Verification of a commercial implementation of the Macro-Monte-Carlo ...

ARTICLE IN PRESS TECHNISCHE MITTEILUNG

Verification of a commercial implementation of the MacroMonte-Carlo electron dose calculation algorithm using the virtual accelerator approach ¨ Wulff2,3, Heiko Karle1, Klemens Zink2 Jakob Tertel,1,2, Jorg 1

Department of Radiation Oncology and Radiation Therapy, Clinical Center of the Johannes Gutenberg University of Mainz, Germany 2 ¨ Medizinische Physik und Strahlenschutz – IMPS, University of Applied Sciences Gießen, Germany Institut fur 3 ¨ Marburg ¨ Strahlendiagnostik, Medizinisches Zentrum fur ¨ Radiologie, Philipps Universitat Klinik fur Received 4 June 2009; accepted 2 November 2009

Abstract In this work, the accuracy of the implementation of the Macro Monte Carlo electron dose calculation algorithm into the radiation therapy treatment planning system Eclipse is evaluated. This implementation – called eMC – uses a particle source based on the Rotterdam Initial Phase-Space model. A three-dimensional comparison of eMC calculated dose to dose distributions resulting from full treatment head simulations with the Monte Carlo code package EGSnrc is performed using the ‘virtual accelerator’ approach. Calculated dose distributions are compared for a homogeneous tissue equivalent phantom and a water phantom with air and bone inhomogeneities. The performance of the eMC algorithm in both phantoms can be considered acceptable within the 2%/2 mm Gamma index criterion. A systematic underestimation of dose by the eMC algorithm within the air inhomogeneity is found.

Keywords: Monte Carlo, electrons, treatment planning

Verifizierung einer kommerziellen Implementierung des Macro-Monte-Carlo Dosisberechnungsalgorithmus unter Anwendung eines virtuellen Beschleunigers Zusammenfassung In dieser Arbeit wird die Implementierung des MacroMonte-Carlo Dosisberechnungsalgorithmus fur ¨ Elektronen im Bestrahlungsplanungssystem Eclipse untersucht, welche dort eMC genannt wird. Als Quellenmodell dient ein modifiziertes ‘‘Rotterdam Initial Phase-Space model’’. Unter Verwendung eines virtuellen Beschleunigers werden dreidimensionale Dosisverteilungen, resultierend aus Monte-Carlo-Beschleunigerkopfsimulationen mit EGSnrc, mit denen des Bestrahlungsplanungssystems verglichen. Ein homogenes gewebeaquivalentes ¨ Phantom und ein Wasserphantom mit Inhomogenitaten ¨ aus Luft und Knochen werden hierzu verwendet. Die Dosisberechnungsgenauigkeit in beiden Phantomen basiert auf einem Gamma-Index-Test mit 2%/2 mm akzeptabel. In Luft findet eine deutliche systematische Unterschatzung der Dosis durch den eMC-Algorithmus ¨ statt. ¨ ¨ Schlusselw orter: Monte Carlo, Elektronen, Bestrahlungsplanung

 Korrespondenzanschrift: Universitatsmedizin der Johannes Gutenberg-Universitat, Langenbeckstraße 1, 55131 Mainz, Germany. ¨ ¨

E-mail: [email protected] (J. Tertel).

