GAMOS/GEANT4 Validation in a Siemens PRIMUS Linac

GAMOS/GEANT4 Validation in a Siemens PRIMUS Linac M. A. Cort´es-Giraldo, P. Arce, J. Salguero, M. I. Gallardo, J. M. Quesada, A. Leal, and R. Arr´ans

Abstract—Geant4.9.0.p01 Monte Carlo code has been used to simulate a Siemens PRIMUS linac. The geometry of the head, including the double-focused multileaf collimator (MLC) developed by TOSHIBA has been introduced using GAMOS.1.9.0 interface. The obtained data have been compared with two different sets of data from BEAMnrc/EGSnrc (V4 Series) simulation results, one of them without using Variance Reduction Techniques (VRT), to compare both MC under the same conditions, and another where Directional Bremsstrahlung Splitting (DBS) is applied. They are compared to the corresponding calibration dose curves for a 10x10 cm2 field, in order to validate the geometry module and the different physics lists, which have been optimized to model transport of photons and charged particles for radiotherapy applications. Phase Space Data (PSD) below the flattening filter and the MLC have been calculated for a 10x10 cm2 field, to analyse the different fluence contributions from the different modules of the head. Discrepancies between the different physics lists have been found, regarding the bremsstrahlung gamma production, as discussed below. We consider these calculations as a first step to use Geant4 for medical applications, to take advantage of its capability to be extended to situations were hadronic processes play a major role.

I. I NTRODUCTION

M

ONTE CARLO simulations have been widely used in medical applications for treatment plannings, in electron and photon machines [1], [2], especially after the development of Variance Reduction Techniques (VRTs), which allow to achieve an acceptable accuracy in the simulations, even in geometries as complex as realistic tumor shapes. GAMOS.1.9.0 [3] has been considered to simulate a Siemens Primus Linac, used at Virgen Macarena Hospital (Seville, Spain). GAMOS.1.9.0 includes Geant4.9.0.p01 [4], [5] as simulation engine. There is an increasing interest in Geant4 among medical physicists, and has been used to Manuscript sent November 14, 2008. This work was supported in part by the Spanish Ministry of Science and Innovation under Grant No. AP200601459. M. A. Cort´es-Giraldo is with the Dep. F´ısica At´omica, Molecular y Nuclear, University of Sevilla, Ap. 1065, E-41080 Sevilla, Spain (telephone: +34954550928, e-mail: [email protected]). P. Arce is with the Dep. of Physics Research, CIEMAT, Av. Complutense 22, E-28040 Madrid, Spain (e-mail: [email protected]). J. Salguero is with the Dep. Fisiolog´ıa M´edica y Biof´ısica, University of Sevilla, Av. S´anchez-Pizju´an 9, E-41009 Sevilla, Spain (e-mail: [email protected]). M. I. Gallardo is with the Dep. F´ısica At´omica, Molecular y Nuclear, University of Sevilla, Ap. 1065, E-41080 Sevilla, Spain (e-mail: [email protected]). J. M. Quesada is with the Dep. F´ısica At´omica, Molecular y Nuclear, University of Sevilla, Ap. 1065, E-41080 Sevilla, Spain (e-mail: [email protected]). A. Leal is with the Dep. Fisiolog´ıa M´edica y Biof´ısica, University of Sevilla, Av. S´anchez-Pizju´an 9, E-41009 Sevilla, Spain (e-mail: [email protected]). R. Arr´ans is with the Servicio de Radiof´ısica, H. U. Virgen Macarena, Av. Doctor Fedriani, s/n, E-41009 Sevilla, Spain (e-mail: [email protected]).

simulate brachitherapy sources [6] and proton therapy machines [7], [8]. In the other hand, Poon and Verhaegen [9] found Geant4.6.1 wasn’t accurate enough to simulate electrons transport at medical energy range. However, that version is now obsolete and it would be necessary to make another verification with a more recent version. With this purpose, a simulation were only electromagnetic physics play a role has been made in Geant4, and compared to experimental data and also to BEAMnrc/EGSnrc [10]-[12] calculation results, with and without Variance Reduction Techniques. These results can help to study the suitability of Geant4 below 6 MeV, before considering higher energies. At higher energies the contamination of neutrons is important, and Geant4 would be able to estimate this neutronic contamination. II. M EASUREMENTS AND S IMULATIONS The experimental set-up consisted on a Siemens Primus Linac configuring a 10×10 cm2 radiation field. The water tank was a 50×50×40 cm3 cube (inplane, crossplane and thickness dimensions), and was placed at SSD 100 cm, with the radiation field centered in the upper surface of the cube. This entire setup, from the electron beam hitting the tungsten target to the water tank, was reproduced in Geant4 and EGSnrc, with both geometry configurations as equal to each other as possible. The electrom beam was characterized by a gaussian-shaped energy spectrum with mean energy 5.8 MeV and sigma equal to 0.29 MeV, and a 2-D gaussian distribution in the plane XY, with FWHM equal to 1.0 mm. The reason for this choice will be explained in subsection IV-A. A phase-space data (PSD) file was created for two different planes. The first one is just after the flattening filter and tungsten collimator, and 5 · 108 histories were considered. The second PSD plane is at SSD 90 cm, between the machine and the water phantom, taking into account 1.5 · 109 histories. To calculate the delivered dose in the water tank, the PSD file at SSD 90 cm was recycled 5 times to get a simulation equivalent to 7.5 · 109 histories. A. Geant4 GAMOS provides several physics lists, based on the ones the user can find at the Hadrontherapy advanced example in the official release. In our simulations, the so called Standard and LowEnergy modular physics lists are considered. The Standard physics list can be used from 1 keV to 100 TeV, and includes the most important physics for photons, electrons and positrons, except Rayleigh scattering and atomic relaxations. In Geant4, this is the most efficient physics list in

