eindhoven university of technology master extraction of ...van elmpt r.f.h. schiffeleers 0478359 r.f...
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Eindhoven University of Technology
MASTER
Extraction of incident energy fluence with portal dosimetry
Schiffeleers, R.F.H.
Award date:2006
Link to publication
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Masters thesis Supervisor TU/e Advisor MAASTRO CLINIC
Student Student nr. Email
Extraction of incident energy fluence with portal dosimetry.
R.F.H. Schiffeleers MRLITPM 03-2006
March 2006
April2006 prof. dr. ir. K. Kopinga ir. W. van Elmpt R.F.H. Schiffeleers 0478359 R.F .H. Schiffeleers@ student. tue. nl
Preface
For my study Applied Physics, at the Eindhoven University of Technology, I finished my master thesis at MAASTRO CLINIC in Heerlen in the Netherlands. My research started in March 2005 and ended in March 2006. My choice for radiotherapy as my research area was enduing due to my interest in radiotherapy, in which a direct combination of the medical world and physics exists. In this report the research I did, for MAASTRO CLINIC, during my master thesis will be explained.
During my master thesis I experienced different aspects within a radiotherapy clinic, like the ambience, and the hierarchy within the clinic. From physicists to technicians everybody was very willing to help during my research. My thanks for this, and very special thanks to my supervisor at the TU/e prof. dr. ir. K. Kopinga and thanks to ir. W. J. C. van Elmpt who supervised me during my research at MAASTRO CLINIC.
I willlook back to my research period for my master thesis with a pleasant feeling.
I
Rob Schiffeleers Eindhoven, March 2006
11
Abstract
Introduction: The verification of a full three dimensional (3-D) dose distribution inside a patient during external radiotherapy is the ultimate goal of in-vivo dosimetry. This goal can be achieved in a two-stage process: (i) Reconstructing the incident energy fluence of the linear accelerator (linsv) by means of portal imaging and (ii) calculating the dose distribution in a patient model with a dose calculation engine based on Monte Carlo. During this study solutions have been found for stage (i) of the problem.
Methods: A model to reconstruct the incident energy fluence of a linac by means of portaldose images has been developed for 6 MV and 10 MV photon beams. An electronic portal imaging device (EPID) mounted to the linac is calibrated to measure the dose equivalent to the dose at 5 cm depth in water at the level op de EPID. These portal dose images obtained with the EPID are composed of primary and scattered dose. Without a phantom in the beam the scattered dose is because of the lateral scattered dose at the EPID. Whit a phantom in the beam the scatter dose is because of the lateral scattered and the patient scattered dose. An in-house developed phantom scatter model and a newly developed lateral scatter model are used for subtracting scatter of the portal dose images. The verification of the model is split up in a situation with and without phantoms in the beam. The energy fluence at the portal imager is directly related to the primary dose. The accuracy of the incident energy fluence reconstruction model without a phantom in the beam is assessed by camparing the primary dose reconstructed from portal dose images with measurements done with a mini phantom. In case of a phantom in the beam model was verified by camparing the reconstructed incident energy fluence with the incident energy fluence extracted in case of an open beam.
Results: The accuracy of the incident energy fluence reconstruction model without a phantom in the beam was assessed. For this situation the primary dose could be reconstructed from portaldose images with a mean difference of -0.2% ± 0.7% (one standard deviation) compared to ionisation measurements in a mini phantom for both photon beam energies. In case of a phantom in the beam the incident energy fluence reconstruction model has an error of 2.6% (mean difference) ± 1,3% (one standard deviation) compared to the incident energy fluence extracted without a phantom in the beam.
Conclusions: An accurate incident energy fluence reconstruction model for 6 MV photon beams and 10 MV photon beams has been developed and validated. The model can use portal dose images with and without phantoms in the beam to derive the incident energy fluence. The model is a step toward 3-D dose reconstruction in a patient model for in-vivo dosimetry purposes.
lil
IV
Contents
1 INTRODUCTION ........................................................................................................................................ 1
1.1 PROBLEMSTATEMENT .............................................................................................................................. 3 1.2 REPORTOUTLINE ..................................................................................................................................... 3
2 THEORY ....................................................................................................................................................... 5
2.1 THE EQUIVALENT HOMOGENEOUS PHANTOM CONCEPT ............................................................................ 5 2.2 INCIDENT ENERGY FLUENCE RECONSTRUCTION ....................................................................................... 7
3 INCIDENT ENERGY FLUENCE RECONSTRUCTION MODEL ....................................................... 9
4 MATERIALS & METHODS .................................................................................................................... 13
4.1 MEASUREMENTS TODETERMINE THE FIXED INPUT PARAMETERS ........................................................... 14 4.1.1 Measurements to delermine the effective attenuation coefficient afwater .................................... 14 4.1. 2 Measurements for experimental determination of lateralP BSK. .................................................. 15 4.1.3 Measurementsfor experimental determination ofphantom PBSK. ............................................... 16
4.2 VERIFICATION MEASUREMENTS ............................................................................................................. 16 4.2.1 Verification ofEP1D calibration model ........................................................................................ 17 4.2.2 Verification of lateral scatter model in case of an open beam ...................................................... 17 4.2.3 Verification ofphantom scatter model .......................................................................................... 18 4.2. 4 Verification of lateral scatter model with phantoms in the beam .................................................. 18 4.2.5 Verification ofthe model in case ofphantoms in the beam ........................................................... 19
5 RESULTS .................................................................................................................................................... 21
5.1 INPUTPARAMETERS FOR THEMODEL ..................................................................................................... 21 5. 1.1 Effective attenuation coefficient .................................................................................................... 21 5.1.2 Derivation ofthe lateral PBSKs .................................................................................................... 22 5. 1.3 Derivation ofthe phantom PBSKs ................................................................................................. 24
5.2 VERIFICATION MEASUREMENTS ............................................................................................................. 25 5.2.1 Verification of EP1D cal i bration model ........................................................................................ 26 5.2.2 Verification ofthe lateral scatter model in case of an open beam . ............................................... 27 5.2.3 Verification ofphantom scatter model .......................................................................................... 28 5.2.4 Verification ofthe lateral scatter model in case ofphantoms in the bemn. ................................... 28 5.2.5 Verification ofthe model in case of a phantom in the beam .......................................................... 29
6 DISCUSSION AND CONCLUSION ........................................................................................................ 33
6.1 DISCUSSION ........................................................................................................................................... 33 6.2 RECOMMENDATIONS .............................................................................................................................. 35 6.3 FUTURE .................................................................................................................................................. 35 6.4 CONCLUSION .......................................................................................................................................... 36
7 REFERENCES. . ................................................................................................................................... 37
8 APPENDICES ...................................................................................................................................... 41
8.1 APPENDIX A; DIMENSIONS OF THE MINI PHANTOM ................................................................................ 41 8.2 APPENDIX B; DERIV A TION OF EQUATION 18 .......................................................................................... 42 8.3 APPENDIX C; DERIVA TION OF EQUA TION 20 .......................................................................................... 44 8.4 APPENDIX D; OUTPUT MEASUREMENTS FOR DERIVATION OF LATERAL PBSKS ..................................... 45 8.5 APPENDIX E; OPEN BEAM PROFILES 6 MV AND 10 MV PHOTON BEAMS ............................................... 4 7 8.6 APPENDIX F; OUTPUT MEASUREMENTS WITH MINI PHANTOM BEHIND PHANTOMS ................................. 48
V
VI
Frequently used abbreviations
PS TPS Linac 2-D 3-D PBSK EHP EPID PDI
IJI;n !.f'exit
IY' D' jjat
T P' r f1 t
polystyrene treatment planning system linear accelerator two-dimensional three-dimensional pencil beam scatter kemel equivalent homogenous phantom electronic portal imaging device portal dose image
Frequently used symbols
incident energy fluence exit energy fluence primary dose at EPID phantom scattered dose at EPID lateral scattered dose at EPID total transmission primary transmission scattered transmission attenuation coefficient radiological thickness
VII
VIII
Introduetion
MAASTRO CLINIC is a radiotherapy centre for the most southem part of the Netherlands. Radiotherapy is the modality for treating cancer with ionizing radiation to destroy tumour cells inside the human body. The aim of the treatment is to deliver a high dose to malignant cells while keeping the dose to healthy tissue as low as possible. MAASTRO CLINIC has its origin in 1977 when the Radio Therapeutic Institute Limburg was founded. The main department of MAASTRO CLINIC is still located at Heerlen next to the Atrium Medica! Centrum. At MAASTRO CLINIC linear accelerators (linacs) are used to produce high energetic photon and electron beams (see figure 1). In 2003 the name of the institute changed into MAASTRO CLINIC. In 2006 all activities will be transferred to a new location in Maastricht. In 2007 the transfer should be finished and MAASTRO CLINIC will have 6 linacs, that are used to produce poly-energetic photon beam for extemal radiotherapy treatment. All linacs will be equipped with electronic portal imaging devices (EPIDs) (see figure 1). The EPIDs used are indirect flat panel imagers based on amorphous silicon designed for detecting MeV photons. EPIDs were originally designed for geometrie verification ofpatient set-up during treatment.
EP!D
Figure I; Linear accelerator with an electronic portal i/naging device.
Introduetion
The efficiency of radiation therapy relies highly on the accuracy of dose delivery. Possible errors in the dose delivery due to for example; variations in the output of the linac and field flatness, uncertainties in the dose calculation by the treatment planning system (TPS). Inaccuracies of the multi-Ieaf-collimator (MLC) leaf movements, and changes in the patients anatomy, creates the necessity for the use of control procedures. These control procedures can be divided in periodic quality control of the linac and patient specific controls before the start of the treatment, i.e. pre-treatment verification, and control procedures during treatment, i.e. in vivo dosimetry.
Periadie quality control ofthe linac: A detailed quality assurance program is essential for high precision dose irradiations. Two weekly perforrned quality control procedures at MAASTRO CLINIC
are; (i) light-field vs. radiation-field verification, and (ii) the positioning of the yaws. The objective of the first quality control procedure is to verify if the light field (light field produced by the linac for positioning of the patient) and the radiation field are in acceptable agreement with each other. The objective of the second quality control procedure is to verify if the start position of each individual yaw has not been changed after several treatments. For both purposes engineers perforrn weekly measurements with radiographic film placed at the isocenter (1 00 cm under the souree of the linac), with 2.5 cm polystyrene on top of the film as build up. Because of their high spatial resolution and two-dimensional (2-D) character, radiographic films are commonly used for quality assurance. Film measurements however, are very Iabour intensive, only make verification possible in a plane, and the dose response can vary due to processing conditions and varies from film batch to another. An alternative for the quality assurance with film involves the use ofEPID images.
Pre treatment verification: For pre-treatment verification, a common way to verify the dose distribution is to deliver the beams to a phantom with a radiographic film placed inside. An alternative for this Iabour intensive pre-treatment verification involves the use of EPID images. A portal image is a measure ofthe photon intensity, or fluence at the level ofthe portal imager. A dosimetrie calibration is necessary to convert this EPID image into a portal dose image (PDI). For this purpose an in-house calibration model was developed [1]. With this calibration model it is possible to deterrnine the absolute dose at the portal imager, equivalent to the full scatter dose measured with an ionization chamber in a water tank at 5 cm depth in water, at a plane at a di stance 150 cm below the souree of the linac (see tigure 2). However, pre-treatment verification with 2-D portal dose images does notprovide inforrnation about the three-dimensional (3-D) dose delivered inside the patient, or how possible differences add up in the total (complex) treatment plan with multiple beams and possible changes in the patients anatomy.
