Macro Monte Carlo Research Articles

Development of an extended Macro Monte Carlo method for efficient and accurate dose calculation in magnetic fields.

Progress in the field of magnetic resonance (MR)-guided radiotherapy has triggered the need for fast and accurate dose calculation in presence of magnetic fields. The aim of this work is to satisfy this need by extending the macro Monte Carlo (MMC) method to enable dose calculation for photon, electron, and proton beams in a magnetic field. The MMC method is based on the transport of particles in macroscopic steps through an absorber by sampling the relevant physical quantities from a precalculated database containing probability distribution functions. To enable MMC particle transport in a magnetic field, a transformation accounting for the Lorentz force is applied for each macro step by rotating the sampled position and direction around the magnetic field vector. The transformed position and direction distributions on local geometries are validated against full MC for electron and proton pencil beams. To enable photon dose calculation, an in-house MC algorithm is used for photon transport and interaction. Emerging secondary charged particles are passed to MMC for transport and energy deposition. The extended MMC dose calculation accuracy and efficiency is assessed by comparison with EGSnrc (photon and electron beams) and Geant4 (proton beam) calculated dose distributions of different energies and homogeneous magnetic fields for broad beams impinging on water phantoms with bone and lung inhomogeneities. The geometric transformation on the local geometries is able to reproduce the results of full MC for all investigated settings (difference in mean value and standard deviation <1%). Macro Monte Carlo calculated dose distributions in a homogeneous magnetic field are in agreement with EGSnrc and Geant4, respectively, with gamma passing rates >99.6% (global 2%, 2mm and 10% threshold criteria) for all situations. MMC achieves a substantial efficiency gain of up to a factor of 21 (photon beam), 66 (electron beam), and 356 (proton beam) compared to EGSnrc or Geant4. Efficient and accurate dose calculation in magnetic fields was successfully enabled by utilizing the developed extended MMC transport method for photon, electron, and proton beams.

36 Monte Carlo simulation of absorbed dose distribution for electron beam using GATE/GEANT4

Introduction Limits of Treatment Planning Systems (TPS) dose calculation for photon beams have been widely studied. There are fewer studies on electron beam dose calculation. Fast Electron Monte Carlo (eMC, Varian, Palo Alto, CA) is a clinical dose distribution calculation algorithm for electron beam, based on an advanced variance reduction technique, Macro Monte Carlo (MMC) [1] . Results for complex cases (heterogeneity, irregular surface contour) are limited. A GATE/GEANT4 model of a radiotherapy linac (Varian, TrueBeam) is implemented. The purpose of this study is to evaluate these algorithms by comparing them to film measurements in complex cases. Methods Validation of GATE model is performed on homogenous water phantom. Percentage depth dose curves (PDD) and lateral dose profiles (LDP) are compared with experimental measurement (6 and 9 MeV). Results of dose distribution calculation for eMC and GATE are comparing with Gafchromic EBT3 (Ashland ISP, Wayne, NJ) films, for complex cases including heterogeneities (lung, bone) and irregular surface (step). Normalization are achieved in a homogenous water region for dose profiles at two different depths (at contact and at a distance of the heterogeneity). Global Gamma Index Pass Rate (GIPR) 1D is used to compare the data sets. Results When comparing GATE and measurements, GIPR 2 % / 2 mm for PDD and LDP in homogenous water phantom is 100% for 6 MeV and 9 MeV. GIPR 3 % / 3 mm (threshold >10% D max ) for complexes cases (lung, bone and step) is >98.5% for GATE (6, 9 MeV) except for only one case at 6 MeV (at contact with lung heterogeneity: 82.9%). But, for eMC in lung case, GIPR are 100% for 9 MeV electrons but only 65.6% and 84.4% at 6 MeV at contact and at 10 mm of the heterogeneity, respectively. In presence of bones, GIPR are 100% (6, 9 MeV) except at 9 MeV, at contact of the heterogeneity (69.7%). For irregular surface cases GIPR of eMC vs. films was superior to 95.2% and 99.2% for 6 and 9 MeV respectively. Conclusions GATE model for electron beams is validated in homogeneous water phantom. In presence of surface irregularities (step) satisfactory results are obtained for both GATE and eMC. Nevertheless, when comparing to measurements for heterogeneous media, and in particular after lung (6 MeV) and bones (9 MeV) eMC was limited while GATE was satisfactory in all configurations. The study is currently carried on for more energy (12 and 18 MeV) and clinical cases (face). GATE could be proposed as a 3D dose check solution for complex electron beams.

