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Comparison of GATE/GEANT4 with EGSnrc and MCNP for electron dose calculations at

energies between 15 keV and 20 MeV

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2011 Phys. Med. Biol. 56 811

(http://iopscience.iop.org/0031-9155/56/3/017)

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IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 56 (2011) 811–827 doi:10.1088/0031-9155/56/3/017

Comparison of GATE/GEANT4 with EGSnrc andMCNP for electron dose calculations at energiesbetween 15 keV and 20 MeV

L Maigne1,2, Y Perrot1,2, D R Schaart3, D Donnarieix2,4 and V Breton2

1 Clermont Universite, Universite Blaise Pascal, LPC, BP 10448, 63000 Clermont-Ferrand,France2 CNRS/IN2P3, UMR 6533, LPC, 63177 Aubiere, France3 Delft University of Technology, Radiation Detection & Medical Imaging, Mekelweg 15,2629 JB, Delft, The Netherlands4 Centre Jean Perrin, Unite de Physique Medicale, Departement de Radiotherapie-Curietherapie,58 rue Montalembert, 63011 Clermont-Ferrand Cedex, France

E-mail: maigne@clermont.in2p3.fr

Received 20 July 2010, in final form 22 November 2010Published 14 January 2011Online at stacks.iop.org/PMB/56/811

AbstractThe GATE Monte Carlo simulation platform based on the GEANT4 toolkithas come into widespread use for simulating positron emission tomography(PET) and single photon emission computed tomography (SPECT) imagingdevices. Here, we explore its use for calculating electron dose distributionsin water. Mono-energetic electron dose point kernels and pencil beam kernelsin water are calculated for different energies between 15 keV and 20 MeV bymeans of GATE 6.0, which makes use of the GEANT4 version 9.2 StandardElectromagnetic Physics Package. The results are compared to the well-validated codes EGSnrc and MCNP4C. It is shown that recent improvementsmade to the GEANT4/GATE software result in significantly better agreementwith the other codes. We furthermore illustrate several issues of generalinterest to GATE and GEANT4 users who wish to perform accurate simulationsinvolving electrons. Provided that the electron step size is sufficiently restricted,GATE 6.0 and EGSnrc dose point kernels are shown to agree to within lessthan 3% of the maximum dose between 50 keV and 4 MeV, while pencil beamkernels are found to agree to within less than 4% of the maximum dose between15 keV and 20 MeV.

1. Introduction

Monte Carlo simulations have become an indispensable tool for radiation transport calculationsin a great variety of applications. In medical physics, the GEANT4 simulation toolkit

0031-9155/11/030811+17$33.00 © 2011 Institute of Physics and Engineering in Medicine Printed in the UK 811

812 L Maigne et al

(Agostinelli et al 2003) is attracting increasing interest because of its great versatility. Itcontains a comprehensive range of physics models for electromagnetic, hadronic and opticalinteractions of a large set of particles over a wide energy range. It furthermore offers adiversity of tools for defining or importing the problem geometry, for modelling complexradiation sources and detection systems—including e.g. electromagnetic fields, electronicdetector responses, time-dependences, etc—and for exporting the required output data. Thecode is continuously being improved and extended with new functionalities.

The reverse side of GEANT4’s versatility is its complexity. New users must spend aconsiderable learning effort before they are able to make effective use of this object-orientedcode written in the C++ programming language. It is therefore not surprising that the GATEMonte Carlo simulation platform (Jan and Morel 2004), making a wide range of GEANT4functionality available through a user-friendly interface, has come into widespread use in thefield of nuclear medicine for simulating PET and SPECT imaging devices.

In this work, we explore the applicability of GATE for calculating electron dosedistributions in water. In fact, GATE could be useful in many other dosimetry applications.Perhaps the most obvious are dose calculations in nuclear medicine, both for diagnosticapplications (e.g. analysis of the radiation burden to patients) and for therapeutic applications(e.g. treatment planning in radionuclide therapy and treatment verification through emissionscans). One may also envisage the use of GATE in external beam therapy, especially inemerging areas such as proton- and light-ion therapy, where the versatility of GEANT4 isof great advantage. To make these benefits fully available to the scientific community, theOpenGATE Collaboration (OpenGATE) is currently implementing new functionality, e.g., foruser-friendly input of the source and patient geometry (voxelized phantoms, etc), and for easygeneration of the required dosimetric output data.

At least as important is a thorough validation of the code’s dosimetric accuracy. This isespecially relevant in radiotherapy, where dose calculations are often required to be accurate towithin 2–3% (Reynaert et al 2007). In a previous paper we have already shown that GATE canaccurately simulate the dose distribution for low-energy photon sources (Thiam et al 2008).In the present paper we validate its use for electron dose calculations. It is noted that accurateMonte Carlo simulation of electron transport has proven to be difficult especially at lowerenergies (Jenkins et al 1988), where it has been shown that differences between the MonteCarlo codes can be quite significant (Chiu-Tsao et al 2007).