In vivo dosimetry: Measurement devices like MOSFETs can be used as point detectors for either entrance or exit dosimetry [2] . Electronic portal imaging devices can not only be used for geometrie verification of the patient's position, multi-leaf collimator settingor leaf trajectory control, but also for in-vivo dosimetry. If the EPID is used for in-vivo dosimetry, it would decrease the workload of the technicians for placing the conventional dosimeters. There are several approaches using EPIDs for in-vivo dosimetry. A proruising method use the portal imager to reconstruct the output of the linac, in order to reconstruct the dose in an on-line patient model , by recalculating the dose with the treatment planning system or an independent dose calculation engine. Several studies suggested making an on-line patient model by means of kilo-Voltage [3] or Mega-Voltage Cone-Beam [4] computed tomography (CT). The output of the linac will be described by means of the incident energy fluence ~n(x,y) (see tigure 2), in a plane below the souree of the linac. The energy fluence, IJ'(x,y), is the quotient dE!dA, where dE is the average kinetic energy of photons incident on a cross-sectional area dA. Several authors have described methods to reconstruct the output of the linac from portal images. Steciw et al. [5] and Warkentin et al. [6] reconstructed the incident energy fluence by means of portal images acquired without a patient in the beam (the situation without an object in the beam will be called "open beam" situation). No attempts were made to reconstruct the incident energy fluence in case of an object in the beam. Chen et al. [7] used a similar calibration method ofthe EPIDas in our clinic in order to obtain portal dose images behind a patient. In this research an iterative algorithm was used for reconstructed the energy fluence at the detector plane by recalculating the dose at the EPID. Louwe et al. [8] used portal dose images to reconstruct the primary dose behind the patient but did not reconstruct the
2
1.1 Problem statement
incident energy fluence by portal images. Patridge et al. [9] and Renner et al. [10] used grey-scale values of the portal imager in order to determine the incident energy fluence, by means of portal images behind a patient. However this technique is not suited for reconstructing the incident energy fluence by means of portal dose images. Me Nutt et al. [11] used an iterative algorithm in order to reconstruct the incident energy fluence by means of portal dose images behind an object in the photon beam, however this method requires a lot of computation time since in each step of the iterative algorithm the dose distribution in an extended phantom must be calculated. Wendling et al. [12] reconstructed the primary dose component at the position of the EPID but didn't use it as input for an independent dose calculation engine.
In this report a new method will be developed for reconstructing the incident energy fluence in case of an open beam and in case of an object in the photon beam, with portal dose images.
1.1 Problem statement At MAASTRO CLINIC the following problem statement has been defined: "Develop and validate a method to reconstruct the incident energy fluence of a linac, by means of portal dose images". The model should be valid for water equivalent phantoms with radiological thicknesses varying from 0-30 cm, with their centre of mass positioned at 40-60 cm above the portal imager, for different field shapes and sizes, and for 6 MV and 10 MV photon beams. The output of the linac must be described by means ofthe incident energy fluence, in a plane 40 cm below the souree ofthe linac.
Complicating factors are that the EPID is calibrated to reconstruct the dose equivalent to the dose measured at 5 cm depth in a water tank with a souree to detector distance of 150 cm. At this depth the incident energy fluence will cause lateral scatter (see figure 2). Another complicating factor is that the incident energy fluence causes phantom scatter at the imager (see figure 2) in case of a phantom in the beam.
The following criteria were given by MAASTRO CLINIC: In case of an open beam the primary dose must be reconstructed within an accuracy of 2% (mean difference), compared to measurements with a mini-phantom. In case of an object in the beam the incident energy fluence must be reconstructed within 3% (mean difference), compared to the incident energy fluence in case of an open beam.
1.2 Report outline This report provides the theory necessary for a solid understanding of the model ( chapter two ), foliowed by the model to reconstruct the three dimensional dose in a phantom (chapter three). In chapter four the experimental set-up consisting of a linac, EPID and measurement devices, i.e. a mm1 phantom, an ionization chamber and a water tank, will be described, as well as the methods used. Results that are obtained are shown in chapter five. Finally, in chapter six the results obtained will be discussed and conclusions will be made.
z (cm)
Phantom {
Water { tank
40cm -!-------------------·
Isocenter
Midplane to detector distance
Water
Figure 2; Schematic representation of scatter caused by the incident energy fluence.
3
Theory
In this chapter the theory necessary for this study will be presented. During this research the souree of the linac is seen as a single point souree (see figure 3) producing poly-energetic ray lines, and the mean energy E (Me V) of the poly-energetic raylines is used in order to describe the energy of the poly-energetic raylines. The distance from a ray line from the central axis (see figure 3), inline with the electron gun is called the inline distance v(z) (cm). The distance of a ray line to the central axis perpendicular to the inline distance will be referred to as the crossline distance u(z) (cm).
2.1 The equivalent homogeneons phantom concept In a plane at a di stance z1 ( 40 cm) below the souree of the linac, the energy fluence will be called the incident energy fluence 'l';m while the energy fluence at a plane at a distance z2 (150 cm) below the source, with 5 cm water equivalent build up, will be called the exit energy fluence 'Fexit· A rayline in a plane at depth z2 has a crossline distance x (see figure 3) and inline distance y. The incident energy fluence is assumed to originate from a point source, therefore the incident energy fluence can be calculated from, by correcting for attenuation along the ray-line and applying the inverse square law
Heterogeneaus phantom
Water tank
.......................................................................................................... ~ .......... ! ........................... . [!) Water . 40 cm
• Polystyrene '!';" 0 Air """!'""'""''"'"' Isocenter
{
,........._ EHP concept ........ ;] ...... ~'[ ..... i~·, ................... ... 'J"~ .. .. ·····--.r········<===>·····::::::::r::::::].~.~x~;·:::::::::::::::·:::.:::.[::::::···· }
Water phantom
Central aûs} / •i . 150 cm
{ ........... ;;;~;: ................................................................. l""'~:;;;~; .. r ............ ::: .. \ ..................................... . .................................................................................... ::;~"'T!,,'i:..... . .................................... .
s
Figure 3; Equivalent homogeneaus phanlom concept.
5
Theory
by re-sealing the inline and crossline distances from the exit plane by means of a factor w=z/z2. as can be seen in equation 1: This projection through the phantom in the direction from the EPID to the souree of the LINAC is also referred to in radiotherapy as; back projection. Projection of the incident energy fluence through the phantom in the direction ofthe EPIDis referred to as forward projection.
. f.-1
x y OJ
effective attenuation coefficient crossline distance in a plane at distance z2
inline distance in a plane at distance z2
rescaling factor
[ cm-1}
[cm} [cm] [ - 1
(1)
The second term in Equation (1) is the quadratic law correcting for beam divergence and the third term in equation 1 account for the attenuation of the ray line by the effective attenuation coefficient. The effective attenuation coefficient depends on the 3-D position because it depends on the material at each 3-D position and the mean energy at each position. Therefore equation 1 requires knowledge about the effective attenuation coefficients for a lot of materials and for different mean energies. As a simplification during the present research the equivalent homogeneaus phantom (EHP) concept is used, as introduced by Pasma et al. [13]. Using this concept, an inhamogeneaus phantom is replaced by a phantom of water (see tigure 3), taking into account the radiological path length, the beam divergence and the centre of mass, using the following relation;
ZJ
f * Jl( OJX, OJy, z)dz = Jl(X, y )t(x, y) .
t
f.-1
water equivalent radiological thickness effective attenuation coefficient of water
(2)
By using the EHP concept the effective attenuation coefficient at the EPID only depends on the mean energy of the rayline at the EP ID. The mean energy at the EPID depends on the position at the EPID due to (i) the beam softening effed [ 14, 15, 16] and (ii) the beam hardening effect2
[ 14, 15, 16].
I) Beam soflening effect: The effect that the mean energy of a ray fine shifts to the lower end ofthe energy spectrum due to the shape of thejlatteningfilter ofthe linac.
2) Beam hardening effect: The effect that the mean energy of a ray fine shifts to the higher end ofthe energy spectrum due to the object in the photon beam that attenuates more low energetic photons than high energe/ie photons.
6
2.2 Incident energy fluence reconstruction
2.2 Incident energy fluence reconstruction The EPIDs at MAASTRO CLINIC are calibrated in such a way that it is possible to determine the absolute dose, equivalent to the full scatter dose measured with an ionization chamber in a water tank at 5 cm depth in water, at a plane at adepthof z2 ( -150 cm) [1]. The full-scatter dose at 5 cm depth in a water tank at a point r(x,y) at the EPID, in case of a phantom in the beam, can be split up in (i) a phantom scatter dose, D', (ii) a lateral scatter dose, rJat, and (iii) a primary dose, IY'. This is reflected by equation 3:
Dfilit (x,y) = DP(x,y) + Ds (x,y) + D 1at (x,y). (3)
The following relation between the primary exit energy fluence, and the primary dose at 5 cm depth in a water tank, IY'(x,y), is valid [17];
D P( )-j3J1(X,y)mp ( ) X,y - T exit X,y
fJ p
p
conversion factor water density
(4)
According to several studies [ 17, 18] the conversion factor fJ in equation 3 is constant and close to unity. Equation 3 shows that if IY' is known, the primary exit energy fluence can be calculated. The incident energy fluence can be derived by projecting the exit energy fluence through the phantom with the EHP concept, as discussed in section 1.
In order to determine rJat a new lateral scatter model has been developed based on the pencil beam concept as described by Ahnesjo et al. [19]. The lateral scatter model assumes that the scatter in the water tank can be replaced by point sourees in a plane at a depth z2 (see figure 4), from which lateral doses spread to other parts of the plane. The amount of lateral dose that spreads from a souree in a point in the plane is given by the product of primary dose, at that position, and a lateral pencil beam scatter kemel. In this model the following assumptions are made; (a) lateral scatter in the EPID is cause by the primary dose (b) kemel tilting can be neglected, (c) the lateral-scatter kemels are assumed to be independent of the beam softening, and beam hardening effect. This way the lateral scatter dose originating from a point souree at a position at the EPIDis given by the product ofthe
uniform waterslab
I ~in
Figure 4; Lateral scatter in water slab in case of an open beam and a ray line perpendicular to the water slab.
7
Theory
primary dose, at that position, and a lateral pencil beam scatter kemel. Because only one pencil beam scatter kemel is used, the lateral scatter dose dat can be determined by the convolution of the primary dose at a plane at a depth z2 with the pencil beam lateral-scatter kemel. This is reflected by equation 5.
Dlat (x,y) = fJDP (x' ,y')Klat ijx'-xl,ly'-yl}ix' dy'.
A
lateral pencil beam scatter kemel EP ID surface area
(5)
In order to determine the phantom scatter dose D' at the EPID, an in-house model has been used based on the pencil beam concept [20,21 ,22]. The model replaces the phantom as the souree of the scatter energy fluence by point sourees in a plane at a depth z2 (see figure 5), from which phantom scatter dose spreads to other parts of the EPID. The amount of phantom scatter dose that spreads from a souree depends on the radiologkal thickness t(x,y) of the phantom, the energy of the linac and the distance of the centre of mass of the phantom to the detector s(x,y) (see figure 2). This way the phantom scatter dose that spreads from a souree in a point in the place is given by the product of the primary dose, at that position, in case of an open beam IY'1~o, and a phantom scatter kemel. The phantom scatter kemel only depends on the radiologkal thickness of the phantom, the energy of the linac and the air gap. The total phantom scatter dose D', at the portal imager can be seen as the superposition of primary dose, in case of an open beam, with pencil beam phantom-scatter kemels. The assumption is made that the phantom pencil beam scatter kernels are independent of the off-axis position.