Monte Carlo based beam model using a photon MLC for modulated electron radiotherapy

Modulated electron radiotherapy (MERT) promises sparing of organs at risk for certain tumor sites. Any implementation of MERT treatment planning requires an accurate beam model. The aim of this work is the development of a beam model which reconstructs electron fields shaped using the Millennium photon multileaf collimator (MLC) (Varian Medical Systems, Inc., Palo Alto, CA) for a Varian linear accelerator (linac). This beam model is divided into an analytical part (two photon and two electron sources) and a Monte Carlo (MC) transport through the MLC. For dose calculation purposes the beam model has been coupled with a macro MC dose calculation algorithm. The commissioning process requires a set of measurements and precalculated MC input. The beam model has been commissioned at a source to surface distance of 70 cm for a Clinac 23EX (Varian Medical Systems, Inc., Palo Alto, CA) and a TrueBeam linac (Varian Medical Systems, Inc., Palo Alto, CA). For validation purposes, measured and calculated depth dose curves and dose profiles are compared for four different MLC shaped electron fields and all available energies. Furthermore, a measured two-dimensional dose distribution for patched segments consisting of three 18 MeV segments, three 12 MeV segments, and a 9 MeV segment is compared with corresponding dose calculations. Finally, measured and calculated two-dimensional dose distributions are compared for a circular segment encompassed with a C-shaped segment. For 15 × 34, 5 × 5, and 2 × 2 cm(2) fields differences between water phantom measurements and calculations using the beam model coupled with the macro MC dose calculation algorithm are generally within 2% of the maximal dose value or 2 mm distance to agreement (DTA) for all electron beam energies. For a more complex MLC pattern, differences between measurements and calculations are generally within 3% of the maximal dose value or 3 mm DTA for all electron beam energies. For the two-dimensional dose comparisons, the differences between calculations and measurements are generally within 2% of the maximal dose value or 2 mm DTA. The results of the dose comparisons suggest that the developed beam model is suitable to accurately reconstruct photon MLC shaped electron beams for a Clinac 23EX and a TrueBeam linac. Hence, in future work the beam model will be utilized to investigate the possibilities of MERT using the photon MLC to shape electron beams.

SU-E-T-528: Beam Model Interface for Treatment Planning in Proton Therapy Using Macro Monte Carlo

Purpose: A previously developed macro Monte Carlo (MC) method for accurate and efficient dose calculations in proton radiotherapy is interfaced with a beam model in order to allow treatment planning for proton beams. Methods: The beam model interface generates particles above the beam modifiers such as block or range shifter plates for the macro MC algorithm and is based on an already existing beam model for modulated scanning beam lines. Based on the beam data of the commissioned beam model and the patient treatment plan, a sampling procedure is defined in order to provide the particle type, position, direction, energy and weight of the starting particle necessary for the macro MC transport through the beam modifiers and for the dose calculation. The new interface is validated by comparing sampled position and energy distributions of single spots with those from the already existing beam model. Furthermore, dose distributions in a water phantom for single spots of different energies calculated using either the new interface with the macro MC or the pencil beam algorithm available in Eclipse are compared. Results: The sampled distributions for the position within a spot as well as the energy distributions are in good agreement with the corresponding distributions of the already existing beam model. The ranges of the depth dose curves for the calculated dose distributions agree within 1 mm, while the dose differences are generally within 2% except close to the phantom surface where the pencil beam overestimates the macro MC dose by 3%. Conclusion: By interfacing a beam model with the macro MC dose calculation algorithm accurate treatment planning for proton radiation therapy beams is realized. This work was supported by Varian Medical Systems. This work was supported by Varian Medical Systems.

