A macro Monte Carlo method for electron beam dose calculations

Auto-commissioning of a Monte Carlo electron beam model with application to photon MLC shaped electron fields

Objective.Presently electron beam treatments are delivered using dedicated applicators. An alternative is the usage of the already installed photon multileaf collimator (pMLC) enabling efficient electron treatments. Currently, the commissioning of beam models is a manual and time-consuming process. In this work an auto-commissioning procedure for the Monte Carlo (MC) beam model part representing the beam above the pMLC is developed for TrueBeam systems with electron energies from 6 to 22 MeV.Approach.The analytical part of the electron beam model includes a main source representing the primary beam and a jaw source representing the head scatter contribution each consisting of an electron and a photon component, while MC radiation transport is performed for the pMLC. The auto-commissioning of this analytical part relies on information pre-determined from MC simulations, in-air dose profiles and absolute dose measurements in water for different field sizes and source to surface distances (SSDs). For validation calculated and measured dose distributions in water were compared for different field sizes, SSDs and beam energies for eight TrueBeam systems. Furthermore, a sternum case in an anthropomorphic phantom was considered and calculated and measured dose distributions were compared at different SSDs.Main results.Instead of the manual commissioning taking up to several days of calculation time and several hours of user time, the auto-commissioning is carried out in a few minutes. Measured and calculated dose distributions agree generally within 3% of maximum dose or 2 mm. The gamma passing rates for the sternum case ranged from 96% to 99% (3% (global)/2 mm criteria, 10% threshold).Significance.The auto-commissioning procedure was successfully implemented and applied to eight TrueBeam systems. The newly developed user-friendly auto-commissioning procedure allows an efficient commissioning of an MC electron beam model and eases the usage of advanced electron radiotherapy utilizing the pMLC for beam shaping.

Efficiency enhancements of a Monte Carlo beamlet based treatment planning process: implementation and parameter study

Objective.The computational effort to perform beamlet calculation, plan optimization and final dose calculation of a treatment planning process (TPP) generating intensity modulated treatment plans is enormous, especially if Monte Carlo (MC) simulations are used for dose calculation. The goal of this work is to improve the computational efficiency of a fully MC based TPP for static and dynamic photon, electron and mixed photon-electron treatment techniques by implementing multiple methods and studying the influence of their parameters.Approach.A framework is implemented calculating MC beamlets efficiently in parallel on each available CPU core. The user can specify the desired statistical uncertainty of the beamlets, a fractional sparse dose threshold to save beamlets in a sparse format and minimal distances to the PTV surface from which 2 × 2 × 2 = 8 (medium) or even 4 × 4 × 4 = 64 (large) voxels are merged. The compromise between final plan quality and computational efficiency of beamlet calculation and optimization is studied for several parameter values to find a reasonable trade-off. For this purpose, four clinical and one academic case are considered with different treatment techniques.Main results.Setting the statistical uncertainty to 5% (photon beamlets) and 15% (electron beamlets), the fractional sparse dose threshold relative to the maximal beamlet dose to 0.1% and minimal distances for medium and large voxels to the PTV to 1 cm and 2 cm, respectively, does not lead to substantial degradation in final plan quality compared to using 2.5% (photon beamlets) and 5% (electron beamlets) statistical uncertainty and no sparse format nor voxel merging. Only OAR sparing is slightly degraded. Furthermore, computation times are reduced by about 58% (photon beamlets), 88% (electron beamlets) and 96% (optimization).Significance.Several methods are implemented improving computational efficiency of beamlet calculation and plan optimization of a fully MC based TPP without substantial degradation in final plan quality.

Virtual particle Monte Carlo: A new concept to avoid simulating secondary particles in proton therapy dose calculation

BACKGROUND

In proton therapy dose calculation, Monte Carlo (MC) simulations are superior in accuracy but more time consuming, compared to analytical calculations. Graphic processing units (GPUs) are effective in accelerating MC simulations but may suffer thread divergence and racing condition in GPU threads that degrades the computing performance due to the generation of secondary particles during nuclear reactions.

PURPOSE

A novel concept of virtual particle (VP) MC (VPMC) is proposed to avoid simulating secondary particles in GPU-accelerated proton MC dose calculation and take full advantage of the computing power of GPU.

METHODS

Neutrons and gamma rays were ignored as escaping from the human body; doses of electrons, heavy ions, and nuclear fragments were locally deposited; the tracks of deuterons were converted into tracks of protons. These particles, together with primary and secondary protons, are considered to be the realistic particles. Histories of primary and secondary protons were replaced by histories of multiple VPs. Each VP corresponded to one proton (either primary or secondary). A continuous-slowing-down-approximation model, an ionization model, and a large angle scattering event model corresponding to nuclear interactions were developed for VPs by generating probability distribution functions (PDFs) based on simulation results of realistic particles using MCsquare. For efficient calculations, these PDFs were stored in the Compute Unified Device Architecture textures. VPMC was benchmarked with TOPAS and MCsquare in phantoms and with MCsquare in 13 representative patient geometries. Comparisons between the VPMC calculated dose and dose measured in water during patient-specific quality assurance (PSQA) of the selected 13 patients were also carried out. Gamma analysis was used to compare the doses derived from different methods and calculation efficiencies were also compared.

RESULTS

Integrated depth dose and lateral dose profiles in both homogeneous and inhomogeneous phantoms all matched well among VPMC, TOPAS, and MCsquare calculations. The 3D-3D gamma passing rates with a criterion of 2%/2 mm and a threshold of 10% was 98.49% between MCsquare and TOPAS and 98.31% between VPMC and TOPAS in homogeneous phantoms, and 99.18% between MCsquare and TOPAS and 98.49% between VPMC and TOPAS in inhomogeneous phantoms, respectively. In patient geometries, the 3D-3D gamma passing rates with 2%/2 mm/10% between dose distributions from VPMC and MCsquare were 98.56 ± 1.09% in patient geometries. The 2D-3D gamma analysis with 3%/2 mm/10% between the VPMC calculated dose distributions and the 2D measured planar dose distributions during PSQA was 98.91 ± 0.88%. VPMC calculation was highly efficient and took 2.84 ± 2.44 s to finish for the selected 13 patients running on four NVIDIA Ampere GPUs in patient geometries.

CONCLUSION

VPMC was found to achieve high accuracy and efficiency in proton therapy dose calculation.