CPU time, since its algorithm are based on some parameterisations based on validated cross section data sets. The LowEnergy package extends the previous application range to lower energy (from 250 eV). Rayleigh scattering and atomic relaxations are included in this case. These models implement cross-section tables obtained from the Lawrence Livermore National Library, including evaluated data for photons (EPDL97, [13]), electrons (EEDL, [14]) and atoms (EADL, [15]), but not for positrons. The production cuts were set to 0.1 mm for all kind of particles in all regions. This means that every secondary particle created will not be explicitely considered when its expected range in the material is below this value. In these cases, Geant4 considers the energy lost by the primary particle as delivered locally at the point of interaction. B. EGSnrc Two simulations with EGSnrc (V4 Series) were considered. In the first one, no VRTs were used in order to make the comparison with Geant4 without VRTs. The simulation parameters were set to: ECUT = 0.521, PCUT = 0.010 and ESTEPE = 0.25. Boundary crossing algorithm was set to EXACT, with electron-step algorithm PRESTA-II, bremsstrahlung angular sampling KM, bremsstrahlung cross sections from NIST and pair angular sampling KM. Spin effects , bound Compton scattering, photoelectron angular sampling, Rayleigh scattering and atomic relaxations were set to ON. The rest of the parameters were set to default. The second simulation used Directional Bremsstrahlung Splitting (DBS), and has been used as a benchmark when no experimental data were available. The DBS parameters were nsplit = 1500, rsplit = 20 cm y zsplit = 100 cm, and 2.0 × 107 histories were considered to calculate the dose curves. C. Measurements The measurements were made during the routinary machine calibration at the Virgen Macarena Hospital. A semiconductor detector (2.5-mm diameter and 0.5-mm thickness) was used to calculate the delivered dose in each point of the water tank. The tolerance in dose is 1%, and the experimental uncertainty in position is 0.1 mm. III. D OSE CALCULATIONS To calculate the delivered dose in the water tank, the cubic phantom was divided into voxels whose dimensions were 2 × 2 × 2 cm3 . The curves in Fig. 1-4 were made considering a parallelepiped volume of size 8 × 8 × 2 cm3 in X, Y and Z for PDD curves, and in Y, Z and X for the profiles. A. Relative dose Fig. 1 shows the PDD curves obtained by each simulation with the callibration data. The experimental data were normalised to a dose of 100 at the maximum, situated at dM = 1.53 cm, being dM the depth where the delivered dose is maximum. But, due to the statistical noise, the curve

