation at 2 Gy/fraction. Sincedoses given to normal tissues in HDR brachytherapy treatments are different from those given to tumor, anormal tissue dose modifying factor (DMF) was applied in this spreadsheet (depending on the anticipated doseto normal tissue) to obtain more realistic equivalent normal tissue effects.Results: The spreadsheet program created requires the clinician to enter only the external beam total dose anddose/fraction, HDR dose, and the number of HDR fractions. It automatically calculates the equivalent doses fortumor and normal tissue effects, respectively. Generally, the DMF applied is< 1 since the doses to normal tissuesare less than the doses to the tumor. However, in certain circumstances, a DMF of > 1 may need to be appliedif the dose to critical normal tissues is higher than the dose to tumor. Additionally, the !/" ratios for tumor andnormal tissues can be changed from their default values of 10 Gy and 3 Gy, respectively. This program has beenused to determine HDR doses needed for treatment of cancers of the cervix, prostate, and other organs. It canalso been used to predict the late normal tissue effects, alerting the clinician to the possibility of undue morbidityof a new HDR regimen.Conclusion: A simple Excel spreadsheet program has been developed to assist clinicians to easily calculateequivalent doses to be used in HDR brachytherapy regimens. The novelty of this program is that the equivalentdoses are expressed as if given at 2 Gy per fraction rather than as BED values and a more realistic equivalentnormal tissue effect is obtained by applying a DMF. Its ease of use should promote the use of LQ radiobiologicalmodeling to determine doses to be used for HDR brachytherapy. The program is to be used judiciously as a guideonly and should be correlated with clinical outcome. © 2000 Elsevier Science Inc.

HDR brachytherapy, Time–dose-effect, Linear-quadratic, Biologically equivalent dose.

INTRODUCTION

Most radiation oncologists are familiar with low-dose-rate(LDR) brachytherapy. Recently, there has been a trendtowards increased use of high-dose-rate (HDR) brachyther-apy due to its advantages, namely that it eliminates radiationexposure to caregivers, requires only short treatment times,and that its dose distribution can be optimized by varyingthe dwell times. HDR is generally given as fractionatedtreatments to decrease normal tissue toxicity. The doseeffect relationship in radiation therapy is not linear, but maybe assumed to follow a linear-quadratic (LQ) function (1).Hence, doses from different treatment modalities cannot beadded linearly to determine the combined effect. Manyradiation oncologists are not very familiar with the fraction-

ation schemes to be used in HDR brachytherapy. Further,there is a marked difference between the biological effectsin the tumor and those in late reacting normal tissue (1).Besides, patients are often treated with external beam ra-diotherapy combined with HDR brachytherapy, whichposes the added challenge of determining the combinedeffect of the two treatments.One way to calculate the biologically equivalent doses

(BEDs) of different dose fractionation schemes is to use theLQ equation (eq. 1 in Appendix 1). In this equation, the !/"ratio is usually taken to be 10 Gy for tumor/early effects and3 Gy for late effects (2). The concept of LQ modeling isfamiliar to most radiation oncologists. However, this calcu-lation is cumbersome, and the resultant BED values are notfamiliar to the clinicians. Further, it does not take into

Reprint requests to: Subir Nag, M.D., Chief of Brachytherapy,The Arthur G. James Cancer Hospital, Ohio State University,300 West Tenth Avenue, Columbus, OH 43210. E-mail:nag.1@osu.eduAcknowledgments—The authors wish to express their gratitude to

David Carpenter for editorial assistance. This study was supportedin part by Grant 5P30CS16058 from the National Cancer Institute,Bethesda, MD.Accepted for publication 29 July 1999.