A hybrid column generation and simulated annealing algorithm for direct aperture optimization

The purpose of this work was to develop a hybrid column generation (CG) and simulated annealing (SA) algorithm for direct aperture optimization (H-DAO) and to show its effectiveness in generating high quality treatment plans for intensity modulated radiation therapy (IMRT) and mixed photon-electron beam radiotherapy (MBRT). The H-DAO overcomes limitations of the CG-DAO with two features improving aperture selection (branch-feature) and enabling aperture shape changes during optimization (SA-feature). The H-DAO algorithm iteratively adds apertures to the plan. At each iteration, a branch is created for each field provided. First, each branch determines the most promising aperture of its assigned field and adds it to a copy of the current apertures. Afterwards, the apertures of each branch undergo an MU-weight optimization followed by an SA-based simultaneous shape and MU-weight optimization and a second MU-weight optimization. The next H-DAO iteration continues the branch with the lowest objective function value. IMRT and MBRT treatment plans for an academic, a brain and a head and neck case generated using the CG-DAO and H-DAO were compared. For every investigated case and both IMRT and MBRT, the H-DAO leads to a faster convergence of the objective function value with number of apertures compared to the CG-DAO. In particular, the H-DAO needs about half the apertures to reach the same objective function value as the CG-DAO. The average aperture areas are 27% smaller for H-DAO than for CG-DAO leading to a slightly larger discrepancy between optimized and final dose. However, a dosimetric benefit remains. The H-DAO was successfully developed and applied to IMRT and MBRT. The faster convergence with number of apertures of the H-DAO compared to the CG-DAO allows to select a better compromise between plan quality and number of apertures.

Validation of spline modeling for calculation of electron insert factors for varian linear accelerators

There are several methods available in the literature for predicting the insert factor for clinical electron beams. The purpose of this work was to build on a previously published technique that uses a bivariate spline model generated from elliptically parameterized empirical measurements. The technique has been previously validated for Elekta linear accelerators for limited clinical electron setups. The same model is applied to Varian machines to test its efficacy for use with these linear accelerators. Insert factors for specifically designed elliptical cutouts were measured to create spline models for 6, 9, 12, 16, and 20 MeV electron energies for four different cone sizes at source-to-surface distances (SSD) of 100, 105, and 110 cm. Insert factor validation measurements of patient cutouts and clinical standard cutouts were acquired to compare to model predictions. Agreement between predicted insert factors and validation measurements averaged 0.8% over all energies, cones, and clinical SSDs, with an uncertainty of 0.6% (1SD), and maximum deviation of 2.1%. The model demonstrated accurate predictions of insert factors using the minimum required amount of input data for small cones, with more input measurements required for larger cones. The results of this study provide expanded validation of this technique to predict insert factors for all energies, cones, and SSDs that would be used in most clinical situations. This level of accuracy and the ease of creating the model necessary for the insert factor predictions demonstrate its acceptability to use clinically for Varian machines.

Implementation and experimental validation of a robust hybrid direct aperture optimization approach for mixed-beam radiotherapy

Purpose

The objectives of the work presented in this paper were to (1) implement a robust‐optimization method for deliverable mixed‐beam radiotherapy (MBRT) plans within a previously developed MBRT planning framework; (2) perform an experimental validation of the delivery of robust‐optimized MBRT plans; and (3) compare PTV‐based and robust‐optimized MBRT plans in terms of target dose robustness and organs at risk (OAR) sparing for clinical head and neck and brain patient cases.

Methods

A robust‐optimization method, which accounts for translational setup errors, was implemented within a previously developed treatment planning framework for MBRT. The framework uses a hybrid direct aperture optimization method combining column generation and simulated annealing. A robust plan was developed and then delivered to an anthropomorphic head phantom using the Developer Mode of a TrueBeam linac. Planar dose distributions were measured and compared to the planned dose. Robust‐optimized and PTV‐based plans were developed for three clinical patient cases consisting of two head and neck cases and one brain case. The plans were compared in terms of the robustness to 5 mm shifts of the target volume dose as well as in terms of OAR sparing.

Results

Using a gamma criterion of 3%/2 mm and a dose threshold of 10%, the agreement between film measurements and dose calculations was better than 97.7% for the total plan and better than 95.5% for the electron component of the plan. For the two head and neck patient cases, the average clinical target volume (CTV) dose homogeneity index (V95%–V107%) over all the considered setup error scenarios was on average 19% lower for the PTV‐based plans and it had a larger standard deviation. The robust‐optimized plans achieved, on average, a 20% reduction in the OAR doses compared to the PTV‐based plans. For the brain patient case, the CTV dose homogeneity index was similar for the two plans, while the OAR doses were 22% lower, on average, for the robust‐optimized plan. No clear trend in terms of electron contributions was found across the three patient cases, although robust‐optimized plans tended toward higher electron beam energies.

Conclusions

A framework for robust optimization of deliverable MBRT plans has been developed and validated. PTV‐based MBRT were found to not be robust to setup errors, while the dose delivered by the robust‐optimized plans were clinically acceptable for all considered error scenarios and had better OAR sparing. This study shows that the robust optimization is a promising alternative to conventional PTV margins for MBRT.

TriB-RT: Simultaneous optimization of photon, electron and proton beams

PURPOSE

To develop a novel treatment planning process (TPP) with simultaneous optimization of modulated photon, electron and proton beams for improved treatment plan quality in radiotherapy.

METHODS

A framework for fluence map optimization of Monte Carlo (MC) calculated beamlet dose distributions is developed to generate treatment plans consisting of photon, electron and spot scanning proton fields. Initially, in-house intensity modulated proton therapy (IMPT) plans are compared to proton plans created by a commercial treatment planning system (TPS). A triple beam radiotherapy (TriB-RT) plan is generated for an exemplary academic case and the dose contributions of the three particle types are investigated. To investigate the dosimetric potential, a TriB-RT plan is compared to an in-house IMPT plan for two clinically motivated cases. Benefits of TriB-RT for a fixed proton beam line with a single proton field are investigated.

RESULTS

In-house optimized IMPT are of at least equal or better quality than TPS-generated proton plans, and MC-based optimization shows dosimetric advantages for inhomogeneous situations. Concerning TriB-RT, for the academic case, the resulting plan shows substantial contribution of all particle types. For the clinically motivated case, improved sparing of organs at risk close to the target volume is achieved compared to IMPT (e.g. myelon and brainstem [Formula: see text] -37%) at cost of an increased low dose bath (healthy tissue V _10% +22%). In the scenario of a fixed proton beam line, TriB-RT plans are able to compensate the loss in degrees of freedom to substantially improve plan quality compared to a single field proton plan.

CONCLUSION

A novel TPP which simultaneously optimizes photon, electron and proton beams was successfully developed. TriB-RT shows the potential for improved treatment plan quality and is especially promising for cost-effective single-room proton solutions with a fixed beamline in combination with a conventional linac delivering photon and electron fields.

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

MOTIVATION

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.

METHODS

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.

RESULTS

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%, 2 mm 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.

CONCLUSION

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.