SU‐E‐T‐659: Inverse Treatment Planning for MERT Using Monte Carlo Calculations

Purpose: The use of electron beams to treat shallow tumors cou ld reduce the dose to the distal organs at risk. To employ modulated electron radiotherapy (MERT) an inverse treatment planning strategy which bases on a Monte Carlo (MC) Electron Beam Model (EBM) has been developed. Methods: The inverse planning process starts with the selection of the SSD, gantry angle and co llimator rotation for each electron field. These fields are then divided into a grid of beamlets. An MC EBM together with the macro MC (MMC) dose calculation algorithm is employed to pre‐calculate the dose distribution for each beamlet. Afterwards a direct aperture optimization (DAO) using simulated annealing minimizes a co st function which is the sum of the squared dose differences in all voxels of the PTV and the OARs between the actual value and a given upper or lower limit. For each step either a weight change or an aperture change is initiated. As the beamlet dose calculation neglects the MLC interaction a post processing weight optimization and MLC aperture adjustment has been carried out after the DAO has been finished. To test the algorithm an inverse treatment plan has been created for an academic situation and co mpared to the obtained results using a previously developed forward planning strategy. Results: The implementation of an inverse optimization inco rporating the home made EBM has been completed successfully. The time needed for the DAO of the academic situation is about 30 min. Compared to the forward planning the inverse optimization is able to reduce the dose to the OAR (mean dose from 41% to 38%) for the academic case. Conclusion: The developed inverse optimization employing the EBM and MMC can be used for treatment planning of MERT. This work was supported by Varian Medical Systems.This work was supported by Varian Medical Systems.

Macro Monte Carlo for dose calculation of proton beams

Although the Monte Carlo (MC) method allows accurate dose calculation for proton radiotherapy, its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations has been developed. The basic principle of the MMC transport is a local to global MC approach. The local simulations using GEANT4 consist of mono-energetic proton pencil beams impinging perpendicularly on slabs of different thicknesses and different materials (water, air, lung, adipose, muscle, spongiosa, cortical bone). During the local simulation multiple scattering, ionization as well as elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement, direction distributions and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, based on local simulations the radiation transport of neutrons and the generated ions are included into the MMC simulations for the dose calculations. In order to validate the MMC transport, calculated dose distributions using the MMC transport and GEANT4 have been compared for different mono-energetic proton pencil beams impinging on different phantoms including homogeneous and inhomogeneous situations as well as on a patient CT scan. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and phantoms considered. For the dose profiles the agreement is within 1% or 1 mm in all phantoms for all energies and depths. The comparison of the dose distribution calculated using either GEANT4 or MMC in the patient also shows an agreement of within 1% or 1 mm. The efficiency of MMC is up to 200 times higher than for GEANT4. The very good level of agreement in the dose comparisons demonstrate that the newly developed MMC transport results in very accurate and efficient dose calculations for proton beams.

MO-F-BRB-02: Macro Monte Carlo for Proton Dose Calculation in Different Materials.

Although the Monte Carlo (MC) method allows accurate dose calculation its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations in homogeneous materials has been developed. The macro MC is based on a local to global MC approach. The local simulations using Geant4 consist of mono-energetic proton pencil beams (10 to 250 MeV) impinging perpendicularly on slabs of different thicknesses (1-10 mm) and different materials (water, lung, muscle, adipose, bone). During the local simulation multiple scattering, ionization, elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, ions and neutrons are taken into account for the dose calculation. In order to validate the MMC, calculated dose distributions using the MMC transport and Geant4 have been compared for different mono-energetic proton pencil beams impinging on phantoms with different homogeneous materials. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and materials considered. For the dose profiles the agreement is within 1% or 1 mm for all energies, depths and materials. The efficiency of MMC is about 200 times higher than for Geant4. The dose comparisons demonstrate that the new MMC results in very accurate and efficient dose calculations for proton beams in homogeneous materials. In future, the MMC method will be extended to inhomogeneous situations in order to allow patient dose calculations for proton beams. This work was supported by Varian Medical Systems.

SU-D-218-06: Acceleration of Optical Photon Monte Carlo Simulations Using the Macro Monte Carlo Method.

The purpose of this work is to demonstrate that optical photon Monte Carlo simulations via a photon transport code called MCML can be accelerated using macro Monte Carlo (MMC) techniques. MCML was modified to incorporate the macro Monte Carlo radiation transport method. The original MCML uses scattering, absorption, reflection and refraction physics to transport optical photons through multi-layered geometries. The code determines transmission, reflection and absorption for the layered geometry specified by the user. To make the code run faster, the MMC version of MCML uses large, multi-interaction steps in regions that are homogeneous. These large steps are pre-computed and stored in a database with many step sizes, materials and photon energies. The MMC version of MCML determines whether large MMC steps or traditional Monte Carlo should be used depending on the photon's current location inthe geometry. The MMC version of MCML was tested against the original MCML code for a number of simple test geometries. It was also tested in anatomical geometries that are often uses in optical photon modeling. This includes skin and skull geometries. In each case, the reflection and transmission results from each code differed by less than 0.5%. The absorption data produced by each code also differed by less than 0.5% in most cases, and never differed by more than 2%. The MMC version of MCML runs between 1-3 times as many particles per unit time comparedto MCML, depending on the geometry. Applying Macro Monte Carlo methods to MCML produces a faster code without compromising accuracy. The speed-gains are greatest in geometries thathave regions that are large relative to the mean scattering length for photons in that region. This work has the potential to accelerate light modeling for both photodynamic therapy and near-infrared spectroscopic imaging.