obtained by each Monte Carlo code was normalised taking into account the average dose in a range of ±5 mm around dM . As one can see, the simulations which don’t apply any VRT give an acceptable curve, reproducing the experimental data, but with a statistical noise between 5% and 10% near the maximum, and above 10% at the end of the tail. As one can expect, the simulation results are better when DBS is applied. This shows that the simulated PDD curves can be improved by a simulation with a higher number of histories, in order to make the statistical noise smaller. In Fig. 2 the profile curve at 5 cm depth is represented for each simulation, and for the experimental dose data as well. The experimental curve was normalised to a dose of 100 at x = 0 cm, and the profiles calculated by the Monte Carlo codes were normalised taking into account the average dose for |x| < 1 cm, due to the statistical noise. As in Fig. 1, the simulations seem to have a good agreement with the experimental profile, but the statistical noise presented here, between 5% and 10% for the simulations without VRTs and below 4% for EGSnrc with DBS, prevents to extract definitive conclusions. It is expected that a good agreement can be achieve with a better statistics. However, it is possible to see that Geant4 is as accurate as EGSnrc, when VRT are not taken into account. Fig. 3 shows another profile at 10 cm depth. The best agreement is achieved for EGSnrc simulation with DBS, as expected. However, it seems that both Geant4 simulations (Standard and LowEnergy) fit better to the experimental data than EGSnrc, when DBS is switched off. In this case, the EGSnrc (without DBS) curve shows a higher noise level. Anyway, a higher number of histories, like 20 · 109 , can make possible the discussion with more reliable results. B. Absolute dose Even without having no experimental data for absolute dose, it is interesting to study the actual dose that is delivered to the water tank per event or history. With this purpose, Fig. 4 shows the absolute dose curves in depth along the beam axis. It is really noticeable that both Geant4 simulations give a higher estimation on the absorbed dose per event, compared to EGSnrc simulations. In particular, the Geant4 Standard results are aprox. 20% higher than the EGSnrc (with DBS) results. The Geant4 LowEnergy physics list also overestimate the EGSnrc results, but in a 5%. This is a really important issue in Geant4, because there is a difference of approx. ∼ 15% between Standard and LowEnergy physics lists, even when working inside the range of energies where these models are considered valid. In order to study what produce this severe discrepancy in absolute dose, a gamma fluence study is made in the following section, using the phase-space data built to complete the dose calculations. IV. P HASE - SPACE ANALYSIS In this section the gamma fluence is studied just below the flattening filter and at SSD 90 cm. In particular, this study is focused on the energy spectrum, angular distribution after the

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flattening filter and spacial distribution at SSD 90 cm, to find out why the discrepancies showed in Fig. 4 happen. A. Below flattening filter In Fig. 5 the energy spectra corresponding to Geant4 simulations and EGSnrc simulation (without DBS) are shown. It is clear that the gamma fluence in Geant4 Standard simulation is above 20% for gamma energies below 2 MeV, and above 15% between 2 MeV and 5 MeV. For Geant4 LowEnergy

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case, the relative discrepancy is near 5% for all energies. The higher discrepancies seen at energies above 5 MeV may be produced by the fact of using not exactly the same spectrum in the primary electrom beam. In EGSnrc, the primary electrom beam energy is modelled by using a spectrum file; in Geant4, the electron beam energy is modelled by the gaussian curve that fits to that spectrum file. Perhaps this issue should be corrected, in order to eliminate this possible error source. Fig. 6 shows the distribution for the angle between the gamma momentum vector and the primary beam axis, θ. The same

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Fig. 8. Top: calculated angular distribution for gammas crossing the plane just below the flattening filter, normalised to particles per (event) history. The width of each bin is 1.5 deg. Bottom: calculated ratios.

B. SSD 90 cm relative discrepancies as in Fig. 5 appear between the different simulations, i. e., about 20% between Geant4 Standard and EGSnrc, and 5% between Geant4 LowEnergy and EGSnrc. These discrepancies are precisely of the same magnitude as found between the calculated absolute dose curve, so it seems that the origin of such discrepancies is the fact of having a higher gamma fluence in Geant4. That could mean that Geant4 produces too many bremsstrahlung photons in the target, compared to EGSnrc.

The photon energy distribution and the fluence between the machine and the water phantom are shown in Fig. 7-8, respectively. Clearly, in Fig. 7 the discrepancies are basically the same as the ones shown in Fig. 5, meaning that the photon transport is modelled in Geant4 as good as EGSnrc. Fig. 8 compares the fluences between the three simulations. Besides having the same discrepancies as in previous figures, Geant4 don’t reproduce the same penumbra as EGSnrc does, being the penumbra simulated by EGSnrc smaller than the one

calculated by Geant4. This effect may be caused by having different spacial distributions for the primary electron beam, but has not been studied yet. In spite of not having experimental data for the phase space analysis, two recent works made by Faddegon et. al. can help to solve this issue. They found a relative difference of 15% regarding photons produced by electron bremsstrahlung [16], and in order to find the origin of such discrepancies, they made a systematic bremsstrahlung analysis [17], finding that Geant4 wasn’t able to fit to the experimental bremsstrahlung data as good as EGSnrc. V. C ONCLUSIONS A Siemens Primus Linac was simulated by EGSnrc and Geant4 Monte Carlo codes, to study the feasibility of Geant4 to simulate a typical photon therapy machine. Despite of having high noise levels in the dose calculations, we have found some issue to be improved in Geant4. Geant4 is capable to reproduce relative dose curves (PDD and profiles) as accurate as EGSnrc, when the Variance Reduction Techniques are switched off. However, the statistical noise level is really high, so in order to be a competitive code in this area, Geant4 should include some of these Variance Reduction Techniques. Although the relative dose curves seem to fit to the experimental data, there are a sizeable relative differences in the simulated absolute dose curves, between the Geant4 physics lists. As shown from the PSD analysis, such differences seem to be due to an overproduction in bremsstrahlung photons in the target. These results have been sent to the Geant4 Collaboration to solve this issue.

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