Poon and Verhaegen (2005a, 2005b) have indicated discrepancies in electron dosecalculations performed with an older version (6.1) of GEANT4. For example, depth–dose distributions in a water phantom for 1 and 10 MeV electron beams calculated withGEANT4 and BEAMnrc showed differences of about 10% and 6%, respectively. Anotherwork, investigating the calculation of electron dose point kernels using GEANT4 version 8.0in comparison to other Monte Carlo calculations (Ferrer et al 2007), also showed differences.The present work focuses on GATE version 6.0, which makes use of GEANT4 version 9.2. Anumber of modifications to the electron transport algorithms have been implemented in recentGEANT4 releases (Urban 2006, Elles et al 2008, Kadri et al 2007). Notably, as of version8.0 the electron multiple-scattering algorithms have undergone major improvements so as toobtain better agreement with other codes (Allison et al 2006).

Therefore, we first investigate how the specifications of the GEANT4 particle transportmanagement and the choice of multiple-scattering model influence the dosimetric accuracy ofGATE 6.0 in comparison with other state-of-the-art Monte Carlo codes such as MCNP4C andEGSnrc, which have already been validated carefully for electron dose calculations (Chibaniand Li 2002, Jeraj et al 1999, Reynaert et al 2002, Schaart et al 2002a, Kawrakow 2000a,2000b). Subsequently, we discuss some modifications made to GATE to improve the accuracy

Comparison of GATE/GEANT4 with EGSnrc and MCNP 813

of electron transport calculations especially in volumes that are not small compared to theelectron range. These investigations highlight several issues of general interest to users ofGATE and GEANT4 who wish to calculate accurate electron dose distributions. Finally, wevalidate GATE by calculating mono-energetic electron dose point kernels and pencil beamkernels in water for different energies between 15 keV and 20 MeV and comparing the resultsto the above, well-validated codes.

2. Material and methods

2.1. GATE Monte Carlo simulations

This work was performed with version 6.0 of the GATE generic Monte Carlo platform (Janand Morel 2004). This version of GATE makes use of GEANT4 version 9.2.p01 (Agostinelliet al 2003, GEANT Collaboration 2008a, 2008b). The GEANT4 Standard ElectromagneticPhysics Package, which is used by default in GATE and which describes electron and photoninteractions between ∼1 keV and 100 TeV, was used in all simulations, taking into accountelectron impact ionization, multiple scattering and bremsstrahlung generation. The electronmultiple-scattering model used by default in GEANT4 version 9.2 is the Urban2 model(GEANT Collaboration 2008a, 2008b), and is a class II condensed-history algorithm accordingto the classification by Berger (1963). The algorithm uses model probability density functionsfor sampling the angular and spatial distributions after each electron step. These modelfunctions have been chosen such that they give the same moments of the angular and spatialdistributions as the Lewis theory (Lewis 1950). This theory is applicable for all scatteringangles and it allows electron step sizes to be arbitrarily small.

It has to be noted that the Standard, Low Energy and Penelope packages available inGEANT4 9.2 all use the same multiple-scattering model (Urban2). The Low Energy andPenelope packages are still under development and therefore this paper presents results for theStandard package only.

GATE inherits the GEANT4 capability to set thresholds for the production of secondaryelectrons, fluorescence x-rays, etc. In contrast with many other codes, all primary andsecondary particles created in GEANT4 are in principle tracked to the end of their range.However, the user can limit the number of secondary particles to be tracked, by inhibiting theproduction of secondary particles whose range would be less than a user-defined value calledthe range cut (Agostinelli et al 2003, GEANT4 Collaboration 2008a, 2008b). A range cut of4.3 μm, corresponding to an electron energy of ∼2 keV in water, was used for incident energies>1 MeV. For incident energies �1 MeV, a range cut of 1 μm, corresponding to an electronenergy of ∼1 keV, was used. The ROOT system analysis tool was used to derive the relevantdosimetric quantities from the results.

2.1.1. Mono-energetic electron dose point kernels. Dose point kernels for 15 keV, 50 keV,100 keV, 1 MeV, 2 MeV and 4 MeV electrons were calculated by scoring the energy depositedper source particle in thin, concentric, spherical shells around an isotropic, mono-energetic,electron point source centred in a 400 mm diameter, spherical water phantom with a massdensity of 1 g cm−3, see figure 1. At each electron energy we used 24 scoring shells with athickness of 0.05RE, where RE is the nominal continuous slowing down approximation (CSDA)range of electrons with initial energy E. Values of RE from NIST and the shell thickness foreach electron energy investigated are given in table 1. Between 5 × 106 and 2 × 107 sourceparticles were generated per simulation.

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Figure 1. Schematic cross section of the concentric scoring shells around the isotropic electronpoint source located at the origin of the coordinate system.

Table 1. CSDA range RE and thickness of dose scoring regions for different electron energies inwater. CSDA ranges were taken from the NIST web database ESTAR (ESTAR).

