Modeling the TrueBeam linac using a CAD to Geant4 geometryimplementation Dose and IAEA-compliant phasespace calculations

Magdalena Constantina)

Department of Radiation Oncology Radiation Physics Division Stanford University StanfordCalifornia 94304

Joseph PerlSLAC National Accelerator Laboratory Menlo Park California 94025

Tom LoSassoMemorial Sloan-Kettering Cancer Center New York 10021

Arthur Salop David Whittum Anisha Narula and Michelle SvatosVarian Medical Systems Inc Palo Alto California 94304

Paul J KeallDepartment of Radiation Oncology Radiation Physics Division Stanford University StanfordCalifornia 94304

(Received 16 June 2010 revised 17 May 2011 accepted for publication 19 May 2011 published20 June 2011)

Purpose To create an accurate 6 MV Monte Carlo simulation phase space for the Varian True-Beam treatment head geometry imported from CAD (computer aided design) without adjusting theinput electron phase space parametersMethods GEANT4 v492p01 was employed to simulate the 6 MV beam treatment head geome-try of the Varian TrueBeam linac The electron tracks in the linear accelerator were simulatedwith Parmela and the obtained electron phase space was used as an input to the Monte Carlobeam transport and dose calculations The geometry components are tessellated solidsincluded in GEANT4 as GDML (generalized dynamic markup language) files obtained via STEP(standard for the exchange of product) export from Pro=Engineering followed by STEPimport in Fastrad a STEPndashGDML converter The linac has a compact treatment head andthe small space between the shielding collimator and the divergent arc of the upperjaws forbids the implementation of a plane for storing the phase space Instead an IAEA(International Atomic Energy Agency) compliant phase space writer was implemented on acylindrical surface The simulation was run in parallel on a 1200 node Linux cluster The 6MV dose calculations were performed for field sizes varying from 4 4 to 40 40 cm2 Thevoxel size for the 60 60 40 cm3 water phantom was 4 4 4 mm3 For the 10 10 cm2

field surface buildup calculations were performed using 4 4 2 mm3 voxels within 20 mmof the surfaceResults For the depth dose curves 98 of the calculated data points agree within 2 with theexperimental measurements for depths between 2 and 40 cm For depths between 5 and 30 cmagreement within 1 is obtained for 99 (4 4) 95 (10 10) 94 (20 20 and 30 30)and 89 (40 40) of the data points respectively In the buildup region the agreementis within 2 except at 1 mm depth where the deviation is 5 for the 10 10 cm2 open fieldFor the lateral dose profiles within the field size for fields up to 30 30 cm2 the agreementis within 2 for depths up to 10 cm At 20 cm depth the in-field maximum dose differencefor the 30 30 cm2 open field is within 4 while the smaller field sizes agree within 2 Out-side the field size agreement within 1 of the maximum dose difference is obtained for allfields The calculated output factors varied from 093860015 for the 4 4 cm2 field to108860024 for the 40 40 cm2 field Their agreement with the experimental output factors iswithin 1Conclusions The authors have validated a GEANT4 simulated IAEA-compliant phase space of theTrueBeam linac for the 6 MV beam obtained using a high accuracy geometry implementationfrom CAD These files are publicly available and can be used for further research VC 2011 AmericanAssociation of Physicists in Medicine [DOI 10111813598439]

Key words Monte Carlo 6 MV photon beam CAD import phase space

4018 Med Phys 38 (7) July 2011 0094-2405201138(7)40187$3000 VC 2011 Am Assoc Phys Med 4018

I INTRODUCTION

An important goal of Monte Carlo dose calculations in medi-cal physics is to provide accurate results for the entire radia-tion therapy process1 While improving the efficiency ofMonte Carlo dose calculations has been recently dis-cussed12 exploring new ways of improving the accuracy ofgeometry representation needs to be further addressed as itrepresents a crucial aspect of any accurate beam transportdose calculation Previous Monte Carlo dose calculationshave shown that inaccurate geometrical representation of thein-field treatment head components such as the primary col-limator the shielding collimator and the ionization cham-ber introduces large errors that propagate throughout thesimulation3 Electron-beam Monte Carlo calculations4 haveaddressed the dose sensitivity to the geometry and positionof scattering foils High energy electron beams at large fieldsizes have been shown4 to be highly sensitive to the geome-trical configuration of the treatment head and changes assmall as 2 mm in component positioning have a significantimpact on the calculated dose profiles The specifications ofthe primary collimator such as the upstream opening have anoticeable effect on the calculated off-axis ratios5 Geometri-cal errors can be minimized through a computer-assistedprocedure that automates the setup of the geometry avoidingmanual data entry Transferring the detailed treatment headgeometry from CAD (computer aided design) drawings toGEANT4 is more accurate and less error prone than interpret-ing the engineering drawings The simplicity of this processmakes it easier to keep the information updated as smallmodifications are made to the design Linking CAD toGEANT4-based Monte Carlo simulations has recently beendescribed in Ref 6 It provides the GDML (generalizeddynamic markup language)7 representations of the headcomponents used as input into GEANT478 a feature not cur-rently supported by other codes such as EGS4 (Ref 9) orBEAM (Ref 10)

Several groups have performed Monte Carlo studies ofradiotherapy beams starting with certain assumptions aboutthe initial electron beam parameters511ndash15 and iterativelyadjusting those parameters to obtain a good match with theexperiment for a specific machine In this work instead ofvarying these parameters we have specified as input to theMonte Carlo model the particle phase space derived by theParmela16 simulation of the waveguide Parmela phase spaceinputs have been used in other studies17ndash21 This approachprovides a realistic approximation for the particle parametersand potentially avoids the need of iterations In our studythe electron energy spectrum along with the target focal spotsize were independently determined through experimentalinvestigations It is estimated that the uncertainty of the Par-mela energy distribution is 4 for the mean energy whilethe beam spot size at the target location has uncertainties upto 10

The goal of the present project was to develop a MonteCarlo application for the complex treatment head geometryimported from CAD for the Varian TrueBeam linac operatedat 6 MV and to quantify the agreement with experimental

dose measurements without tuning the parameters of theinput Parmela electron phase space The output of our simu-lations is an International Atomic Energy Agency (IAEA)-compliant phase space file which is generic not tuned for spe-cific machine parameters yet gives dose results in good agree-ment with experimental measurements We also demonstratethe necessity to score the phase space on a cylindrical surfacerather than conventional flat geometry due to the compacttreatment head geometry

II METHODS AND MATERIALS

IIA Linac simulation

The TrueBeam medical accelerator employs a biperiodicstanding wave accelerator incorporating an ldquoenergyswitchrdquo and a 270 bending magnet The system is capableof achieving a sharp spectrum at energies ranging from 4 to20 MeV for treatment and down to 2 MeV for imaging22

The linac consists of a linear array of microwave cavitiesin which RF fields at frequencies corresponding to thecavity resonance frequencies are maintained with theappropriate magnitude and phasing so as to accelerate alarge fraction of the particles in their passage through thelinac guide

The simulation of the waveguide included the followingfour parts (a) a simulation of an electron beam source forthe guide to provide an input beam injected at a specifiedcurrent and energy (b) a means of generating the cavity RFfields (c) a method for computing the trajectories of the vari-ous beam particles as they experience the accelerating Lor-entz forces from their interaction with the various cavity andspace charge fields and (d) a provision for superimposing afocusing solenoidal magnetic field along the length of theguide

(a) To model the input beam from the truebeam triode gunin Parmela a macroparticle simulation was createdbased on measurements made using an electron beamanalyzer The device was used to examine the variationin the outer radius (envelope) of the beam generated ina field-free drift region as a function of the distancedownstream from the gun From this data the Twissparameters of the emittance ellipses23 at the accelera-tor entrance could be inferred and the phase space dis-tribution of the input beam determined The injectedbeam is monoenergetic corresponding to the gun highvoltage setting appropriate for the mode studied Thegun current was a nominal value measured with a to-roidal current monitor

(b) The Superfish code24 a 2D RF finite difference cavityfield solver was used to generate the cavity fieldpatterns

(c) Parmela16 a multiparticle time-dependent beam dy-namics simulation code was used to track the particlesthrough the accelerator The version used in this workwas modified from an early 1980rsquos version of the LosAlamos developed code and has been specialized forthe linac development program at Varian The input

4019 Constantin et al Varian TrueBeam Linac 4019

Medical Physics Vol 38 No 7 July 2011

parameters to Parmela include the number and thetypes of cavities cavity RF information electron beaminput specifications solenoidal magnetic field parame-ters and various global parameters The iterative proce-dure that was used to initially develop a design modelfor the guide consisted of a series of Parmela simula-tions adjusting one or more of the guide parametersparticularly the cavity field levels and electron sourceparameters at each step until the specified output beamcharacteristics were achieved The field profileemployed matches the nominal design as verified oneach guide via a beadpull measurement25 The sole-noid field profile matches the profile obtained fromHall probe measurements

(d) The actual solenoid field level is adjustable in practicevia the solenoid current For this simulation work itwas left at the nominal setting where fair agreement isobtained with spot size measurements taken with astacked multichannel plate assembly (ie ldquospotcamerardquo)

On exit from the RF structure model the beam is sub-jected to collimation on a 3 mm diameter followed by acoordinate map to the target26 This map represents theaction of the achromatic 270 stepped field bending magnetTransport through the bending magnet also affects collima-tion at 63 in energy representing the effect of the watercooled energy slit designed to provide a well-defined energyin all modes including electron modes

The beam output data after the bending magnet resultingfrom the Parmela run with the design model as input werein fair agreement with the measurements of beam energy (asinferred from experimental measurements of dose in a water

tank) electron beam spot size and target current obtainedwith an actual accelerator system

A plot of the Parmela phase space is shown in Fig 1 Thebeam energy measured in the central portion of the energyspectrum using calibration data for the bending magnetagreed within 4 with the calculated value obtained fromthe cumulative acceleration of the particles by the longitudi-nal components of the cavity electric fields The calculatedspot size diameter was about 2 mm and an exact comparisonwith the spot camera measurements was performed The Par-mela coordinate and momenta distributions in this work arein agreement with previous studies51112 However theenergy spectrum after the bending magnet indicates a non-Gaussian distribution with a large narrow peak at 613 MeVand a smaller peak at 63 MeV The presence of the twopeaks is analogous to the bimodal structure obtained byAubin et al21 although unlike their results the high energypeak in the present work is much smaller in amplitude thanthe peak at the lower energy As explained by Aubin21 thebimodal structure of the energy spectrum results from twostable (but separate) phase regions in the RF bucket for thecaptured electrons This distribution is very different fromthe Gaussian model assumed in other studies11ndash1519

IIB Components implemented from CAD

The electronic engineering drawings of the treatmenthead were provided by Varian Medical Systems The treat-ment head components exported from CAD (Ref 6) were thetarget block holder the two vacuum windows (at the exitfrom the bending magnet and at the entrance into the targetholder) the protective window of the target the target thex-ray window the primary collimator the flattening filter

FIG 1 (a) Part of the TrueBeam treatment head showing the shielding collimator the cylindrical phase space surface the upper jaws and the lower jaw blockThe middle trapezoid tangent to the jaws is the x-ray field for a 40 40 cm2 open field (at isocenter) The tessellated representation of the movable upper jawsis displayed Labels one and two point to the bar canal and the mounting holes of the jaws (b) Phase space of the input Parmela electrons (using 71 712 pri-mary electrons) The plots of the y coordinate and y direction cosine are not displayed due to their similarity with the x correspondent

4020 Constantin et al Varian TrueBeam Linac 4020

Medical Physics Vol 38 No 7 July 2011

friction ring the relevant components of the ion chamber6

the backscatter filter the shielding collimator the upper andlower jaws the base plate and the clipped corners Theseclipped corners intersect only the 40 40 cm2 field and areconnected to the base plate Note that the flattening filteritself was modeled in GEANT4 using a polycone due to techni-cal difficulties encountered during the standard for theexchange of product (STEP) to GDML conversion6 Part of thetreatment head geometry is displayed in Fig 1(a) Noticethat there is very little space between the shielding collima-tor and the divergent arc of the jaws Only a cylindrical ge-ometry of the phase space ensures no collisions between thestored phase space the shielding collimator and the upperjaws even for the largest field The geometrical complexityof the CAD imported treatment head components used in thisstudy is apparent Note that while TrueBeam can be operatedin a flattening filter free (FFF) mode in this work the valida-tion of the CAD import into GEANT4 is performed only for theconventional 6 MV flattened beam