WE‐C‐BRB‐10: Acceleration of Proton Monte Carlo Simulations Using the Macro Monte Carlo Method

Purpose: This work describes a new macro Monte Carlo method for proton beam dose calculation. Originally developed for electron beams, macro Monte Carlo (MMC) is designed to provide better computational efficiency than traditional MC without sacrificing accuracy. Methods: The proton MMC method performs dose calculation using pre‐calculated steps derived from MCNPX simulations. Simulations of mono‐energetic proton pencil beams ranging from 5–200 MeV impinging on homogenous cylinders of varying length, radius and material were carried out using MCNPX. The energy loss, trajectory and exit position of the exiting protons and secondary particles have been determined and used to create a pre‐calculated step database. The database is used to transport protons through an absorbing geometry in a step‐by‐step manner. Energy loss is scored in a 3D dose grid during each step. The creation of secondary particles is tracked as well. For validation purposes, the dose distributions for many monoenergetic proton beams have been calculated using proton MMC and MCNPX for single‐ and multi‐layered phantoms. The resulting central‐axis depth dose curves and dose profiles have been compared. The materials tested include water, bone, fat, soft tissue and lung. Results: The calculated central‐axis depth dose curves agree better than 1% or 1 mm for all pencil beams near the Bragg peak. The lateral dose profiles agree to better than 1% or 1 mm for all pencil beams near the Bragg peak. Away from the Bragg peak, the depth dose curves and lateral profiles agree better than 1% or 1 mm for energies below 100 MeV. Above 100 MeV, disagreement can reach 5%. The computational efficiency of proton MMC is about 100 times greater than for MCNPX. Conclusions: The results from the dose comparisons show that proton MMC is accurate and more efficient than traditional Monte Carlo.

SU‐E‐T‐672: Macro Monte Carlo for Protons: Proof of Principle

Purpose: For electron beams the macro Monte Carlo (MC) technique is well‐established. This work describes the proof of principle of a new macro MC method for proton beams in order to gain computational efficiency. Methods: The proof of principle is performed for the transport of primary protons in water. Pre‐simulations of mono‐energetic proton pencil beams ranging from 10 to 250 MeV impinging perpendicularly on water slabs of different thicknesses (1–10 mm) have been carried out using Geant4. The lateral displacement, the energy‐loss and the direction of all exiting primary protons have been scored and converted into probability density functions (PDFs). The macro MC method consists of stepwise transporting protons by selecting appropriate slab thicknesses and by means of sampling from corresponding PDFs. The sampled energy‐loss is deposited along the path between the entrance and exit positions of the proton for the current step. For validation purposes, different mono‐energetic proton pencil beams impinging on a water phantom, the dose distributions for the primary protons have been calculated using the macro MC transport and Geant4. The resulting integral depth dose curves and dose profiles have been compared. Results: The calculated integral depth dose curves agree better than 1% or 1 mm for all pencil beams considered. The agreement between the dose profiles at several depths in water is within 1% or 1 mm for all energies and depths. The computational efficiency for the macro MC method is about 200 times higher than for Geant4. Conclusions: The results of the dose comparisons demonstrate the very accurate and efficient dose calculation of primary protons using the macro MC method. In future, the macro MC method will be extended to include patient materials and the secondary particle transport in order to allow patient dose calculations for proton beams.This work was supported by Varian Medical Systems.