Electron Scoring shell thickness Scoring slice thicknessenergy (MeV) RE (g cm−2) 0.05RE (g cm−2) 0.025RE (g cm−2)

0.015 5.147 × 10−4 2.573 × 10−5 1.290 × 10−5

0.05 4.320 × 10−3 2.160 × 10−4 1.080 × 10−4

0.1 1.431 × 10−2 7.155 × 10−4 3.578 × 10−4

1.0 4.367 × 10−1 2.184 × 10−2 1.092 × 10−2

2.0 9.785 × 10−1 4.893 × 10−2 2.446 × 10−2

4.0 2.037 1.018 × 10−1 5.093 × 10−2

10 4.975 2.487 × 10−1 1.244 × 10−1

15 7.219 3.610 × 10−1 1.805 × 10−1

20 9.320 4.660 × 10−1 2.330 × 10−1

As suggested by Cross et al (1992), all dose point kernel results are represented using thedimensionless quantity

J (r /RE,E) = 4π r2D(r,E)RE/E (1)

where D(r,E) is the dose per source particle at radial distance r, while RE is the nominalCSDA range of electrons with initial energy E in units of mass per unit area (see table 1).The quantity J (r /RE,E) thus represents the fraction of the emitted energy deposited in aninfinitesimally thin spherical shell of scaled radius r /RE to r /RE + d(r /RE). Scaling of theradial distances has the advantage that J (r /RE,E) becomes a slowly varying quantity withenergy, making interpolation over relatively wide energy intervals more accurate.

2.1.2. Mono-energetic electron pencil beam kernels. Pencil beam kernels for 15 keV,50 keV, 100 keV, 1 MeV, 2 MeV, 4 MeV, 10 MeV, 15 MeV and 20 MeV electrons werecalculated by scoring the energy deposited per source particle in thin slices of an effectivelysemi-infinite water phantom with a mass density of 1 g cm−3 located 5 cm from the beamsource. The beam source and the water phantom were both located in vacuum. The 48scoring slices each had a thickness of 0.025RE. One million source particles were generatedper simulation. All pencil beam kernels are represented using the dimensionless quantity

J (z/RE,E) = RED(z,E)/�E (2)

where � is the incident electron fluence.

Comparison of GATE/GEANT4 with EGSnrc and MCNP 815

2.2. EGSnrc simulations

Simulations were also performed with EGSnrc (Rogers et al 2003), based on the user-codeexample EDKnrc developed by Mainegra et al (2005) for the calculation of photon and electrondose point kernels and on the user-code example DOSRZnrc (Rogers and Bielajew 1986) forthe pencil beam kernels. The same geometries as in the GATE simulations were used (seesections 2.1.1 and 2.1.2, respectively).

EGSnrc has been shown to produce dose deposition kernels in excellent agreement withmeasurements in water (Mainegra et al 2005). It uses the exact multiple-scattering theorybased on the screened Rutherford cross section and takes into account spin effects in electronscattering. We applied the PRESTA II electron-step algorithm and the EXACT boundary-crossing algorithm (Kawrakow 2000a) to switch to an approximate single-scattering modelwhen an electron comes close to a boundary. The ‘skin depth’ parameter was fixed to 3.This parameter represents the number of elastic mean free paths (which are equal to theinverse of the total cross section per atom for Moller scattering) to the next boundary at whichlateral correlations will be switched off. We restricted the maximum fractional continuousenergy loss per step ESTEPE to 1% of the kinetic energy of the particles, except when notedotherwise. The electron tracking cut was set to ECUT = 10 keV for energies >1 MeV. Forincident energies �1 MeV, ECUT was set to 1 keV. We produced a PEGS4 file containing datareproducing the ICRU collision stopping powers and cross sections for energies �1 MeV.

In addition to the energy deposited in each scoring shell, the user-code example EDKnrcalso estimates the effective centre rp of the shell as described by Mackie et al (1988):

rp =∑

n

rn[�Ep]n

/∑n

[�Ep]n (3)

where rn is the radius corresponding to the middle of the nth step taking place in the shell and[�Ep]n is the amount of primary generated energy deposited in that step.

2.3. MCNP4C simulations

The calculations described in sections 2.1.1 and 2.1.2 were also performed using MCNP4C(Briesmeister 2000). Several issues associated with MCNP4C electron transport havepreviously been discussed by Schaart et al (2002a). For example, the ITS energy indexingalgorithm should be used instead of the default algorithm. Furthermore, it was shown thatthe repeated interruption of electron tracks at the boundaries of scoring volumes (voxels)may significantly distort the transport of electrons. To avoid these boundary-crossingartefacts, Schaart et al developed and validated an electron track length estimator of absorbeddose that can be used in combination with non-interrupting, so-called segment boundaries(Briesmeister 2000) to define the scoring geometry. This method has been used successfullyfor the calculation of the dose distributions for several therapeutic beta sources (Schaart et al2002b, Schaart and Marijnissen 2002c, Schaart 2002) and has also been used in the presentcalculations.