IIC Computing facilities and numerical procedures

A load sharing facility (LSF) batch cluster has been usedfor the Monte Carlo simulation of the phase space and dosecalculations GEANT4 version v492p01 was used Thousandtwo hundred batches were launched independently on the LSFcluster Our GEANT4 Monte Carlo application was divided intwo parts (1) We first simulated the transport of the particlesstarting with the Parmela phase space and ending with theshielding collimator We developed a phase space writerwhich stores the phase space information on a cylindrical sur-face as shown in Fig 1(a) (2) Then starting with this patient-independent phase space file the particles were transportedthrough the rest of the treatment head components and thedose deposited in the water phantom was recorded For part(1) the Parmela input was recycled 80 times (ie a combined69 109 primary histories) For part (2) we imposed a recy-cling factor R between 4 and 20 The voxel size used for thesecalculations was 4 4 4 mm3 in order to have a dose reso-lution similar to that corresponding to the experimental ionchamber measurements In the dose buildup region the voxelvolume was 4 4 2 mm3 The CPU time for each of thebatch jobs was 111 h for part 1 and 28 h for part 2 Theobtained IAEA-compliant phase space files contain the parti-cle index (0 for photon 1 for electron 2 for positron and 3for neutron) the x y and z coordinates the direction cosinespx and py the sign of pz and the particle energy The GEANT4physics list was based on the standard electromagnetic proc-esses We used the newest GEANT4 multiple scattering modelG4UrbanMscModel2 which gives the best results for electronscatter in external beam radiotherapy18 A value of 01 mm18

was chosen for the particle range cutoff parameter hence theenergy threshold in water was 111 keV (for photons) 8466keV (for electrons) and 8353 keV (for positrons)

IID Experimental data acquisition and uncertainties

All measurements were made in water with a compactchamber CC04 (IBA Dosimetry) except for the depth doses

in the first 7 mm from the surface where a photon diode(IBA Dosimetry) was used for the 4 4 cm2 field and a par-allel ion chamber (MSKCC design) was used for largerfields Polarity effects ion recombination effects and X-Yjaw profile dependence were observed during the truebeamcommissioning procedure for the CC04 ion chamber No sig-nificant in-field variation is observed however the periph-eral dose is influenced by all three of these effects Usingone polarity the peripheral dose was over-measured by03 of the CAX dose for the 30 30 cm2 field Asexpected this error decreased with field size Due to ionrecombination the doses in peripheral dose regions normal-ized to the CAX was over-measured by up to 03 Periph-eral doses normalized to the CAX are 1 greater under theY-jaws in these data than under the X-jaws Also uncor-rected polarity and recombination effects increased themeasured depth dose up to 03 each at large depthsFinally mechanical accuracy was determined to be less than1 mm over 30 cm in all three scanning dimensions

IIE Conversion to dose and data comparison

We converted the simulations results to dose (cGy=MU)to allow a direct comparison with ionization chamber meas-urements We divided the deposited dose to the total numberof primary particles used in the simulation for a particularfield size The obtained dose distributions DMC for all openfields were scaled with the dimensionless area under the curvecorresponding to the 10 10 cm2 field Aexpt

frac12525$cm=AMCfrac12525$cm C

where A MC and Aexpt represent the calculated and experimentalvalues for a depth between 5 and 25 cm We have also cor-rected the measured dose values for the effective point of mea-surement for different field sizes The experimental outputfactor OFexpt was measured at dmax frac14 14 cm The compari-son between experimental measurements and calculationswas performed by analyzing the dose difference

frac12DexptethzTHORN OFexpt ) DMCethzTHORN C$=frac12DMCdmax C$ for depth

dose curves and frac12Dexpt OFexpt ) DMC C$=frac12DMCdcenter C$

for dose profiles

III RESULTS

Monte Carlo simulations were performed for differentfield sizes including small (4 4 cm2) medium (10 10and 20 20 cm2) and large (30 30 and 40 40 cm2)fields For clarity reasons in Figs 2 and 3 only the dose dis-tributions corresponding to the 4 4 10 10 and 40 40cm2 open fields are displayed All calculations used a sourceto surface distance of 100 cm For the dose profiles both thein-plane and cross-plane directions were considered No dif-ference was observed between these two directions for thein-field dose profiles while the out-of-field dose displayedsmall differences no larger than 1 The profile depthswere 25 5 10 20 and 30 cm

The depth dose results are shown in Fig 2 The curvesrepresent the experimental measurements while the pointscorrespond to the Monte Carlo calculations Note that 98of the calculated data points agree within 2 with the

4021 Constantin et al Varian TrueBeam Linac 4021

Medical Physics Vol 38 No 7 July 2011

experimental measurements for depths between 2 and 40cm For depths between 5 and 30 cm agreement within 1with experiment is obtained for 99 (for 4 4 cm2 field)95 (for 10 10 cm2 field) 94 (for 20 20 and 30 30cm2 fields) and 89 (for 40 40 cm2 field) of the MonteCarlo data points respectively For the surface buildupregion Monte Carlo calculations were performed using a

2 mm wide voxel up to 20 mm depth and the results werecompared against both the CC04 and the plane parallel ionchamber experimental data The agreement in the buildupregion is within 2 for the dose difference between themeasurements using the ion chamber and Monte Carlo datasets Only the point corresponding to the first voxel at 1 mmdepth from the surface is characterized by a 5 deviationNote however that the experimental accuracy in the surfacebuildup region is estimated to be within 5

The dose profiles are shown in Fig 3 at 25 cm depthThe continuous curves represent the experimental measure-ments For the dose profiles at 25 and 10 cm depths themaximum dose difference is within 2 for the in-fieldregions and within 1 for the out-of-field values for fieldsizes up to 30 30 cm2 The 30 30 cm2 open field showsdose differences in the horn region up to 3 At even largerdepth (ie 20 cm) the in-field maximum dose difference forthe 30 30 cm2 open field is within 4 while the smallerfield sizes preserve the same level of agreement (ie within2) At both small and large depths a few exceptions appearfor the interpolated points corresponding to the field edgesand penumbra regions where the interpolation was per-formed using a simple linear function For the 40 40 cm2

field the maximum dose difference between the experimentand Monte Carlo deviates from the 2 accuracy goal espe-cially in the horn region for the dose measurements corre-sponding to the smaller depths (25 and 50 cm) The largestdeviations are equal to 55 This could be due to the statis-tical imprecision associated with the x and y coordinates ofthe Parmela simulated electron phase space which can be aslarge as 10 As explained in Sec IV these errors can sig-nificantly affect the radial spread of the electron beam andhave a direct impact on the magnitude of the horns511ndash13 Over-all the off-axis ratio calculated with GEANT4 at large fieldsare low by 3 for the 30 30 cm2 open field and by 5for the largest field of 40 40 cm2 with an uncertaintyof lt 15 This is consistent with the results by Faddegonet al27

The experimental output factors measured at the maxi-mum dose depth dmax frac14 14 cm together with the MonteCarlo output factors OFc and their standard errors are shownin Table I for field sizes varying from 4 4 to 40 40 cm2The agreement between the experimental and calculated val-ues is well within 1

The statistical uncertainty of our dose calculations wasestimated using the recommendations from TG-1052 Forreporting the statistical uncertainty over a certain volume

FIG 2 (a) Experimental (lines) and GEANT4 (points) calculated depth dosecurves The Monte Carlo dose was averaged over 3 3 voxels with a totalarea of (12 cm)2 (b) The maximum dose differences between the experi-ment and GEANT4 calculations (c) The buildup region for the 10 10 cm2

field Both the CC04 and the parallel chamber measurements are displayedThe dose difference between the parallel chamber results and the calculationis shown in (d)

FIG 3 Experimental (lines) and GEANT4 (points) calculated dose profiles for25 cm depth The Monte Carlo dose was averaged over three voxels with atotal length of 12 cm The dose differences (ie experimentmdashMonte Carlo)are shown in the bottom panel

TABLE I Experimental and calculated output factors at dmaxfrac14 14 cm as afunction of field size

Field(cm2) OFexpt OFc (OFexpt-OFc)=OFc

4 4 0934 0938 6 0015 )0004

10 10 10 100 00

20 20 1050 1043 6 0016 0007

30 30 1076 1067 6 0017 0008

40 40 1085 1088 6 0024 -0003

4022 Constantin et al Varian TrueBeam Linac 4022

Medical Physics Vol 38 No 7 July 2011

the voxels receiving a dose larger than 50 of the maximumdose Dmax were considered and the fractional uncertainty inthe average dose for these particular voxels FDgt05Dmax

wascalculated The values we obtained for FDgt05Dmax

using avoxel volume of 04 04 04 cm3 as a function of thefield size are 192 (4 4 cm2) 123 (10 10 cm2)144 (20 20 cm2) 199 (30 30 cm2) and 288(40 40 cm2) However rebinning the data using largervoxels (ie 12 12 04 cm3 for the PDDs) reduces thefractional uncertainties to 050 (4 4 cm2) 061(10 10 cm2) 060 (20 20 cm2) 050 (30 30 cm2)and 122 (40 40 cm2)

The cumulative number of histories used in this study var-ied between 27 1010 and 13 1011 based on the valuesof the recycling factor R which varied between 4 and 20Since the same input phase space file was reused a largenumber of times which could in principle introduce latentvariance effects2829 we have calculated the average dosevariance for the 10 10 cm2 open field and looked at its de-pendence on R The variance was calculated by summing thecontributions of all the voxels in 5 5 cm2 central region ofthe phantom We have verified that as R increases the var-iance of the average dose decreases A saturation at large Rwould be an indication of latent variance effects notobserved in our study Instead a linear dependence of the av-erage dose variance on the inverse of the recycling factor isobtained indicating that the current calculations do not suf-fer from latent variance effects

IV DISCUSSIONS AND CONCLUSIONS

In this study we validated the 6 MV beam Monte Carlodose simulations using high precision geometry implementa-tion from CAD and input electron beam parameters fixed bythe Parmela phase space The adjustable Parmela parameterswere fixed based on their experimental correspondents set inpractice by the operation of the linac We have generatedphase space files scoring to a cylindrical geometry such thatwe can record particle characteristics upstream of the mova-ble jaws The phase space files are available on the IAEAphase space database30

The agreement with experiment mostly within 2 iswithin the dose accuracy goals set by the Report of TaskGroup 65 (Ref 31) ldquothe accuracy of computed dose distri-butions should be between 1 and 2rdquo The calculated andexperimental output factors agree well within 1

While previous Monte Carlo studies have obtained agree-ment within 111122132 it is important to note the differen-ces in the input phase space and the geometryimplementation used as well as in the data analysis involv-ing dose normalization using field dependent quanti-ties122132 (instead of a unique field independent scaling11)multiple iterations to determine the optimal electron spec-trum as well as smoothing techniques21

There are four possible factors affecting the level ofagreement obtained in this study the approximations used inthe Parmela simulations the uncertainties in componentpositioning and material composition the physics used in

GEANT4 and the uncertainties in experimental dataacquisition

The uncertainty in Parmela simulations are estimated tobe within 4 for the energy distribution and up to 10 forthe transverse coordinates Let us assume that the peak ofthe Parmela energy spectrum shifts by 4 As shown byTzedakis12 a 4 decrease in the mean energy value of theGaussian energy distribution from 64 to 61 MeV leads tohigher ldquohornsrdquo and produces a dose difference as large as2 The impact of the more predominant error in the trans-verse coordinates can be estimated as well Since theFWHM of the spatial coordinate distributions is 14 mm forboth x and y a 10 residual error means that FWHM canfluctuate by 6014 mm A decrease in the FWHM value ofthe spatial coordinate distribution from 11 to 09 mm leadsto higher horns12 and a dose difference as large as 1 Eitherone of these scenarios may bring our simulations into closeragreement with experiment

The possible residual errors in GEANT4 are due to thephysics list and=or the choice for the range cutoff A rangecutoff reduction from 1 to 001 mm produces less than a 2effect on the calculated relative dose distributions in the highdose region as shown by Faddegon et al18 This effect is notnegligible and it would be useful to have more detailed stud-ies to decide the optimal range cut for a particular energyHowever this study was performed for a different physicslist with an older version of GEANT4 and we stress the needfor additional studies for the current version of the toolkit

Moreover the component positioning can significantlychange the dose distributions4 and in addition material com-positions from manufacturers are not known exactly Forexample the primary collimator the jaws and the multileafcollimator are made of a tungsten alloy which contains 95W and the remaining 5 containing a metallic binder madeof Ni Fe and Cu For our simulations the following combi-nation was selected 28 Ni 12 Fe and 1 Cu whichwas one of the three options provided by the manufacturerIt is important to point out that the ratios of these elementscan vary and will slightly affect the radiation transport prop-erties It would be useful to know the impact of this type ofmaterial composition uncertainty on the output data