Z. Med. Phys. 20 (2010) 51–60 doi: 10.1016/j.zemedi.2009.11.001 http://www.elsevier.de/zemedi

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1. Introduction

2. Methods

Monte Carlo (MC) algorithms are widely accepted as being the most precise method to calculate dose distributions for radiation therapy [1]. MC codes are able to track individual particles and their secondary particles based on the underlying physical laws. Interactions can be explicitly simulated for every particle. This property makes MC calculations very accurate, but also time consuming. During the last decade MC based algorithms for electron beam treatment planning have been developed that allow for accurate dose calculation while keeping calculation times reasonably short, thereby enabling clinical usage. This is achieved with variance reduction techniques [2] or by making simplifications to the MC particle transport for instance by precalculating data and appropriately applying it to the specific patient geometry. Available algorithms include: MMC [3], VMC [4], DPM [5] and PEREGRINE [6]. Reviews on MC in radiation therapy treatment planning have been provided by Chetty et al. [1] and by the Netherlands Commission on Radiation Dosimetry [7]. The Macro Monte Carlo algorithm (MMC) [3,8] has been implemented into the treatment planning system (TPS) Eclipse by Varian, where it is named eMC (electron Monte Carlo). So far the performance of this algorithm has been investigated by comparing calculated dose distributions to measurements [9,10] and by using a standard verification data set for several different phantoms [11]. When comparing measurements in a water tank at the accelerator site to dose calculation results from the TPS, uncertainties in detector position, detector response, accelerator output constancy and voxel size versus detector size need to be considered [12]. These uncertainties can be minimized, but not eleminated, requiring experience and care for detail. Especially steep dose gradients produced by electron beams may produce non-negligible diffences between TPS-calculation and measurements. In this work the performance of the eMC algorithm is being evaluated by comparisons with EGSnrc calculations employing the ‘virtual accelerator’ approach [13]. This method bypasses the mentioned uncertainties by building a MC model of an accelerator using the MC code BEAMnrc [14] and scoring dose in phantoms with DOSXYZnrc [15]. By defining the same voxel sizes and positions for calculations in the TPS and with DOSXYZnrc, it is possible to achieve proper comparability of the respective dose calculation results. Calculated dose distributions for a homogeneous tissue equivalent phantom and the socalled ‘trachea and spine phantom’ are used to evaluate the MMC implementation in Eclipse 8.2.23 with dose calculation framework version 8.2.22. The TPS is running on a workstation with Windows XP SP2, a 2.5 GHz Intel Xeon processor and 3 GB RAM.

2.1. Electron Monte Carlo (eMC) Algorithm The eMC algorithm is comprised of an adapted version of the Rotterdam IPS (Initial Phase-Space) model [16] and the MMC dose calculation algorithm. The IPS model acts as the particle source for the MMC. Electrons and photons are generated according to a mathematical model of the beam, which is adapted to measured electron beam data. Four sub-sources describe the properties of the electron beam in a plane at a distance of 95 cm from the focus, just below the applicator. For configuration, open beam and applicator-specific depth dose curves have to be supplied for each energy, including absolute dose in cGy/ MU at a defined point on the depth dose curve. Furthermore profiles in air measured in an open beam without applicator are required. The MMC algorithm uses precalculated data to track electrons through the patient geometry. The precalculated data arises from EGSnrc MC calculations for a sphere geometry. Repeated simulations of a single electron being tracked through the sphere are performed to determine the probability distribution functions (PDF) for exit position, direction and energy of the primary electron emerging from the sphere dependent on its density and material as well as the initial energy of the electron. The electron transport in the TPS is based on sampling values from the PDF database. The electrons trajectory through matter is transformed into a chain of spheres, where the location of each sphere is dependent on the position and direction of the primary electron exiting the previous sphere. A simplified scattering model is used to account for energy deposited by secondary particles [3,8]. The density value of a sphere in the patient geometry is determined by the average density of the voxels it covers. For the dose calculation this density is randomly substituted with one of two densities for which precalculated PDF exist. These two densities are the adjacent densities of the average voxel density available in the PDF database. This method is used because of the limited amount of densities and materials for which PDFs have been precalculated [17]. In the eMC implementation, the user is enabled to adjust several parameters that affect calculation times and accuracy [17]. The most important ones being the target statistical accuracy, calculation grid size, smoothing method and smoothing strength. The significant impact of these parameters on dose distributions has been shown by Ding et al. [10], Pemler et al. [9] and Popple et al. [11]. The target statistical accuracy is defined as the average statistical uncertainty of all voxels with doses larger than 50% of Dmax . Smoothing is optional and can be performed by means of a 3-D Gaussian filter or a 2-D