Ds (x,y) = fJD/:0 (x' ,y')Kpat ~(x' ,y'),s(x' ,y'),lx'-xi,IY'-yl)ix' dy'.
K!'at
s
A
phantom pencil beam scatter kemel air gap
Figure 5; Schematic representation ofpatient scatter in case of a ray line perpendicular b.
8
(6)
Incident energy finenee reconstruction model
In this chapter a new procedure for reconstructing the incident energy fluence is presented, based on electronic portal imaging measurements. The input parameters for the iterative procedure are a portal dose image (PDI) derived from the image measured with the EPID, the effective attenuation coefficient of water, the water equivalent radiological thickness of the phantom, and finally the phantom and lateral pencil beam scatter kemels. The input parameters for the model and their experimental derivation will be explained in the next chapter. For a schematic representation of the model see tigure 6, in which the symbol18J denotes a convolution!superposition. Each procedure ofthe 3-D dose reconstruction model is explained in detail below.
Step 1: Estimate starting values for iterative procedure. In the first step of the iterative procedure (N = 1) the initial values for the primary dose and phantom scatter dose are estimated to be 100% and 0% of rfi'11(x,y), respectively.
Step 2: Calculate lateral scatter dose. In the second step of the iterative procedure, the lateral scatter dose at each position at the EPID is estimated. In order to do this equation 5 is used in the iterative procedure to determine D 1ar reflected by equation 7.
N D1a
1(x,y) =JIN DP(x',y')K1a
1(1x'-xl,lx'-xl)dx'dy'. (7) A
Step 3: Calculate primary dose. After the calculation ofthe lateral scatter dose at the EPID a more accurate estimation for the primary dose at the EPID is made by using equation 3 in the iterative procedure reflected by equation 8.
NDp( ) = Dfii/1( )-NDs( )-ND/at( ) x,y x,y x,y x,y . (8)
9
Incident energy fluence reconstruction model
Step 4: Calculate phantom scatter dose. In the next step of the iterative procedure the phantom scatter dose at each position at the EPID is calculated by means of equation 9 derived from equations 4 and 6. In case of an open beam K!'a1=0.
N Ds (x,y) = fJ N DP (x' ,y')e,u(x',y')t(x',y') Kpat &ex' ,y'),s(x' ,y'),lx'-xi,IY'-yl}:ix' dy' A
Step 6: Calculate primary dose.
(9)
After the calculation of the phantom scatter dose at the EPID a more accurate estimation for the primary dose at the EPID is made by using equation 3 in the iterative procedure reflected by equation 10.
Step 7: Repeat steps 2-6 until the solution converges. Steps 2-6 should be repeated for a fixed number of iterations or they should be repeated until the salution converges below a pre-determined objective value.
Yrnax Xmax
LLIN DP(x,y)-N-!Dp(x,y)l :s; & .
Ymin xmin
Step 8: Calculate exit-energy-fluence.
(10)
(11)
In case the objective is reached at iterative step N =6, the incident energy fluence can be calculated by using equation 4 in the iterative procedure reflected by equation 12.
(12)
Step 9: Calculate incident energy fluence. The incident energy fluence in a plane at a height z1 originating from an point souree can be calculated by means the next equation.
(13)
10
Incident energy fluence reconstruction model
N Dlat (x,y)=N []P (x,y) 0 Klat (x,y) I I J
Estimate initial dose Distribution: N IY(x,y) =Dfu11(x,y)-N D 5 (x,y)-N D 1a'(x,y) I
N=J
N IJP(x,y)=d""(x,y)
N D'(x,y)=O NDs(x,y)=NDp(x,y)e!J(x,y)t(x,y) ®Kpat(x,y,t,s J 8 t J -K)at -rf"11(x,y)
_J<:at -t(x,y) N IY(x,y) =nfi'11(x,y)-N D 5 (x,y)-ND!at(x,y) I -jl(x,y) -s(x,y)
DATAlN YmaxXma'\ No L:LjN D"(x,y)-N-IIJP(x,y)[5,c 1--
YminXmm
Yes I N []P (x,y) =Df""(x,y)-N D' (x,y)-N D'a'(x,y) I
\{I:Xit(x,y) N=<S []P (x,y)p
;l(x,y)/3
~ [ 2 2 2 ) - p z2 +x + y IJ(x,y)t(x,y)
~n(OA:,cy)-\{lexilx,y) 2 ( r ( )2 e zi + OA: + cy
DATAOUT
Figure 6: Representation incident energy fluence reconstruction mode/,
11
12
Materials & methods
In this chapter the equipment that was used and the measurements that were performed are described. Field si zes are defined as the surface area within 50% of the maximum dose produced by the photon beam at the isocenter (100 cm under the souree ofthe linac) and the penumbra region is defined as the region within 80% and 20% ofthe maximum dose. All measurements presented in this report are done with a 6 and 10 MV photon beam produced by a Siemens Oncor Avant Garde linear accelerator (Siemens Medica! Solutions, Concord, USA). During this study measurements at fixed positions have been performed (point measurements), as well as 1-D dose (profiles) and 2-D full scatter dose measurements (PD!s). Each measurement technique will bedescribed below.
Point measurements to determine the relative full scatter dose and the relative primary dose are performed, with an ionization chamber (CC13, Scanditronix Wellhofer, Schwarzenbruck, Germany) at a reference depthof 5 cm in water, in a water tank and a mini phantom respectively. The mini phantom consists of a cylinder made of polystyrene (see Appendix A), with the CC13 placed inside at a depth of 5 cm [23,24,25]. The ionisation chamber was read out with a UNIDOS E electrometer (PTW, Freiburg, Germany). Possible variations in detector response with time are estimated by performing the same measurements with the same ionization chamber approximately an hour later. From these measurements the variation ofthe detector response with time is estimated to be within 0.2%. For all point measurements 100 monitor units3 (MU) are given. The following relations are used for the relative full scatter dose measurements in a water tank Jvfu", and the relative dose measurements with the mini phantom M, both normalized at the on-axis position (xr,yJ=(O,O), for an open field of 1 Oxl 0 cm2
:
D fu/1( )
M fu/1( ) _ c,x,y,t,s c,x,y,t,s - fill
D u (cr,xr,Yr,t"sr)
DP (c,x,y,t) + Ds (c,x,y,t,s) MP(c,x,y,t,s) = -------------
DP (Cr' Xr' Y r ,fr) + Ds (Cr' X r' Y r' tr ,Sr)
Xr Yr tr Sr Cr
reference inline distance (xr = 0 cm) reference crossfine distance Ó'r = 0 cm) reference radiological thickness (tr = 0 cm) reference midplane to detector distance (sr = 50 cm) reference collimator setting, equal to a square field centred around the axis, with a size of 1 Oxl 0 cm2
3) MU: One monitor unit is defined as the dose as measured under reference conditions.
13
[cm] [cm] [cm] [cm]
[cm2}
(14)
(15)
Materials & methods
Possible dependenee of the detector response with the angle between the ionisation chamber and the ray lines is estimated by performing measurements with the ionisation chamber placed under various angles with its effective point of measurement kept at the same location. This way the angle dependenee ofthe detector response is estimated to be within 0.01%.
Profiles are scanned with the ionisation chamber placed in the mini phantom and with the ionisation chamber placed at 5 cm depth in water, in order to obtain primary dose profiles and full scatter dose profiles respectively. A water tank (Blue Phantom, Scanditronix Wellhofer, Schwarzenbruck, Germany) was used for positioning. Ouring scanning an additional ionization chamber (CC13) has been positioned inside the field to correct for possible variations in the output of the linac with time. The accuracy of the profiles is estimated by scanning the same profile a number of times. This way the accuracy is estimated to be within 0.2 % in between the two penumbra regions. The profiles are considered to be unreliable in the penumbra regions for reasons explained in chapter 6.
Portaldose images have been obtained with a Siemens OptiVue 1000 amorphous silicon type EPID (Siemens Medica! Solutions, Concord, USA), mounted on the linear accelerator. The EPID was calibrated to measure dose similar to the dose at 5 cm depth in a water tank at a souree to detector distance of 150 cm. The grid size of the EPID after dosimetrie calibration is 256x256 pixels with an effective detector area of 41x41 cm. The distance from the EPID to the souree was fixed at 150 cm. The accuracy of a POl is assessed insection 4.2.1.
The measurements can be further divided into measurements performed in order to experimentally determine the input parameters, and measurements performed in order to assess the accuracy of the incident energy fluence method. The measurements done are described in detail in section 4.1.
4.1 Measurements todetermine the fixed input parameters To reconstruct the incident energy fluence the following input parameters should be known: (a) The full scatter dose at 5 cm depth in water at a souree to detector distance of 150 cm, (b) the radiological thickness of the phantom, ( c) the effective attenuating coefficient, ( d) the lateral scatter kemel, and finally ( e) the phantom scatter kemels.
The full scatter dose of an open beam is obtained with the EPID and converting this image into a POl with an in-house developed calibration model. In case of a phantom in the beam the calibration model needs the portal image in case of an open beam as well as the portal image bebind the phantom, in order to be able to reconstruct the full scatter dose at the EPID. The equivalent homogeneous phantom (EHP) concept is used for calculating the radiological thickness as described in section 2.1. The effective attenuation coefficient and the pencil beam scatter kemels (PBSKs) are experimentally derived as described in the next sections.
4.1.1 Measurements todetermine the effective attenuation coefficient of water The total transmission T of a pboton beam through a homogeneous phantom, with radiologkal thickness t (cm) and its center ofmass at a distance s (cm) from the EPID, is defined as the ratio ofthe dose measured with the phantom in the beam and the dose measured without the phantom in the beam. When transmission measurements are performed with a mini phantom, the transmission consists of a primary component P and a component T arising from phantom scatter:
_ DP(c,x,y,t)+Ds(c,x,y,t,s,) _ P s T(c,x,y,t,s,)- - T (c,x,y,t) + T (c,x,y,t,s,).
DP(c,x,y,t,) (16)
The primary component of the transmission is only related to the radiological thickness of the phantom and the effective attenuation coefficient. This primary component can be estimated by
14
4.1.2 Measurements for experimental determination of lateral PBSK
extrapolating tbe total transmission toa field size c ofO x 0 cm2•
TP(c = OxO x y t) = lim T(c x y t) = e-J-l(x,y)t ' ' ' cJ.o ' ' '
(17)
In order to obtain tbe primary transmission, point measurements are taken at on- and off-axis locations relative to tbe beam axis, witb polystyrene pbantoms placed in tbe beam, for field sizes 3x3 cm and 4x4 cm centered around tbe on-axis and off-axis locations. Tbe extrapolation is done by taking a first order linear fit througb tbe measured data. Tbe off-axis distances expressed at tbe isocenter plane are; 0, 3, 6 and 9 cm. Measurements are done witb polystyrene pbantoms witb tbicknesses of: 4.0, 7.5, 11.6, 17.0, 22.4, 30.2 and 37.8 cm.