Future work will address the simulation of 6 MV FFF andhigher energy photon beams the implementation of variancereduction techniques along with a framework to run the sim-ulation on a cloud computing cluster

ACKNOWLEDGMENTS

This work was supported in part by Varian Medical Sys-temsThe authors would like to thank Dragos Constantin forhis contribution to the bash scripting procedure developedfor this study and the GEANT4 user support group at CERN inparticular Gabriele Cosmo The authors also acknowledgeuseful conversations with Magdalena Bazalova

a)Author to whom correspondence should be addressed Electronicmailmagdalenaconstantinvariancom

1D W O Rogers ldquoFifty years of Monte Carlo simulations for medicalphysicsrdquo Phys Med Biol 51 R287ndashR301 (2006)

4023 Constantin et al Varian TrueBeam Linac 4023

Medical Physics Vol 38 No 7 July 2011

I INTRODUCTION

An important goal of Monte Carlo dose calculations in medi-cal physics is to provide accurate results for the entire radia-tion therapy process1 While improving the efficiency ofMonte Carlo dose calculations has been recently dis-cussed12 exploring new ways of improving the accuracy ofgeometry representation needs to be further addressed as itrepresents a crucial aspect of any accurate beam transportdose calculation Previous Monte Carlo dose calculationshave shown that inaccurate geometrical representation of thein-field treatment head components such as the primary col-limator the shielding collimator and the ionization cham-ber introduces large errors that propagate throughout thesimulation3 Electron-beam Monte Carlo calculations4 haveaddressed the dose sensitivity to the geometry and positionof scattering foils High energy electron beams at large fieldsizes have been shown4 to be highly sensitive to the geome-trical configuration of the treatment head and changes assmall as 2 mm in component positioning have a significantimpact on the calculated dose profiles The specifications ofthe primary collimator such as the upstream opening have anoticeable effect on the calculated off-axis ratios5 Geometri-cal errors can be minimized through a computer-assistedprocedure that automates the setup of the geometry avoidingmanual data entry Transferring the detailed treatment headgeometry from CAD (computer aided design) drawings toGEANT4 is more accurate and less error prone than interpret-ing the engineering drawings The simplicity of this processmakes it easier to keep the information updated as smallmodifications are made to the design Linking CAD toGEANT4-based Monte Carlo simulations has recently beendescribed in Ref 6 It provides the GDML (generalizeddynamic markup language)7 representations of the headcomponents used as input into GEANT478 a feature not cur-rently supported by other codes such as EGS4 (Ref 9) orBEAM (Ref 10)

Several groups have performed Monte Carlo studies ofradiotherapy beams starting with certain assumptions aboutthe initial electron beam parameters511ndash15 and iterativelyadjusting those parameters to obtain a good match with theexperiment for a specific machine In this work instead ofvarying these parameters we have specified as input to theMonte Carlo model the particle phase space derived by theParmela16 simulation of the waveguide Parmela phase spaceinputs have been used in other studies17ndash21 This approachprovides a realistic approximation for the particle parametersand potentially avoids the need of iterations In our studythe electron energy spectrum along with the target focal spotsize were independently determined through experimentalinvestigations It is estimated that the uncertainty of the Par-mela energy distribution is 4 for the mean energy whilethe beam spot size at the target location has uncertainties upto 10

The goal of the present project was to develop a MonteCarlo application for the complex treatment head geometryimported from CAD for the Varian TrueBeam linac operatedat 6 MV and to quantify the agreement with experimental

dose measurements without tuning the parameters of theinput Parmela electron phase space The output of our simu-lations is an International Atomic Energy Agency (IAEA)-compliant phase space file which is generic not tuned for spe-cific machine parameters yet gives dose results in good agree-ment with experimental measurements We also demonstratethe necessity to score the phase space on a cylindrical surfacerather than conventional flat geometry due to the compacttreatment head geometry

II METHODS AND MATERIALS

IIA Linac simulation

The TrueBeam medical accelerator employs a biperiodicstanding wave accelerator incorporating an ldquoenergyswitchrdquo and a 270 bending magnet The system is capableof achieving a sharp spectrum at energies ranging from 4 to20 MeV for treatment and down to 2 MeV for imaging22

The linac consists of a linear array of microwave cavitiesin which RF fields at frequencies corresponding to thecavity resonance frequencies are maintained with theappropriate magnitude and phasing so as to accelerate alarge fraction of the particles in their passage through thelinac guide

The simulation of the waveguide included the followingfour parts (a) a simulation of an electron beam source forthe guide to provide an input beam injected at a specifiedcurrent and energy (b) a means of generating the cavity RFfields (c) a method for computing the trajectories of the vari-ous beam particles as they experience the accelerating Lor-entz forces from their interaction with the various cavity andspace charge fields and (d) a provision for superimposing afocusing solenoidal magnetic field along the length of theguide

(a) To model the input beam from the truebeam triode gunin Parmela a macroparticle simulation was createdbased on measurements made using an electron beamanalyzer The device was used to examine the variationin the outer radius (envelope) of the beam generated ina field-free drift region as a function of the distancedownstream from the gun From this data the Twissparameters of the emittance ellipses23 at the accelera-tor entrance could be inferred and the phase space dis-tribution of the input beam determined The injectedbeam is monoenergetic corresponding to the gun highvoltage setting appropriate for the mode studied Thegun current was a nominal value measured with a to-roidal current monitor

(b) The Superfish code24 a 2D RF finite difference cavityfield solver was used to generate the cavity fieldpatterns

(c) Parmela16 a multiparticle time-dependent beam dy-namics simulation code was used to track the particlesthrough the accelerator The version used in this workwas modified from an early 1980rsquos version of the LosAlamos developed code and has been specialized forthe linac development program at Varian The input

4019 Constantin et al Varian TrueBeam Linac 4019

Medical Physics Vol 38 No 7 July 2011

parameters to Parmela include the number and thetypes of cavities cavity RF information electron beaminput specifications solenoidal magnetic field parame-ters and various global parameters The iterative proce-dure that was used to initially develop a design modelfor the guide consisted of a series of Parmela simula-tions adjusting one or more of the guide parametersparticularly the cavity field levels and electron sourceparameters at each step until the specified output beamcharacteristics were achieved The field profileemployed matches the nominal design as verified oneach guide via a beadpull measurement25 The sole-noid field profile matches the profile obtained fromHall probe measurements

(d) The actual solenoid field level is adjustable in practicevia the solenoid current For this simulation work itwas left at the nominal setting where fair agreement isobtained with spot size measurements taken with astacked multichannel plate assembly (ie ldquospotcamerardquo)

On exit from the RF structure model the beam is sub-jected to collimation on a 3 mm diameter followed by acoordinate map to the target26 This map represents theaction of the achromatic 270 stepped field bending magnetTransport through the bending magnet also affects collima-tion at 63 in energy representing the effect of the watercooled energy slit designed to provide a well-defined energyin all modes including electron modes

The beam output data after the bending magnet resultingfrom the Parmela run with the design model as input werein fair agreement with the measurements of beam energy (asinferred from experimental measurements of dose in a water

tank) electron beam spot size and target current obtainedwith an actual accelerator system

A plot of the Parmela phase space is shown in Fig 1 Thebeam energy measured in the central portion of the energyspectrum using calibration data for the bending magnetagreed within 4 with the calculated value obtained fromthe cumulative acceleration of the particles by the longitudi-nal components of the cavity electric fields The calculatedspot size diameter was about 2 mm and an exact comparisonwith the spot camera measurements was performed The Par-mela coordinate and momenta distributions in this work arein agreement with previous studies51112 However theenergy spectrum after the bending magnet indicates a non-Gaussian distribution with a large narrow peak at 613 MeVand a smaller peak at 63 MeV The presence of the twopeaks is analogous to the bimodal structure obtained byAubin et al21 although unlike their results the high energypeak in the present work is much smaller in amplitude thanthe peak at the lower energy As explained by Aubin21 thebimodal structure of the energy spectrum results from twostable (but separate) phase regions in the RF bucket for thecaptured electrons This distribution is very different fromthe Gaussian model assumed in other studies11ndash1519

IIB Components implemented from CAD

The electronic engineering drawings of the treatmenthead were provided by Varian Medical Systems The treat-ment head components exported from CAD (Ref 6) were thetarget block holder the two vacuum windows (at the exitfrom the bending magnet and at the entrance into the targetholder) the protective window of the target the target thex-ray window the primary collimator the flattening filter

FIG 1 (a) Part of the TrueBeam treatment head showing the shielding collimator the cylindrical phase space surface the upper jaws and the lower jaw blockThe middle trapezoid tangent to the jaws is the x-ray field for a 40 40 cm2 open field (at isocenter) The tessellated representation of the movable upper jawsis displayed Labels one and two point to the bar canal and the mounting holes of the jaws (b) Phase space of the input Parmela electrons (using 71 712 pri-mary electrons) The plots of the y coordinate and y direction cosine are not displayed due to their similarity with the x correspondent

4020 Constantin et al Varian TrueBeam Linac 4020

Medical Physics Vol 38 No 7 July 2011

friction ring the relevant components of the ion chamber6

the backscatter filter the shielding collimator the upper andlower jaws the base plate and the clipped corners Theseclipped corners intersect only the 40 40 cm2 field and areconnected to the base plate Note that the flattening filteritself was modeled in GEANT4 using a polycone due to techni-cal difficulties encountered during the standard for theexchange of product (STEP) to GDML conversion6 Part of thetreatment head geometry is displayed in Fig 1(a) Noticethat there is very little space between the shielding collima-tor and the divergent arc of the jaws Only a cylindrical ge-ometry of the phase space ensures no collisions between thestored phase space the shielding collimator and the upperjaws even for the largest field The geometrical complexityof the CAD imported treatment head components used in thisstudy is apparent Note that while TrueBeam can be operatedin a flattening filter free (FFF) mode in this work the valida-tion of the CAD import into GEANT4 is performed only for theconventional 6 MV flattened beam

IIC Computing facilities and numerical procedures

A load sharing facility (LSF) batch cluster has been usedfor the Monte Carlo simulation of the phase space and dosecalculations GEANT4 version v492p01 was used Thousandtwo hundred batches were launched independently on the LSFcluster Our GEANT4 Monte Carlo application was divided intwo parts (1) We first simulated the transport of the particlesstarting with the Parmela phase space and ending with theshielding collimator We developed a phase space writerwhich stores the phase space information on a cylindrical sur-face as shown in Fig 1(a) (2) Then starting with this patient-independent phase space file the particles were transportedthrough the rest of the treatment head components and thedose deposited in the water phantom was recorded For part(1) the Parmela input was recycled 80 times (ie a combined69 109 primary histories) For part (2) we imposed a recy-cling factor R between 4 and 20 The voxel size used for thesecalculations was 4 4 4 mm3 in order to have a dose reso-lution similar to that corresponding to the experimental ionchamber measurements In the dose buildup region the voxelvolume was 4 4 2 mm3 The CPU time for each of thebatch jobs was 111 h for part 1 and 28 h for part 2 Theobtained IAEA-compliant phase space files contain the parti-cle index (0 for photon 1 for electron 2 for positron and 3for neutron) the x y and z coordinates the direction cosinespx and py the sign of pz and the particle energy The GEANT4physics list was based on the standard electromagnetic proc-esses We used the newest GEANT4 multiple scattering modelG4UrbanMscModel2 which gives the best results for electronscatter in external beam radiotherapy18 A value of 01 mm18

was chosen for the particle range cutoff parameter hence theenergy threshold in water was 111 keV (for photons) 8466keV (for electrons) and 8353 keV (for positrons)

IID Experimental data acquisition and uncertainties

All measurements were made in water with a compactchamber CC04 (IBA Dosimetry) except for the depth doses

in the first 7 mm from the surface where a photon diode(IBA Dosimetry) was used for the 4 4 cm2 field and a par-allel ion chamber (MSKCC design) was used for largerfields Polarity effects ion recombination effects and X-Yjaw profile dependence were observed during the truebeamcommissioning procedure for the CC04 ion chamber No sig-nificant in-field variation is observed however the periph-eral dose is influenced by all three of these effects Usingone polarity the peripheral dose was over-measured by03 of the CAX dose for the 30 30 cm2 field Asexpected this error decreased with field size Due to ionrecombination the doses in peripheral dose regions normal-ized to the CAX was over-measured by up to 03 Periph-eral doses normalized to the CAX are 1 greater under theY-jaws in these data than under the X-jaws Also uncor-rected polarity and recombination effects increased themeasured depth dose up to 03 each at large depthsFinally mechanical accuracy was determined to be less than1 mm over 30 cm in all three scanning dimensions