SU‐GG‐T‐420: Electron Monte Carlo Dose Calculation in Eclipse for Elekta Linear Accelerators

Purpose: The macro Monte Carlo (MC) method as implemented in Eclipse (Varian Medical Systems), named eMC, is only released for Varian accelerators. This is due to limitations in accuracy if eMC is applied to Elekta machines. This work describes improvements made in eMC to achieve accurate dose calculations of electron beams for Elekta accelerators. Method and Materials: Several changes recently implemented in the original eMC algorithm for low electron beam energies of Varian linear accelerators have been applied for the modeling of Elekta machines. In order to make eMC available for Elekta machines, the second divergent photon and electron source in the beam model for Varian accelerators have to be replaced with a line source to model the head scatter radiation more accurately. With respect to the dose calculation algorithm, the transport of the secondary electron component has been improved including modifications in the database of the transport code. Calculated and measured dose distributions are compared for Elekta machines using electron energies of 6, 8, 9, 12 and 15 MeV and applicators ranging from 6×6 to 20×20 cm2. Results: Calculated and measured absolute depth dose curves agree generally within 1.5% or 1 mm at a source to surface distance (SSD) of 100 cm. For SSD = 110 cm the differences are usually within 2% or 2 mm. Calculated and measured absolute dose profiles at depths of dmax and in the photon tail generally agree to within 2%. Some dose values close to the field edge show slightly larger differences. Conclusion: The results of the dose comparisons using the newly developed version of eMC suggest that this new eMC is now suitable to predict dose distributions for Elekta linear accelerators within sufficient accuracy. Conflict of Interest: This work was supported by Varian Medical Systems.

SU‐FF‐T‐429: Electron Monte Carlo Dose Calculation in Eclipse for Siemens Linear Accelerators

Purpose: Initially, the implementation of the macro Monte Carlo (MC) method into Eclipse (Varian Medical Systems), named eMC, was only carried out for Varian accelerators. This leads to limitations in accuracy if eMC is applied to Siemens machines. In this work eMC has been adjusted in order to allow accurate dose calculations of electron beams for Siemens accelerators. Method and Materials: Several changes have been implemented into the eMC algorithm. First, the beam model has been modified by introducing a 2D fluence instead of a 1D radial fluence distribution for the primary electrons and by including all scrapers of the applicator. Second, the resolution of mono‐energetic depth dose curves used during beam configuration has been increased to determine the initial electron energy spectrum. Furthermore, the size of the sphere within the macro MC transport has been reduced when the incident energy of the electron is below certain thresholds. Calculated and measured dose distributions are compared for Siemens machines using electron energies of 6, 7, 9, 13, 17, 20 and 21 MeV and applicators ranging from 10×10 to 25×25 cm2. Results: Calculated and measured absolute depth dose curves agree within 1% or 1 mm for all energy and applicator combinations investigated. Calculated and measured absolute dose profiles at depths of dmax, R50 and in the photon tail generally agree to within 2%. Some dose values close to the field edge show slightly larger differences. Conclusion: In this work several improvements have been implemented into the eMC algorithm. Due to these improvements the eMC algorithm was able to successfully configure electron beams from Siemens machines. The results of the dose comparison suggest that eMC is suitable to predict dose distributions also for Siemens linear accelerators. Conflict of Interest: This work was supported by Varian Medical Systems.

SU‐FF‐T‐314: Macro Monte Carlo Simulation of Visible Light Transport in Heterogeneous Media

Purpose: Although Monte Carlo (MC) simulation has become the gold standard in the transport of visible and near infra‐red photons in turbid media such as tissue, its computational intensity limits its practical application. To increase the computational efficiency of visible MC, we have adapted a macro‐Monte Carlo (MMC) method (Neuenschwander, et al. 1995, Phys. Med. Biol. 40, 543–574) to the modeling of light transport in heterogeneous media. Method and Materials: Traditional MC routines trace individual photons step‐by‐step through the tissue. Instead, the MMC approach relies on a data set consisting of spheres or ‘kugels’ in which the light absorbed in each voxel is pre‐calculated using a traditional MC routine. At each MMC step, the pre‐calculated absorbed light dose in the appropriate sphere, aligned to the current position and direction of the sphere, is recorded in the dose matrix. The position and direction of the photon exiting the sphere are chosen from the exit distribution of the pre‐calculated sphere, and the process is repeated. By choosing the size of the pre‐calculated sphere appropriately, arbitrarily complex boundary geometries can be simulated. To allow the simulation to remain accurate arbitrarily close to boundaries, we have it automatically switch to photon‐by‐photon MC for points less than one kugel radius. Results: We compare the accuracy and calculation time of the MMC method with a traditional MC algorithm for a variety of tissue optical properties and geometries. We find that the MMC algorithm can increase the speed of calculation by as much as two orders of magnitude, depending on the optical properties and geometry being simulated, without a significant loss in accuracy. Conclusions: The drastic improvement in efficiency accomplished by implementing the Macro Monte Carlo algorithm for visible photons makes it fast enough to be potentially useful in photodynamic therapy treatment planning and optical measurement analysis.