ARTICLE IN PRESS J. Tertel et al. / Z. Med. Phys. 20 (2010) 51–60

Median filter. Both can be applied with three different smoothing strengths. Furthermore the maximum amount of particle histories and the random generator seed can be chosen, as well as an accuracy limit for the monitor unit (MU) calculation (this prevents the dose calculation from voxels with dose of low accuracy). 2.2. Virtual Accelerator Approach Typically the accuracy of dose calculation algorithms is evaluated by comparing dose calcuations from the TPS with measurements at the accelerator site. The virtual accelerator approach [13] substitutes measurements with MC dose calculations using a BEAMnrc model of an accelerator treatment head. The needed commissioning data such as depth dose curves and profiles for the dose calculation algorithm of the TPS have to be calculated with the BEAMnrc model. The major challenge is to ensure identical phantoms for both the treatment planning system and DOSXYZnrc. A procedure similar to the one described by Wieslander and Kno¨ os ¨ [13] is employed. First the DICOM phantoms are imported to the TPS where an electron field is calculated and the corresponding plan, including image data and dose distribution, is exported. In Matlab 7.0.0 (R14) (www.mathworks.com) an .egsphant file [15] is created with the voxel boundaries defined by the eMC calculation grid and densities derived from the DICOM images. The .egsphant file defines the materials, densities and voxel boundaries for the phantoms used in simulations with DOSXYZnrc. In this work spatial trilinear interpolation is used to reduce the slice resolution from the original 1  1 mm2 to the resolution of the calculation grid of 2  2 mm2 . Hence, dose calculations can be performed with BEAMnrc/DOSXYZnrc and the eMC algorithm with the same geometrical setup and the same phantoms. 2.3. EGSnrc calculations The MC modeling of electron beams has been reviewed by Ma and Jiang [18]. BEAMnrc and DOSXYZnrc are codes based on the EGSnrc MC code [19]. In BEAMnrc a linear accelerator treatment head can be modeled. DOSXYZnrc enables the scoring of dose in a voxelized volume with a cartesian coordinate system. Voxel sizes, densities and materials can be defined by the user. The code comes with a set of predefined sources. The particle source can also be a BEAMnrc accelerator model when linked as a shared library [15]. The information needed to accurately model the Varian accelerator (high energy type) in BEAMnrc is provided by Varian Medical Systems. The respective energies of the primary electron beams are chosen to produce depth dose curves on the central axis coinciding with measurements

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from a Varian Clinac 2100C at the depth of 50% of the maximum dose (R50 ). No further efforts regarding agreement to measurements are made. In BEAMnrc the primary electron beam is defined as a parallel, circular and monoenergetic beam with a Gaussian radial distribution and a full width at half maximum of 0.2 cm [20]. For the nominal energies of 6 MeV, 12 MeV and 20 MeV the energy of the primary electron beam is set to 6.5 MeV, 13.2 MeV and 21.8 MeV respectively. The voxel size for depth dose curves in water (density: 1.0 g/ ccm) of the input data for the eMC is chosen to be X  Y  Z 5  5  1 mm3 (accelerator coordinate system) and for profiles in air (density: 0.0012 g/ccm) 5  5  5 mm3 . For the open beam calculations the jaws are set to a 40  40 cm2 field with no applicator. All simulations for input data calculation employ the ‘dsurround’ option in DOSXYZnrc [15]. For the calculation of depth dose curves and profiles in homogeneous media only dose is scored in a column or row of voxels respectively, which is enclosed by a material with dimensions defined by ‘dsurround’. This greatly reduces calculation times in combination with the variance reduction technique ‘HOWFARLESS’ [21]. A cut-off energy for photons (PCUT) of 10 keV and for electrons (ECUT) of 700 keV for the calculation of commissioning data and the homogeneous phantom are chosen. ECUT is 521 keV for the trachea and spine phantom. The photon cross sections are set to ‘xcom’, and ‘NIST’ brems cross sections are used. The default values of the other EGSnrc transport parameters [15] are not changed. For the calculation of in air profiles and depth dose curves, the variance reduction techniques ‘HOWFARLESS’ and range rejection (with ESAVE = 2 MeV) [14] are switched on. The PRESTA-I boundary crossing algorithm is chosen in order to reduce calculation times. PRESTA-I is known to introduce calculation artifacts under certain conditions [22]. Preliminary calculations with differenct parameter combinations have been performed for the trachea and spine phantom. The previously stated settings were found to be most efficient while not introducing artifacts.