4.1.2 Measurements for experimental determination of lateral PBSK
Tbe lateral PBSKs are derived from on-axis measurements witb a mini pbantom and measurements in a water tank at 5 cm deptb, for different square fields in an open beam. By fitting equation 18 (see appendix B for a full derivation) as valid as possible tbe coefficients of a predefined kemel and an additional coefficient are derived. Tbe additional coefficient c1 represents tbe proportion of tbe primary dose compared witb tbe full scatter dose, on-axis, in a plane at a deptb z2, fora 10x10 cm2
field. Tbe fitting is performed in Matlab (Matlab 7.04, Tbe Matbworks, Natick, USA).
c,x,,y,, ,, r - ffMP( , ' )Klat( , •)d 'd, 1 M fiût ( t s ) [ ) --------C1 c,2 ,X ,y ,t,,s, X ,y X y+ MP(c,x,,y"t,,s,) c
(18)
In tbe derivation of equation 18, tbe assumption is made tbat tbe sbape of a normalized open beam profile is independent of tbe field size (see figure 7). Tbis way a large collimator setting Crz (20x20 cm2
) can be used. Tbe following radial symmetrie kemel function bas been investigated to describe tbe lateral PBSK:
(19)
Tbe fitting parameters IJ (cm--2) and K (cm-1
) are dependent on tbe energy of tbe pboton beam. Point measurements witb tbe ionisation cbamber intbewater tank and in tbe mini pbantom are performed in order to obtain lateral scatter kemels. Botb are done for a set of square fields: 3x3, 6x6, 1 Ox1 0, 15x 15, 20x20, 25x25, 30x30 and 35x35 cm2
, witb tbe ionisation cbamber centred at tbe central axis of tbe collimator. An open beam profile bas been measured witb tbe mini pbantom by scanning tbe diagonal profile in a field of20x20 cm2
•
2 1.00 <!)
.g 0.80 "0
-~ ~ 0.60 g
0.40
0.20
-square field with a width of Scm
-square field with a width of 20cm square field with a width of 10 cm
-18 -14 -10 -6 -2 2 6 10 14 180ff-axisdistance (cm)
Figure 7: Primary dose profiles normali::ed at the on-axis positionfor different squarefield si::es.
15
Materials & methods
4.1.3 Measurements for experimental determination of phantom PBSK The phantom PBSKs are derived by on-axis measurements done with a mini phantom, for square fields with polystyrene phantoms in the beam with different thicknesses positioned with their centre of mass at a constant distance s, of 50 cm. The phantom PBSKs are derived by these measurements by fitting the coefficients of a predefined kemel in equation 20 (See Appendix C for a full derivation). The fitting is implemented in Matlab (Matlab 7.04, The Mathworks, Natick, USA).
MP (c,x,,y,,t,s,) -limc-1-o MP (c,x,,y,,t,s ,) = JJM ~0 (c,2 ,x' ,y' ,t,,s,)Kpat (x' ,y' ,t,s,)dx' dy' (20)
For the derivation of the phantom PBSK the same assumption is made as in section 4.1.2 that the shape of a normalized open beam profile is independent of the field size (see tigure 7). This way the largest collimator setting possible c,2 (20x20 cm2
) can be used. The following radial symmetrie kemel function has been used to describe the phantom PBSKs;
(21)
With d =(sis/ a sealing factor taking into account the midplane to detector distance of the phantom. The fitting parameters y (cm--2
) and w (cm) are dependent on the energy of the photon beam and the thickness of the phantom. In order to obtain phantom scatter kemels on-axis point measurements with the mini phantom are performed with phantoms in the beam, at a souree to detector distance of 150 cm. Measurements are done fora set of square fields: 3x3, 6x6, 10x10, 15x15, 20x20, 25x25 and 30x30 cm2
, centred at the central axis of the collimator, with phantoms with polystyrene thicknesses of: 4.0, 7.5, 11.6, 17.0, 22.4, 30.2 and 37.8 cm. All combinations have been measured. The open beam profile is known from measurements as described in section 4.1.2. The polystyrene plates are placed symmetrically around the isocenter resulting in a fixed centre of mass to detector di stance of 50.0 cm.
4.2 Verification measurements The measurements performed to assess the accuracy of the incident energy tluence reconstruction model can be divided into three categories.
In the first category the EPID calibration model is verified in case of an open beam and in case of phantoms in the photon beam. The accuracy of the full scatter dose from portal dose images are assessed with verification measurements with the ionisation chamber in the water tank.
Second the extraction of the primary dose is verified in case of an open beam. The incident energy tluence is assumed to be directly related to the primary dose at the EPID (see equation 4) [ 17, 18]. The accuracy of the primary dose reconstructed from portal dose images in case of an open beam is assessed with verification measurements with the mini-phantom.
Third the model is verified in case of a phantom in the beam. In order to do this the accuracy of the phantom scatter model and the lateral scatter model are assessed. The mean difference of the reconstructed incident energy tluence compared to the incident energy tluence extracted in case of an open beam is determined and should be within 3% (mean difference).
16
4.2.1 Verification of EPID calibration model
4.2.1 Verification ofEPID calibration model The EPID calibration model has been verified with and without phantoms in the beam for a field size of 20x20 cm2
• The accuracy of the EPID calibration has been assessed by camparing portal dose images (PDls) fora field size of 20x20 cm2 with profiles measured along the y-axis (y-profiles) with the ionisation chamber at 5 cm depth in the water tank (see tigure 8). The polystyrene thicknesses used are; 9 .6, 21.4 and 31.6 cm. All phantoms were placed symmetrically around the central axis.
z (cm)
: : :
Campare Jul! scatter dose
measured in a water tank with Jul! scatter dose
oJPDI.
~~;~ s;ta;:; {: ::1::;_'._~==.~~--.· ;;:_,_;:},:_,_:_,I::::::::::::: ···d•"ll••=: =} cm depth in l jf:( ;~ ·· )' ~~ _ a water
Full scatter dose reconstructed fromportal images.
Figure 8: Schematic representation ofthe verification ofthe portaldose ca/i bration model in case of an open beam.
4.2.2 Verification oflateral scatter model in case ofan open beam To assess the accuracy of the lateral scatter model in case of an open beam (see figure 9), POls have been obtained for the following fields: 5x5, 10x10, and 20x20 cm2 centred around the central axis. With the lateral scatter model the primary dose at the EPID for the different fields has been determined. Primary dose profiles (y-profiles) have been scanned for each field and are compared with the reconstructed primary dose.
z (cm)
Subtract lateral
scatter dose.
rf"/1 _ JJat
: :
~ortal dose {===--d-"11
•=============j::!:::,:::'H:::} Image. . • ( ) \ r
Figure 9: Schematic representation ofthe verification ofthe lateral scatter model in case of an open beam.
17
Primary dose at five cm depth in mini-phantom.
Materials & methods
4.2.3 Verification of phantom scatter model To assess the accuracy of the phantom scatter model (see figure 10), the phantom scatter was calculated with the model for various phantoms. y-Profiles are scanned with the mini phantom behind these phantoms and the phantom scatter was subtracted from these measurements in order to obtain the primary dose profiles. These calculated primary dose profiles are compared with point measurements with the mini phantom at different positions as described in section 4.1.1. The phantom thicknesses used are 4.0, 4.1, 9.6, 11.6, 15.3 and 31.6 cm. All phantoms are positioned at a midplane to detector distance of 50 cm.
r(cm) z(cm)
Subtract phantom scatter dose.;
- D- D' -Mini phantom f 7
/ \ ! ;
{
D=Ii'+D' lf me~uremenl.< _ -t _ 1 _____ --, _ -~- _______ -----~- _____ •. · ____ t--} behznd a --- --,--- ----,-- ------------- ------ , , ------ ---phantom. ! ( • \ i \
Figure I 0: Schematic representation of the verification of the patient scatter model.
4.2.4 Verification of lateral scatter model with phantoms in the beam
Mini-phantom measurements with 3x3 cm2
field
To assess the accuracy of the lateral scatter model in case of homogeneaus phantoms in the beam, PDis have been obtained for homogenous phantoms with different thicknesses in the beam for a 20x20 cm2 field centred around the central axis (see figure 11). The phantoms were all positioned at an air gap of 50 cm. With the lateral scatter and the phantom scatter model the primary dose has been reconstructed from these PDis. y-profiles have been scanned with the mini phantom behind each phantom and are converted into primary dose profiles by subtracting the patient scatter. A comparison between the reconstructed primary dose of the PDis with the reconstructed primary dose profiles of the mini phantom will be made. The phantom thicknesses used are 9.6, 21.4 and 31.6 cm.
;~
. \. Subtract phantom Subtract phantom f scatter dose scatter dose.
PDL {=
; \ and lateral scatter dose. , \
- duli_Jjat_D' D-JY -
~~~\ j d"
11 \ _________ !!_ ____ !!_ ________ j-!{~ _J!..+_ !ti,--~_·} ~~:ec~
--------------------------- --;-(-----;-r -· dep:h_in · · mmz-
z (cm)
phantom.
Figure 11: Schematic representation of the verification of the lateral scatter model in case of a phantom in the beam.
18
4.2.5 verification ofthe model in case ofphantoms in the beam
4.2.5 Verification ofthe model in case ofphantoms in the beam To verizy the accuracy of the incident energy fluence reconstruction model in case of homogeneaus phantoms in the beam, PDis with various phantoms in the beam have been obtained fora 20x20 cm2
field (see figure 12). The phantoms were all positioned at an midplane to detector distance of 50 cm. The incident energy fluence was reconstructed from each PDI and each case was compared with the incident energy fluence reconstructed in case of an open beam. To determine the convergence of the iterative algorithm in the incident energy fluence reconstruction model the progress of the iterative algorithm has been investigated. The phantom thicknesses used are 9 .6, 21.4 and 31.6 cm.
Reconstruct incident energy
fluence.
Portaldose Image.
{ U~ -j_- ':'"IJ)n
Reconstruct incident energy
fluence.
{ ===dll"l'f·····==============-·····\I.Ifl";=} f;:;; dose
Figure 12: Schematic representation ofthe incident energy jluence reconstruction model in case of a phantom in the beam.
19
20
Results
In this chapter, the results obtained from the measurements done as described in the previous chapter will be shown. The numbering of the sections is the same as in chapter 4. The results of the measurements are presented along with a short discussion of the particular measurement. The general discussion ofthe total reconstruction model with the conclusions is shown in chapter 6. Unless stated otherwise, dose profiles are normalised at the on-axis position relative to the dose value of a 20x20 cm2 field in case of an open beam. Relative differences of a measurement M relative to a standard H are expressed as (M-H)/H. The results in this chapter are expressed as the relative mean difference (MD) ± 1 standard deviation (SD).
5.1 Input parameters for the model The input parameters have been obtained from measurements as described in section 4.1. Results have been obtained for the effective attenuation coefficient, the lateral PBSKs and the phantom PBSKs. All results obtained for the input parameters will be shown in this section.
5.1.1 Effective attenuation coefficient
The obtained primary transmission values are shown in table 1 for a 6 MV beam for different off-axis positions and different polystyrene (PS) thicknesses investigated. Results for a 10 MV beam are
Tabel I :Primary transmission 6 MV. Tabe/2:Primary transmission JO MV.