Beam modeling and beam model commissioning for Monte Carlo dose calculation-based radiation therapy treatment planning: Report of AAPM Task Group 157

Dose calculation plays an important role in the accuracy of radiotherapy treatment planning and beam delivery. The Monte Carlo (MC) method is capable of achieving the highest accuracy in radiotherapy dose calculation and has been implemented in many commercial systems for radiotherapy treatment planning. The objective of this task group was to assist clinical physicists with the potentially complex task of acceptance testing and commissioning MC-based treatment planning systems (TPS) for photon and electron beam dose calculations. This report provides an overview on the general approach of clinical implementation and testing of MC-based TPS with a specific focus on models of clinical photon and electron beams. Different types of beam models are described including those that utilize MC simulation of the treatment head and those that rely on analytical methods and measurements. The trade-off between accuracy and efficiency in the various source-modeling approaches is discussed together with guidelines for acceptance testing of MC-based TPS from the clinical standpoint. Specific recommendations are given on methods and practical procedures to commission clinical beam models for MC-based TPS.

Adaptive step size algorithm to increase efficiency of proton macro Monte Carlo dose calculation

Purpose

To provide fast and accurate dose calculation in voxelized geometries for proton radiation therapy by implementing an adaptive step size algorithm in the proton macro Monte Carlo (pMMC) method.

Methods

The in-house developed local-to-global MMC method for proton dose calculation is extended with an adaptive step size algorithm for efficient proton transport through a voxelized geometry by sampling transport parameters from a pre-simulated database. Adaptive choice of an adequate slab size in dependence of material interfaces in the proton’s longitudinal and lateral vicinity is investigated. The dose calculation algorithm is validated against the non-adaptive pMMC and full MC simulation for pencil and broad beams with various energies impinging on academic phantoms as well as a head and neck patient CT.

Results

For material interfaces perpendicular to a proton’s direction, choice of nearest neighbor slab thickness shows best trade-off between dosimetric accuracy and calculation efficiency. Adaptive reduction of chosen slab size is shown to be required for material interfaces closer than 0.5 mm in lateral direction. For the academic phantoms, dose differences of within 1% or 1 mm compared to full Geant4 MC simulation are found, while achieving an efficiency gain of up to a factor of 5.6 compared to the non-adaptive algorithm and 284 compared to Geant4. For the head and neck patient CT, dose differences are within 1% or 1 mm with an efficiency gain factor of up to 3.4 compared to the non-adaptive algorithm and 145 compared to Geant4.

Conclusion

An adaptive step size algorithm for proton macro Monte Carlo was implemented and evaluated. The dose calculation provides the accuracy of full MC simulations, while achieving an efficiency gain factor of three compared to the non-adaptive algorithm and two orders of magnitude compared to full MC for a complex patient CT.

Part 2: Dynamic mixed beam radiotherapy (DYMBER): Photon dynamic trajectories combined with modulated electron beams

PURPOSE

The purpose of this study was to develop a treatment technique for dynamic mixed beam radiotherapy (DYMBER) utilizing increased degrees of freedom (DoF) of a conventional treatment unit including different particle types (photons and electrons), intensity and energy modulation and dynamic gantry, table, and collimator rotations.

METHODS

A treatment planning process has been developed to create DYMBER plans combining photon dynamic trajectories (DTs) and step and shoot electron apertures collimated with the photon multileaf collimator (pMLC). A gantry-table path is determined for the photon DTs with minimized overlap of the organs at risk (OARs) with the target. In addition, an associated dynamic collimator rotation is established with minimized area between the pMLC leaves and the target contour. pMLC sequences of photon DTs and electron pMLC apertures are then simultaneously optimized using direct aperture optimization (DAO). Subsequently, the final dose distribution of the electron pMLC apertures is calculated using the Swiss Monte Carlo Plan (SMCP). The pMLC sequences of the photon DTs are then re-optimized with a finer control point resolution and with the final electron dose distribution taken into account. Afterwards, the final photon dose distribution is calculated also using the SMCP and summed together with the one of the electrons. This process is applied for a brain and two head and neck cases. The resulting DYMBER dose distributions are compared to those of dynamic trajectory radiotherapy (DTRT) plans consisting only of photon DTs and clinically applied VMAT plans. Furthermore, the deliverability of the DYMBER plans is verified in terms of dosimetric accuracy, delivery time and collision avoidance. For this purpose, The DYMBER plans are delivered to Gafchromic EBT3 films placed in an anthropomorphic head phantom on a Varian TrueBeam linear accelerator.

RESULTS

For each case, the dose homogeneity in the target is similar or better for DYMBER compared to DTRT and VMAT. Averaged over all three cases, the mean dose to the parallel OARs is 16% and 28% lower, D2% to the serial OARs is 17% and 37% lower and V10% to normal tissue is 12% and 4% lower for the DYMBER plans compared to the DTRT and VMAT plans, respectively. The DYMBER plans are delivered without collision and with a 4-5 min longer delivery time than the VMAT plans. The absolute dose measurements are compared to calculation by gamma analysis using 2% (global)/2 mm criteria with passing rates of at least 99%.

CONCLUSIONS

A treatment technique for DYMBER has been successfully developed and verified for its deliverability. The dosimetric superiority of DYMBER over DTRT and VMAT indicates utilizing increased DoF to be the key to improve brain and head and neck radiation treatments in future.

Monte Carlo simulations in radiotherapy dosimetry

BACKGROUND

The use of the Monte Carlo (MC) method in radiotherapy dosimetry has increased almost exponentially in the last decades. Its widespread use in the field has converted this computer simulation technique in a common tool for reference and treatment planning dosimetry calculations.

METHODS

This work reviews the different MC calculations made on dosimetric quantities, like stopping-power ratios and perturbation correction factors required for reference ionization chamber dosimetry, as well as the fully realistic MC simulations currently available on clinical accelerators, detectors and patient treatment planning.

CONCLUSIONS

Issues are raised that include the necessity for consistency in the data throughout the entire dosimetry chain in reference dosimetry, and how Bragg-Gray theory breaks down for small photon fields. Both aspects are less critical for MC treatment planning applications, but there are important constraints like tissue characterization and its patient-to-patient variability, which together with the conversion between dose-to-water and dose-to-tissue, are analysed in detail. Although these constraints are common to all methods and algorithms used in different types of treatment planning systems, they make uncertainties involved in MC treatment planning to still remain "uncertain".

Predicting Heart Dose in Breast Cancer Patients Who Received 3D Conformal Radiation Therapy

Cardiac late effects are a major health concern for long-term survivors after radiotherapy for breast cancer. Large cohort studies to better understand the exact dose-response relationship require individual estimates of radiation dose to the heart. To predict individual cardiac dose from information that is typically available for all members of a retrospective epidemiological cohort study, 774 female breast cancer patients treated with megavoltage tangential field radiotherapy in 1998-2008 were examined. All dose distributions were calculated using Eclipse with the anisotropic analytical algorithm (AAA) for photon fields and the electron Monte Carlo algorithm for electron boost fields. Based on individual dose volume histograms, the authors calculated absorbed dose in the complete heart as well as in six functional substructures. Statistical models were developed to predict absorbed dose using only covariate information from patients' clinical records on tumor location, patient anatomy and radiotherapy prescription. The out-of-sample prediction error for mean heart dose was 54% (coefficient of variation). The prediction error in functional substructures ranged from 49-68% for mean dose and from 52-86% for extreme dose. The authors conclude that based on a patient sample with exact heart dosimetry, it is possible to use clinical information alone to predict absorbed heart dose in the remaining cohort with a quantified error suitable for dose-response analyses of cardiac late effects.