2.4. Phantoms To verify the commissioned beam model, dose distributions are calculated with the eMC and EGSnrc in a simple homogeneous tissue equivalent phantom. The trachea and spine phantom (Fig. 1), which has been successfully used in previous works [10,23,24] for ion chamber measurements, is used to evaluate the performance of the eMC algorithm in the presence of inhomogeneities. Both phantoms are built as a discrete three-dimensional matrix of Hounsfield Units (HU) with Matlab and exported as a series of DICOM images. The slice

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Figure 1. The original DICOM trachea and spine phantom with 1  5  1 mm3 voxels (a) and the interpolated phantom used for calculations in DOSXYZnrc and (b) in 2  5  2 mm2 resolution. The central XZ-plane (Y=0 cm) is shown on the left and a YZplane through a bone (X=1.5 cm) on the right. The trilinear interpolation introduces new density values. PMMA (next to the bone) and Lung (along the border of the air tube) are assigned to these voxels.

thickness is 5 mm and the resolution within a slice is set to 1  1 mm2 . 50 slices are used for both phantoms. The homogeneous phantom is made of tissue equivalent material with a density of 0.979 g/cc. The original trachea and spine phantom consists of a tube of air and four hard bone disks embedded in a slab of solid water with a total thickness of 47 mm. The tube of air has a diameter of 26 mm and is located 2 mm below the surface. 5 mm below the tube, the disks are located with an interspace of 5 mm. The disks have a diameter of 25 mm and a thickness of 14 mm [10]. The following HU and corresponding densities are assigned to the used materials in the trachea and spine phantom: Air: 1000 HU (0.001 g/cc), Water: 0 HU (1 g/cc) and bone: 1000 HU (1.61 g/cc). The interpolation introduces new density values at some material interfaces. Polymethyl methacrylate (PMMA, next to the bone) and lung (around the air tube) are assigned to these voxels. A proper conversion of HU to density values was ensured by using the same HUto-density ramps in DOSXYZnrc, Eclipse and Matlab for each phantom. The cross section data for the DOSXYZnrc calculations (PEGS data file [19]) in the trachea and spine phantom is taken from the cross section library used in the calculations of the PDF for the MMC. 2.5. Dose comparison Dose calculated with eMC and BEAMnrc/DOSXYZnrc are both reported as dose to medium. All calculations with BEAMnrc/DOSXYZnrc and eMC for dose comparison

are performed with a gantry angle of 0 degrees and a field size of 10  10 cm2 at an SSD of 100 cm. The statistical uncertainty for the DOSXYZnrc calculations in the homogeneous phantom is 0.6 % or less at the practical range Rp (including error propagation through normalizing), resulting in 6:4  108 histories calculated for 6 MeV, 10  108 for 12 MeV and 25  108 for 20 MeV. The same number of histories is used in the case of the trachea and spine phantom. In Eclipse dose distributions are calculated with target statistical accuracies of 2% for the tissue equivalent phantom and 1% and 2% for the trachea and spine phantom, all with a calculation grid size of X  Y  Z 2  5  2 mm3 (accelerator coordinate system) and the default random generator seed of 39916801. Calculations with 2% accuracy are repeated using Gaussian smoothing in medium strength. Data analysis is performed with Matlab. A voxel near the maximum on the central axis is used for normalization. This procedure is suggested by Pemler et al. for MC calculated dose distributions of single electron fields [9]. Depth dose curves as well as profiles are extracted from the normalized data. Gamma Index values [25] are calculated by an algorithm that compares single slices of the three-dimensional data. Thus, the Gamma index in this work is a conservative approximated three-dimensional evaluation of the dose distributions. The dose difference for the Gamma index calculation is the absolute difference of the normalized dose. To make the Gamma index calculation reasonably sensitive, the evaluated volume is