IIE Conversion to dose and data comparison

We converted the simulations results to dose (cGy=MU)to allow a direct comparison with ionization chamber meas-urements We divided the deposited dose to the total numberof primary particles used in the simulation for a particularfield size The obtained dose distributions DMC for all openfields were scaled with the dimensionless area under the curvecorresponding to the 10 10 cm2 field Aexpt

frac12525$cm=AMCfrac12525$cm C

where A MC and Aexpt represent the calculated and experimentalvalues for a depth between 5 and 25 cm We have also cor-rected the measured dose values for the effective point of mea-surement for different field sizes The experimental outputfactor OFexpt was measured at dmax frac14 14 cm The compari-son between experimental measurements and calculationswas performed by analyzing the dose difference

frac12DexptethzTHORN OFexpt ) DMCethzTHORN C$=frac12DMCdmax C$ for depth

dose curves and frac12Dexpt OFexpt ) DMC C$=frac12DMCdcenter C$

for dose profiles

III RESULTS

Monte Carlo simulations were performed for differentfield sizes including small (4 4 cm2) medium (10 10and 20 20 cm2) and large (30 30 and 40 40 cm2)fields For clarity reasons in Figs 2 and 3 only the dose dis-tributions corresponding to the 4 4 10 10 and 40 40cm2 open fields are displayed All calculations used a sourceto surface distance of 100 cm For the dose profiles both thein-plane and cross-plane directions were considered No dif-ference was observed between these two directions for thein-field dose profiles while the out-of-field dose displayedsmall differences no larger than 1 The profile depthswere 25 5 10 20 and 30 cm

The depth dose results are shown in Fig 2 The curvesrepresent the experimental measurements while the pointscorrespond to the Monte Carlo calculations Note that 98of the calculated data points agree within 2 with the

4021 Constantin et al Varian TrueBeam Linac 4021

Medical Physics Vol 38 No 7 July 2011

experimental measurements for depths between 2 and 40cm For depths between 5 and 30 cm agreement within 1with experiment is obtained for 99 (for 4 4 cm2 field)95 (for 10 10 cm2 field) 94 (for 20 20 and 30 30cm2 fields) and 89 (for 40 40 cm2 field) of the MonteCarlo data points respectively For the surface buildupregion Monte Carlo calculations were performed using a

2 mm wide voxel up to 20 mm depth and the results werecompared against both the CC04 and the plane parallel ionchamber experimental data The agreement in the buildupregion is within 2 for the dose difference between themeasurements using the ion chamber and Monte Carlo datasets Only the point corresponding to the first voxel at 1 mmdepth from the surface is characterized by a 5 deviationNote however that the experimental accuracy in the surfacebuildup region is estimated to be within 5

The dose profiles are shown in Fig 3 at 25 cm depthThe continuous curves represent the experimental measure-ments For the dose profiles at 25 and 10 cm depths themaximum dose difference is within 2 for the in-fieldregions and within 1 for the out-of-field values for fieldsizes up to 30 30 cm2 The 30 30 cm2 open field showsdose differences in the horn region up to 3 At even largerdepth (ie 20 cm) the in-field maximum dose difference forthe 30 30 cm2 open field is within 4 while the smallerfield sizes preserve the same level of agreement (ie within2) At both small and large depths a few exceptions appearfor the interpolated points corresponding to the field edgesand penumbra regions where the interpolation was per-formed using a simple linear function For the 40 40 cm2

field the maximum dose difference between the experimentand Monte Carlo deviates from the 2 accuracy goal espe-cially in the horn region for the dose measurements corre-sponding to the smaller depths (25 and 50 cm) The largestdeviations are equal to 55 This could be due to the statis-tical imprecision associated with the x and y coordinates ofthe Parmela simulated electron phase space which can be aslarge as 10 As explained in Sec IV these errors can sig-nificantly affect the radial spread of the electron beam andhave a direct impact on the magnitude of the horns511ndash13 Over-all the off-axis ratio calculated with GEANT4 at large fieldsare low by 3 for the 30 30 cm2 open field and by 5for the largest field of 40 40 cm2 with an uncertaintyof lt 15 This is consistent with the results by Faddegonet al27

The experimental output factors measured at the maxi-mum dose depth dmax frac14 14 cm together with the MonteCarlo output factors OFc and their standard errors are shownin Table I for field sizes varying from 4 4 to 40 40 cm2The agreement between the experimental and calculated val-ues is well within 1

The statistical uncertainty of our dose calculations wasestimated using the recommendations from TG-1052 Forreporting the statistical uncertainty over a certain volume

FIG 2 (a) Experimental (lines) and GEANT4 (points) calculated depth dosecurves The Monte Carlo dose was averaged over 3 3 voxels with a totalarea of (12 cm)2 (b) The maximum dose differences between the experi-ment and GEANT4 calculations (c) The buildup region for the 10 10 cm2

field Both the CC04 and the parallel chamber measurements are displayedThe dose difference between the parallel chamber results and the calculationis shown in (d)

FIG 3 Experimental (lines) and GEANT4 (points) calculated dose profiles for25 cm depth The Monte Carlo dose was averaged over three voxels with atotal length of 12 cm The dose differences (ie experimentmdashMonte Carlo)are shown in the bottom panel

TABLE I Experimental and calculated output factors at dmaxfrac14 14 cm as afunction of field size

Field(cm2) OFexpt OFc (OFexpt-OFc)=OFc

4 4 0934 0938 6 0015 )0004

10 10 10 100 00

20 20 1050 1043 6 0016 0007

30 30 1076 1067 6 0017 0008

40 40 1085 1088 6 0024 -0003

4022 Constantin et al Varian TrueBeam Linac 4022

Medical Physics Vol 38 No 7 July 2011

the voxels receiving a dose larger than 50 of the maximumdose Dmax were considered and the fractional uncertainty inthe average dose for these particular voxels FDgt05Dmax

wascalculated The values we obtained for FDgt05Dmax

using avoxel volume of 04 04 04 cm3 as a function of thefield size are 192 (4 4 cm2) 123 (10 10 cm2)144 (20 20 cm2) 199 (30 30 cm2) and 288(40 40 cm2) However rebinning the data using largervoxels (ie 12 12 04 cm3 for the PDDs) reduces thefractional uncertainties to 050 (4 4 cm2) 061(10 10 cm2) 060 (20 20 cm2) 050 (30 30 cm2)and 122 (40 40 cm2)

The cumulative number of histories used in this study var-ied between 27 1010 and 13 1011 based on the valuesof the recycling factor R which varied between 4 and 20Since the same input phase space file was reused a largenumber of times which could in principle introduce latentvariance effects2829 we have calculated the average dosevariance for the 10 10 cm2 open field and looked at its de-pendence on R The variance was calculated by summing thecontributions of all the voxels in 5 5 cm2 central region ofthe phantom We have verified that as R increases the var-iance of the average dose decreases A saturation at large Rwould be an indication of latent variance effects notobserved in our study Instead a linear dependence of the av-erage dose variance on the inverse of the recycling factor isobtained indicating that the current calculations do not suf-fer from latent variance effects

IV DISCUSSIONS AND CONCLUSIONS

In this study we validated the 6 MV beam Monte Carlodose simulations using high precision geometry implementa-tion from CAD and input electron beam parameters fixed bythe Parmela phase space The adjustable Parmela parameterswere fixed based on their experimental correspondents set inpractice by the operation of the linac We have generatedphase space files scoring to a cylindrical geometry such thatwe can record particle characteristics upstream of the mova-ble jaws The phase space files are available on the IAEAphase space database30

The agreement with experiment mostly within 2 iswithin the dose accuracy goals set by the Report of TaskGroup 65 (Ref 31) ldquothe accuracy of computed dose distri-butions should be between 1 and 2rdquo The calculated andexperimental output factors agree well within 1

While previous Monte Carlo studies have obtained agree-ment within 111122132 it is important to note the differen-ces in the input phase space and the geometryimplementation used as well as in the data analysis involv-ing dose normalization using field dependent quanti-ties122132 (instead of a unique field independent scaling11)multiple iterations to determine the optimal electron spec-trum as well as smoothing techniques21

There are four possible factors affecting the level ofagreement obtained in this study the approximations used inthe Parmela simulations the uncertainties in componentpositioning and material composition the physics used in

GEANT4 and the uncertainties in experimental dataacquisition

The uncertainty in Parmela simulations are estimated tobe within 4 for the energy distribution and up to 10 forthe transverse coordinates Let us assume that the peak ofthe Parmela energy spectrum shifts by 4 As shown byTzedakis12 a 4 decrease in the mean energy value of theGaussian energy distribution from 64 to 61 MeV leads tohigher ldquohornsrdquo and produces a dose difference as large as2 The impact of the more predominant error in the trans-verse coordinates can be estimated as well Since theFWHM of the spatial coordinate distributions is 14 mm forboth x and y a 10 residual error means that FWHM canfluctuate by 6014 mm A decrease in the FWHM value ofthe spatial coordinate distribution from 11 to 09 mm leadsto higher horns12 and a dose difference as large as 1 Eitherone of these scenarios may bring our simulations into closeragreement with experiment

The possible residual errors in GEANT4 are due to thephysics list and=or the choice for the range cutoff A rangecutoff reduction from 1 to 001 mm produces less than a 2effect on the calculated relative dose distributions in the highdose region as shown by Faddegon et al18 This effect is notnegligible and it would be useful to have more detailed stud-ies to decide the optimal range cut for a particular energyHowever this study was performed for a different physicslist with an older version of GEANT4 and we stress the needfor additional studies for the current version of the toolkit

Moreover the component positioning can significantlychange the dose distributions4 and in addition material com-positions from manufacturers are not known exactly Forexample the primary collimator the jaws and the multileafcollimator are made of a tungsten alloy which contains 95W and the remaining 5 containing a metallic binder madeof Ni Fe and Cu For our simulations the following combi-nation was selected 28 Ni 12 Fe and 1 Cu whichwas one of the three options provided by the manufacturerIt is important to point out that the ratios of these elementscan vary and will slightly affect the radiation transport prop-erties It would be useful to know the impact of this type ofmaterial composition uncertainty on the output data

Future work will address the simulation of 6 MV FFF andhigher energy photon beams the implementation of variancereduction techniques along with a framework to run the sim-ulation on a cloud computing cluster

ACKNOWLEDGMENTS

This work was supported in part by Varian Medical Sys-temsThe authors would like to thank Dragos Constantin forhis contribution to the bash scripting procedure developedfor this study and the GEANT4 user support group at CERN inparticular Gabriele Cosmo The authors also acknowledgeuseful conversations with Magdalena Bazalova

a)Author to whom correspondence should be addressed Electronicmailmagdalenaconstantinvariancom

1D W O Rogers ldquoFifty years of Monte Carlo simulations for medicalphysicsrdquo Phys Med Biol 51 R287ndashR301 (2006)

4023 Constantin et al Varian TrueBeam Linac 4023

Medical Physics Vol 38 No 7 July 2011

parameters to Parmela include the number and thetypes of cavities cavity RF information electron beaminput specifications solenoidal magnetic field parame-ters and various global parameters The iterative proce-dure that was used to initially develop a design modelfor the guide consisted of a series of Parmela simula-tions adjusting one or more of the guide parametersparticularly the cavity field levels and electron sourceparameters at each step until the specified output beamcharacteristics were achieved The field profileemployed matches the nominal design as verified oneach guide via a beadpull measurement25 The sole-noid field profile matches the profile obtained fromHall probe measurements

(d) The actual solenoid field level is adjustable in practicevia the solenoid current For this simulation work itwas left at the nominal setting where fair agreement isobtained with spot size measurements taken with astacked multichannel plate assembly (ie ldquospotcamerardquo)

On exit from the RF structure model the beam is sub-jected to collimation on a 3 mm diameter followed by acoordinate map to the target26 This map represents theaction of the achromatic 270 stepped field bending magnetTransport through the bending magnet also affects collima-tion at 63 in energy representing the effect of the watercooled energy slit designed to provide a well-defined energyin all modes including electron modes

The beam output data after the bending magnet resultingfrom the Parmela run with the design model as input werein fair agreement with the measurements of beam energy (asinferred from experimental measurements of dose in a water

tank) electron beam spot size and target current obtainedwith an actual accelerator system

A plot of the Parmela phase space is shown in Fig 1 Thebeam energy measured in the central portion of the energyspectrum using calibration data for the bending magnetagreed within 4 with the calculated value obtained fromthe cumulative acceleration of the particles by the longitudi-nal components of the cavity electric fields The calculatedspot size diameter was about 2 mm and an exact comparisonwith the spot camera measurements was performed The Par-mela coordinate and momenta distributions in this work arein agreement with previous studies51112 However theenergy spectrum after the bending magnet indicates a non-Gaussian distribution with a large narrow peak at 613 MeVand a smaller peak at 63 MeV The presence of the twopeaks is analogous to the bimodal structure obtained byAubin et al21 although unlike their results the high energypeak in the present work is much smaller in amplitude thanthe peak at the lower energy As explained by Aubin21 thebimodal structure of the energy spectrum results from twostable (but separate) phase regions in the RF bucket for thecaptured electrons This distribution is very different fromthe Gaussian model assumed in other studies11ndash1519