Int. J. Radiation Oncology Biol. Phys., Vol. 46, No. 2, pp. 507–513, 2000Copyright © 2000 Elsevier Science Inc.Printed in the USA. All rights reserved

0360-3016/00/$–see front matter

507

SUMMARY

A simple Excel spreadsheet program has been developedto assist clinicians to easily calculate equivalent doses to beused in HDR brachytherapy regimens. The novelty of thisprogram is that the equivalent doses are expressed as ifgiven at 2 Gy per fraction rather than as BED values, and a

more realistic equivalent normal tissue effect is obtained byapplying a DMF. Its ease of use should promote the use ofLQ radiobiological modeling to determine HDR brachyther-apy doses. The program is to be used judiciously as a guideonly and should be correlated with clinical outcome.

REFERENCES

1. Hall EJ. Time, dose, and fractionation in radiotherapy. In: HallEJ, editor. Radiobiology for the radiobiologist. 4th ed. Phila-delphia: J.B. Lippincott; 1994. 211–229.

2. Dale RG. The application of the linear quadratic dose-effectequation to fractionated and protracted radiotherapy. Br JRadiol 1985;58:515–528.

3. Nag S, Young D, Orton C, Erickson B. Survey of the Brachy-therapy Practice for Carcinoma of the Cervix: A Report of theClinical Research Committee of the American BrachytherapySociety. Gynecol Oncol 1999;73:111–118.

4. Gaspar LE, Qian C, Kocha WI, Coia LR, Herskovic A, Gra-ham M. A phase I/II study of external beam radiation, brachy-therapy and concurrent chemotherapy in localized cancer ofthe esophagus (RTOG 92-07): Preliminary toxicity report. IntJ Radiat Oncol Biol Phys 1997;37:593–599.

5. Ellis F. Is NSD-TDF useful to radiotherapy? Int J RadiatOncol Biol Phys 1985;11:1685–1697.

6. Barendsen GW. Dose fractionation, dose-rate and iso-effectrelationships for normal tissue responses. Int J Radiat OncolBiol Phys 1982;8:1981–1997.

7. Fowler JF. The linear-quadratic formula and progress in frac-tionation. Br J Radiol 1985;58:515–528.

8. Thames HD. An “incomplete-repair” model for survival afterfractionated and continuous irradiation. Int J Radiat Biol1985;47:319–339.

9. Brenner DJ, Hall EJ. The origins and basis of the linear-quadratic model. Int J Radiat Oncol Biol Phys 1992;23:252.

10. Brenner DJ, Hlatky LR, Hahnfedlt PJ, Huang Y, Sachs RK.The linear-quadratic model and most other common radiobi-ological models result in similar predictions of time–doserelationships. Radiat Res 1998;150:83–91.

11. Dale RJ, Jones B. The clinical radiobiology of brachytherapy.Br J Radiol 1998;71:465–483.

12. Orton C. Radiobiology. In: Nag S, editor. Principles andpractice of brachytherapy. Armonk, NY: Futura; 1997. 27–45.

13. Barton M. Tables of equivalent dose in 2 Gy fractions: Asimple application of the linear quadratic formula. Int J RadiatOncol Biol Phys 1995;31:371–78.

14. Brenner DJ, Hall EJ. Fractionation and protraction for radio-therapy of prostate carcinoma. Int J Radiat Oncol Biol Phys1999;43:1095–1101.

APPENDIX 1:BIO-EQUIVALENCE CALCULATIONS FOR

MULTIPLE MODALITY RADIATION TREATMENTS

The dose effect relationship in radiation therapy is not alinear relationship, but follows a LQ function. Hence, dosesdelivered by different modalities cannot be added to eachother to predict the effect of the combined modality treat-ment. One way to calculate the BEDs of different dosefractionation schemes is to use the LQ equation, using theformula

BED! nd !1 "d(!/"" (1)

where n ! the number of fractions and d ! the dose perfraction. To express the results in terms more familiar toclinicians, the BED was converted back to equivalent doses(DEq) as though given as conventionally fractionated irra-diation given at 2 Gy/day for tumor and late effects respec-tively using the formula