Thickness Off-Axis Distance Thickness Off-Axis Distance [cm] Ocm 3cm 6cm 9cm [cm] Ocm 3cm 6cm 9cm
0.0 1.000 1.000 1.000 1.000 0.0 1.000 1.000 1.000 1.000 4.0 0.776 0.792 0.804 0.806 4.0 0.821 0.820 0.815 0.810 7.5 0.658 0.666 0.677 0.676 7.5 0.722 0.719 0.712 0.706 11.6 0.541 0.549 0.555 0.551 11.6 0.623 0.620 0.611 0.603 17.0 0.421 0.426 0.428 0.424 17.0 0.513 0.509 0.500 0.490 22.4 0.322 0.324 0.325 0.319 22.4 0.416 0.412 0.403 0.393 30.2 0.229 0.231 0.231 0.225 30.2 0.322 0.318 0.310 0.300 37.8 0.161 0.162 0.161 0.157 37.8 0.247 0.244 0.236 0.228
21
Results
shown in table 2. Other values for the primary transmission can be obtained by means of linear interpolation. From these primary transmission values the effective attenuation coefficient is derived as explained in chapter 4. The attenuation coefficient is plotled with an expanded scale against the offaxis position in tigure 13A for 6 MV and in tigure 13B for 10 MV. The effective attenuation
A B
Ot=4.0an ~ t=7.5an ot=!7.0an ~t=Z2Aan Ot=4.0an ~ t=7.5an ot=l7.0an Jt=224an
o t=30.2an + t=37.8an x t=O.Oan ot=30.2an +t=37.8an Xt=O.Oan
6.5 5.5 ~
a x x a u 6.0 <;u 5.0 b 0 0
0 ~ '3: 0
5.5 ~ 4.5 0
~ ~
~
5.0 *
4.0 0 ~
+ ~
4.5 3.5 ~
4.0 3.0 0 2 4 6 8 10 0 2 4 6 8 10
Off-axis distance (cm) Off-axis distance (cm)
Figure 13: The effective attenuation coe.fficientfor a 6MV photon beam (A) andfor a IOMV photon beam (B).
coefficient for an infinitely thin phantom is estimated by means of linear extrapolation. As can be seen in bath figures the effective attenuation coefficient increases because of the beam softening effect and the effective attenuation coefficient decreases for thicker phantoms because of the beam hardening effect.
5.1.2 Derivation of the lateral PBSKs The lateral PBSKs are derived by on-axis measurements with a mini phantom and measurements in a water tank at 5 cm depth, in an open beam, for different square fields. The coefficients are fitled to a pre-defined kemel as described in the previous chapter. An exponential relation described by six parameters has been used to descri he the lateral pencil beam Tabel3: coe.fficients lateral PBSKs.
scatter kemels. The function descrihing the kemel is shown again in equation 22 for convenience.
coefficients 6 MV j ~
K lat ( ) _ ~ -K.-vx-+y-exp X, Y - L.../l;e
i=l
(22) -3 -2
TJ1(10 cm ) 6.6350 -4 -2
TJ2(10 cm ) 13.723 The on-axis measurements with the mini phantom and the on-axis _
4 _2
measurements in the water tank are normalised for the value of a fJJ(lO cm ) 1.0679 10x10 cm2 field and are shown in Appendix D. The open beam K1(10-1cm-1) 8.8738 profiles for 6 and 10 MV, measured with the mini phantom, are shown in Appendix E. The open beam profiles are normalized at the beam axis, and are extrapolated for off-axis positions larger than 18 cm, since the dimensions of the water tank do not allow scans for larger ranges. From the raw data presented in
-1 -1 K2(10 cm )
-1 -1 KJ(lO cm )
C1 (-)
3.0911
0.9468
0.8825
lOMV
11.321
2.4679
1.1905
9.3365
1.7922
1.4860
0.8952
Appendices D and E, the lateral PBSKs are derived for the function investigated. The coefficients of the lateral PBSKs are shown in table 3. The function is plotled in tigure 14A fora 6 MV and 10 MV photon beam at a semi-logarithmical scale. The ratios between the full scatter dose measurements and the measurements with the mini phantom (the expression at the left hand side of equation 18) are
22
5.1.2 Derivation of lateral PBSKs
plotted in tigure 14B for 6 MV and 10 MV, along with the calculated ratio (the expression at the right hand side of equation 18). The error of the calculated ratio is below 0.2% (maximum difference) compared to the measured ratio for both energies. A comparison between the different lateral PBSKs in tigure 14A shows that the lateral PBSKs are more forward peaked for higher energies.
"'a -:::, ~ Vl CQ Q..
ë
* ~
A B o measured (6 MV) o measured (10 MV)
-kemel (6MV) ··· kemel (IOMV) fitted(6MV) -fitted(10MV)
J0-2 ~ 1.08 ~ 0
.", _o
<l)
>
JO"' ·~ 1.04 03
/ ..:: /
1.00 i'
J0-4 if 0.96 I
I
1 JO"' 0.92
0 JO 15 20 0 10 20 30 40
Off-axis distance (cm) Off-axis distance (cm)
Figure 14: Resultsfor the lateral PBSK A) The lateral PBSKs plotted against the off-a:xis distancefor a 6 MV and a JO MV photon beam. B) The ratios between the Juli scatter dose measurements and the measurements with the mini phantom plotted for differentfielcl si= es for a 6 MV and a I 0 MV photon beam.
The dependenee of the mini-phantom with its dimensions has been investigated for a 6 MV beam by performing the same on-axis point measurements with mini-phantoms with diameters of 3,4,5,6 and 7 cm. The results are shown in tigure 32 in Appendix D. Larger dimensions of the mini phantom cause the mini-phantom to he more urneliabie for smaller field sizes. This will he further discusses in chapter 6.
23
Results
5.1.3 Derivation of the phantom PBSKs.
The phantom PBSKs are derived by on-axis measurements clone with a mini phantom, for square fields with polystyrene phantoms in the beam with different thicknesses positioned with their centre of mass at a constant midplane to detector distance of 50 cm. The phantom PBSKs are derived from these measurements by fitting the coefficients of a pre-defined kemel shown again in equation 23 for convenience.
(23)
The derivation of the phantom PBSKs requires the open beam profiles, and on-axis measurements with the mini phantom as described in the previous chapter. The results for the open beam profiles measured with the ionization chamber in the mini phantom are shown in Appendix E. The transmission measurements normalised for a 10x10 cm2 field are shown in Appendix F. The experimentally derived phantom PBSKs are shown in tigure 15A for 6 MV and 16A for 10 MV. The measured scatter transmission is shown in tigure 15B for 6 MValong with the calculated/fitted scatter transmission. In tigure 16B the measured scatter transmission is shown for a 10 MV photon beam along with the calculated/fitted scatter transmission. The fitled coefficients of the different lateral scatter kemels are shown in table 4. For field widths larger than 6 cm and all PS thicknesses the scatter transmission could be fitled within 0.3% for both photon beam energies. For smaller field sizes larger deviations could be seen. However the scattered transmission is very low for small field sizes.
The shape ofthe phantom PBSKs can be expressed by the magnitude y and the width ro ofthe kernels [20]. For both energies the magnitude is increasing with phantom thickness. This is due to the increased amount of scatter that is created by the primary beam because there is more phantom materiaL For the 6 MV beam the amount of scatter gradually levels off with larger phantom thicknesses due to the loss of intensity of the primary beam and the attenuation of the scattered photons becomes larger than the generation of new scattered photons by the weakening primary beam. The width decreases for larger phantom thicknesses. This decrease is a result of two effects. The first effect is that the beam hardens for larger phantom thicknesses (increase in mean energy) and the scatter is more forward peaked for higher energies. The second effect is that the air gap is smaller for
8.00
C'E 6.00 u
b ~
"' 28 4.00
"" E
~ f 2.00
0
A -e--t=4.0cm -+-t=7.5cm -t=ll.Scm--$-t=l7.0cm -e-t= 22.4 cm ~t = 30.2 cm -6-t = 37.8 cm
5 10 15 20 25 30
B o t = 7.5 cm " t = 11.6 cm + t = 17.0 cm - t = 22.4 cm
ot=30.2cm xt=37.8cm ot=4.0cm 0.10
~
'
= 0.08 0 ·~
-~ 0.06 = .ê
.",
~ ~ 0.04 "' u
"' 0.02
0.00
0 5 10 15 20 25 30 35 Off-axis distance (cm) Beam width (cm)
Figure 15: The resultsfor the phantom PBSKs in case of a 6 MVphoton beam. A) The di.fferentphantom PBSKs plotted against the offaxis distance for PS thicknesses of 4.0, 7.5, 11.6, 17.0, 22.4, 30.2 and 37.8 cm, B) The measured scatter transmission for PS thicknesses of 4.0, 7.5, 11.6, 17.0, 22.4, 30.2 and 37.8 cm, alongwith thejitted scatter transmission represented by the dashed lines.
24
5.2 Verification measurements
larger phantom thicknesses and the angular spread of scatter photons is thus smaller. For the 10 MV beam the amount of scatter also gradually level off with larger phantom thicknesses. For 10 MV the loss of intensity of the primary beam is less then for the 6 MV beam. A comparison between the phantom PBSKs for the 6 MV photon beam and the 10 MV photon beam shows that the width decreases for the 10 MV photon beam. This decreaseis aresult ofthe more forward peaked scatter for higher energies. Concluding, for both energies the magnitude of the phantom PBSK first increases rapidly with phantom thickness and levels off for larger phantom thickness. The width of the PBSKs decreases with phantom thickness due to the increase in the mean energy of the beam and the smaller air gap between phantom and detector. Tabe/4: Coe.fficients phantom PBSKs.
5.2 Verification measurements The measurements performed to assess the accuracy of the incident energy fluence reconstruction model is divided into three categories. In the first category the EPID calibration model is verified with and without phantoms in the beam (section 5.2.1).
Second the model is verified in case of an open beam. The incident energy fluence is directly related to the primary dose at the EPID. The accuracy of the primary dose reconstructed from portal dose images with the lateral scatter
Thickness
cm
0.0 4.0 7.5
11.6 17.0 22.4 30.2 37.8
6MV y(l0-5 cm-2
)
0.00 3.16 4.63 6.07 6.93 7.32 7.50 7.21
ro(cm)
0.00 25.87 25.95 24.85 24.35 23.59 22.21 21.01
10 MV
0.00 2.90 4.51 5.94 7.21 8.18 8.90 9.12
model is assessed by means ofmeasurements with the mini phantom (section 5.2.2).
ro(cm)
0.00 24.96 24.37 23.26 22.46 21.60 20.28 19.03
Third the model is verified in case of a phantom in the beam. In order to do this the accuracy ofthe phantom scatter model (section 5.2.3) and the lateral scatter model (section 5.2.4) are assessed. The mean difference of the reconstructed incident energy fluence compared to the incident energy fluence extracted in case of an open beam is determined and should be within 3% (mean difference) (section 5.2.5).
::-- 1.00
'§ -; 0 ::::- 0.80 ~
"' §3 a o.6o B §
..:::
"" 0.40
0.20
A
+-t = 4.0 cm -B-t= 7.5 cm -6--t= II 6 cm -+-t = 17.0 cm
-t = 22.4 cm -&-t=30.2 cm"*"" t= 37.8 cm
10 15 20 25
";" 0.10
s:: -~
0.08 -~ s:: El "ei 0.06 ~ <!) ;:
"' u
"' 0.04
0.02
0.00 30
r (cm)
B
o t~7.6cm 6 t~ 11.6cm "t~22.4 cm o t~30.2 cm
+t~37.8cm ot~4.0cm +t~J7.0cm
; -: 6
~ / "'r/
h~r5' /' 'f'/
f/ / ~15" ,ft
h f/ / Jt / / c('
/ j-/15" / / /
1)_..>3__-
.."f~ /
~""' 0 10 15 20 25 30 35
r(cm)
Figure 16: The resu/tsfor the phantom PBSKs in case of a JO MVphoton beam. A) The different phantom PBSKs plotted against the off-axis distancefor PS thicknesses of 4.0, 7.5, 11.6, 17.0, 22.4, 30.2 and 37.8 cm, B) The measured scatter transmission/ar PS thicknesses of 4.0, 7.5, I 1.6, 17.0, 22.4, 30.2 and 37.8 cm, a/ongwith thefitted scatter transmission represented by the dashed /ines.