For this work, all calculations were performed in coupled electron–photon mode, usingthe el03 and mcnplib2 electron and photon interaction data libraries and using ITS energyindexing. For all electron energies, the simulation geometries were the same as those describedin sections 2.1.1 and 2.1.2. The photon and electron cut-off energies were set slightly above1 keV. Other simulation parameters were left at the default setting (Briesmeister 2000). Onemillion source particles were generated in each simulation.

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2.4. Computing time comparisons

To compare the different codes in terms of computational efficiency, dose point kernels andpencil beam kernels for 1 MeV electrons were simulated using GATE 6.0, MCNP4C andEGSnrc on a PC with a 64 bit 2 GHz dual core processor, using the geometries described insections 2.1.1 and 2.1.2, respectively. All simulations were run on a single core. For a faircomparison, the cuts for photons and electrons were set to 1 keV in all codes. Furthermore,the expected energy loss per electron step, given by ESTEPE in EGSnrc and linearLossLimitin GATE, was set equal to 2−1/8. This is the default value used by MCNP, which cannot bechanged easily by the user. In the MCNP calculations the default ∗F8 method was used fordose scoring. No variance reduction methods were used with any of the codes.

2.5. Uncertainty evaluation

The uncertainties in the GATE simulations were evaluated in line with the principlesrecommended in NIST Technical Note 1297 (Taylor and Kuyatt 1994). The combined relativeuncertainty in the absorbed dose D was calculated as

uc(D)

D=

√(uS(D)

D

)2

+

(ustat(D)

D

)2

(4)

where uS(D) and ustat(D) are the uncertainties in D due to stopping power uncertainties andstatistical variations, respectively.

The total mass stopping powers for electrons used in the Standard ElectromagneticPackage of GEANT4 were compared to those in the ESTAR database given by NIST (ESTAR)for energies between 15 keV and 20 MeV. (EGSnrc uses the mass stopping powers and crosssections from NIST.) The relative deviation between the NIST and GEANT4 values is lessthan ±2.0% at all energies. Hence we assume that the relative uncertainty in the stoppingpower S equals u(S)/S = 2% (2σ ). The relative uncertainty in D due to stopping poweruncertainties is then given by

uS(D)

D= S

D

∂D

∂S

u(S)

S. (5)

We estimated the relative uncertainty propagation factor (S/D) (∂D/∂S) by comparingdose point kernels calculated using cross sections of GEANT4 and of the NIST ESTARdatabase over the range of radial distances concerned in our simulations. The mean value of(S/D) (∂D/∂S) over all radial distances of interest equals ∼1.2. Consequently, we estimatethat uS(D)/D = 2.4% (2σ ). The maximum relative statistical uncertainty ustat(D)/D waskept negligible compared to uS(D)/D in all simulations. Hence, the combined, relativeuncertainty does not exceed uc(D)/D ≈ 2.4% (2σ ). The EGSnrc code uses the mass stoppingpowers and cross sections from NIST.

2.6. Influence of GATE/GEANT4 electron transport parameters

In this work we study the influence of several GATE/GEANT4 input parameters on theaccuracy of GATE 5.0 electron dose calculations. For clarity, a description of these parametersand related terminology is presented in the following.

2.6.1. Particle transport management in GATE/GEANT4. One may distinguish severallevels in the management of particle transport in GATE/GEANT4: run, event, track andstep (GEANT Collaboration 2008a, 2008b). The run level is the top level at which problem

Comparison of GATE/GEANT4 with EGSnrc and MCNP 817

Table 2. Default values of the parameters determining the electron step size in GATE 6.0 usingGEANT4 version 9.2. These values were used for the simulations performed in this work unlessnoted otherwise.

GATE version 6.0

GEANT4 version 9.2

Name Symbol Value

Ionization process options dRoverRange αR 0.2finalRange ρR 1 mmlinearLossLimit ξ 10−2

Multiple-scattering options MSC Model – Urban2StepLimitType – UseSafetyRangeFactor fR 0.02GeomFactor fg 2.5skin – 3

initialization, termination and overall control of running a pre-defined number of histories ismanaged. The event level concerns the simulation of a single history. Each history involves thesimulation of the tracks of each of the primary and secondary particles created in that history.A step is the smallest unit of particle propagation, in which a particle is linearly displaced overa certain distance, possibly depositing energy and/or generating secondary particles.

2.6.2. Step size limitations in GEANT4. The step size is a critical parameter, especially in thecase of multiple-scattering electron simulations. On one hand, the step size should be smallenough that changes in all relevant interaction cross sections between the beginning and theend of each step remain small, and that the (curvy) electron tracks are accurately representedgeometrically. On the other hand, computational efficiency requires that the step size is notmade too small.