Full Monte Carlo and measurement-based overall performance assessment of improved clinical implementation of eMC algorithm with emphasis on lower energy range

New version 13.6.23 of the electron Monte Carlo (eMC) algorithm in Varian Eclipse™ treatment planning system has a model for 4MeV electron beam and some general improvements for dose calculation. This study provides the first overall accuracy assessment of this algorithm against full Monte Carlo (MC) simulations for electron beams from 4MeV to 16MeV with most emphasis on the lower energy range. Beams in a homogeneous water phantom and clinical treatment plans were investigated including measurements in the water phantom. Two different material sets were used with full MC: (1) the one applied in the eMC algorithm and (2) the one included in the Eclipse™ for other algorithms. The results of clinical treatment plans were also compared to those of the older eMC version 11.0.31. In the water phantom the dose differences against the full MC were mostly less than 3% with distance-to-agreement (DTA) values within 2mm. Larger discrepancies were obtained in build-up regions, at depths near the maximum electron ranges and with small apertures. For the clinical treatment plans the overall dose differences were mostly within 3% or 2mm with the first material set. Larger differences were observed for a large 4MeV beam entering curved patient surface with extended SSD and also in regions of large dose gradients. Still the DTA values were within 3mm. The discrepancies between the eMC and the full MC were generally larger for the second material set. The version 11.0.31 performed always inferiorly, when compared to the 13.6.23.

Latent uncertainties of the precalculated track Monte Carlo method

PURPOSE

While significant progress has been made in speeding up Monte Carlo (MC) dose calculation methods, they remain too time-consuming for the purpose of inverse planning. To achieve clinically usable calculation speeds, a precalculated Monte Carlo (PMC) algorithm for proton and electron transport was developed to run on graphics processing units (GPUs). The algorithm utilizes pregenerated particle track data from conventional MC codes for different materials such as water, bone, and lung to produce dose distributions in voxelized phantoms. While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from the limited number of unique tracks in the pregenerated track bank is missing from the paper. With a proper uncertainty analysis, an optimal number of tracks in the pregenerated track bank can be selected for a desired dose calculation uncertainty.

METHODS

Particle tracks were pregenerated for electrons and protons using EGSnrc and geant4 and saved in a database. The PMC algorithm for track selection, rotation, and transport was implemented on the Compute Unified Device Architecture (cuda) 4.0 programming framework. PMC dose distributions were calculated in a variety of media and compared to benchmark dose distributions simulated from the corresponding general-purpose MC codes in the same conditions. A latent uncertainty metric was defined and analysis was performed by varying the pregenerated track bank size and the number of simulated primary particle histories and comparing dose values to a "ground truth" benchmark dose distribution calculated to 0.04% average uncertainty in voxels with dose greater than 20% of Dmax. Efficiency metrics were calculated against benchmark MC codes on a single CPU core with no variance reduction.

RESULTS

Dose distributions generated using PMC and benchmark MC codes were compared and found to be within 2% of each other in voxels with dose values greater than 20% of the maximum dose. In proton calculations, a small (≤ 1 mm) distance-to-agreement error was observed at the Bragg peak. Latent uncertainty was characterized for electrons and found to follow a Poisson distribution with the number of unique tracks per energy. A track bank of 12 energies and 60000 unique tracks per pregenerated energy in water had a size of 2.4 GB and achieved a latent uncertainty of approximately 1% at an optimal efficiency gain over DOSXYZnrc. Larger track banks produced a lower latent uncertainty at the cost of increased memory consumption. Using an NVIDIA GTX 590, efficiency analysis showed a 807 × efficiency increase over DOSXYZnrc for 16 MeV electrons in water and 508 × for 16 MeV electrons in bone.

CONCLUSIONS

The PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty of 1% with a large efficiency gain over conventional MC codes. Before performing clinical dose calculations, models to calculate dose contributions from uncharged particles must be implemented. Following the successful implementation of these models, the PMC method will be evaluated as a candidate for inverse planning of modulated electron radiation therapy and scanned proton beams.

Accuracy of pencil-beam redefinition algorithm dose calculations in patient-like cylindrical phantoms for bolus electron conformal therapy

PURPOSE

The purpose of this study was to document the improved accuracy of the pencil beam redefinition algorithm (PBRA) compared to the pencil beam algorithm (PBA) for bolus electron conformal therapy using cylindrical patient phantoms based on patient computed tomography (CT) scans of retromolar trigone and nose cancer.

METHODS

PBRA and PBA electron dose calculations were compared with measured dose in retromolar trigone and nose phantoms both with and without bolus. For the bolus treatment plans, a radiation oncologist outlined a planning target volume (PTV) on the central axis slice of the CT scan for each phantom. A bolus was designed using the planning.decimal(®) (p.d) software (.decimal, Inc., Sanford, FL) to conform the 90% dose line to the distal surface of the PTV. Dose measurements were taken with thermoluminescent dosimeters placed into predrilled holes. The Pinnacle(3) (Philips Healthcare, Andover, MD) treatment planning system was used to calculate PBA dose distributions. The PBRA dose distributions were calculated with an in-house C++ program. In order to accurately account for the phantom materials a table correlating CT number to relative electron stopping and scattering powers was compiled and used for both PBA and PBRA dose calculations. Accuracy was determined by comparing differences in measured and calculated dose, as well as distance to agreement for each measurement point.

RESULTS

The measured doses had an average precision of 0.9%. For the retromolar trigone phantom, the PBRA dose calculations had an average ± 1σ dose difference (calculated - measured) of -0.65% ± 1.62% without the bolus and -0.20% ± 1.54% with the bolus. The PBA dose calculation had an average dose difference of 0.19% ± 3.27% without the bolus and -0.05% ± 3.14% with the bolus. For the nose phantom, the PBRA dose calculations had an average dose difference of 0.50% ± 3.06% without bolus and -0.18% ± 1.22% with the bolus. The PBA dose calculations had an average dose difference of 0.65% ± 6.21% without bolus and 1.75% ± 5.94% with the bolus. From a clinical perspective an agreement of 5% or better between planned (calculated) and delivered (measured) dose is desired. Statistically, this was true for 99% (± 2σ) of the dose points for three of the four cases for the PBRA dose calculations, the exception being the nose without bolus for which this was true for 89% (± 1.6σ) of the dose points. For the retromolar trigone, with and without bolus, the PBA showed agreement of 5% or better for approximately 86% (± 1.5σ) of the dose points. For the nose, with and without bolus, the PBA showed agreement of 5% or better for only approximately 58% (± 0.8σ) of the dose points.