DEq !BED

#1" dREF(!/")$

(2)

where dREF ! the reference dose per fraction for a conven-tionally fractionated external beam treatment to be used for

calculating the equivalent dose (which for the purposes ofthis paper has been assumed to be 2 Gy/fraction).If the equivalent dose for late effects is calculated using

eq. 2 above, the implicit assumption in this calculation isthat doses delivered to the normal tissues were equal todoses delivered to the tumor (which is true for externalbeam radiotherapy). However, under certain circumstances(e.g., with HDR brachytherapy), this assumption may not betrue, because the dose given to normal tissues is reduced dueto the fall-off in dose with distance. For example, if the doseto normal tissue is estimated to be 70% of the prescribeddose to the tumor in HDR brachytherapy, a dose reductionfactor (DMF) of 0.7 would need to be applied to obtain themodified, more realistic late normal tissue effects using theformulas

BEDHDR ! n*d*DMF*#1"#d*DMF!/" $$ (3)

DEq!BEDHDR

#1"dREF!/"$#

n*d*DMF*#"1#d*DMF!/" $$#1"dREF!/"$

(4)

512 I. J. Radiation Oncology ● Biology ● Physics Volume 46, Number 2, 2000

SUMMARY

A simple Excel spreadsheet program has been developedto assist clinicians to easily calculate equivalent doses to beused in HDR brachytherapy regimens. The novelty of thisprogram is that the equivalent doses are expressed as ifgiven at 2 Gy per fraction rather than as BED values, and a

more realistic equivalent normal tissue effect is obtained byapplying a DMF. Its ease of use should promote the use ofLQ radiobiological modeling to determine HDR brachyther-apy doses. The program is to be used judiciously as a guideonly and should be correlated with clinical outcome.

REFERENCES

1. Hall EJ. Time, dose, and fractionation in radiotherapy. In: HallEJ, editor. Radiobiology for the radiobiologist. 4th ed. Phila-delphia: J.B. Lippincott; 1994. 211–229.

2. Dale RG. The application of the linear quadratic dose-effectequation to fractionated and protracted radiotherapy. Br JRadiol 1985;58:515–528.

3. Nag S, Young D, Orton C, Erickson B. Survey of the Brachy-therapy Practice for Carcinoma of the Cervix: A Report of theClinical Research Committee of the American BrachytherapySociety. Gynecol Oncol 1999;73:111–118.

4. Gaspar LE, Qian C, Kocha WI, Coia LR, Herskovic A, Gra-ham M. A phase I/II study of external beam radiation, brachy-therapy and concurrent chemotherapy in localized cancer ofthe esophagus (RTOG 92-07): Preliminary toxicity report. IntJ Radiat Oncol Biol Phys 1997;37:593–599.

5. Ellis F. Is NSD-TDF useful to radiotherapy? Int J RadiatOncol Biol Phys 1985;11:1685–1697.

6. Barendsen GW. Dose fractionation, dose-rate and iso-effectrelationships for normal tissue responses. Int J Radiat OncolBiol Phys 1982;8:1981–1997.

7. Fowler JF. The linear-quadratic formula and progress in frac-tionation. Br J Radiol 1985;58:515–528.

8. Thames HD. An “incomplete-repair” model for survival afterfractionated and continuous irradiation. Int J Radiat Biol1985;47:319–339.

9. Brenner DJ, Hall EJ. The origins and basis of the linear-quadratic model. Int J Radiat Oncol Biol Phys 1992;23:252.

10. Brenner DJ, Hlatky LR, Hahnfedlt PJ, Huang Y, Sachs RK.The linear-quadratic model and most other common radiobi-ological models result in similar predictions of time–doserelationships. Radiat Res 1998;150:83–91.

11. Dale RJ, Jones B. The clinical radiobiology of brachytherapy.Br J Radiol 1998;71:465–483.

12. Orton C. Radiobiology. In: Nag S, editor. Principles andpractice of brachytherapy. Armonk, NY: Futura; 1997. 27–45.

13. Barton M. Tables of equivalent dose in 2 Gy fractions: Asimple application of the linear quadratic formula. Int J RadiatOncol Biol Phys 1995;31:371–78.