25
Results
5.2.1 Verification of EPID calibration model
The EPID calibration model has been verified with and without phantoms in the beam for a field size of 20x20 cm2
• The accuracy of the EPID calibration has been assessed by camparing PDis with profiles scanned along the y-axis with the ionisation chamber at 5 cm depth in the water tank. The close profiles for the 6 MV pboton beam are shown in figure 17 A and the close profiles for the 10 MV pboton beam are shown in figure 17B. All profiles are relative to the
Table 5: Mean differences between the reconstructedfull scatter dose and thefull scatter dose measured with the ionisation chamber, along with one time the standard deviations.
on-axis value of a 20x20 cm2 field without a phantom in the beam.
Comparison between the close value of the PDI along the y-axis and the measured profiles has been made by calculating the mean difference between both profiles with one times the standard deviation. The results are shown in table 5. The penumbra regions are excluded from the calculations of the mean
FS Thickness
0.0 cm 9.6 cm 21.4 cm 31.6 cm
6MV 10 MV
0.6 0.9 0.4 0.7 3.4 0.7 1.4 1.2 -2.2 0.6 0.9 1.1
differences along with the standard deviations since measurements with the ionisation chamber have proven to be unreliable in the penumbra regions [12]. The full scatter close of a PDI has a steeper close gradient then the ionisation measurements. This will be further discussed in chapter 6.
The EPID calibration model uses a sensitivity [1] correction in order to obtain the beam profile from the grey values of the portal images. In case of an open beam the inaccuracy in the EPID cal i bration model is higher for the 6 MV pboton beam compared to the 10 MV pboton beam. This can be because of a small error in the sensitivity correction for the 6 MV pboton beam. In case of phantoms in the beam the model uses a non-linearity correction. The deviation for different phantom thicknesses can be cause by an error in the non-linearity correction [1].
~
~
~ 0 0 '0
.~ 0.8 -;;; ê
0.6 0 z
A
o Full scatter close bebind a phantom with a thickness of9.6 cm o Full scatter close bebind a phantom with a thickness of 21.4 cm
~ ~~~J ~~~: ~~~= fne~~ ~f:::,~: b!na thickness of31.6 cm
~ 0 0
] ~ ê 0 z
-18 -14 -10 -6 -2 2 6 10 14 18 y(cm)
B
o Full scatter close bebind a phantom w!th a th!ckness of9.6 cm o Full scatter close beh~nd a phantom W!th a th1ckness of 21.4 cm
~ ~~H ~~g=~ ~~~: f;~~~~ ~f:::,~: b!na thickness of31.6 cm
-18 -14 -10 -6 -2 2 6 10 14 18 y(cm)
Figure 17: Portaldose images along the y a:xis compared with ionisation chamber measurements in the water tankfor 6 MV (A) and JO MV (B). Jonisation chamber measurements are plotted with thin solid lines.
26
5.2.2 Verification ofthe lateral scatter model in case ofan open beam
5.2.2 Verification of the lateral scatter model in case of an open beam. For the verification of the lateral scatter model primary dose profiles along the y-axis have been obtained from POls and the lateral scatter model for different field sizes (FS), as described in chapter 4. The maximum beam width used for the fitting procedure is 35 cm. This results, due to beam divergence, in a distance off-axis of 26.25 cm at the EPID. The kemel values for distances at the EPID larger than 26.25 cm are extrapolated from the coefficients of the scatter kemel that are fitted in the region 0-26.25 cm. In figure 18A the relative primary dose profiles along the y-axis of the EPID are shown, reconstructed in case of 6 MV photon beams. In figure 18B results are show in case of 10 MV photon beams. All profiles are normalised at the on-axis position. All profiles are compared with relative primary dose profiles obtained with the mini phantom and
Table 6: Mean differences between the calculated primary dose and the measured primary dose with the ionisation chamber. along with one time the standard deviations.
FS
5x5 10x10 20x20
6MV
MD(%
-0.1 -0.1 -0.2
0.7 0.7
10 MV
0.0 -0.1 0.0 0.2
expressed as the mean differences (MD) ± 1 SD between predicted and measured primary dose values. The results are shown in table 6. The penumbra regions are excluded from the calculations ofthe mean differences along with the standard deviations since the mini phantom has proven to be unreliable in the penumbra regions. The differences between reconstructed and measured primary dose are small. The mean difference and its standard deviation increases for larger field sizes. However, the mean difference for the 20x20 cm2 field size is within the inaccuracy of the PDI. From figure 18A and 18B can be seen that the ionisation chamber measurements shows less steep dose gradients then the primary dose reconstructed from the PDI. This will be further discussed in chapter 6.
>, 0
A
t:. Reconstructcd prim~ dose from a PDI of a square field with a width of5 cm o Reconstructcd primary dose from a PDI of a squarefield with a width of 10 cm a Reconstructcd primary dose from a PDI of a square field with a width of 20 cm
1.20
'i 1.00 0 oo oo 0
0 Cl
0.80
0.60
0.40
-18 -12 -6 0 6 12
B
.o. Reconstructed primat") dosc from PDI fora square field with a width of 5 cm o Reconstructcd primary dosc from POlfora square f!Cld with a \\idth of 10 cm o Rcconstructcd primary dose from PDI for beam with of 20 cm
18 -18 -12 -6 0 6 12
y(cm) y(cm)
Figure 18: Primary dose profiles along the y-axis compared with ionisation chamber measurements in the mini-phantom for 6 MV (A) and 10 MV (B). Ionisation chamber measurements are p/otted with thin solid lines.
27
18
Results
5.2.3 Verification ofphantom scatter model To assess the accuracy of the patient scatter model the phantom scatter was subtracted from mini phantom measurements behind the phantoms in order to obtain primary dose profiles. These primary dose profiles are compared with the primary dose values obtained in section 5.1.1. With linear interpolation in table 1 and 2 the primary dose was determined for the phantom thicknesses and for off-axis distauces of 0, 3, 6 and 9 cm. The reconstructed primary dose values and the measured primary dose from the look-up tables are shown in tigure 19. The reconstructed primary dosevalues are all within 0.6% ofthe primary dose determined with the look-up tables. This is in agreement with the research done by W.v.Elmpt et al. [20].
~ 1.20
iJl 0
"0 1.00 "0
iJl
~ 0.80 0 z
0.60
0.40
0.20
0.00
A
- t ~ 0 cm (reconstructed)
o t ~ 4.1 cm (look-up table
-- t = 4.1 cm (reconstructed) · · · · t = 9.6 cm (reconstructed) ~ t = 31 cm (reconstructed?.
o t ~ 9.6 cm (look-up table o t ~ 31.6 cm (look-up tab e)
-- t = 15 cm (reconstructed?.
t. t ~ 15.3 cm (look-up tab e)
r--D--- -o.. ___ ".._--IJ- -B---
'ro-- -<&·· •••• -<>-- ·- -- -o-- .... 4·- .. -o-- -- --~
I. . ' .
r. ---fr-·-~--zs---.ll.-....---~---·-----&----zt-..\ ,. i ,.-o--<>--····<>-···---o-----<>--~ ~
1 \
... ~!JJ
0 ~
iJl 0 "0 "0 & ~ ê 0 z
-20 -16 -12 -8 -4 0 4 8 12 16 20
y(cm)
1.20
1.00
0.80
0.60
0.40
0.20
8
-- t = 4.1 cm (reconstructed) · · · · · t = 15 cm ( reconstructed~ ----- t = 31 cm ( reconstructed
o t ~ 9.6 cm (look-up table o t ~ 31.6 cm (look-up tab e)
· · · · t ~ 9.6 cm (reconstructed) - t = 0 cm (reconstructed)
o t ~ 4.1 cm (look-up tablel t. t ~ 15.3 cm (look-up tabfe)
rr--e----Q... _n..---e---1 ----e----1 <>" ~ - - - <& ••• - -- 'lC> •• -- -- -<& •• -- - 0- .. -- <&. - - - ···o.
~ ' f";····· ····"-··· ... "' ....... /:o. . .. t.· ... ··{!, ..•........ " •. :
t' :Î ~-~-_"\
I \ .?f!l \~ 0 00 4===r---.--.--,--,----.,--,---,---.==;-
-20 -16 -12 -8 -4 0 4 8 12 16 20 y(cm)
Figure 19: Primary dose profiles represented by thin solid /i nes, a long with the dose values derived from the look-up tables for a 6 MY beam (A) and a JO MV beam (B)
5.2.4 Verification ofthe lateral scatter model in case of phantoms in the beam. To assess the accuracy of the lateral scatter model in case of homogeneous phantoms in the beam, POls have been obtained for homogenous phantoms with different thicknesses in the beam for a 20x20 cm2 field centred on the axis. The phantoms were all positioned at a midplane to detector distance of 50 cm. With the lateral scatter and the phantom scatter model the primary dose has been reconstructed from these PDis. y-Profiles have been scanned with the mini-phantom behind each phantom and are converted into primary dose profiles by subtracting the phantom scatter. The results are expressed as the mean difference between measured and reconstructed profiles along with one time the standard deviation. These results are shown in table 7. The profiles are shown in tigure 20. The error in the primary dose is related to the error in the EPID calibration model as can be seen after comparing table 5 and 7.
Table 7: Mean differences between the calculated primary dose and the measured primary dose with the ionisation chamber, along with one time the standard deviations.
PS 6MV (cm)
9.6 -0.1 0.5 21.4 3.5 0.7 1.7 0.8 31.6 -2.8 0.7 -0.4 0.9
28
5.2.2 Verification of the lateral scatter model in case of an open beam
5.2.5 Verification of the model in case of a phantom in the beam.
To verify the accuracy of the incident energy fluence reconstruction model in case of homogeneous phantoms in the beam. PDis with various phantoms in the beam have been obtained for a 20x20 cm2
field. The phantoms were all positioned at a midplane to detector distance of 50 cm. The incident energy fluence was reconstructed from each PDI and each case was compared with the incident energy fluence reconstructed in case of an open beam with the mean difference, along with one time the standard deviation. Results for the different phantom thicknesses are shown in table 7. The incident energy fluence could be reconstructed from all PDis within 5 iterative steps. The deviation between the reconstructed incident energy fluence and the incident energy tluence in case of an open beam are shown in figures 21-26 for all phantom thicknesses. The deviations are
o Reconstructed primary dose behind a~antom with a thickness of9.6 cm . . B . .
o Reconstructed prunary dose behmd a phantom w1th a thiCkness of9.6 cm o Reconstructed primary dose behind a phantom with a thickness of21.4 cm o Reconstructed primary dose behind a phantom with a thickness of21.4 cm o Reconstructed primary dose behind a phantom with a thickness of31.6 cm - Primary dose in case of an open beam
o Reconstructed primary dose behind a phantom with a thickness of 3 1.6 cm - Primary dose in case of an open beam
» 1.2 s ~ 0 Cl
0.8
0.6
0.4
0.2
0
-16 -12 -8 -4 0 4 8 12
» 1.2 s ~ 0 Cl
16 y(cm)
0.8
0.6
0.4
0.2
0
-1 6 -12 -8 -4 0 4 8 12 16 y(cm)
Figure 20: Reconstructed primary dose profiles along with profiles measured with the mini-phantom. The measurements with the mini phantom are represented by thin solid /i nes fora 6 MV beam (A) and a I 0 MV beam (B).
relative to the on-axis value of the incident energy fluence in case of an open beam. In the 10 MV photon beam case the incident energy fluence can be reconstructed better along the y-axis. This can be explained by the EPID calibration model. For the sensitivity correction of the EPID an array of ionization chambers was used. It is likely that the ionization chambers along the y-axis deviated compared to the others. In figures 21-26 discontinuity can be seen along x = 5 a.nd x = -5. This is because the EPID is divided into 16 section. Small deviation at the edges of the sectio.ns can be detected since each section of the EPID is slightly different. In figures 21-26 a " ring" effect has been observed. This effect can be explained by the EPID calibration model. In order to correct the EPID images for the beam profile [2] the EPTD calibratio.n uses a sensitivity matrix. This matrix uses interpolated values between measured values.