CONCLUSIONS

The measured data, whose high precision makes them useful for evaluation of the accuracy of electron dose algorithms, will be made publicly available. Based on the spread in dose differences, the PBRA has at least twice the accuracy of the PBA. From a clinical perspective the PBRA accuracy is acceptable in the retromolar trigone and nose for electron therapy with and without bolus.

A review on the use of grid-based Boltzmann equation solvers for dose calculation in external photon beam treatment planning

Deterministic linear Boltzmann transport equation (D-LBTE) solvers have recently been developed, and one of the latest available software codes, Acuros XB, has been implemented in a commercial treatment planning system for radiotherapy photon beam dose calculation. One of the major limitations of most commercially available model-based algorithms for photon dose calculation is the ability to account for the effect of electron transport. This induces some errors in patient dose calculations, especially near heterogeneous interfaces between low and high density media such as tissue/lung interfaces. D-LBTE solvers have a high potential of producing accurate dose distributions in and near heterogeneous media in the human body. Extensive previous investigations have proved that D-LBTE solvers were able to produce comparable dose calculation accuracy as Monte Carlo methods with a reasonable speed good enough for clinical use. The current paper reviews the dosimetric evaluations of D-LBTE solvers for external beam photon radiotherapy. This content summarizes and discusses dosimetric validations for D-LBTE solvers in both homogeneous and heterogeneous media under different circumstances and also the clinical impact on various diseases due to the conversion of dose calculation from a conventional convolution/superposition algorithm to a recently released D-LBTE solver.

Gd@C82 metallofullerenes for neutron capture therapy-fullerene solubilization by poly(ethylene glycol)-block-poly(2-(N, N-diethylamino)ethyl methacrylate) and resultant efficacy in vitro

Poly(ethylene glycol)-block-poly(2-(N,N-diethylamino)ethyl methacrylate) (PEG-b-PAMA) was found to solubilize fullerenes such as C60, and this technique was applied to metallofullerenes. Gd@C82 was easily dissolved in water in the presence of PEG-b-PAMA without any covalent derivatization, forming a transparent complex about 20-30 nm in diameter. Low cytotoxicity was confirmed in vitro. Neutron irradiation of cultured cells (colon-26 adenocarcinoma) with Gd@C82-PEG-b-PAMA-complexed nanoparticles showed effective cytotoxicity, indicating the effective emission of gamma rays and internal conversion electrons produced from the neutron capture reaction of Gd. This result suggests a potentially valuable approach to gadolinium-based neutron capture therapy.

A contemporary review of stereotactic radiotherapy: inherent dosimetric complexities and the potential for detriment

OBJECTIVE

The advantages of highly localised, conformal treatments achievable with stereotactic radiotherapy (SRT) are increasingly being extended to extracranial sites as stereotactic body radiotherapy with advancements in imaging and beam collimation. One of the challenges in stereotactic treatment lies in the significant complexities associated with small field dosimetry and dose calculation. This review provides a comprehensive overview of the complexities associated with stereotactic radiotherapy and the potential for detriment.

METHODS

This study is based on a comprehensive review of literature accessible via PubMed and other sources, covering stereotactic radiotherapy, small-field dosimetry and dose calculation.

FINDINGS

Several key issues were identified in the literature. They pertain to dose prescription, dose measurement and dose calculation within and beyond the treatment field. Field-edge regions and penumbrae occupy a significant portion of the total field size. Spectral and dosimetric characteristics are difficult to determine and are compounded by effects of tissue inhomogeneity. Measurement of small-fields is made difficult by detector volume averaging and energy response. Available dosimeters are compared, and emphasis is given to gel dosimetry which offers the greatest potential for three-dimensional small-field dosimetry. The limitations of treatment planning system algorithms as applied to small-fields (particularly in the presence of heterogeneities) is explained, and a review of Monte Carlo dose calculation is provided, including simplified treatment planning implementations. Not incorporated into treatment planning, there is evidence that far from the primary field, doses to patients (and corresponding risks of radiocarcinogenesis) from leakage/scatter in SRT are similar to large fields.

CONCLUSIONS

Improved knowledge of dosimetric issues is essential to the accurate measurement and calculation of dose as well as the interpretation and assessment of planned and delivered treatments. This review highlights such issues and the potential benefit that may be gained from Monte Carlo dose calculation and verification via three-dimensional dosimetric methods (such as gel dosimetry) being introduced into routine clinical practice.

Monte Carlo dose calculation improvements for low energy electron beams using eMC

The electron Monte Carlo (eMC) dose calculation algorithm in Eclipse (Varian Medical Systems) is based on the macro MC method and is able to predict dose distributions for high energy electron beams with high accuracy. However, there are limitations for low energy electron beams. This work aims to improve the accuracy of the dose calculation using eMC for 4 and 6 MeV electron beams of Varian linear accelerators. Improvements implemented into the eMC include (1) improved determination of the initial electron energy spectrum by increased resolution of mono-energetic depth dose curves used during beam configuration; (2) inclusion of all the scrapers of the applicator in the beam model; (3) reduction of the maximum size of the sphere to be selected within the macro MC transport when the energy of the incident electron is below certain thresholds. The impact of these changes in eMC is investigated by comparing calculated dose distributions for 4 and 6 MeV electron beams at source to surface distance (SSD) of 100 and 110 cm with applicators ranging from 6 x 6 to 25 x 25 cm(2) of a Varian Clinac 2300C/D with the corresponding measurements. Dose differences between calculated and measured absolute depth dose curves are reduced from 6% to less than 1.5% for both energies and all applicators considered at SSD of 100 cm. Using the original eMC implementation, absolute dose profiles at depths of 1 cm, d(max) and R50 in water lead to dose differences of up to 8% for applicators larger than 15 x 15 cm(2) at SSD 100 cm. Those differences are now reduced to less than 2% for all dose profiles investigated when the improved version of eMC is used. At SSD of 110 cm the dose difference for the original eMC version is even more pronounced and can be larger than 10%. Those differences are reduced to within 2% or 2 mm with the improved version of eMC. In this work several enhancements were made in the eMC algorithm leading to significant improvements in the accuracy of the dose calculation for 4 and 6 MeV electron beams of Varian linear accelerators.

Verification of a commercial implementation of the Macro-Monte-Carlo electron dose calculation algorithm using the virtual accelerator approach

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.