In the absence of any other restrictions, the step size would be limited only by volumeboundaries and discrete interactions. In many simulations this would result in steps that aretoo large to meet the above criteria. In GEANT4 9.2, additional electron step size limitationsare therefore applied, which can be controlled by several parameters (Elles et al 2008, GEANTCollaboration 2008a, 2008b). In the GATE 6.0 simulations performed in this work the valuesof these parameters were equal to those given in table 2, unless otherwise noted.

The first step size limitation arises from StepFunction, which is common to all chargedparticles. It controls the step size using two parameters: dRoverRange and finalRange. Thestep size s is limited to (GEANT Collaboration 2008a, 2008b):

s < max{ρR, αRR + ρR(1 − αR)(2 − ρR/R)} (6)

where αR ∈ [0, 1] is the parameter dRoverRange, which has a default value of 0.2, while ρR

is the parameter finalRange, having a default value of 1 mm and R is the particle range at thebeginning of the step. At high energies (i.e. αRR � ρR), this equation can be approximatedby

s < αRR. (7)

As the particle slows down, the step size gradually decreases until its range becomes lowerthan finalRange, upon which the remaining range R < ρR is completed in a single, final step.

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In the GATE 6.0 simulations performed here, the value of finalRange used was ρR = 1 mm(see table 2), unless otherwise noted.

The GEANT4 multiple-scattering (MSC) algorithms impose additional step sizelimitations (GEANT Collaboration 2008a, 2008b). Here we concentrate on the limitationsimplemented in the Urban2 model, which is the default model in GEANT4 9.2 for electronsand positrons and which will be renamed the Urban93 model in future GEANT4 versions. Inthis model the user can choose between three types of step size limitation: Minimal, UseSafetyand UseDistanceToBoundary.

If Minimal is selected, the MSC algorithm restricts the step size at the start of a new trackand each time the particle enters a new volume to

s < fR · max{R, λ} (8)

where fR ∈ [0, 1] is the parameter RangeFactor, which has a default value of 0.02, while λ

is the transport mean free path calculated by the multiple-scattering model as described in theGEANT4 Physics Reference Manual (GEANT Collaboration 2008a). For completion, it isnoted that a lower limit to the step size is also applied so as to avoid excessively small steps(inconsistent with the MSC theory).

If UseSafety is selected, which is the default in GEANT4 9.2, the MSC algorithm appliesan additional restriction to ensure that a minimum number of steps are performed in anygeometrical volume, even in low-density media or very thin layers. Similar to the previousone, this limit is computed at the start of each new track and recomputed only when enteringa new volume. At the start of a track the step size is limited to

s < 2dgeom/fg (9)

where fg is the parameter GeomFactor, which has a default value of 2.5, while dgeom isthe linear distance to the next geometrical boundary (in the direction of the particle). Afterentering a new volume this restriction takes the form

s < dgeom/fg (10)

If UseDistanceToBoundary is selected, a third restriction is added that increases theaccuracy of simulation in the immediate vicinity of interfaces. It reduces the step size tothe mean free path of elastic scattering λelastic in a small region around the boundary. In thisregion the particle is transported using an (approximate) single Coulomb scattering algorithm(i.e. multiple scattering is not used). This restriction is only applied if the parameter Skin >

0. It is active in layers of thickness Skin · λelastic before boundary crossing and of thickness(Skin − 1) · λelastic after boundary crossing (in other words, for Skin = 1 essentially only onesmall step occurs just before the boundary). There is no upper limit for the parameter Skin butthe use of large values (∼10) is not recommended since the single Coulomb scattering modelis approximate and should therefore not be applied to a large thickness of medium (Elles et al2008).

For completion, we briefly discuss how the energy loss after each step is calculated (Elleset al 2008, GEANT Collaboration 2008a, 2008b). If the mean energy loss �T < ξT0, whereξ is the parameter linearLossLimit with default value ξ = 0.01, while T0 is the particle kineticenergy at the beginning of the step, a linear approximation is applied based on the assumptionthat the stopping power dT/dx varies negligibly along the length s of the step:

�T = dT

dxs (11)

where the stopping power is taken from the dT/dx table via interpolation.If �T > ξT0, the mean energy loss is calculated using

�T = T0 − fT (R − s) (12)

Comparison of GATE/GEANT4 with EGSnrc and MCNP 819

where the function fT (R) is the (interpolated) inverse of the Range table (i.e. it gives thekinetic energy of the particle T for a range value of R).

In GATE 6.0 the user has the possibility to modify the dRoverRange, finalRange, LinearLoss Limit and the skin parameter.

2.6.3. Step size limits in GATE 6.0 (GEANT4 9.2). The step size limitations described in thesection 2.6.2 are only calculated at the beginning of a new track and when crossing a volumeboundary. Therefore, if there are no, or relatively few, boundaries within a simulation, so thatthe simulation geometry includes volumes that are not small compared to the electron range,it is possible that the electron steps become too large. To remedy this problem, GATE userscan set the parameter StepMax, representing the maximum step size in units of length, to avalue lower than the electron range.