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reduced to a box that contains the whole field and excludes the large volume of the phantom with low dose caused by scattered radiation. Acceptance criteria of 2%/ 2mm and 3%/3mm are chosen. The Gamma index calculations are performed for 2 volumes of interest (VOI) in the trachea and spine phantom. TrVOI1 encompasses the whole field (voxels with dose above 0.05), TrVOI2 has the same outer dimensions but excludes the voxels of the airfilled tube.

3.1. eMC Input Data The statistical uncertainty of the open beam profiles in air is below 0.5% for dose above 50% of the central axis value, all depth dose curves for configuration show a statistical uncertainty of less than 0.5 % up to Rp . These depth dose curves are normalized to 100% at their

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3. Results and Discussion

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Figure 2. Depth dose curves (a, c and e) and profiles for three depths (b, d and f) of the 6 MeV, 12MeV and 20 MeV beams in the tissue equivalent phantom (density: 0.979 g/cc). eMC dose is plotted for 2% target accuracy (eMC 2%) and 2% target accuracy with three-dimensional Gaussian smoothing in medium strength (eMC 2% sm.).

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Depth dose curves and profiles for various depths in crossplane direction (X) are shown for all three energies and a field size of 10  10 cm2 in Figure 2, one profile being in the Dmax region, one near R50 and another one close to Rp of the respective beam. Smoothed and unsmoothed eMC dose with 2% target accuracy is shown in these plots. The standard deviation of the depth dose curves of the EGSnrc data is below 0.5% up to Rp and the range of 5.5 cm to 5.5 cm in crossplane direction for the shown profiles except for the profile close to practical range, where the standard deviation is below 1% in the same interval. The normalisation points are in depths of 1.1 cm for 6 MeV, 2.5 cm for 12MeV and 3.3 cm for 20 MeV on the central axis. For the 12 and 20 MeV beams, depth dose curves and profiles are in excellent agreement with the DOSXYZnrc calculated dose. The 6 MeV plots reveal larger deviations of up to 10% in the fall off region (Fig. 2). Deviations of several millimeters are found for the isodose lines in the high dose region for all three energies (Fig. 3). This is also the region where most of the voxels are located that fail the Gamma index test for both chosen criteria (Table 1). Smoothing slightly improves the Gamma index results for 12 MeV and 20 MeV. The location of the larger deviations found for 6 MeV especially in the fall-off region can be partially attributed to the location of the normalisation point. Shifting the position of the normalisation point will also change the location of the differences, mainly due to the the differing slope in the fall off region. Calculation times summarized in Table 2 are clinically acceptable overall.

3.3. Trachea and Spine Phantom A comparison of depth dose curves through the center of a bone disc ([X,Y]=(1.5,0)) and crossplane profiles are presented in Figure 4. The normalization depths on the central axis are 3.3 cm for 6 MeV, 3.5 cm for 12 MeV and 5.9 cm 20 MeV. The standard deviation of the dose in all voxels included in the profiles calculated with EGSnrc is well below 0.5% for voxels with dose above 0.3. In general, the agreement of the depth dose curves is acceptable. Considerable deviations are found at material interfaces for 6 and 20 MeV. The accuracy of the eMC dose calculation is in general rather poor in air for all energies, but this finding is not of clinical significance. This deviation has not been observed

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maximum and the profiles are normalized to their central axis value. The eMC is successfully commissioned using the calculated data.