Fast, accurate photon beam accelerator modeling using BEAMnrc: a systematic investigation of efficiency enhancing methods and cross-section data

In this work, an investigation of efficiency enhancing methods and cross-section data in the BEAMnrc Monte Carlo (MC) code system is presented. Additionally, BEAMnrc was compared with VMC++, another special-purpose MC code system that has recently been enhanced for the simulation of the entire treatment head. BEAMnrc and VMC++ were used to simulate a 6 MV photon beam from a Siemens Primus linear accelerator (linac) and phase space (PHSP) files were generated at 100 cm source-to-surface distance for the 10 x 10 and 40 x 40 cm2 field sizes. The BEAMnrc parameters/techniques under investigation were grouped by (i) photon and bremsstrahlung cross sections, (ii) approximate efficiency improving techniques (AEITs), (iii) variance reduction techniques (VRTs), and (iv) a VRT (bremsstrahlung photon splitting) in combination with an AEIT (charged particle range rejection). The BEAMnrc PHSP file obtained without the efficiency enhancing techniques under study or, when not possible, with their default values (e.g., EXACT algorithm for the boundary crossing algorithm) and with the default cross-section data (PEGS4 and Bethe-Heitler) was used as the "base line" for accuracy verification of the PHSP files generated from the different groups described previously. Subsequently, a selection of the PHSP files was used as input for DOSXYZnrc-based water phantom dose calculations, which were verified against measurements. The performance of the different VRTs and AEITs available in BEAMnrc and of VMC++ was specified by the relative efficiency, i.e., by the efficiency of the MC simulation relative to that of the BEAMnrc base-line calculation. The highest relative efficiencies were approximately 935 (approximately 111 min on a single 2.6 GHz processor) and approximately 200 (approximately 45 min on a single processor) for the 10 x 10 field size with 50 million histories and 40 x 40 cm2 field size with 100 million histories, respectively, using the VRT directional bremsstrahlung splitting (DBS) with no electron splitting. When DBS was used with electron splitting and combined with augmented charged particle range rejection, a technique recently introduced in BEAMnrc, relative efficiencies were approximately 420 (approximately 253 min on a single processor) and approximately 175 (approximately 58 min on a single processor) for the 10 x 10 and 40 x 40 cm2 field sizes, respectively. Calculations of the Siemens Primus treatment head with VMC++ produced relative efficiencies of approximately 1400 (approximately 6 min on a single processor) and approximately 60 (approximately 4 min on a single processor) for the 10 x 10 and 40 x 40 cm2 field sizes, respectively. BEAMnrc PHSP calculations with DBS alone or DBS in combination with charged particle range rejection were more efficient than the other efficiency enhancing techniques used. Using VMC++, accurate simulations of the entire linac treatment head were performed within minutes on a single processor. Noteworthy differences (+/- 1%-3%) in the mean energy, planar fluence, and angular and spectral distributions were observed with the NIST bremsstrahlung cross sections compared with those of Bethe-Heitler (BEAMnrc default bremsstrahlung cross section). However, MC calculated dose distributions in water phantoms (using combinations of VRTs/AEITs and cross-section data) agreed within 2% of measurements. Furthermore, MC calculated dose distributions in a simulated water/air/water phantom, using NIST cross sections, were within 2% agreement with the BEAMnrc Bethe-Heitler default case.

Recommendations for clinical electron beam dosimetry: supplement to the recommendations of Task Group 25

The goal of Task Group 25 (TG-25) of the Radiation Therapy Committee of the American Association of.Physicists in Medicine (AAPM) was to provide a methodology and set of procedures for a medical physicist performing clinical electron beam dosimetry in the nominal energy range of 5-25 MeV. Specifically, the task group recommended procedures for acquiring basic information required for acceptance testing and treatment planning of new accelerators with therapeutic electron beams. Since the publication of the TG-25 report, significant advances have taken place in the field of electron beam dosimetry, the most significant being that primary standards laboratories around the world have shifted from calibration standards based on exposure or air kerma to standards based on absorbed dose to water. The AAPM has published a new calibration protocol, TG-51, for the calibration of high-energy photon and electron beams. The formalism and dosimetry procedures recommended in this protocol are based on the absorbed dose to water calibration coefficient of an ionization chamber at 60Co energy, N60Co(D,w), together with the theoretical beam quality conversion coefficient k(Q) for the determination of absorbed dose to water in high-energy photon and electron beams. Task Group 70 was charged to reassess and update the recommendations in TG-25 to bring them into alignment with report TG-51 and to recommend new methodologies and procedures that would allow the practicing medical physicist to initiate and continue a high quality program in clinical electron beam dosimetry. This TG-70 report is a supplement to the TG-25 report and enhances the TG-25 report by including new topics and topics that were not covered in depth in the TG-25 report. These topics include procedures for obtaining data to commission a treatment planning computer, determining dose in irregularly shaped electron fields, and commissioning of sophisticated special procedures using high-energy electron beams. The use of radiochromic film for electrons is addressed, and radiographic film that is no longer available has been replaced by film that is available. Realistic stopping-power data are incorporated when appropriate along with enhanced tables of electron fluence data. A larger list of clinical applications of electron beams is included in the full TG-70 report available at http://www.aapm.org/pubs/reports. Descriptions of the techniques in the clinical sections are not exhaustive but do describe key elements of the procedures and how to initiate these programs in the clinic. There have been no major changes since the TG-25 report relating to flatness and symmetry, surface dose, use of thermoluminescent dosimeters or diodes, virtual source position designation, air gap corrections, oblique incidence, or corrections for inhomogeneities. Thus these topics are not addressed in the TG-70 report.

Validation of calculations for electrons modulated with conventional photon multileaf collimators

Treating shallow tumors with a homogeneous dose while simultaneously minimizing the dose to distal critical organs remains a challenge in radiotherapy. One promising approach is modulated electron radiotherapy (MERT). Due to the scattering properties of electron beams, the commercially provided secondary and tertiary photon collimation systems are not conducive for electron beam delivery when standard source-to-surface distances are used. Also, commercial treatment planning systems may not accurately model electron-beam dose distributions when collimated without the standard applicators. However, by using the photon multileaf collimators (MLCs) to create segments to modulate electron beams, the quality of superficial tumor dose distributions may improve substantially. The purpose of this study is to develop and evaluate calculations for the narrow segments needed to modulate megavoltage electron beams using photon beam multileaf collimators. Modulated electron radiotherapy (MERT) will be performed with a conventional linear accelerator equipped with a 120 leaf MLC for 6-20 MeV electron beam energies. To provide a sharp penumbra, segments were delivered with short SSDs (70-85 cm). Segment widths (SW) ranging from 1 to 10 cm were configured for delivery and planning, using BEAMnrc Monte Carlo (MC) code, and the DOSXYZnrc MC dose calculations. Calculations were performed with voxel size of 0.2 x 0.2 x 0.1 cm3. Dosimetry validation was performed using radiographic film and micro- or parallel-plate chambers. Calculated and measured data were compared using technical computing software. Beam sharpness (penumbra) degraded with decreasing incident beam energy and field size (FS), and increasing SSD. A 70 cm SSD was found to be optimal. The PDD decreased significantly with decreasing FS. The comparisons demonstrated excellent agreement for calculations and measurements within 3%, 1 mm. This study shows that accurate calculations for MERT as delivered with existing photon MLC are feasible and allows the opportunity to take advantage of the dynamic leaf motion capabilities and control systems, to provide conformal dose distributions.