2.6.4. Electron energy deposition along the step. A second point of concern is themanagement of energy deposition by electrons at the step level. At this level, the GEANT4G4SteppingManager class manages the particle transport (GEANT4 Collaboration 2008a,2008b). The GetPhysicalInteractionLength (GPIL) functions of all registered processes forthe current type of particle in transport are invoked, a step size for each process is obtainedand the process with the smallest step size is selected. Next, the appropriate AlongStepDoItand PostStepDoIt methods are invoked and the particle state (i.e. its spatial position, energy,direction, spin, travelling time, etc.) is updated.

By default, the energy is deposited at the end of a step (i.e. energy deposition is taken careof by the PostStepDoIt method). When the electron step size is not small compared to thedimensions of interest and in the absence of charged-particle equilibrium (CPE), this meansthat the dose may be deposited, on average, at the wrong position.

To solve this problem, as suggested in the GEANT4 example TestEm12 (GEANT4Collaboration 2008a, 2008b), we modified the GateSteppingAction class in GATE 6.0 suchthat the energy is not deposited at the end of a step but at a point randomly chosen along thelength of the step. Under the assumption that the stopping power dE/dx varies negligiblyalong the length of the step, the dose should on average be deposited correctly with thismethod. In GATE 6.0 the user has the possibility to choose energy deposition to occur at thePreStepPoint, PostStepPoint (default value) or randomly along the step.

3. Results

3.1. Validation of GATE 6.0 electron transport

We first illustrate how the electron transport parameters in GATE6.0/GEANT4 9.2 can havea significant impact on a 1 MeV dose point kernel calculation. To this end the dose pointkernel was computed in a large volume of water without any boundaries. The coordinatesand energy deposited corresponding to each energy deposition were written to a ROOT outputfile and, upon completion of the simulation, the dose distribution was calculated from thisoutput file by binning the energy deposited in concentric spherical shells with a thickness of0.05 RE.

Figure 2 shows a comparison of the 1 MeV electron dose point kernel obtained withEGSnrc and with, respectively, GATE 6.0 using default settings, GATE 6.0 using low valuesof dRoverRange = 0.0001 and finalRange = 1 μm, GATE 6.0 using a step size limitation ofStepMax = 3 μm, and GATE 6.0 using random energy deposition along the step. Significantdifferences are found between the default version of GATE 6.0 and the other calculations. If

820 L Maigne et al

Figure 2. Comparison between 1 MeV electron dose point kernels in water calculated using GATE6.0 with default settings (squares), GATE 6.0 with dRoverRange αR = 0.0001 and finalRange ρR =1 μm (circles), GATE 6.0 with a maximum step size stepMax = 3 μm (diamonds) and GATE 6.0with random energy deposition along the electron steps (stars) in a large volume of water withoutany volume boundaries.

we quantify the difference between dose DA(r) at distance r calculated with code A and doseDB(r) at the same distance calculated with code B, as a percentage of the maximum valuemax(DA,DB) of the two calculated dose distributions:

|DA(r) − DB(r)|max(DA,DB)

× 100%, (13)

differences between r/RE = 0 and r/RE = 0.75 of up to 13% are found between GATE 6.0 andEGSnrc. In general, the default GATE 6.0 dose point kernel appears to be less penetrating thanthose obtained with EGSnrc or with GATE 6.0 with modified electron transport parameters.

The relatively low first data point at r/RE = 0.05 of the default GATE 6.0 calculationcan be explained as follows. In this simulation the energy is deposited at the end of each step.Thus, for steps crossing the surface of the first spherical bin, the energy is always depositedin the second bin. Since in this calculation the steps are not very small compared to the binwidth, this means that a significant fraction of the energy that should be deposited in the firstbin is carried over to the second bin. Note that for the second bin, the extra energy carriedinto it from the first bin is at least partly cancelled by the energy carried over to the thirdbin by the same mechanism. Furthermore, the net influence of this mechanism is expected todepend strongly on the electron directions and, therefore, on the value of r/RE . For r/RE � 1the electrons are strongly forward directed (i.e. away from the source) so the effect can beexpected to be large. In contrast, for r/RE ≈ 1 the electron directions are distributed muchmore randomly so a situation closer to charged particle equilibrium can be expected betweenneighbouring bins.

3.1.1. Electron step size restriction. The diamonds in figure 2 show the result of a simulationwith the maximum step size set to 3 μm in a large volume of water without boundaries. With amaximum step size of 3 μm (much smaller than the scoring shell thickness of ∼0.02 mm), thedose deposition profile is shifted to significantly larger radial distances which leads to betteragreement with EGSnrc, at the expense of increased CPU time.

Comparison of GATE/GEANT4 with EGSnrc and MCNP 821

3.1.2. Random electron energy deposition. The stars in figure 2 represent a 1 MeVelectron dose point kernel simulated with random energy deposition along the step in alarge volume of water. We indeed obtain essentially the same results as when we imposea maximum step length that is much shorter than the dimensions of the scoring shells(diamonds).