IIB Components implemented from CAD

The electronic engineering drawings of the treatmenthead were provided by Varian Medical Systems The treat-ment head components exported from CAD (Ref 6) were thetarget block holder the two vacuum windows (at the exitfrom the bending magnet and at the entrance into the targetholder) the protective window of the target the target thex-ray window the primary collimator the flattening filter

FIG 1 (a) Part of the TrueBeam treatment head showing the shielding collimator the cylindrical phase space surface the upper jaws and the lower jaw blockThe middle trapezoid tangent to the jaws is the x-ray field for a 40 40 cm2 open field (at isocenter) The tessellated representation of the movable upper jawsis displayed Labels one and two point to the bar canal and the mounting holes of the jaws (b) Phase space of the input Parmela electrons (using 71 712 pri-mary electrons) The plots of the y coordinate and y direction cosine are not displayed due to their similarity with the x correspondent

4020 Constantin et al Varian TrueBeam Linac 4020

Medical Physics Vol 38 No 7 July 2011

friction ring the relevant components of the ion chamber6

the backscatter filter the shielding collimator the upper andlower jaws the base plate and the clipped corners Theseclipped corners intersect only the 40 40 cm2 field and areconnected to the base plate Note that the flattening filteritself was modeled in GEANT4 using a polycone due to techni-cal difficulties encountered during the standard for theexchange of product (STEP) to GDML conversion6 Part of thetreatment head geometry is displayed in Fig 1(a) Noticethat there is very little space between the shielding collima-tor and the divergent arc of the jaws Only a cylindrical ge-ometry of the phase space ensures no collisions between thestored phase space the shielding collimator and the upperjaws even for the largest field The geometrical complexityof the CAD imported treatment head components used in thisstudy is apparent Note that while TrueBeam can be operatedin a flattening filter free (FFF) mode in this work the valida-tion of the CAD import into GEANT4 is performed only for theconventional 6 MV flattened beam

IIC Computing facilities and numerical procedures

A load sharing facility (LSF) batch cluster has been usedfor the Monte Carlo simulation of the phase space and dosecalculations GEANT4 version v492p01 was used Thousandtwo hundred batches were launched independently on the LSFcluster Our GEANT4 Monte Carlo application was divided intwo parts (1) We first simulated the transport of the particlesstarting with the Parmela phase space and ending with theshielding collimator We developed a phase space writerwhich stores the phase space information on a cylindrical sur-face as shown in Fig 1(a) (2) Then starting with this patient-independent phase space file the particles were transportedthrough the rest of the treatment head components and thedose deposited in the water phantom was recorded For part(1) the Parmela input was recycled 80 times (ie a combined69 109 primary histories) For part (2) we imposed a recy-cling factor R between 4 and 20 The voxel size used for thesecalculations was 4 4 4 mm3 in order to have a dose reso-lution similar to that corresponding to the experimental ionchamber measurements In the dose buildup region the voxelvolume was 4 4 2 mm3 The CPU time for each of thebatch jobs was 111 h for part 1 and 28 h for part 2 Theobtained IAEA-compliant phase space files contain the parti-cle index (0 for photon 1 for electron 2 for positron and 3for neutron) the x y and z coordinates the direction cosinespx and py the sign of pz and the particle energy The GEANT4physics list was based on the standard electromagnetic proc-esses We used the newest GEANT4 multiple scattering modelG4UrbanMscModel2 which gives the best results for electronscatter in external beam radiotherapy18 A value of 01 mm18

was chosen for the particle range cutoff parameter hence theenergy threshold in water was 111 keV (for photons) 8466keV (for electrons) and 8353 keV (for positrons)

IID Experimental data acquisition and uncertainties

All measurements were made in water with a compactchamber CC04 (IBA Dosimetry) except for the depth doses

in the first 7 mm from the surface where a photon diode(IBA Dosimetry) was used for the 4 4 cm2 field and a par-allel ion chamber (MSKCC design) was used for largerfields Polarity effects ion recombination effects and X-Yjaw profile dependence were observed during the truebeamcommissioning procedure for the CC04 ion chamber No sig-nificant in-field variation is observed however the periph-eral dose is influenced by all three of these effects Usingone polarity the peripheral dose was over-measured by03 of the CAX dose for the 30 30 cm2 field Asexpected this error decreased with field size Due to ionrecombination the doses in peripheral dose regions normal-ized to the CAX was over-measured by up to 03 Periph-eral doses normalized to the CAX are 1 greater under theY-jaws in these data than under the X-jaws Also uncor-rected polarity and recombination effects increased themeasured depth dose up to 03 each at large depthsFinally mechanical accuracy was determined to be less than1 mm over 30 cm in all three scanning dimensions

IIE Conversion to dose and data comparison

We converted the simulations results to dose (cGy=MU)to allow a direct comparison with ionization chamber meas-urements We divided the deposited dose to the total numberof primary particles used in the simulation for a particularfield size The obtained dose distributions DMC for all openfields were scaled with the dimensionless area under the curvecorresponding to the 10 10 cm2 field Aexpt

frac12525$cm=AMCfrac12525$cm C

where A MC and Aexpt represent the calculated and experimentalvalues for a depth between 5 and 25 cm We have also cor-rected the measured dose values for the effective point of mea-surement for different field sizes The experimental outputfactor OFexpt was measured at dmax frac14 14 cm The compari-son between experimental measurements and calculationswas performed by analyzing the dose difference

frac12DexptethzTHORN OFexpt ) DMCethzTHORN C$=frac12DMCdmax C$ for depth

dose curves and frac12Dexpt OFexpt ) DMC C$=frac12DMCdcenter C$

for dose profiles

III RESULTS

Monte Carlo simulations were performed for differentfield sizes including small (4 4 cm2) medium (10 10and 20 20 cm2) and large (30 30 and 40 40 cm2)fields For clarity reasons in Figs 2 and 3 only the dose dis-tributions corresponding to the 4 4 10 10 and 40 40cm2 open fields are displayed All calculations used a sourceto surface distance of 100 cm For the dose profiles both thein-plane and cross-plane directions were considered No dif-ference was observed between these two directions for thein-field dose profiles while the out-of-field dose displayedsmall differences no larger than 1 The profile depthswere 25 5 10 20 and 30 cm

The depth dose results are shown in Fig 2 The curvesrepresent the experimental measurements while the pointscorrespond to the Monte Carlo calculations Note that 98of the calculated data points agree within 2 with the

4021 Constantin et al Varian TrueBeam Linac 4021

Medical Physics Vol 38 No 7 July 2011

experimental measurements for depths between 2 and 40cm For depths between 5 and 30 cm agreement within 1with experiment is obtained for 99 (for 4 4 cm2 field)95 (for 10 10 cm2 field) 94 (for 20 20 and 30 30cm2 fields) and 89 (for 40 40 cm2 field) of the MonteCarlo data points respectively For the surface buildupregion Monte Carlo calculations were performed using a

2 mm wide voxel up to 20 mm depth and the results werecompared against both the CC04 and the plane parallel ionchamber experimental data The agreement in the buildupregion is within 2 for the dose difference between themeasurements using the ion chamber and Monte Carlo datasets Only the point corresponding to the first voxel at 1 mmdepth from the surface is characterized by a 5 deviationNote however that the experimental accuracy in the surfacebuildup region is estimated to be within 5

The dose profiles are shown in Fig 3 at 25 cm depthThe continuous curves represent the experimental measure-ments For the dose profiles at 25 and 10 cm depths themaximum dose difference is within 2 for the in-fieldregions and within 1 for the out-of-field values for fieldsizes up to 30 30 cm2 The 30 30 cm2 open field showsdose differences in the horn region up to 3 At even largerdepth (ie 20 cm) the in-field maximum dose difference forthe 30 30 cm2 open field is within 4 while the smallerfield sizes preserve the same level of agreement (ie within2) At both small and large depths a few exceptions appearfor the interpolated points corresponding to the field edgesand penumbra regions where the interpolation was per-formed using a simple linear function For the 40 40 cm2

field the maximum dose difference between the experimentand Monte Carlo deviates from the 2 accuracy goal espe-cially in the horn region for the dose measurements corre-sponding to the smaller depths (25 and 50 cm) The largestdeviations are equal to 55 This could be due to the statis-tical imprecision associated with the x and y coordinates ofthe Parmela simulated electron phase space which can be aslarge as 10 As explained in Sec IV these errors can sig-nificantly affect the radial spread of the electron beam andhave a direct impact on the magnitude of the horns511ndash13 Over-all the off-axis ratio calculated with GEANT4 at large fieldsare low by 3 for the 30 30 cm2 open field and by 5for the largest field of 40 40 cm2 with an uncertaintyof lt 15 This is consistent with the results by Faddegonet al27

The experimental output factors measured at the maxi-mum dose depth dmax frac14 14 cm together with the MonteCarlo output factors OFc and their standard errors are shownin Table I for field sizes varying from 4 4 to 40 40 cm2The agreement between the experimental and calculated val-ues is well within 1

The statistical uncertainty of our dose calculations wasestimated using the recommendations from TG-1052 Forreporting the statistical uncertainty over a certain volume

FIG 2 (a) Experimental (lines) and GEANT4 (points) calculated depth dosecurves The Monte Carlo dose was averaged over 3 3 voxels with a totalarea of (12 cm)2 (b) The maximum dose differences between the experi-ment and GEANT4 calculations (c) The buildup region for the 10 10 cm2

field Both the CC04 and the parallel chamber measurements are displayedThe dose difference between the parallel chamber results and the calculationis shown in (d)

FIG 3 Experimental (lines) and GEANT4 (points) calculated dose profiles for25 cm depth The Monte Carlo dose was averaged over three voxels with atotal length of 12 cm The dose differences (ie experimentmdashMonte Carlo)are shown in the bottom panel

TABLE I Experimental and calculated output factors at dmaxfrac14 14 cm as afunction of field size

Field(cm2) OFexpt OFc (OFexpt-OFc)=OFc

4 4 0934 0938 6 0015 )0004

10 10 10 100 00

20 20 1050 1043 6 0016 0007

30 30 1076 1067 6 0017 0008

40 40 1085 1088 6 0024 -0003

4022 Constantin et al Varian TrueBeam Linac 4022

Medical Physics Vol 38 No 7 July 2011

the voxels receiving a dose larger than 50 of the maximumdose Dmax were considered and the fractional uncertainty inthe average dose for these particular voxels FDgt05Dmax

wascalculated The values we obtained for FDgt05Dmax

using avoxel volume of 04 04 04 cm3 as a function of thefield size are 192 (4 4 cm2) 123 (10 10 cm2)144 (20 20 cm2) 199 (30 30 cm2) and 288(40 40 cm2) However rebinning the data using largervoxels (ie 12 12 04 cm3 for the PDDs) reduces thefractional uncertainties to 050 (4 4 cm2) 061(10 10 cm2) 060 (20 20 cm2) 050 (30 30 cm2)and 122 (40 40 cm2)

The cumulative number of histories used in this study var-ied between 27 1010 and 13 1011 based on the valuesof the recycling factor R which varied between 4 and 20Since the same input phase space file was reused a largenumber of times which could in principle introduce latentvariance effects2829 we have calculated the average dosevariance for the 10 10 cm2 open field and looked at its de-pendence on R The variance was calculated by summing thecontributions of all the voxels in 5 5 cm2 central region ofthe phantom We have verified that as R increases the var-iance of the average dose decreases A saturation at large Rwould be an indication of latent variance effects notobserved in our study Instead a linear dependence of the av-erage dose variance on the inverse of the recycling factor isobtained indicating that the current calculations do not suf-fer from latent variance effects

IV DISCUSSIONS AND CONCLUSIONS

In this study we validated the 6 MV beam Monte Carlodose simulations using high precision geometry implementa-tion from CAD and input electron beam parameters fixed bythe Parmela phase space The adjustable Parmela parameterswere fixed based on their experimental correspondents set inpractice by the operation of the linac We have generatedphase space files scoring to a cylindrical geometry such thatwe can record particle characteristics upstream of the mova-ble jaws The phase space files are available on the IAEAphase space database30

The agreement with experiment mostly within 2 iswithin the dose accuracy goals set by the Report of TaskGroup 65 (Ref 31) ldquothe accuracy of computed dose distri-butions should be between 1 and 2rdquo The calculated andexperimental output factors agree well within 1