Fifty years of Monte Carlo simulations for medical physics

Monte Carlo techniques have become ubiquitous in medical physics over the last 50 years with a doubling of papers on the subject every 5 years between the first PMB paper in 1967 and 2000 when the numbers levelled off. While recognizing the many other roles that Monte Carlo techniques have played in medical physics, this review emphasizes techniques for electron-photon transport simulations. The broad range of codes available is mentioned but there is special emphasis on the EGS4/EGSnrc code system which the author has helped develop for 25 years. The importance of the 1987 Erice Summer School on Monte Carlo techniques is highlighted. As an illustrative example of the role Monte Carlo techniques have played, the history of the correction for wall attenuation and scatter in an ion chamber is presented as it demonstrates the interplay between a specific problem and the development of tools to solve the problem which in turn leads to applications in other areas.

Review of electron beam therapy physics

For over 50 years, electron beams have been an important modality for providing an accurate dose of radiation to superficial cancers and disease and for limiting the dose to underlying normal tissues and structures. This review looks at many of the important contributions of physics and dosimetry to the development and utilization of electron beam therapy, including electron treatment machines, dose specification and calibration, dose measurement, electron transport calculations, treatment and treatment-planning tools, and clinical utilization, including special procedures. Also, future changes in the practice of electron therapy resulting from challenges to its utilization and from potential future technology are discussed.

Evaluation of a commercial electron treatment planning system based on Monte Carlo techniques (eMC)

A commercial electron beam treatment planning system on the basis of a Monte Carlo algorithm (Varian Eclipse, eMC V7.2.35) was evaluated. Measured dose distributions were used for comparison with dose distributions predicted by eMC calculations. Tests were carried out for various applicators and field sizes, irregular shaped cut outs and an inhomogeneity phantom for energies between 6 Me V and 22 MeV Monitor units were calculated for all applicator/energy combinations and field sizes down to 3 cm diameter and source-to-surface distances of 100 cm and 110 cm. A mass-density-to-Hounsfield-Units calibration was performed to compare dose distributions calculated with a default and an individual calibration. The relationship between calculation parameters of the eMC and the resulting dose distribution was studied in detail. Finally, the algorithm was also applied to a clinical case (boost treatment of the breast) to reveal possible problems in the implementation. For standard geometries there was a good agreement between measurements and calculations, except for profiles for low energies (6 MeV) and high energies (18 Me V 22 MeV), in which cases the algorithm overestimated the dose off-axis in the high-dose region. For energies of 12 MeV and higher there were oscillations in the plateau region of the corresponding depth dose curves calculated with a grid size of 1 mm. With irregular cut outs, an overestimation of the dose was observed for small slits and low energies (4% for 6 MeV), as well as for asymmetric cases and extended source-to-surface distances (12% for SSD = 120 cm). While all monitor unit calculations for SSD = 100 cm were within 3% compared to measure-ments, there were large deviations for small cut outs and source-to-surface distances larger than 100 cm (7%for a 3 cm diameter cut-out and a source-to-surface distance of 10 cm).

Monte Carlo source model for photon beam radiotherapy: photon source characteristics

A major barrier to widespread clinical implementation of Monte Carlo dose calculation is the difficulty in characterizing the radiation source within a generalized source model. This work aims to develop a generalized three-component source model (target, primary collimator, flattening filter) for 6- and 18-MV photon beams that match full phase-space data (PSD). Subsource by subsource comparison of dose distributions, using either source PSD or the source model as input, allows accurate source characterization and has the potential to ease the commissioning procedure, since it is possible to obtain information about which subsource needs to be tuned. This source model is unique in that, compared to previous source models, it retains additional correlations among PS variables, which improves accuracy at nonstandard source-to-surface distances (SSDs). In our study, three-dimensional (3D) dose calculations were performed for SSDs ranging from 50 to 200 cm and for field sizes from 1 x 1 to 30 x 30 cm2 as well as a 10 x 10 cm2 field 5 cm off axis in each direction. The 3D dose distributions, using either full PSD or the source model as input, were compared in terms of dose-difference and distance-to-agreement. With this model, over 99% of the voxels agreed within +/-1% or 1 mm for the target, within 2% or 2 mm for the primary collimator, and within +/-2.5% or 2 mm for the flattening filter in all cases studied. For the dose distributions, 99% of the dose voxels agreed within 1% or 1 mm when the combined source model-including a charged particle source and the full PSD as input-was used. The accurate and general characterization of each photon source and knowledge of the subsource dose distributions should facilitate source model commissioning procedures by allowing scaling the histogram distributions representing the subsources to be tuned.

ORANGE: a Monte Carlo dose engine for radiotherapy

This study presents data for the verification of ORANGE, a fast MCNP-based dose engine for radiotherapy treatment planning. In order to verify the new algorithm, it has been benchmarked against DOSXYZ and against measurements. For the benchmarking, first calculations have been done using the ICCR-XIII benchmark. Next, calculations have been done with DOSXYZ and ORANGE in five different phantoms (one homogeneous, two with bone equivalent inserts and two with lung equivalent inserts). The calculations have been done with two mono-energetic photon beams (2 MeV and 6 MeV) and two mono-energetic electron beams (10 MeV and 20 MeV). Comparison of the calculated data (from DOSXYZ and ORANGE) against measurements was possible for a realistic 10 MV photon beam and a realistic 15 MeV electron beam in a homogeneous phantom only. For the comparison of the calculated dose distributions and dose distributions against measurements, the concept of the confidence limit (CL) has been used. This concept reduces the difference between two data sets to a single number, which gives the deviation for 90% of the dose distributions. Using this concept, it was found that ORANGE was always within the statistical bandwidth with DOSXYZ and the measurements. The ICCR-XIII benchmark showed that ORANGE is seven times faster than DOSXYZ, a result comparable with other accelerated Monte Carlo dose systems when no variance reduction is used. As shown for XVMC, using variance reduction techniques has the potential for further acceleration. Using modern computer hardware, this brings the total calculation time for a dose distribution with 1.5% (statistical) accuracy within the clinical range (less then 10 min). This means that ORANGE can be a candidate for a dose engine in radiotherapy treatment planning.