Tab/e 8: Mean dijferences between the Juli scatter dose in case of a phantom in the beam and thefii/1 scatter dose measured with the ionisation chamber, a/ong with one time the standard deviations.
PS 6MV 10 MV Thickness MD %) ± I SD % MD(%) ± I SD (%
9.6 cm 1.4 1.0 2.0 1.1 21.4 cm 2.0 1.8 2.6 1.3 31.6 cm -1.6 1.9 0.2
29
Results
-20
-15
-10
-5
x( cm) 0 0
5 -1
10
15
20 -20 -15 -10 -5 0 10 15
y(cm)
Figure 21: The deviation of the incident energy jluence reconstructedfrom a PDI behind a phantom with a thickrless of9.6 cmfor the 6 MV photon beam case, relative to the onaxis value of the incident energy jluence in case of an open beam.
y(cm)
Figure 23: The deviarion of rhe incident energy jluence reconstructed from a PDI behind a phantom with a thickness of 21.4 cmfor rhe 6 MV phoron beam case, relarive to the onaxis value of rhe incident energy jluence in case of an open beam.
30
% -20
-15
-10
-5
x(cm) 0
5
10
15
20 -20 -15 -10 -5 0 5 10 15
y(cm)
Figure 22: The deviation of the incident energy jluence reconstructed from a PDI behind a phantom with a thickness of9.6 cmfor the 10 MV photon beam case, relative to the onaxis value of the incident energy jluence in case of an open beam.
y(cm)
Figure 24: The deviation of the incident energy jluence reconstructed from a PDI behind a phantom with a thickrless of21.4 cmfor the JO MV photon beam case, relative to the onaxis value of !he incident energy jluence in case of an open beam.
%
%
5.2.2 Verification of the lateral scatter model in case of an open beam
y(cm)
Figure 25: The deviation of the incident energy jluence reconstmcted from a PDI behind a phantom with a thickness of 31 .6 cm for the 6 MV photon beam case, relative to the onaxis value of the incident energy jluence in case of an open beam.
31
% -20
-15
-1 0
-5
x( cm) 0
5
10
15
20 -20 -15 -10 -5 0 5 10 15 20
y(cm)
Figure 26: The deviation of the incident energy jluence reconstructed from a PDI behind a phantom with a thickness of 31.6 cm for the I 0 MV photon beam case, relative to the onaxis va/ue of the incident energy jluence in case of an open beam.
32
Discussion and Coneinsion
In this chapter the results derived in the previous chapter will be discussed and recommadations will be made for further research. Futher developments will be discussed and at the end of this chapter conclusions are made based on the research done.
6.1 Discussion Mini phantom: In the back-projection algorithm, the primary dose component at the level ofthe EPID is needed. An ionization chamber in a mini-phantom at the EPID position as a reference detector, because in this way only the primary dose component is measured. J.J.M. van Gasteren et al. [23] already showed that the following conclusions could be made for measurements with a mini phantom; (i) MP is almost independent ofthe souree to surface distance (ii) MP does notdepend on the depthof the ionization chamber in the polystyrene cylinder ifthe depth is beyond the range ofthe contaminated electrans (iii) MP is only a function of the collimator setting. (iv) MP is not influenced by irradiation obliquely incident on the lateral phantom wall.
Within the water tank, lateral scatter takes place. For that reason, the uncorrected PDI has a steeper field size dependent response compared to the ionization chamber in a mini phantom. However, the primary dose profiles reconstructed with the lateral scatter model for an open beam, deviate in the region ofthe edges ofthe fields from the profiles measured with the ionization chamber in a mini-phantom. This has also been observed by Wendling et al. [12]. Moreover, the primary dose profiles reconstructed with the lateral scatter model for an open beam had a steeper penumbra. These differences may have the following causes: (i) An ionization chamber needs an electron equilibrium. In the penumbra region there is a lack
of electron equilibrium. The same problem occurs for small fields. So on one hand the diameter ofthe mini-phantom should be large enough in order to achieve electron equilibrium, while on the other hand it has to be small compared to the field size, so that negligible lateral scatter takes place.
(ii) The EPID has a higher resolution compared to the ionization chamber because ofthe larger dimensions ofthe ionization chamber.
(iii) EPIDs are known to have an over-response at low-energy photons. So in the penumbra region this could be a problem. However, at the EPIDs used during this research an additional 3 mm Copper plate has been place at the EPID surface in order to filter out the low energetic photons
33
Attenuation coefficient: The attenuation coefficient for on- and off-axis distances is measured for small fields and extrapolated to the transmission of zero field size. The results have been put in a look up table from which other values of the attenuation coefficient can be extracted by means of linear interpolation. This interpolation step can be removed by fitting the measurements to a model that takes into account both off-axis distance and thickness. Tailor et al. [14] proposed to describe the effective attenuation coefficient at an off-axis angle by descrihing the on-axis attenuation coefficient multiplied by an off-axis correction factor. However the model as proposed by Tailor et al. [14] showed deviations up to 5% compared to the effective attenuation coefficient measured with the miniphantom. This can be explained by the fact that the model is a general description of the off-axis energy correction for linac photon beams.
PBSK: A comparison between the different lateral PBSKs in tigure 14 shows that the lateral PBSK are more forward peaked for higher energies and that the primary dose to full scatter dose ratio increases for higher photon beam energies. Both results are in agreement with literature [17]. The shape of the phantom PBSK can be expressed by the magnitude y and the width ro of the kemels [27]. From figures 15 and 16 can beseen that the magnitude first increases rapidly with phantom thickness and levels off for 1arger phantom thickness. The width decreases with phantom thickness due to the increase in mean energy of the beam and the smaller air gap between phantom and detector. A comparison between the different phantom PBSKs in tigure 15 and 16 shows that the lateral PBSKs are more forward peaked for higher energies and that the primary dose to full scatter dose ratio increases for higher photon beam energies. Both results are in agreement with literature [21,22,27].
Verification of the PBSK with Monte Carlo simulations was not possible since the Monte Carlo code available at our institute is not yet able to distinct scatter from primary dose, and the accuracy of the Monte Carlo code at 150 cm depth has not been verified. Adaptations of the code and verifications of the new implementations in the Monte Carlo code are beyond the scope of this research.
Incident energy jluence reconstruction in case of an open beam: The incident energy fluence depends on the primary dose at the level of the EPID. The inaccuracy in the reconstructed primary dose is used to asses the accuracy of the incident energy fluence reconstruction model. The inaccuracy in the reconstruction of the incident energy fluence in case of an open beam is caused by the EPID calibration and the lateral scatter model. Results insection 5.2.6 show that the EPID calibration has an error in case of an open beam of 0.3 (MD) ± 0.9% (SD) for the 6 MV photon beam and 0.4 (MD) ± 0.6% (SD) for the 10 MV photon beam. This makes the PDI accurate enough for further use in the open beam situation. Moreover the PDI is what is going to be used in the future as starting point.
By means of PDis the primary dose could be reconstructed with the lateral scatter model within -0.2 (MD)± 0.7% (SD) for the 6 MV photon beam and -0.1(MD) ± 0.3% (SD) for the 10 MV photon beam. This is within the criteria of MAASTRO CLINIC of 3% (MD). The error in the lateral scatter model can be caused by the fact that the lateral PBSKs are only fitted by on-axis point measurements. This way the solution for the fitting parameters of the kemel are not unique. Multiple scatter kemels can result in the same on-axis accuracy. This could be made more accurate by fitting the lateral PBSK for on- and off-axis values at the same time. This will require more computational time. Because the calculations and measurements are performed numerically with discrete data points, the resolution ofthe grid size ofthe primary dose and thus the grid size ofthe incident energy fluence can be of importance. The primary dose is scaled to the dimensions of the portal dose grid. This grid is fixed as a result of the pixel size in the EPID. v. Elmpt et al. [26] investigated the incident energy fluence with the same grid size and found that the dose in a water phantom could be reconstructed within 0.2% (absoluut difference) compared to ionisation chamber measurements.
Incident energy jluence reconstruction in case of a phantom in the beam: For both photon beam energies the inaccuracy of the incident energy fluence reconstruction model in case of an object in the beam is within 3.0% ± 1 SD compared to the incident energy fluence reconstructed in case of an open beam. The inaccuracy in the reconstruction ofthe incident energy fluence in case of a phantom in the
34
beam is caused by the EPID calibration model, the phantom scatter model, the lateral scatter model and the inaccuracy in the thickness ofthe phantoms. Results insection 5.2.6 show that the inaccuracy of the EPID calibration increases for thinner phantoms for the 6 MV beam. This is probably due to a small error in the non-linearity correction of the EPID calibration model for the 6 MV beam. The EPID calibration model showed good results for the 10 MV photon beam. The phantom scatter model has an inaccuracy on-axis within 0.6% for both photon beam energies.
The lateral scatter model has an error of 3.8% (MD) and 1,7% (MD) in case of a 6 and 10 MV photon beams. The error in the lateral scatter model can be caused by two reasons. The first reasons is that the fitting parameters ofthe lateral PBSK are not unique as explained earlier. The second reason is that the assumption is made that the lateral scatter caused by patient scatter can be ignored. Since the patient scatter is only 10% on-axis in case of a phantom with a water equivalent thickness of 20 cm, the lateral scatter due to phantom scatter is estimated to be no more then 1 %. The exact PS thickness can deviate from the used PS thickness. This is estimated to be approximately 1 mm, which results in a error ofthe primary dose of0.4%.
6.2 Recommendations The following recommendations can be made for further research. If the model is going to be used for intensity modulated radiation therapy further research is necessary. Intensity modulated radiation therapy uses highly irregular MLC shaped fields to radiate patients. These field are the composition of many small fields. The incident energy fluence reconstruction model should be verified for the penumbra region and for very small fields before it is being implemented in the clinic for intensity modulated radiation therapy purposes. A method to verif)r the model in the penumbra areas is by means of small ionisation chambers or by means of film measurements. The lateral scatter model can be made more accurate in the penumbra region by making use of a second lateral scatter kemel as proposed by M.Wendling et al. [21]. In intensity modulated radiation therapy organs at risk (organs that should be spared during radiation treatments) are shielded by the multi leafs. Therefore it is also important to know how the incident energy fluence can be reconstructed outside the field. The stability ofthe EPID should be investigated because EPID are know to have a response in time and finally, the model should be investigated for highly inhomogeneous phantoms positioned at different midplane to detector distances.