While previous Monte Carlo studies have obtained agree-ment within 111122132 it is important to note the differen-ces in the input phase space and the geometryimplementation used as well as in the data analysis involv-ing dose normalization using field dependent quanti-ties122132 (instead of a unique field independent scaling11)multiple iterations to determine the optimal electron spec-trum as well as smoothing techniques21

There are four possible factors affecting the level ofagreement obtained in this study the approximations used inthe Parmela simulations the uncertainties in componentpositioning and material composition the physics used in

GEANT4 and the uncertainties in experimental dataacquisition

The uncertainty in Parmela simulations are estimated tobe within 4 for the energy distribution and up to 10 forthe transverse coordinates Let us assume that the peak ofthe Parmela energy spectrum shifts by 4 As shown byTzedakis12 a 4 decrease in the mean energy value of theGaussian energy distribution from 64 to 61 MeV leads tohigher ldquohornsrdquo and produces a dose difference as large as2 The impact of the more predominant error in the trans-verse coordinates can be estimated as well Since theFWHM of the spatial coordinate distributions is 14 mm forboth x and y a 10 residual error means that FWHM canfluctuate by 6014 mm A decrease in the FWHM value ofthe spatial coordinate distribution from 11 to 09 mm leadsto higher horns12 and a dose difference as large as 1 Eitherone of these scenarios may bring our simulations into closeragreement with experiment

The possible residual errors in GEANT4 are due to thephysics list and=or the choice for the range cutoff A rangecutoff reduction from 1 to 001 mm produces less than a 2effect on the calculated relative dose distributions in the highdose region as shown by Faddegon et al18 This effect is notnegligible and it would be useful to have more detailed stud-ies to decide the optimal range cut for a particular energyHowever this study was performed for a different physicslist with an older version of GEANT4 and we stress the needfor additional studies for the current version of the toolkit

Moreover the component positioning can significantlychange the dose distributions4 and in addition material com-positions from manufacturers are not known exactly Forexample the primary collimator the jaws and the multileafcollimator are made of a tungsten alloy which contains 95W and the remaining 5 containing a metallic binder madeof Ni Fe and Cu For our simulations the following combi-nation was selected 28 Ni 12 Fe and 1 Cu whichwas one of the three options provided by the manufacturerIt is important to point out that the ratios of these elementscan vary and will slightly affect the radiation transport prop-erties It would be useful to know the impact of this type ofmaterial composition uncertainty on the output data

Future work will address the simulation of 6 MV FFF andhigher energy photon beams the implementation of variancereduction techniques along with a framework to run the sim-ulation on a cloud computing cluster

ACKNOWLEDGMENTS

This work was supported in part by Varian Medical Sys-temsThe authors would like to thank Dragos Constantin forhis contribution to the bash scripting procedure developedfor this study and the GEANT4 user support group at CERN inparticular Gabriele Cosmo The authors also acknowledgeuseful conversations with Magdalena Bazalova

a)Author to whom correspondence should be addressed Electronicmailmagdalenaconstantinvariancom

1D W O Rogers ldquoFifty years of Monte Carlo simulations for medicalphysicsrdquo Phys Med Biol 51 R287ndashR301 (2006)

4023 Constantin et al Varian TrueBeam Linac 4023

Medical Physics Vol 38 No 7 July 2011

friction ring the relevant components of the ion chamber6

the backscatter filter the shielding collimator the upper andlower jaws the base plate and the clipped corners Theseclipped corners intersect only the 40 40 cm2 field and areconnected to the base plate Note that the flattening filteritself was modeled in GEANT4 using a polycone due to techni-cal difficulties encountered during the standard for theexchange of product (STEP) to GDML conversion6 Part of thetreatment head geometry is displayed in Fig 1(a) Noticethat there is very little space between the shielding collima-tor and the divergent arc of the jaws Only a cylindrical ge-ometry of the phase space ensures no collisions between thestored phase space the shielding collimator and the upperjaws even for the largest field The geometrical complexityof the CAD imported treatment head components used in thisstudy is apparent Note that while TrueBeam can be operatedin a flattening filter free (FFF) mode in this work the valida-tion of the CAD import into GEANT4 is performed only for theconventional 6 MV flattened beam

IIC Computing facilities and numerical procedures

A load sharing facility (LSF) batch cluster has been usedfor the Monte Carlo simulation of the phase space and dosecalculations GEANT4 version v492p01 was used Thousandtwo hundred batches were launched independently on the LSFcluster Our GEANT4 Monte Carlo application was divided intwo parts (1) We first simulated the transport of the particlesstarting with the Parmela phase space and ending with theshielding collimator We developed a phase space writerwhich stores the phase space information on a cylindrical sur-face as shown in Fig 1(a) (2) Then starting with this patient-independent phase space file the particles were transportedthrough the rest of the treatment head components and thedose deposited in the water phantom was recorded For part(1) the Parmela input was recycled 80 times (ie a combined69 109 primary histories) For part (2) we imposed a recy-cling factor R between 4 and 20 The voxel size used for thesecalculations was 4 4 4 mm3 in order to have a dose reso-lution similar to that corresponding to the experimental ionchamber measurements In the dose buildup region the voxelvolume was 4 4 2 mm3 The CPU time for each of thebatch jobs was 111 h for part 1 and 28 h for part 2 Theobtained IAEA-compliant phase space files contain the parti-cle index (0 for photon 1 for electron 2 for positron and 3for neutron) the x y and z coordinates the direction cosinespx and py the sign of pz and the particle energy The GEANT4physics list was based on the standard electromagnetic proc-esses We used the newest GEANT4 multiple scattering modelG4UrbanMscModel2 which gives the best results for electronscatter in external beam radiotherapy18 A value of 01 mm18

was chosen for the particle range cutoff parameter hence theenergy threshold in water was 111 keV (for photons) 8466keV (for electrons) and 8353 keV (for positrons)

IID Experimental data acquisition and uncertainties

All measurements were made in water with a compactchamber CC04 (IBA Dosimetry) except for the depth doses

in the first 7 mm from the surface where a photon diode(IBA Dosimetry) was used for the 4 4 cm2 field and a par-allel ion chamber (MSKCC design) was used for largerfields Polarity effects ion recombination effects and X-Yjaw profile dependence were observed during the truebeamcommissioning procedure for the CC04 ion chamber No sig-nificant in-field variation is observed however the periph-eral dose is influenced by all three of these effects Usingone polarity the peripheral dose was over-measured by03 of the CAX dose for the 30 30 cm2 field Asexpected this error decreased with field size Due to ionrecombination the doses in peripheral dose regions normal-ized to the CAX was over-measured by up to 03 Periph-eral doses normalized to the CAX are 1 greater under theY-jaws in these data than under the X-jaws Also uncor-rected polarity and recombination effects increased themeasured depth dose up to 03 each at large depthsFinally mechanical accuracy was determined to be less than1 mm over 30 cm in all three scanning dimensions

IIE Conversion to dose and data comparison

We converted the simulations results to dose (cGy=MU)to allow a direct comparison with ionization chamber meas-urements We divided the deposited dose to the total numberof primary particles used in the simulation for a particularfield size The obtained dose distributions DMC for all openfields were scaled with the dimensionless area under the curvecorresponding to the 10 10 cm2 field Aexpt

frac12525$cm=AMCfrac12525$cm C

where A MC and Aexpt represent the calculated and experimentalvalues for a depth between 5 and 25 cm We have also cor-rected the measured dose values for the effective point of mea-surement for different field sizes The experimental outputfactor OFexpt was measured at dmax frac14 14 cm The compari-son between experimental measurements and calculationswas performed by analyzing the dose difference

frac12DexptethzTHORN OFexpt ) DMCethzTHORN C$=frac12DMCdmax C$ for depth

dose curves and frac12Dexpt OFexpt ) DMC C$=frac12DMCdcenter C$

for dose profiles

III RESULTS

Monte Carlo simulations were performed for differentfield sizes including small (4 4 cm2) medium (10 10and 20 20 cm2) and large (30 30 and 40 40 cm2)fields For clarity reasons in Figs 2 and 3 only the dose dis-tributions corresponding to the 4 4 10 10 and 40 40cm2 open fields are displayed All calculations used a sourceto surface distance of 100 cm For the dose profiles both thein-plane and cross-plane directions were considered No dif-ference was observed between these two directions for thein-field dose profiles while the out-of-field dose displayedsmall differences no larger than 1 The profile depthswere 25 5 10 20 and 30 cm

The depth dose results are shown in Fig 2 The curvesrepresent the experimental measurements while the pointscorrespond to the Monte Carlo calculations Note that 98of the calculated data points agree within 2 with the

4021 Constantin et al Varian TrueBeam Linac 4021

Medical Physics Vol 38 No 7 July 2011

experimental measurements for depths between 2 and 40cm For depths between 5 and 30 cm agreement within 1with experiment is obtained for 99 (for 4 4 cm2 field)95 (for 10 10 cm2 field) 94 (for 20 20 and 30 30cm2 fields) and 89 (for 40 40 cm2 field) of the MonteCarlo data points respectively For the surface buildupregion Monte Carlo calculations were performed using a

2 mm wide voxel up to 20 mm depth and the results werecompared against both the CC04 and the plane parallel ionchamber experimental data The agreement in the buildupregion is within 2 for the dose difference between themeasurements using the ion chamber and Monte Carlo datasets Only the point corresponding to the first voxel at 1 mmdepth from the surface is characterized by a 5 deviationNote however that the experimental accuracy in the surfacebuildup region is estimated to be within 5

The dose profiles are shown in Fig 3 at 25 cm depthThe continuous curves represent the experimental measure-ments For the dose profiles at 25 and 10 cm depths themaximum dose difference is within 2 for the in-fieldregions and within 1 for the out-of-field values for fieldsizes up to 30 30 cm2 The 30 30 cm2 open field showsdose differences in the horn region up to 3 At even largerdepth (ie 20 cm) the in-field maximum dose difference forthe 30 30 cm2 open field is within 4 while the smallerfield sizes preserve the same level of agreement (ie within2) At both small and large depths a few exceptions appearfor the interpolated points corresponding to the field edgesand penumbra regions where the interpolation was per-formed using a simple linear function For the 40 40 cm2

field the maximum dose difference between the experimentand Monte Carlo deviates from the 2 accuracy goal espe-cially in the horn region for the dose measurements corre-sponding to the smaller depths (25 and 50 cm) The largestdeviations are equal to 55 This could be due to the statis-tical imprecision associated with the x and y coordinates ofthe Parmela simulated electron phase space which can be aslarge as 10 As explained in Sec IV these errors can sig-nificantly affect the radial spread of the electron beam andhave a direct impact on the magnitude of the horns511ndash13 Over-all the off-axis ratio calculated with GEANT4 at large fieldsare low by 3 for the 30 30 cm2 open field and by 5for the largest field of 40 40 cm2 with an uncertaintyof lt 15 This is consistent with the results by Faddegonet al27

The experimental output factors measured at the maxi-mum dose depth dmax frac14 14 cm together with the MonteCarlo output factors OFc and their standard errors are shownin Table I for field sizes varying from 4 4 to 40 40 cm2The agreement between the experimental and calculated val-ues is well within 1

The statistical uncertainty of our dose calculations wasestimated using the recommendations from TG-1052 Forreporting the statistical uncertainty over a certain volume

FIG 2 (a) Experimental (lines) and GEANT4 (points) calculated depth dosecurves The Monte Carlo dose was averaged over 3 3 voxels with a totalarea of (12 cm)2 (b) The maximum dose differences between the experi-ment and GEANT4 calculations (c) The buildup region for the 10 10 cm2

field Both the CC04 and the parallel chamber measurements are displayedThe dose difference between the parallel chamber results and the calculationis shown in (d)

FIG 3 Experimental (lines) and GEANT4 (points) calculated dose profiles for25 cm depth The Monte Carlo dose was averaged over three voxels with atotal length of 12 cm The dose differences (ie experimentmdashMonte Carlo)are shown in the bottom panel

TABLE I Experimental and calculated output factors at dmaxfrac14 14 cm as afunction of field size

Field(cm2) OFexpt OFc (OFexpt-OFc)=OFc

4 4 0934 0938 6 0015 )0004

10 10 10 100 00

20 20 1050 1043 6 0016 0007

30 30 1076 1067 6 0017 0008

40 40 1085 1088 6 0024 -0003

4022 Constantin et al Varian TrueBeam Linac 4022

Medical Physics Vol 38 No 7 July 2011

the voxels receiving a dose larger than 50 of the maximumdose Dmax were considered and the fractional uncertainty inthe average dose for these particular voxels FDgt05Dmax

wascalculated The values we obtained for FDgt05Dmax

using avoxel volume of 04 04 04 cm3 as a function of thefield size are 192 (4 4 cm2) 123 (10 10 cm2)144 (20 20 cm2) 199 (30 30 cm2) and 288(40 40 cm2) However rebinning the data using largervoxels (ie 12 12 04 cm3 for the PDDs) reduces thefractional uncertainties to 050 (4 4 cm2) 061(10 10 cm2) 060 (20 20 cm2) 050 (30 30 cm2)and 122 (40 40 cm2)