3.1.3. Step size restriction versus random energy deposition. For dose calculations performedin voxelized phantoms, e.g. for radiotherapy treatment planning, random energy depositionwill avoid systematic errors in the assignment of energy deposited to voxels. The advantage ofrandom energy deposition is that it generally results in a much faster simulation (we reacheda factor 10) than reduction of the step size to 3 μm because the average number of steps perelectron is much lower.

It is emphasized that if the phantom is not subdivided into small volumes, the electronstep size still needs to be restricted such that the electron tracks are well-representedgeometrically, especially if the user is interested in the dose distribution at the sub-millimetrescale. By choosing a step limitation the computing time of the simulations is increased by afactor 4.

3.2. Comparison of GATE 6.0 electron dose point kernels with EGSnrc and MCNP4C

All dose point kernels and pencil beam kernels presented in the remainder of this workwere simulated using GATE 6.0 (making use of GEANT4 version 9.2) with the defaultsettings shown in table 2. In these simulations the phantom was subdivided as explained insection 2.1.1, such that the interruption of the electron steps at the volume boundaries andthe subsequent recalculation of the step size limitations given in equations (6) through (12) ofsection 2.6.2 automatically force GATE 6.0/GEANT4 9.2 to deposit the energy in the correctscoring volume.

Figure 3 shows a comparison of electron dose point kernels obtained with GATE 6.0 withthose obtained with EGSnrc and MCNP4C, for various electron energies between 15 keV and4 MeV. For all codes, the r-coordinate corresponding to each scoring shell was taken equal toits effective centre rp as calculated by EDKnrc (see section 2.2).

The GATE 6.0 results are compared to the kernels calculated with EGSnrc (seesection 2.2), at each of the energies investigated. The EGSnrc results, considered as the goldstandard in this study, are quite well reproduced by GATE 6.0. The maximum differencesbetween the different codes at distances 0 � r/RE � 1.075 as a percentage of the maximumdose are shown in figure 4. Between 50 keV and 4 MeV, the differences between GATE6.0 and EGSnrc are <3%. These results should be seen in light of the combined relativeuncertainty of 2.4% (2σ ) estimated in section 2.5. At 15 keV the difference is larger than 8%,suggesting that at energies <50 keV the Standard Electromagnetic package of GEANT4 9.2becomes less reliable for electron dose calculations.

In figure 3 the GATE 6.0 results are also compared to the kernels calculated with MCNP4C(see section 2.3). The MCNP4C results were obtained using ITS energy indexing and usingthe electron track length estimator of absorbed dose that was introduced by Schaart et al(2002a) and that has been carefully validated for electron dose calculations (Schaart et al2002b, Schaart and Marijnissen 2002c, Schaart 2002). The agreement between GATE 6.0 andMCNP4C is less good than that between GATE 6.0 and EGSnrc. It is, however, interesting tonote that the MCNP4C agrees similarly well with EGSnrc as GATE 6.0, see figure 4. Again,we see that the best agreement is obtained at energies above 100 keV.

822 L Maigne et al

(a) (b)

(c)

(e) (f)

(d)

Figure 3. Comparison of dose point kernels for mono-energetic electrons with initial energies of(a) 15 keV, (b) 50 keV, (c) 100 keV, (d) 1 MeV, (e) 2 MeV and (f) 4 MeV calculated with GATE6.0 (closed squares), with EGSnrc (open triangles) and with MCNP4C (open diamonds).

3.3. Comparison of GATE 6.0 electron pencil beam kernels with EGSnrc and MCNP4C

Figure 5 shows a comparison of mono-energetic electron pencil beam kernels obtained withGATE 6.0 (making use of GEANT4 version 9.2) with those obtained with EGSnrc andMCNP4C, at various incident electron energies between 15 keV and 20 MeV.

The maximum differences between the different codes at distances 0 � r/RE � 1.075 asa percentage of the maximum dose are shown in figure 6. Differences between GATE 6.0and EGSnrc are <4% of the maximum dose at all energies between 15 keV and 20 MeV.Again, these results should be seen in light of the combined relative uncertainty of 2.4% (2σ )estimated in section 2.5.

Comparison of GATE/GEANT4 with EGSnrc and MCNP 823

Figure 4. Differences between electron dose points kernels as a percentage of the maximum doseat various energies between 15 keV and 4 MeV, for GATE 6.0 versus EGSnrc (black), GATE 6.0versus MCNP4C (light grey) and MCNP4C versus EGSnrc (dark grey).

Table 3. Comparison of computing time needed by GATE 6.0, MCNP4C and EGSnrc for thecalculation of a 1 MeV dose point kernel (DPK) and 1 MeV pencil beam kernel (PBK) on a 64 bit2 GHz CPU.