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Figure 3. Isodose plots of the central XZ-plane (Y=0 cm) for the 6 MeV (a), 12 MeV (b) and 20 MeV (c) beams in a tissue equivalent phantom (density: 0.979 g/cc). Isodose lines for 0.1, 0.3, 0.5, 0.7, 0.8 and 0.95 are shown. DOSXYZnrc isodose lines are plotted thick, eMC is plotted thin for 2% (left hand side) and 2% smoothed (right hand side) target accuracy.

in an earlyer version of the eMC algorithm, therefor it is expected to be caused by an error in this specific implementation of the MMC. Isodose overlays of EGSnrc and unsmoothed eMC dose are presented in Figure 5. The profiles and isodose plots show that the eMC algorithm is capable of predicting the location and magnitude of steep dose gradients caused by inhomogeneities. Increasing the

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Table 1 Gamma Index Table for the homogeneous phantom (Hom.) and the Trachea Phantom (TrVOI1 encompasses the whole field (voxels with dose above 0.05), TrVOI2 has the same outer dimensions but excludes the voxels of the air-filled tube). The percentage of voxels passing the respective criterion are shown for all energies and chosen settings. 2%/2mm

3%/3mm

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Target Accuracy

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TrVOI1

TrVOI2

Hom.

TrVOI1

TrVOI2

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2% sm. 2% 1% 2% sm. 2% 1% 2% sm. 2% 1%

94:9% 96:6% 93:9% 91:8% 97:6% 96:4% -

89:0% 92:8% 91:3% 87:9% 94:0% 92:6% 75:6% 92:5% 94:1%

93:5% 96:9% 96:3% 91:5% 97:0% 96:5% 78:1% 94:9% 97:4%

98:8% 99:6% 98:0% 97:3% 99:9% 99:9% -

93:2% 96:5% 95:1% 93:7% 97:5% 96:1% 89:1% 97:5% 96:7%

97:5% 99:6% 99:5% 96:8% 99:6% 99:4% 91:8% 99:3% 97:7%

Table 2 eMC calculation times (Calc. Time) and histories calculated in the homogeneous phantom (Hom.) and the trachea and spine phantom (Tr.) for the respective energies and eMC target accuracies. Energy [MeV]

Phantom Target Accuracy

Calc. Time [s]

Histories ½106 

6 6 6 12 12 12 20 20 20

Hom. Tr. Tr. Hom. Tr. Tr. Hom. Tr. Tr.

42/38 25/22 77 80/76 58/55 180 205/202 109/105 416

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2%/2% sm. 2%/2% sm. 1% 2%/2% sm. 2%/2% sm. 1% 2%/2% sm. 2%/2% sm. 1%

eMC target accuracy from 2% to 1% produces smoother isodose lines with better agreement to the DOSXYZ reference. Again, larger deviations are found for the 0.8 and 0.95 isodose lines and in air. The results of the Gamma index calculations are shown in Table 1. Excluding the air-filled volume increases the percentage of voxels that pass the criteria. For TrVOI2 the results are already acceptable for the 2%/2mm criterion. The results for 1% target accuracy is slightly better only for 20 MeV. The calculation times and calculated histories are summarized in Table 2. For the trachea and spine phantom less histories need to be calculated for the same target accuracy than for the homogeneous phantom. Changing the eMC target accuracy from 2% to 1% increases the amount of calculated histories by about a factor of four. The resulting calculation times are acceptable overall (Table 2).