The cumulative number of histories used in this study var-ied between 27 1010 and 13 1011 based on the valuesof the recycling factor R which varied between 4 and 20Since the same input phase space file was reused a largenumber of times which could in principle introduce latentvariance effects2829 we have calculated the average dosevariance for the 10 10 cm2 open field and looked at its de-pendence on R The variance was calculated by summing thecontributions of all the voxels in 5 5 cm2 central region ofthe phantom We have verified that as R increases the var-iance of the average dose decreases A saturation at large Rwould be an indication of latent variance effects notobserved in our study Instead a linear dependence of the av-erage dose variance on the inverse of the recycling factor isobtained indicating that the current calculations do not suf-fer from latent variance effects

IV DISCUSSIONS AND CONCLUSIONS

In this study we validated the 6 MV beam Monte Carlodose simulations using high precision geometry implementa-tion from CAD and input electron beam parameters fixed bythe Parmela phase space The adjustable Parmela parameterswere fixed based on their experimental correspondents set inpractice by the operation of the linac We have generatedphase space files scoring to a cylindrical geometry such thatwe can record particle characteristics upstream of the mova-ble jaws The phase space files are available on the IAEAphase space database30

The agreement with experiment mostly within 2 iswithin the dose accuracy goals set by the Report of TaskGroup 65 (Ref 31) ldquothe accuracy of computed dose distri-butions should be between 1 and 2rdquo The calculated andexperimental output factors agree well within 1

While previous Monte Carlo studies have obtained agree-ment within 111122132 it is important to note the differen-ces in the input phase space and the geometryimplementation used as well as in the data analysis involv-ing dose normalization using field dependent quanti-ties122132 (instead of a unique field independent scaling11)multiple iterations to determine the optimal electron spec-trum as well as smoothing techniques21

There are four possible factors affecting the level ofagreement obtained in this study the approximations used inthe Parmela simulations the uncertainties in componentpositioning and material composition the physics used in

GEANT4 and the uncertainties in experimental dataacquisition

The uncertainty in Parmela simulations are estimated tobe within 4 for the energy distribution and up to 10 forthe transverse coordinates Let us assume that the peak ofthe Parmela energy spectrum shifts by 4 As shown byTzedakis12 a 4 decrease in the mean energy value of theGaussian energy distribution from 64 to 61 MeV leads tohigher ldquohornsrdquo and produces a dose difference as large as2 The impact of the more predominant error in the trans-verse coordinates can be estimated as well Since theFWHM of the spatial coordinate distributions is 14 mm forboth x and y a 10 residual error means that FWHM canfluctuate by 6014 mm A decrease in the FWHM value ofthe spatial coordinate distribution from 11 to 09 mm leadsto higher horns12 and a dose difference as large as 1 Eitherone of these scenarios may bring our simulations into closeragreement with experiment

The possible residual errors in GEANT4 are due to thephysics list and=or the choice for the range cutoff A rangecutoff reduction from 1 to 001 mm produces less than a 2effect on the calculated relative dose distributions in the highdose region as shown by Faddegon et al18 This effect is notnegligible and it would be useful to have more detailed stud-ies to decide the optimal range cut for a particular energyHowever this study was performed for a different physicslist with an older version of GEANT4 and we stress the needfor additional studies for the current version of the toolkit

Moreover the component positioning can significantlychange the dose distributions4 and in addition material com-positions from manufacturers are not known exactly Forexample the primary collimator the jaws and the multileafcollimator are made of a tungsten alloy which contains 95W and the remaining 5 containing a metallic binder madeof Ni Fe and Cu For our simulations the following combi-nation was selected 28 Ni 12 Fe and 1 Cu whichwas one of the three options provided by the manufacturerIt is important to point out that the ratios of these elementscan vary and will slightly affect the radiation transport prop-erties It would be useful to know the impact of this type ofmaterial composition uncertainty on the output data

Future work will address the simulation of 6 MV FFF andhigher energy photon beams the implementation of variancereduction techniques along with a framework to run the sim-ulation on a cloud computing cluster

ACKNOWLEDGMENTS

This work was supported in part by Varian Medical Sys-temsThe authors would like to thank Dragos Constantin forhis contribution to the bash scripting procedure developedfor this study and the GEANT4 user support group at CERN inparticular Gabriele Cosmo The authors also acknowledgeuseful conversations with Magdalena Bazalova

a)Author to whom correspondence should be addressed Electronicmailmagdalenaconstantinvariancom

1D W O Rogers ldquoFifty years of Monte Carlo simulations for medicalphysicsrdquo Phys Med Biol 51 R287ndashR301 (2006)

4023 Constantin et al Varian TrueBeam Linac 4023

Medical Physics Vol 38 No 7 July 2011

experimental measurements for depths between 2 and 40cm For depths between 5 and 30 cm agreement within 1with experiment is obtained for 99 (for 4 4 cm2 field)95 (for 10 10 cm2 field) 94 (for 20 20 and 30 30cm2 fields) and 89 (for 40 40 cm2 field) of the MonteCarlo data points respectively For the surface buildupregion Monte Carlo calculations were performed using a

2 mm wide voxel up to 20 mm depth and the results werecompared against both the CC04 and the plane parallel ionchamber experimental data The agreement in the buildupregion is within 2 for the dose difference between themeasurements using the ion chamber and Monte Carlo datasets Only the point corresponding to the first voxel at 1 mmdepth from the surface is characterized by a 5 deviationNote however that the experimental accuracy in the surfacebuildup region is estimated to be within 5

The dose profiles are shown in Fig 3 at 25 cm depthThe continuous curves represent the experimental measure-ments For the dose profiles at 25 and 10 cm depths themaximum dose difference is within 2 for the in-fieldregions and within 1 for the out-of-field values for fieldsizes up to 30 30 cm2 The 30 30 cm2 open field showsdose differences in the horn region up to 3 At even largerdepth (ie 20 cm) the in-field maximum dose difference forthe 30 30 cm2 open field is within 4 while the smallerfield sizes preserve the same level of agreement (ie within2) At both small and large depths a few exceptions appearfor the interpolated points corresponding to the field edgesand penumbra regions where the interpolation was per-formed using a simple linear function For the 40 40 cm2

field the maximum dose difference between the experimentand Monte Carlo deviates from the 2 accuracy goal espe-cially in the horn region for the dose measurements corre-sponding to the smaller depths (25 and 50 cm) The largestdeviations are equal to 55 This could be due to the statis-tical imprecision associated with the x and y coordinates ofthe Parmela simulated electron phase space which can be aslarge as 10 As explained in Sec IV these errors can sig-nificantly affect the radial spread of the electron beam andhave a direct impact on the magnitude of the horns511ndash13 Over-all the off-axis ratio calculated with GEANT4 at large fieldsare low by 3 for the 30 30 cm2 open field and by 5for the largest field of 40 40 cm2 with an uncertaintyof lt 15 This is consistent with the results by Faddegonet al27

The experimental output factors measured at the maxi-mum dose depth dmax frac14 14 cm together with the MonteCarlo output factors OFc and their standard errors are shownin Table I for field sizes varying from 4 4 to 40 40 cm2The agreement between the experimental and calculated val-ues is well within 1

The statistical uncertainty of our dose calculations wasestimated using the recommendations from TG-1052 Forreporting the statistical uncertainty over a certain volume

FIG 2 (a) Experimental (lines) and GEANT4 (points) calculated depth dosecurves The Monte Carlo dose was averaged over 3 3 voxels with a totalarea of (12 cm)2 (b) The maximum dose differences between the experi-ment and GEANT4 calculations (c) The buildup region for the 10 10 cm2

field Both the CC04 and the parallel chamber measurements are displayedThe dose difference between the parallel chamber results and the calculationis shown in (d)

FIG 3 Experimental (lines) and GEANT4 (points) calculated dose profiles for25 cm depth The Monte Carlo dose was averaged over three voxels with atotal length of 12 cm The dose differences (ie experimentmdashMonte Carlo)are shown in the bottom panel

TABLE I Experimental and calculated output factors at dmaxfrac14 14 cm as afunction of field size

Field(cm2) OFexpt OFc (OFexpt-OFc)=OFc

4 4 0934 0938 6 0015 )0004

10 10 10 100 00

20 20 1050 1043 6 0016 0007

30 30 1076 1067 6 0017 0008

40 40 1085 1088 6 0024 -0003

4022 Constantin et al Varian TrueBeam Linac 4022

Medical Physics Vol 38 No 7 July 2011

the voxels receiving a dose larger than 50 of the maximumdose Dmax were considered and the fractional uncertainty inthe average dose for these particular voxels FDgt05Dmax

wascalculated The values we obtained for FDgt05Dmax

using avoxel volume of 04 04 04 cm3 as a function of thefield size are 192 (4 4 cm2) 123 (10 10 cm2)144 (20 20 cm2) 199 (30 30 cm2) and 288(40 40 cm2) However rebinning the data using largervoxels (ie 12 12 04 cm3 for the PDDs) reduces thefractional uncertainties to 050 (4 4 cm2) 061(10 10 cm2) 060 (20 20 cm2) 050 (30 30 cm2)and 122 (40 40 cm2)

The cumulative number of histories used in this study var-ied between 27 1010 and 13 1011 based on the valuesof the recycling factor R which varied between 4 and 20Since the same input phase space file was reused a largenumber of times which could in principle introduce latentvariance effects2829 we have calculated the average dosevariance for the 10 10 cm2 open field and looked at its de-pendence on R The variance was calculated by summing thecontributions of all the voxels in 5 5 cm2 central region ofthe phantom We have verified that as R increases the var-iance of the average dose decreases A saturation at large Rwould be an indication of latent variance effects notobserved in our study Instead a linear dependence of the av-erage dose variance on the inverse of the recycling factor isobtained indicating that the current calculations do not suf-fer from latent variance effects

IV DISCUSSIONS AND CONCLUSIONS

In this study we validated the 6 MV beam Monte Carlodose simulations using high precision geometry implementa-tion from CAD and input electron beam parameters fixed bythe Parmela phase space The adjustable Parmela parameterswere fixed based on their experimental correspondents set inpractice by the operation of the linac We have generatedphase space files scoring to a cylindrical geometry such thatwe can record particle characteristics upstream of the mova-ble jaws The phase space files are available on the IAEAphase space database30

The agreement with experiment mostly within 2 iswithin the dose accuracy goals set by the Report of TaskGroup 65 (Ref 31) ldquothe accuracy of computed dose distri-butions should be between 1 and 2rdquo The calculated andexperimental output factors agree well within 1

While previous Monte Carlo studies have obtained agree-ment within 111122132 it is important to note the differen-ces in the input phase space and the geometryimplementation used as well as in the data analysis involv-ing dose normalization using field dependent quanti-ties122132 (instead of a unique field independent scaling11)multiple iterations to determine the optimal electron spec-trum as well as smoothing techniques21

There are four possible factors affecting the level ofagreement obtained in this study the approximations used inthe Parmela simulations the uncertainties in componentpositioning and material composition the physics used in

GEANT4 and the uncertainties in experimental dataacquisition

The uncertainty in Parmela simulations are estimated tobe within 4 for the energy distribution and up to 10 forthe transverse coordinates Let us assume that the peak ofthe Parmela energy spectrum shifts by 4 As shown byTzedakis12 a 4 decrease in the mean energy value of theGaussian energy distribution from 64 to 61 MeV leads tohigher ldquohornsrdquo and produces a dose difference as large as2 The impact of the more predominant error in the trans-verse coordinates can be estimated as well Since theFWHM of the spatial coordinate distributions is 14 mm forboth x and y a 10 residual error means that FWHM canfluctuate by 6014 mm A decrease in the FWHM value ofthe spatial coordinate distribution from 11 to 09 mm leadsto higher horns12 and a dose difference as large as 1 Eitherone of these scenarios may bring our simulations into closeragreement with experiment

The possible residual errors in GEANT4 are due to thephysics list and=or the choice for the range cutoff A rangecutoff reduction from 1 to 001 mm produces less than a 2effect on the calculated relative dose distributions in the highdose region as shown by Faddegon et al18 This effect is notnegligible and it would be useful to have more detailed stud-ies to decide the optimal range cut for a particular energyHowever this study was performed for a different physicslist with an older version of GEANT4 and we stress the needfor additional studies for the current version of the toolkit