6.3 Future Three dimensional dose reconstruction is the ultimate goal in radiotherapy. Measurement devices like MOSPETs can be used as point detectors for either entrance or exit dosimetry and portal dose images can be used for 2-D dose verification. However, pre-treatment verification by point detectors or with 2-D portal dose images do notprovide information about the three-dimensional (3-D) dose delivered inside the patient, or how possible differences add up in the total (complex) treatment plan with multiple beams and changes in the patients anatomy. Reconstructing the incident energy fluence by portal dose images as described in this master thesis is a step toward 3-D dose reconstruction in an online patient model for dose guide radiation therapy purposes.
At MAASTRO CLINIC the possibility for using a Mega-Voltage Cone-Beam CT is currently under investigation. Recently, the incident energy fluence reconstruction model has been used for 3-D dose calculations by W.v.Elmpt et al. [26], who used the same relation between the primary dose and the incident energy fluence as in this research. The model was used in order to reconstruct the incident energy fluence in case of an open beam and the reconstructed incident energy fluence was used as input for an independent Monte Carlo dose calculation engine in order to calculate the dose in a water phantom, which was verified with ionisation chamber measurements in the water phantom at different depths. Figures 27 and 28 show reconstructed and measured beam profiles for 6 and 10 MV photons. The agreement between ionisation chamber measurements and reconstructed data is within a few percent..
35
6.4 Condusion A model to reconstruct tbe incident energy fluence of a linac by means of portal dose images bas been presented. The model is able to reconstruct tbe incident energy fluence by means of portal dose images bebind a pbantom for 6 MV and 10 MV pboton beams. Tbe error of tbe model was witbin of 0.2% (mean difference) in case of an open beam and 2.6% (mean difference) in case of a pbantom in tbe beam.
20ll20 cm2 field size, 6 MV 150.--.~-------------.------~------~~
I 100
~ l ~ 50 '~ .--"'"" '"" ;11
-10 -5 0 5 10 Off-ax1s distance lcm)
Figure 27: Dose profiles at different depths in a water phantoms with ionisation chamber measurements as comparison for a 6 MV photon beam. The crosses, doted, square and triangular markers represent the reconstructed profi/es at depths of20,5,10 and 30 cm, respectively.
36
20x20 cm2 field size, 10 MV 150.--.---------------.------~------~~
i 100
i l ~ 50
' "'~·
~ o~~------------~----~------~~
-10 -5 0 5 10 Off-ax1s distance lcmj
Figure 28: Dose profiles at different depths in a water phantoms with ionisation chamber measurements as comparison for a 10 MV photon beam. The crosses, doted, square and triangular markers represent the reconstructed profi/es at depths of20,5,10 and 30 cm, respectively.
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[15] M.K. Yu, R.S. Sloboda, and B. Murray. Linear accelerator pboton beam quality at off-axis points. Med.Phys., 24(2):233-239, 1997
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[17] F.M. Khan. The physics of radiation therapy. Lippeneort Williams & Wilkins., Third edition, ISBN 0-7817-3065-1,2003.
[18] R. Loevinger. A formalism for calculation of absorbed dose toa medium from pboton and electron beams. Med.Phys. 8(1 ): 1-12, 1980.
[19] A. Ahnesjo, M. Saxner, and A. Trepp. A pencil beam model for photon dose calculation. Med.Phys., 19(2):263-273, 1992.
[20] W.J.C. van Elmpt, S.M.J.J.G. Nijsten, B.J. Mijnheer, and A.W.H. Minken. Experimental verification of a portal dose prediction model. Med. Phys., 32 (9):2805-2818, 2005.
[21] B.M.C. McCurdy and S.Pitorius. Pboton scatter in portal images: Accuracy of a fluence based pencil beam superposition algorithm. Med. Phys., 27 (5):913-921, 2000.
[22] B.M.C. McCurdy and S.Pitorius. Pboton scatter in portal images: Physical characteristics of pencil beam kernels generated using the EGS Monte Carlo code. Med. Phys., 27 (2):312-320, 2000.
[23] J.J.M. van Gasteren, S. Heukelom, H.N. Jager, B.J. Mijnheer, R. van der Laarse, H.J. van Kleffens, J.L.M. Venselaar and C.F. Westermann. Determination and use of scatter correction factors of megavoltage pboton beams. Netherlands Commission on Radiation Dosimetry. 1998.
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40
Appendices
In the appendix the dimensions ofthe mini phantom are shown, raw measurement data from the various pint measurements are shown and the derivation of equitation 18 and 20 are shown.
8.1 Appendix A; Dimensions ofthe mini phantom.
3cm
10
r------ I I I I I I I I
-. 6~:I~~~t ----m---- _-_-_-_-x.,-!:_~~~----- ---I I I I
5cm
I
10,25cm I I I I 15.lcm I I I I I I
I I 1~1
: ldn : I I
I
1 4cm 1
Figure 29:Dimensions ofthe mini phantom.
41
8.2 Appendix B; Derivation of equation 18 In this appendix equation 18 will be derived. In case of in an open beam (D' = 0) equation 3 for the 2-D full dose becomes:
Dfilil (c, x,y) = Dlat (c, x, y)+ DP (c, x,y). (24)
Substituting equation 5 for the lateral scatter dose in the previous equation gives the following 2-D expression for the full dose in an open beam,
(25)
Substituting x= 0, and y = 0 in the previous equation gives the on-axis expression for the full dose in an open beam.
(26)
Dividing equiation 26 by D P (c, x = 0, y = 0) gives the next result.
nfull(c,x=O,y=O) JJ DP(c,x',y') I ( ) -------= Kat x',y' dx'dy'+1 DP(c,x=O,y=O) c DP(c,x=O,y=O)
(27)
For the derivation of the lateral PBSK the following relations for the full scatter measurements in a water tank lvl'" and the measurements with the mini phantom M both normalized at the on-axis position for a 1 Ox1 0 cm field are used,
nfi"l< ) Mfi"l(cx )= c,x,y , ,y nfi"l< ) , c,,x,,y,
(28)
MP( )- DP(c,x,y) c,x,y - .
DP(c"x"y,) (29)
Using equation 28 and 29 at the on-axis position and substituting them in equation 27 gives the following result:
Mfi"1(c,x,,y,)Dfi"
1(c,x,,y,) JJ DP(c,x',y') lat( )d
-----------= K x',y' x'dy'+1. MP (c,x,,y,)DP(c,x,,y,) c DP(c,x = O,y = 0)
The constant c1 is introduced.
DP(c,x,,y,) c --.,...,.,.;..-:........:.....:....;_ ' - nfi"l ( x Y ) C, r' r
42
(30)
(31)
Substituting the constant in equation 30 gives the following result;
Mfi"'( ) DP( '') c,XnYr = c JJ c,x ,y Klat(x' y')dx'dy'+c _M_P_( ___ )_ I DP( ) ' I
c,x,,y, c c,x,,y, (32)
The assumption is made that D P (c, x, y) I D P (c, x = 0, y = 0) is independent on c. This way equation 32 can be rewritten as can be seen in equation 33, by making use of the largest collimator setting possible, Crz (20x20 cm).
Mfi"'(c x y ) , r' r _ JJMP( , ')Ktat( , •)d 'd, ------c1 c,2 ,x ,y x ,y x y+c1
MP(c,x,,y,) c (33)
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8.3 Appendix C; Derivation of equation 20. In this appendix equation 20 will he derived hy means of equation 6 as stated helow for convenience:
Ds (x,y) = fJD/:0 (c,x' ,y')Kpat Clx'-xi,IY'-yl,s(x,y),t(x,y))dx'dy'. (34)
Suhstituting x= 0, and y = 0 in the previous equation gives the on-axis expression for the full dose in an open heam.
(35)
Dividing hy DP1~o (c, Xr, Yr) gives the following result:
D"(c x y t s ) DP ( ' ') ' r' r' ' r = JJ t=O C,X ,y Kpat( t t )d 'd ' X ,y ,t,sr X y . Df:o(c,xr,Yr) c D/:o(c,xr,Yr)
(36)
For the derivation of the lateral PBSK the following relations for the full scatter measurements in a water tank, Jv!ull and the measurements with the mini phantom, M , hoth normalized at the on-axis position fora 10x10 cm field are used.
(37)
(38)
The assumption is made that D P (c, x, y) I D P (c, x = 0, y = 0) is independent on c. This way equation 36 can he rewritten as can he seen in equation 39, hy mak.ing use of the largest collimator setting possihle, Cr2 (20x20 cm).
MP (c,x"yr,t,sr) -1imcto MP (c,xr,Yr,t,sr) = JJM /:0 (cr2 ,x' ,y')Kpat (x' ,y' ,t,sr)dx' dy' (39)
44
8.4 Appendix D; Output measurements for derivation of lateral PBSKs
'-' "' 0
-o -o '-' N
<ïi ê 0 ;z:
'-' "' 0 -o
-o '-' .~ <ïi E :.... 0 ;z:
1.15
1.10
1.05
1.00
0.95
0.90
0.85
0 10 20 30 40 50
Width ofthe square fie lds (cm)
Figure 30: On-axis point measurements with !he mini phantom in case of a 6 MV photon beam represented by the solid pink fine and on-axis point measurements with the CC / 3 in the water tank represented by the so fid bfue line. All measurements are normalisedfor a /Ox / 0 cmjie fd.
1.15
1.10
1.05
1.00
0.95
0.90
0.85
0 10 20 30 40 50 Width ofthe square fie lds (cm)
Figure 31: On-axis point measurements with the mini phantom in case of a JO MV photon beam represented by the so/id pink fine and on-axis point measurements with the CC/ 3 in !he water tank represented by the so/id bfue fine . All measurements are norma/isedfor a fOxfO cmjiefd.
45
1.06
' '-' <I)
"' 1.04 0 -o -o <I)
1.02 .~ ca E ,_
1.00 0 z 0.98
0.96
0.94
0.92
0.90
-+- diameter 4 cm diameter 7 cm
--diameter 5 cm _._ diameter 6 cm -+- diameter 3 cm
0 10 15 20 25 30 35 40
Width ofthe square fields (cm)
Figure 32: On-axis point measurements with mini-phantoms with different diameters for a 6 MV photon beam. All measurements are norma/isedfor a /Ox /0 cm field..
46
8.5 Appendix E; Open beam profiles 6 MV and 10 MV pboton beams.
1.09
V <ll 0
'"0 1.07 '"0 V
-~ <;;
E 1.05 0 z
1.03
1.01
0.99
0 4 8 12
~ ~
16
Off-axis di stance (cm)
Figure 33: Open beam profiles norma/ised at the on-axis positionfor the 6 MV photon beam represented by the blue solid fine and the 10 MV photon beam represented by the red solid fin e.
47
8.6 Appendix F; Output measurements with mini phantom bebind phantoms
I 2.00 'E 0 ë c;j
..c 0.
s:: 1.50 .Ë :; 0
~ 1.00
0.50
0.00
0 5 10
•
15 20 25 30 Width ofthe square fields (cm)
Figure 34: On-axis point measurements with the mini phantom in case of a 6 MV photon beam with different phantom thickness in the photon beam ..
'E 0 ë c;j
..c 0.
s:: .Ë :; 0
-o c;j Cl)
0:::
2.00 -+- t=O .......... t=4.0
t=7.5 -+t- t= 11.6 .-----· - t=17.0
1.50 ........ t=22.4 -+- t=30.2 - t=37.8
1.00
~ 0.50
0.00
0 5 10 15 20 25 30
Width of the square fi elds (cm)
Figure 35: On-axis point measurements with the mini phanrom in case of a 6 MV photon beam with different phantom thickness in the photon beam ..
48