Monte Carlo as a four-dimensional radiotherapy treatment-planning tool to account for respiratory motion

Four-dimensional (4D) radiotherapy is the explicit inclusion of the temporal changes in anatomy during the imaging, planning and delivery of radiotherapy. Temporal anatomic changes can occur for many reasons, though the focus of the current investigation was respiration motion for lung tumours. The aims of the current research were first to develop a 4D Monte Carlo methodology and second to apply this technique to an existing 4D treatment plan. A 4D CT scan consisting of a series of 3D CT image sets acquired at different respiratory phases was used. Deformable image registration was performed to map each CT set from the end-inhale respiration phase to the CT image sets corresponding with subsequent respiration phases. This deformable registration allowed the contours drawn on the end-inhale CT to be automatically drawn on the other respiratory phase CT image sets. A treatment plan was created on the end-inhale CT image set and then automatically created on each of the 3D CT image sets corresponding with subsequent respiration phases, based on the beam arrangement and dose prescription in the end-inhale plan. Dose calculation using Monte Carlo was simultaneously performed on each of the N (=8) 3D image sets with 1/N fewer particles per calculation than for a 3D plan. The dose distribution from each respiratory phase CT image set was mapped back to the end-inhale CT image set for analysis. This use of deformable image registration to merge all the statistically noisy dose distributions back onto one CT image set effectively yielded a 4D Monte Carlo calculation with a statistical uncertainty equivalent to a 3D calculation, with a similar calculation time for the 3D and 4D methods. Monte Carlo as a dose calculation tool for 4D radiotherapy planning has two advantages: (1) higher accuracy for calculation in electronic disequilibrium conditions, such as those encountered during lung radiotherapy, and (2) if deformable image registration is used, the calculation time for Monte Carlo is independent of the number of 3D CT image sets constituting a 4D CT, unlike other algorithms for which the calculation time scales linearly with the number of 3D CT image sets constituting a 4D CT.

A virtual photon energy fluence model for Monte Carlo dose calculation

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.

The effect of dose calculation accuracy on inverse treatment planning

The effect of dose calculation accuracy during inverse treatment planning for intensity modulated radiotherapy (IMRT) was studied in this work. Three dose calculation methods were compared: Monte Carlo, superposition and pencil beam. These algorithms were used to calculate beamlets. which were subsequently used by a simulated annealing algorithm to determine beamlet weights which comprised the optimal solution to the objective function. Three different cases (lung, prostate and head and neck) were investigated and several different objective functions were tested for their effect on inverse treatment planning. It is shown that the use of inaccurate dose calculation introduces two errors in a treatment plan, a systematic error and a convergence error. The systematic error is present because of the inaccuracy of the dose calculation algorithm. The convergence error appears because the optimal intensity distribution for inaccurate beamlets differs from the optimal solution for the accurate beamlets. While the systematic error for superposition was found to be approximately 1% of Dmax in the tumour and slightly larger outside, the error for the pencil beam method is typically approximately 5% of Dmax and is rather insensitive to the given objectives. On the other hand, the convergence error was found to be very sensitive to the objective function, is only slightly correlated to the systematic error and should be determined for each case individually. Our results suggest that because of the large systematic and convergence errors, inverse treatment planning systems based on pencil beam algorithms alone should be upgraded either to superposition or Monte Carlo based dose calculations.

[Foundations of the Monte Carlo method for dose calculation in radiotherapy]

Monte Carlo (MC) methods applied in dose calculation are based on fundamental principles of radiation interaction with matter. In contrast to other methods, the accuracy of dose calculation achievable with MC depends only on the determination of the beam quality and the interaction coefficients. Using MC techniques it is possible to predict the dose for clinical photon and electron beams with an accuracy of > +/- 2%. Especially for inhomogeneous regions like head, neck, and lung, the MC technique can significantly improve the accuracy compared to conventional algorithms. Therefore, in the present paper the basic features of the MC method are reviewed in the context of treatment planning in radiation therapy. The main shortcoming in the past, i.e., that MC algorithms are too slow to be acceptable for clinical purposes, could be solved by using faster computers and by introducing new variance reduction (VR) techniques. These techniques decrease the statistical fluctuations without increasing the number of particle histories. Therefore, MC calculation times in the order of a few minutes are possible. A brief overview of VR methods is provided.

A multiple source model for 6 MV photon beam dose calculations using Monte Carlo

A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.

Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy

Monte Carlo (code GEANT) produced 6 and 15 MV phase space (PS) data were used to define several simple photon beam models. For creating the PS data the energy of starting electrons hitting the target was tuned to get correct depth dose data compared to measurements. The modeling process used the full PS information within the geometrical boundaries of the beam including all scattered radiation of the accelerator head. Scattered radiation outside the boundaries was neglected. Photons and electrons were assumed to be radiated from point sources. Four different models were investigated which involved different ways to determine the energies and locations of beam particles in the output plane. Depth dose curves, profiles, and relative output factors were calculated with these models for six field sizes from 5x5 to 40x40cm2 and compared to measurements. Model 1 uses a photon energy spectrum independent of location in the PS plane and a constant photon fluence in this plane. Model 2 takes into account the spatial particle fluence distribution in the PS plane. A constant fluence is used again in model 3, but the photon energy spectrum depends upon the off axis position. Model 4, finally uses the spatial particle fluence distribution and off axis dependent photon energy spectra in the PS plane. Depth dose curves and profiles for field sizes up to 10x10cm2 were not model sensitive. Good agreement between measured and calculated depth dose curves and profiles for all field sizes was reached for model 4. However, increasing deviations were found for increasing field sizes for models 1-3. Large deviations resulted for the profiles of models 2 and 3. This is due to the fact that these models overestimate and underestimate the energy fluence at large off axis distances. Relative output factors consistent with measurements resulted only for model 4.

Accuracy of the phase space evolution dose calculation model for clinical 25 MeV electron beams

The phase space evolution (PSE) model is a dose calculation model for electron beams in radiation oncology developed with the aim of a higher accuracy than the commonly used pencil beam (PB) models and with shorter calculation times than needed for Monte Carlo (MC) calculations. In this paper the accuracy of the PSE model has been investigated for 25 MeV electron beams of a MM50 racetrack microtron (Scanditronix Medical AB, Sweden) and compared with the results of a PB model. Measurements have been performed for tests like non-standard SSD, irregularly shaped fields, oblique incidence and in phantoms with heterogeneities of air, bone and lung. MC calculations have been performed as well, to reveal possible errors in the measurements and/or possible inaccuracies in the interaction data used for the bone and lung substitute materials. Results show a good agreement between PSE calculated dose distributions and measurements. For all points the differences--in absolute dose--were generally well within 3% and 3 mm. However, the PSE model was found to be less accurate in large regions of low-density material and errors of up to 6% were found for the lung phantom. Results of the PB model show larger deviations, with differences of up to 6% and 6 mm and of up to 10% for the lung phantom; at shortened SSDs the dose was overestimated by up to 6%. The agreement between MC calculations and measurement was good. For the bone and the lung phantom maximum deviations of 4% and 3% were found, caused by uncertainties about the actual interaction data. In conclusion, using the phase space evolution model, absolute 3D dose distributions of 25 MeV electron beams can be calculated with sufficient accuracy in most cases. The accuracy is significantly better than for a pencil beam model. In regions of lung tissue, a Monte Carlo model yields more accurate results than the current implementation of the PSE model.