Possible explanations for the found deviations at material interfaces are the sphere radii, which are limited to a minimum of 0.5 mm, and the method of material assignment. The way the eMC algorithm assigns densities to spheres, especially at material interfaces, dose is calculated for densities and materials that might differ significantly from the ones that are defined in the DOSXYZnrc phantom. Generalizations made with respect to the scattering angle while precalculating the PDF for the MMC in air may account partially for the dose deviations found in the air tube (Fix, personal communication). In addition, the dimension of the air inhomogeneity allows for large sphere sizes, leading to the electrons being transported in just a few steps across the air inhomogeneity, hence underestimating lateral scatter and depositing too little energy in air. The standard deviation of the dose values in air also seems to be compromised by the small amount of simulated spheres. The overestimation of dose below the bones can be explained by the lack of lateral scatter of the electrons in air. It needs to be mentioned that Version 8.6.14 of the dose eMC algorithm has been released in 2008 but was not accessible to the authors.

4. Conclusion The eMC algorithm of Varians TPS Eclipse has been commissioned using depth dose curves and profiles from a virtual BEAMnrc accelerator model. This model is also used to calculate DOSXYZnrc dose distributions in the homogeneous and the trachea and spine phantom, thereby generating reference dose distributions for adequate comparison to eMC dose calculations in the same phantoms. The observed differences and calculation times

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Figure 4. Depth dose curves (a, c and e) and profiles (b, d and f) for two depths of the 6 MeV, 12 MeV and 20 MeV beams in the trachea and spine phantom. Depth dose curves run through the center of the middle right bone (X=1.5 cm). eMC dose is plotted for 1% target accuracy (eMC 1%) and 2% target accuracy (eMC 2%).

are acceptable overall. Dose calculation in air is flawed but clinically not relevant. The results for the profiles in this work are compareable to the findings of Ding et al.

[10], where a similar trachea and spine phantom was used for measurements in a water tank for three different energies, but the analysis of the accuracy of the eMC

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Acknowledgement

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The authors would like to thank Dr. Michael Fix of the University Bern, Switzerland for useful suggestions and providing the interpolated trachea and spine phantom for DOSXYZnrc, as well as David Jany of the IMPS Giessen and Florian Griff of Varian Medical Systems. This work was partially financed by a ‘MAIFOR’ research grant by the Johannes Gutenberg University of Mainz.

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Figure 5. Isodose plots of the 6 MeV, 12 MeV and 20 MeV beams in the trachea and spine phantom’s central XZ-plane (Y=0). Isodose lines for 0.1, 0.3, 0.5, 0.7, 0.8 and 0.95 are shown. DOSXYZnrc isodose lines are plotted thick, eMC is plotted thin for 1% (left hand side) and 2% (right hand side) target accuracy. Voxels between 2 and 28 mm depth are air.

algorithm with the virtual accelerator approach proved to enable a more thorough evaluation than water tank measurements.