14. Brenner DJ, Hall EJ. Fractionation and protraction for radio-therapy of prostate carcinoma. Int J Radiat Oncol Biol Phys1999;43:1095–1101.

APPENDIX 1:BIO-EQUIVALENCE CALCULATIONS FOR

MULTIPLE MODALITY RADIATION TREATMENTS

The dose effect relationship in radiation therapy is not alinear relationship, but follows a LQ function. Hence, dosesdelivered by different modalities cannot be added to eachother to predict the effect of the combined modality treat-ment. One way to calculate the BEDs of different dosefractionation schemes is to use the LQ equation, using theformula

BED! nd !1 "d(!/"" (1)

where n ! the number of fractions and d ! the dose perfraction. To express the results in terms more familiar toclinicians, the BED was converted back to equivalent doses(DEq) as though given as conventionally fractionated irra-diation given at 2 Gy/day for tumor and late effects respec-tively using the formula

DEq !BED

#1" dREF(!/")$

(2)

where dREF ! the reference dose per fraction for a conven-tionally fractionated external beam treatment to be used for

calculating the equivalent dose (which for the purposes ofthis paper has been assumed to be 2 Gy/fraction).If the equivalent dose for late effects is calculated using

eq. 2 above, the implicit assumption in this calculation isthat doses delivered to the normal tissues were equal todoses delivered to the tumor (which is true for externalbeam radiotherapy). However, under certain circumstances(e.g., with HDR brachytherapy), this assumption may not betrue, because the dose given to normal tissues is reduced dueto the fall-off in dose with distance. For example, if the doseto normal tissue is estimated to be 70% of the prescribeddose to the tumor in HDR brachytherapy, a dose reductionfactor (DMF) of 0.7 would need to be applied to obtain themodified, more realistic late normal tissue effects using theformulas

BEDHDR ! n*d*DMF*#1"#d*DMF!/" $$ (3)

DEq!BEDHDR

#1"dREF!/"$#

n*d*DMF*#"1#d*DMF!/" $$#1"dREF!/"$

(4)

512 I. J. Radiation Oncology ● Biology ● Physics Volume 46, Number 2, 2000

The�Linear-Quadratic�Model�Is�anAppropriate�Methodology�for�DeterminingIsoeffective�Doses�at�Large�Doses�Per�FractionDavid�J.�Brenner,�PhD,�DSc

The�tool�most�commonly�used�for�quantitative�predictions�of�dose/fractionation�dependen-cies� in� radiotherapy� is� the� mechanistically� based� linear-quadratic� (LQ)� model.� The� LQformalism�is�now�almost�universally�used�for�calculating�radiotherapeutic�isoeffect�dosesfor�different�fractionation/protraction�schemes.�In�summary,�the�LQ�model�has�the�follow-ing� useful� properties� for� predicting� isoeffect� doses:� (1)� it� is� a� mechanistic,� biologicallybased�model;�(2)�it�has�sufficiently�few�parameters�to�be�practical;�(3)�most�other�mecha-nistic�models�of�cell�killing�predict�the�same�fractionation�dependencies�as�does�the�LQmodel;�(4)�it�has�well-documented�predictive�properties�for�fractionation/dose-rate�effectsin�the�laboratory;�and�(5)�it�is�reasonably�well�validated,�experimentally�and�theoretically,�upto�about�10�Gy/fraction�and�would�be�reasonable�for�use�up�to�about�18�Gy�per�fraction.�Todate,�there�is�no�evidence�of�problems�when�the�LQ�model�has�been�applied�in�the�clinic.Semin�Radiat�Oncol�18:234-239�©�2008�Elsevier�Inc.�All�rights�reserved.