A Macro-Monte Carlo method for the simulation of diffuse light transport in tissue.

The Monte Carlo (MC) method of calculating light distributions in turbid media such as tissue has become the gold standard, especially in complex geometries and heterogeneous tissue. The utility of the MC method, however, is limited by is computational intensity. In an effort to reduce the time needed for MC calculations, we have adapted a macro-Monte Carlo (MMC) method (Neuenschwander, et al. 1995, Phys. Med. Biol. 40, 543-574) to the solution of tissue optics problems. Traditional MC routines trace individual photons step-by-step through the tissue. Instead, the MMC approach relies on a data set consisting of spheres in which the light absorbed in each voxel is pre-calculated using a traditional MC routine. At each MMC step, the pre-calculated absorbed light dose in the appropriate sphere, aligned to the current position and direction of the sphere, is recorded in the dose matrix. The position and direction of the photon exiting the sphere are chosen from the exit distribution of the pre-calculated sphere, and the process is repeated. By choosing the size of the pre-calculated sphere appropriately, arbitrarily complex boundary geometries can be simulated. We compare the accuracy and calculation time of the MMC method with a traditional MC algorithm for a variety of tissue optical properties and geometries. We find that the MMC algorithm can increase the speed of calculation by as much as two orders of magnitude, depending on the optical properties being simulated, without a significant loss in accuracy.

Parallelizing a powerful Monte Carlo method for electron beam dose calculations

The Macro Monte Carlo (MMC) method has been developed to improve the speed of traditional Monte Carlo calculations without significant loss in accuracy. MMC runs about one order of magnitude faster for clinically relevant irradiation situations. For routine use in a clinical environment a further speedup is necessary. The MMC code was therefore parallelized and implemented on PowerPC based Parsytec PowerXplorer and GC Power Plus systems. The performance of the parallel code is presented and compared to the sequential implementations on standard hardware platforms. Almost linear speedup is achieved for the parallel sections of the code. Furthermore the performance of the interprocessor communication based on a virtual topology is demonstrated for the two different machine architectures.

MMC-a high-performance Monte Carlo code for electron beam treatment planning

The macro Monte Carlo (MMC) method has been developed to improve the speed of traditional Monte Carlo (MC) high-energy electron transport calculations without loss in accuracy. The MMC algorithm uses results derived from conventional MC simulations of electron transport through macroscopic spheres of various radii and consisting of a variety of media. Based on these results, electrons are transported in macroscopic steps through the absorber. The absorber geometry is represented by a three-dimensional (3D) density matrix, typically derived from computer tomographic (CT) data. Energy lost by the electrons along their paths through the absorber is scored in a 3D dose matrix. Transport of secondary electrons and bremsstrahlung photons is taken into account. Major modifications of the original implementation of the MMC algorithm have resulted in an improved version of the code, resolving earlier problems with electron transport across interfaces of different materials, and running at a substantially higher speed. Furthermore, the code has been integrated into a clinical 3D treatment planning system. MMC results are in good agreement with results from conventional MC codes and are obtained with a speed gain of about one order of magnitude for clinically relevant irradiation situations. Calculation times to obtain a relative statistical accuracy of 2% per dose grid voxel for small electron field sizes are short enough to be routinely useful in radiotherapy clinics on present day affordable workstation computers. Considering speed, accuracy and memory requirements, MMC is a promising alternative to currently available electron dose planning algorithms.

A macro Monte Carlo method for electron beam dose calculations

The macro Monte Carlo (MMC) method is a fast Monte Carlo (MC) algorithm for high energy electron transport in an absorbing medium. Incident electrons are transported in large-scale macroscopic steps through the absorber. Electron parameters after each step are calculated from probability distributions. Transport of secondary electrons and bremsstrahlung photons is taken into account. For electron beam dose calculations, the energy, angular and spatial distributions of primary electrons have to be provided. The absorber geometry is represented by a 3D density matrix and the energy lost by the electrons along their paths is scored in a 3D dose matrix of user-definable resolution. Measurements in the beam of a Philips SL75-20 linear accelerator incident on homogeneous and simple inhomogeneous phantoms are in good agreement with MMC simulations.