References [1] Chetty IJ, Curran B, Cygler J, DeMarco JJ, Ezzell G, Faddegon BA, et al. Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning. Med Phys 2007;34:4818–53. [2] Sheikh-Bagheri D, Kawrakow I, Walters B, Rogers DWO. Monte Carlo Simulations: Efficiency Improvement Techniques and Statistical Considerations, Published in: Integrating New Technologies into the Clinic: Monte Carlo and Image-Guided Radiation Therapy, Proceedings of 2006 AAPM Sommer School. Madison WI: Medical Physics Publishing; 2006. [3] Neuenschwander H, Born EJ. A macro Monte Carlo method for electron beam dose calculations. Phys Med Biol 1992;37:107–25. [4] Kawrakow I, Fippel M, Friedrich K. 3D electron dose calculation using a Voxel based Monte Carlo algorithm (VMC). Med Phys 1996;23:445–57. [5] Sempau J. DPM, a fast, accurate Monte Carlo code optimized for photon and electron radiotherapy treatment planning dose calculations. Phys Med Biol 2000;45:2263–91. [6] Hartmann Siantar CL. Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom. Med Phys 2001;7: 1322–37. [7] Reynaert N, Marck Svd, Schaart D, Zee Wvd, Tomsej M, VlietVroegindeweij CV, et al. Monte Carlo Treatment Planning – An Introduction: Report 16 of the Netherlands Commission on Radiation Dosimetry. Netherlands Commission on Radiation Dosimetry, Subcommittee Monte Carlo Treatment Planning, Delft, Netherlands: 2006. [8] Neuenschwander H, Mackie TR, Reckwerdt PJ. MMC – A highperformance Monte Carlo code for electron beam treatment planning. Phys Med Biol 1995;40:543–74. [9] Pemler P, Besserer J, Schneider U, Neuenschwander H. Evaluation of a commercial electron treatment planning system based on Monte Carlo techniques (eMC). Zeitschrift fur ¨ Medizinische Physik 2006;16:313–29. [10] Ding GX, Duggan DM, Coffey CW, Shokrani P, Cygler J. First macro Monte Carlo based commercial dose calculation module for electron beam treatment planning – new issues for clinical consideration. Phys Med Biol 2006;51:2781–99. [11] Popple RA, Weinber R, Antolak JA, Ye SJ, Pareek PN, Duan J, et al. Comprehensive evaluation of a commercial macro Monte Carlo electron dose calculation implementation using a standard verification data set. Med Phys 2006;33:1540–51. [12] Blomquist M, Karlsson M, Karlsson M. Test procedures for verification of an electron pencil beam algorithm implemented for treatment planning. Radiother Oncol 1996;39:271–86. [13] Wieslander E, Kno¨ os ¨ T. A virtual linear accelerator for verification of treatment planning systems. Phys Med Biol 2000;45:2887–96. [14] Rogers DWO, Faddegon BA, Ding GX, Ma CM, We J, Mackie TR. BEAM: a Monte Carlo code to simulate radiotherapy treatment units. Med Phys 1995;22:503–24.

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J. Tertel et al. / Z. Med. Phys. 20 (2010) 51–60

[15] Walters B, Kawrakow I, Rogers DWO. Report PIRS-794revB, DOSXYZnrc Users Manual. National Research Council of Canada; 2007. [16] Janssen JJ, Korevaar EW, van Battum LJ, Storchi PR, Huizenga H. A model to determine the initial phase space of a clinical electron beam from measured beam data. Phys Med Biol 2001;46:269–86. [17] Eclipse Planning Reference Guide for Algorithms P/N B401653R01I; 2004. [18] Ma CM, Jiang SB. Monte Carlo modelling of electron beams from medical accelerators. Phys Med Biol 1999;44:R157–89. [19] Kawrakow I, Rogers DWO. Report PIRS-701, The EGSnrc Code System: Monte Carlo Simulation of Electron and Photon Transport. Ottawa: National Research Council of Canada; 2006. [20] Huang VW, Seuntjens J, Devic S, Verhaegen F. Experimental determination of electron source parameters for accurate Monte Carlo calculation of large field electron therapy. Phys Med Biol 2005;50:779–86.

[21] Walters B, Kawrakow I. A ‘‘HOWFARLESS’’ option to increase efficiency of homogeneous phantom calculations with DOSXYZnrc. Med Phys 2007;34:3794–807. [22] Walters B, Kawrakow I. Technical note: Overprediction of dose with default PRESTA-I boundary crossing in DOSXYZnrc and BEAMnrc. Med Phys 2007;34:647–50. [23] Ding GX, Cygler J, Zhang GG, Yu MK. Evaluation of a commercial three-dimensional electron beam treatment planning system. Med Phys 1999;26:2571–80. [24] Cygler J, Battista JJ, Scrimger JW, Mah E, Antolak J. Electron dose distributions in experimental phantoms: a comparison with 2D pencil beam calculations. Phys Med Biol 1987;32:1073–86. [25] Low DA, Harms WB, Mutic S, Purdy JA. A technique for the quantitative evaluation of dose distributions. Med Phys 1998;25: 656–61.