Number ofparticles

Statisticaluncertainty for

0 < r < 0.75 RE

Computingtime (min)

DPK PBK DPK PBK DPK PBK

GATE 6.0 105 2.5 × 105 <0.4% <0.5% 1.0 4.2MCNP4C 105 2.5 × 105 <0.4% <0.5% 0.6 1.7EGSnrc 105 2.5 × 105 <0.4% <0.5% 1.0 3.0

The agreement between GATE 6.0 and MCNP4C is less good, especially at energies <1MeV. For energies �1 MeV, the discrepancies remain within 4%. Interestingly, MCNP4C andEGSnrc are found to agree very well at energies >1 MeV. At these energies the agreementis even better than between GATE 6.0 and EGSnrc, see figure 6. However, at energies�100 keV the situation is reversed in that MCNP4C agrees less well with EGSnrc than GATE6.0.

3.4. Computing time comparisons

The computational efficiency of the different codes was compared as described in section 2.4.The results are shown in table 3. The statistical uncertainties listed indicate the maximumstandard deviations estimated by the different codes per scoring bin over the region 0 < r <

RE. While the different codes provide similar degrees of uncertainty with equal numbers ofsource particles, it appears that EGSnrc and MCNCP are faster than GATE 6.0, with MCNP4Cbeing the fastest.

824 L Maigne et al

(a) (b)

(c)

(e)

(g) (h)

(f)

(d)

Figure 5. Comparison of pencil beam kernels for electrons with initial energies of (a) 15 keV, (b)50 keV, (c) 100 keV, (d) 1 MeV, (e) 2 MeV, (f) 4 MeV, (g) 10 MeV and (h) 20 MeV calculated withGATE 6.0 (closed squares), with EGSnrc (open triangles) and with MCNP4C (open diamonds).

Comparison of GATE/GEANT4 with EGSnrc and MCNP 825

Figure 6. Differences between electron pencil beam kernels as a percentage of the maximum doseat various energies between 15 keV and 4 MeV, for GATE 6.0 versus EGSnrc (black), GATE 6.0versus MCNP4C (light grey) and MCNP4C versus EGSnrc (dark grey).

4. Discussion and conclusions

Making GEANT4 physics models available through a user-friendly interface, the GATEMonte Carlo simulation platform has recently come into widespread use for simulating PETand SPECT imaging devices. In this work, we explore its use for calculating electron dosedistributions in water.

Since electrons are charged particles with a relatively low mass, accurate Monte Carlosimulation of their transport through matter has proven notoriously difficult, especially atlower energies (Jenkins et al 1988). It requires not only the implementation and validationof highly refined electron multiple-scattering algorithms, but also that the user of the codesufficiently understands these algorithms and is able to cautiously set the relevant electrontransport parameters. The present paper highlights some issues of general interest to users ofboth GATE and GEANT4 who wish to perform accurate simulations involving electrons.

An important conclusion from this work is that GATE 6.0 (making use of the StandardElectromagnetic package of GEANT4 9.2) agrees much better with EGSnrc and MCNP4Cthan previous versions of GATE/GEANT4 (Poon and Verhaegen 2005a, 2005b). Nevertheless,the user needs to be aware of several possible sources of error.

Since most of GEANT4’s step size limitations are updated only when an electron crossesa volume boundary (see section 2.6.2), the step size may become very large (relative to theelectron range) when transporting electrons through large (i.e. not small compared to theelectron range) volumes. Furthermore, since the energy lost during a step is deposited atthe end of the step by default (see section 2.6.4), relatively large systematic errors may occurin the spatial distribution of the energy deposited under these circumstances.

In such cases the results may be improved by applying a fixed step size limitation(stepMax), random energy deposition along the steps, and/or reduced values of thedRoverRange and finalRange parameters. In GATE 6.0 all these parameters can be set by theuser.

Alternatively, the user may subdivide the simulation geometry into volumes thin enoughthat the step size limitations are updated sufficiently often, in order to ensure a correctsimulation of the dose deposition.

826 L Maigne et al

If the electron step size is sufficiently restricted, good agreement is found between electrondose point kernels calculated with GATE 6.0/GEANT4 9.2 and those calculated with EGSnrcand MCNP4C, except at energies <50 keV. For energies >50 keV, we conclude that GATE6.0 is useful for the calculation of electron dose distributions and gives results comparable towell-validated codes such as EGSnrc and MCNP4C.

Acknowledgments

We wish to thank Dr Vladimir Ivantchenko, Dr Michel Maire, and Dr Laszlo Urban for helpfuldiscussion about the multiple-scattering model in GEANT4. We also thank the OpenGATECollaboration for their technical support. This work was partly supported by grants from theEuropean Commission (through the EGEE project), and regional authorities (Conseil Regionald’Auvergne, Conseil General du Puy-de-Dome, Conseil General de l’Allier). The EnablingGrids for E-sciencE (EGEE) project is co-funded by the European Commission under contractINFSO-RI-031688. Auvergrid is a project funded by the Conseil Regional d’Auvergne.

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