Moreover the component positioning can significantlychange the dose distributions4 and in addition material com-positions from manufacturers are not known exactly Forexample the primary collimator the jaws and the multileafcollimator are made of a tungsten alloy which contains 95W and the remaining 5 containing a metallic binder madeof Ni Fe and Cu For our simulations the following combi-nation was selected 28 Ni 12 Fe and 1 Cu whichwas one of the three options provided by the manufacturerIt is important to point out that the ratios of these elementscan vary and will slightly affect the radiation transport prop-erties It would be useful to know the impact of this type ofmaterial composition uncertainty on the output data

Future work will address the simulation of 6 MV FFF andhigher energy photon beams the implementation of variancereduction techniques along with a framework to run the sim-ulation on a cloud computing cluster

ACKNOWLEDGMENTS

This work was supported in part by Varian Medical Sys-temsThe authors would like to thank Dragos Constantin forhis contribution to the bash scripting procedure developedfor this study and the GEANT4 user support group at CERN inparticular Gabriele Cosmo The authors also acknowledgeuseful conversations with Magdalena Bazalova

a)Author to whom correspondence should be addressed Electronicmailmagdalenaconstantinvariancom

1D W O Rogers ldquoFifty years of Monte Carlo simulations for medicalphysicsrdquo Phys Med Biol 51 R287ndashR301 (2006)

4023 Constantin et al Varian TrueBeam Linac 4023

Medical Physics Vol 38 No 7 July 2011

the voxels receiving a dose larger than 50 of the maximumdose Dmax were considered and the fractional uncertainty inthe average dose for these particular voxels FDgt05Dmax

wascalculated The values we obtained for FDgt05Dmax

using avoxel volume of 04 04 04 cm3 as a function of thefield size are 192 (4 4 cm2) 123 (10 10 cm2)144 (20 20 cm2) 199 (30 30 cm2) and 288(40 40 cm2) However rebinning the data using largervoxels (ie 12 12 04 cm3 for the PDDs) reduces thefractional uncertainties to 050 (4 4 cm2) 061(10 10 cm2) 060 (20 20 cm2) 050 (30 30 cm2)and 122 (40 40 cm2)

The cumulative number of histories used in this study var-ied between 27 1010 and 13 1011 based on the valuesof the recycling factor R which varied between 4 and 20Since the same input phase space file was reused a largenumber of times which could in principle introduce latentvariance effects2829 we have calculated the average dosevariance for the 10 10 cm2 open field and looked at its de-pendence on R The variance was calculated by summing thecontributions of all the voxels in 5 5 cm2 central region ofthe phantom We have verified that as R increases the var-iance of the average dose decreases A saturation at large Rwould be an indication of latent variance effects notobserved in our study Instead a linear dependence of the av-erage dose variance on the inverse of the recycling factor isobtained indicating that the current calculations do not suf-fer from latent variance effects

IV DISCUSSIONS AND CONCLUSIONS

In this study we validated the 6 MV beam Monte Carlodose simulations using high precision geometry implementa-tion from CAD and input electron beam parameters fixed bythe Parmela phase space The adjustable Parmela parameterswere fixed based on their experimental correspondents set inpractice by the operation of the linac We have generatedphase space files scoring to a cylindrical geometry such thatwe can record particle characteristics upstream of the mova-ble jaws The phase space files are available on the IAEAphase space database30

The agreement with experiment mostly within 2 iswithin the dose accuracy goals set by the Report of TaskGroup 65 (Ref 31) ldquothe accuracy of computed dose distri-butions should be between 1 and 2rdquo The calculated andexperimental output factors agree well within 1

While previous Monte Carlo studies have obtained agree-ment within 111122132 it is important to note the differen-ces in the input phase space and the geometryimplementation used as well as in the data analysis involv-ing dose normalization using field dependent quanti-ties122132 (instead of a unique field independent scaling11)multiple iterations to determine the optimal electron spec-trum as well as smoothing techniques21

There are four possible factors affecting the level ofagreement obtained in this study the approximations used inthe Parmela simulations the uncertainties in componentpositioning and material composition the physics used in

GEANT4 and the uncertainties in experimental dataacquisition

The uncertainty in Parmela simulations are estimated tobe within 4 for the energy distribution and up to 10 forthe transverse coordinates Let us assume that the peak ofthe Parmela energy spectrum shifts by 4 As shown byTzedakis12 a 4 decrease in the mean energy value of theGaussian energy distribution from 64 to 61 MeV leads tohigher ldquohornsrdquo and produces a dose difference as large as2 The impact of the more predominant error in the trans-verse coordinates can be estimated as well Since theFWHM of the spatial coordinate distributions is 14 mm forboth x and y a 10 residual error means that FWHM canfluctuate by 6014 mm A decrease in the FWHM value ofthe spatial coordinate distribution from 11 to 09 mm leadsto higher horns12 and a dose difference as large as 1 Eitherone of these scenarios may bring our simulations into closeragreement with experiment

The possible residual errors in GEANT4 are due to thephysics list and=or the choice for the range cutoff A rangecutoff reduction from 1 to 001 mm produces less than a 2effect on the calculated relative dose distributions in the highdose region as shown by Faddegon et al18 This effect is notnegligible and it would be useful to have more detailed stud-ies to decide the optimal range cut for a particular energyHowever this study was performed for a different physicslist with an older version of GEANT4 and we stress the needfor additional studies for the current version of the toolkit

Moreover the component positioning can significantlychange the dose distributions4 and in addition material com-positions from manufacturers are not known exactly Forexample the primary collimator the jaws and the multileafcollimator are made of a tungsten alloy which contains 95W and the remaining 5 containing a metallic binder madeof Ni Fe and Cu For our simulations the following combi-nation was selected 28 Ni 12 Fe and 1 Cu whichwas one of the three options provided by the manufacturerIt is important to point out that the ratios of these elementscan vary and will slightly affect the radiation transport prop-erties It would be useful to know the impact of this type ofmaterial composition uncertainty on the output data

Future work will address the simulation of 6 MV FFF andhigher energy photon beams the implementation of variancereduction techniques along with a framework to run the sim-ulation on a cloud computing cluster

ACKNOWLEDGMENTS

This work was supported in part by Varian Medical Sys-temsThe authors would like to thank Dragos Constantin forhis contribution to the bash scripting procedure developedfor this study and the GEANT4 user support group at CERN inparticular Gabriele Cosmo The authors also acknowledgeuseful conversations with Magdalena Bazalova

a)Author to whom correspondence should be addressed Electronicmailmagdalenaconstantinvariancom

1D W O Rogers ldquoFifty years of Monte Carlo simulations for medicalphysicsrdquo Phys Med Biol 51 R287ndashR301 (2006)

4023 Constantin et al Varian TrueBeam Linac 4023

Medical Physics Vol 38 No 7 July 2011

2I J Chetty et al ldquoReport of the AAPM task group no 105 Issues associ-ated with clinical implementation of Monte Carlo-based photon and electronexternal beam treatment planningrdquo Med Phys 34 4818ndash4853 (2007)

3O Chibani and C-M Ma ldquoOn the discrepancies between Monte Carlodose calculations and measurements for the 18 MV Varian photon beamrdquoMed Phys 34 1206ndash1216 (2007)

4M Bieda J A Antolak and K R Hogstrom ldquoThe effect of scatteringfoil parameters on the electron-beam Monte Carlo calculationsrdquo MedPhys 28 2527ndash2534 (2001)

5D Sheikh-Bagheri and D W O Rogers ldquoSensitivity of megavoltage pho-ton beam Monte Carlo simulations to electron beam and other parame-tersrdquo Med Phys 29(3) 379ndash390 (2002)

6M Constantin D Constantin P J Keall A Narula M Svatos and JPerl ldquoLinking computer-aided design (CAD) to Geant4-based MonteCarlo simulations for precise implementation of complex treatment headgeometriesrdquo Phys Med Biol 55 N211ndashN220 (2010)

7GDML USERSrsquoS GUIDE Version 20 is available at http==lcgappcernch=project=simu=framework=GDML=

8The official page of the Geant4 organization is http==wwwgeant4org=geant4=

9W R Nelson H Hirayama and D W O Rogers The EGS4 code systemReport No 265 (Stanford Linear Accelerator Center pp1ndash398 1985)

10D W O Rogers B A Faddegon G X Ding C M Ma J We and T RMackie Beam ldquoA Monte Carlo code to simulate radiotherapy treatmentunitsrdquo Med Phys 22 503ndash524 (1995)

11P J Keall J V Siebers B Libby and R Mohan ldquoDetermining the inci-dent electron fluence for Monte Carlo-based photon treatment planningusing a standard measured data setrdquo Med Phys 30 574ndash582 (2003)

12A Tzedakis J E Damilakis M Mazonakis J Stratakis H Varveris andN Gourtsoyiannis ldquoInfluence of initial electron beam parameters onMonte Carlo calculated absorbed dose distributions for radiotherapy pho-ton beamsrdquo Med Phys 31 907ndash913 (2004)

13B De Smedt et al ldquoDecoupling initial electron beam parameters forMonte Carlo photon beam modelling by removing beam-modifying filtersfrom the beam pathrdquo Phys Med Biol 50 5935ndash5951 (2005)

14J Pena et al ldquoAutomatic determination of primary electron beam parame-ters in Monte Carlo simulationrdquo Med Phys 34(3) 1076ndash1084 (2007)

15L Lilie W Wang and Konrad Leszczynski ldquoEstimation of the focal spotsize and shape for a medical linear accelerator by Monte Carlo simu-lationrdquo Med Phys 34(2) 485ndash488 (2007)

16L Young and J Billen Parmela code http==laacglanlgov=laacg=services=parmela (1996)

17B A Faddegon E Schreiber and X Ding ldquoMonte Carlo simulation oflarge electron fieldsrdquo Phys Med Biol 50 741ndash53 (2005)

18B A Faddegon J Perl and M Asai ldquoMonte Carlo simulation of largeelectron fieldsrdquo Phys Med Biol 53 1497ndash1510 (2008)

19B A Faddegon D Sawkey T OrsquoShea M McEwen and C RossldquoTreatment head disassembly to improve the accuracy of large electronfield simulationrdquo Med Phys 36 4577ndash91 (2009)

20Joel St Aubin S Steciw and B G Fallone ldquoThe design of a simulatedin-line side-coupled 6 MV linear accelerator waveguiderdquo Med Phys 37466ndash476 (2010)

21Joel St Aubin S Steciw C Kirkby and B G Fallone ldquoAn integrated 6MV linear accelerator model from electron gun to dose in a water tankrdquoMed Phys 37 2279ndash2288 (2010)

22G E Meddaugh M E Trail and D H Whittum ldquoStanding-wave particlebeam acceleratorrdquo US patent 7339320 (March 4 2008)

23M Reiser ldquoTheory and design of charged particle beamsrdquo pp 202ndash203219ndash220 (1994)

24J H Billen and L M Young ldquoPoisson Superfishrdquo LANL Report NoLA-UR-96-1834 (2006)

25A W Chao and M Tigner ldquoHanbook of accelerator physics and engi-neeringrdquo p 442-450 (2006)

26S Johnsen and R McIntyre ldquoIn-line electron beam energy monitor andcontrolM US patent 4877961 (October 31 1989)

27B Faddegon et al ldquoBenchmarking of Monte Carlo simulation of brems-strahlung from thick targets at radiotherapy energiesrdquo Phys Med 354308ndash4317 (2008)

28 D Sheikh-Bagheri I Kawrakow B Walters and D W O RogersldquoMonte Carlo simulations Efficiency improvement techniques and statis-tical considerationsrdquo Integrating New Technologies into the Clinic MonteCarlo and Image-Guided Radiation TherapymdashProceedings of 2006 AAPMSummer School (2006) pp 1ndash21 University of Windsor Ontario Canada

29B R B Walters I Kawrakow and D W O Rogers ldquoHistory by historystatistical estimators in the BEAM code systemrdquo NRCC Report NoPIRS-0791 (2002)

30http==www-ndsiaeaorg=phsp=phsphtmlx31N Papanikolaou et al ldquoReport of task group no 65 of the radiation ther-

apy committee of the American Association of Physicists in MedicineTissue inhomogeneity corrections for megavoltage photon beamsrdquo MedPhys pp 1ndash130 (2004)

32J Pena et al ldquoCommissioning of a medical accelerator photon beamMonte Carlo simulation using wide-field profilesrdquo Phys Med Biol 494929ndash42 (2004)

4024 Constantin et al Varian TrueBeam Linac 4024

Medical Physics Vol 38 No 7 July 2011