L�et�us�start�from�the�premise�that�we�need�some�model�forcalculating� isoeffect� doses�when� alternate� fractionation

schemes�are�considered.�In�addition,�apart�from�increasinginterest�in�alternative�fractionation/protraction�schemes,�it�isessential�that�we�know�how�to�compensate�appropriately�formissed�radiotherapy�treatments.

The�tool�most�commonly�used�for�quantitative�predic-tions�of�dose/fractionation�dependencies�is�the�linear-qua-dratic�(LQ)�formalism.1-5�In�radiotherapeutic�applications,the�LQ�formalism�is�now�almost�universally�used�for�cal-culating�isoeffect�doses�for�different�fractionation/protrac-tion�schemes.

In�contrast�to�earlier�methodologies,�such�as�cumulativeradiation�effect,�nominal�standard�dose,�and�time-dose�fac-tor,6,7� which�were�essentially�empirical�descriptions�of�pastclinical�data,�the�LQ�formalism�has�become�the�preferred�toollargely�because�it�has�a�somewhat�more�biological�basis,�withtumor�control�and�normal�tissue�complications�specificallyattributed� to�cell�killing.�By�contrast,�descriptive�empiricalmodels�can�go�disastrously�wrong�if�used�outside�the�dose/

fractionation�range�from�which�they�were�derived,�as�whenNSD�was�applied�to�large�doses�per�fraction.8,9

MechanisticBackground�to�the�LQ�ModelIt� is� clear� that� radiotherapeutic� response,� both� for� tumorcontrol� and� for� complications,� is� dominated� by� cell� kill-ing,2,10,11� and�LQ�is�a�mechanistic�model�of�cell�killing.�Un-derlying� the� application�of� LQ� to� fractionation/protractioneffects�is�pairwise�misrepair�of�primary�lesions�such�as�dou-ble-strand�breaks�(DSBs)�or�base�damage�(hereon�in�we�shallrefer�to�DSB�as�the�primary�lesion,�but�base�damage�sites�maywell�also�be�relevant�here12).�As�schematized�in�Figure�1,�cellkilling�occurs�via�chromosome�aberrations�such�as�dicentricaberrations,13� which�are�formed�when�pairs�of�nearby�DSBwrongly� rejoin� to� one� another.14� Protracting� the� exposuretime�potentially�allows�the�first�DSB�to�be�repaired�before�thesecond� is� produced,� and� the� LQ� approach� quantifies� thiseffect.5� Nowadays,� this�binary�DSB�misrepair�model� is� themost�usual�way�to�motivate�the�standard�LQ�approach,�butdifferent�biological�rationales�for�the�same�mathematical�for-malism�have�also�been�given,�as�we�will�discuss.

It�is�important�to�stress�here�that�the�standard�LQ�formal-ism, as applied to time-dose relationships, is not merely atruncated power series in dose. Its key feature here is a spe-cific mechanistically based functional form for the protrac-

Center for Radiological Research, Columbia University Medical Center, 630West 168th Street, New York, NY.

Supported by NIH grants U19 AI-067773 and P41 RR-11623.Address reprint requests to David J. Brenner, PhD, Center for Radiological

Research, Columbia University Medical Center, 630 West 168th Street,New�York,�NY�10032.�E-mail:�djb3@columbia.edu

234 1053-4296/08/$-see front matter © 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.semradonc.2008.04.004

AAPM REPORT NO. 166

The Use and QA of Biologically RelatedModels for Treatment Planning

Report of AAPM Task Group 166of the Therapy Physics Committee

March 2012

© 2012 by American Association of Physicists in Medicine

DISCLAIMER: This publication is based on sourcesand information believed to be reliable, but theAAPM, the authors, and the editors disclaim any war-ranty or liability based on or relating to the contents ofthis publication.

The AAPM does not endorse any products, manufac-turers, or suppliers. Nothing in this publication shouldbe interpreted as implying such endorsement.

CONCLUSIONS