José Ramos-Méndez

Geometrical splitting technique to improve the computational efficiency in Monte Carlo calculations for proton therapy

PURPOSE To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation. METHODS The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique. RESULTS A normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria. CONCLUSIONS The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.

The effect of beam purity and scanner complexity on proton CT accuracy

Purpose: To determine the dependence of the accuracy in reconstruction of relative stopping power (RSP) with proton computerized tomography (pCT) scans on the purity of the proton beam and the technological complexity of the pCT scanner using standard phantoms and a digital representation of a pediatric patient. Methods: The Monte Carlo method was applied to simulate the pCT scanner, using both a pure proton beam (uniform 200 MeV mono‐energetic, parallel beam) and the Northwestern Medicine Chicago Proton Center (NMCPC) clinical beam in uniform scanning mode. The accuracy of the simulation was validated with measurements performed at NMCPC including reconstructed RSP images obtained with a preclinical prototype pCT scanner. The pCT scanner energy detector was then simulated in three configurations of increasing complexity: an ideal totally absorbing detector, a single stage detector and a multi‐stage detector. A set of 15 cm diameter water cylinders containing either water alone or inserts of different material, size, and position were simulated at 90 projection angles (4° steps) for the pure and clinical proton beams and the three pCT configurations. A pCT image of the head of a detailed digital pediatric phantom was also reconstructed from the simulated pCT scan with the prototype detector. Results: The RSP error increased for all configurations for insert sizes under 7.5 mm in radius, with a sharp increase below 5 mm in radius, attributed to a limit in spatial resolution. The highest accuracy achievable using the current pCT calibration step phantom and reconstruction algorithm, calculated for the ideal case of a pure beam with totally absorbing energy detector, was 1.3% error in RSP for inserts of 5 mm radius or more, 0.7 mm in range for the 2.5 mm radius inserts, or better. When the highest complexity of the scanner geometry was introduced, some artifacts arose in the reconstructed images, particularly in the center of the phantom. Replacing the step phantom used for calibration with a wedge phantom led to RSP accuracy close to the ideal case, with no significant dependence of RSP error on insert location or material. The accuracy with the multi‐stage detector and NMCPC beam for the cylindrical phantoms was 2.2% in RSP error for inserts of 5 mm radius or more, 0.7 mm in range for the 2.5 mm radius inserts, or better. The pCT scan of the pediatric phantom resulted in mean RSP values within 1.3% of the reference RSP, with a range error under 1 mm, except in exceptional situations of parallel incidence on a boundary between low and high density. Conclusions: The pCT imaging technique proved to be a precise and accurate imaging tool, rivaling the current x‐rays based techniques, with the advantage of being directly sensitive to proton stopping power rather than photon interaction coefficients. Measured and simulated pCT images were obtained from a wobbled proton beam for the first time. Since the in‐silico results are expected to accurately represent the prototype pCT, upcoming measurements using the wedge phantom for calibration are expected to show similar accuracy in the reconstructed RSP.

Dose assessment for the fetus considering scattered and secondary radiation from photon and proton therapy when treating a brain tumor of the mother.

The goal of this work was to determine the scattered photon dose and secondary neutron dose and resulting risk for the sensitive fetus from photon and proton radiotherapy when treating a brain tumor during pregnancy. Anthropomorphic pregnancy phantoms with three stages (3-, 6-, 9-month) based on ICRP reference parameters were implemented in Monte Carlo platform TOPAS, to evaluate the scattered dose and secondary neutron dose and dose equivalent. To evaluate the dose equivalent, dose averaged quality factors were considered for neutrons. This study compared three treatment modalities: passive scattering and pencil beam scanning proton therapy (PPT and PBS) and 6-MV 3D conformal photon therapy. The results show that, for 3D conformal photon therapy, the scattered photon dose equivalent to the fetal body increases from 0.011 to 0.030 mSv per treatment Gy with increasing stage of gestation. For PBS, the neutron dose equivalent to the fetal body was significantly lower, i.e. increasing from 1.5 × 10(-3) to 2.5 × 10(-3) mSv per treatment Gy with increasing stage of gestation. For PPT, the neutron dose equivalent of the fetus decreases from 0.17 to 0.13 mSv per treatment Gy with the growing fetus. The ratios of dose equivalents to the fetus for a 52.2 Gy(RBE) course of radiation therapy to a typical CT scan of the mothers head ranged from 3.4-4.4 for PBS, 30-41 for 3D conformal photon therapy and 180-500 for PPT, respectively. The attained dose to a fetus from the three modalities is far lower than the thresholds of malformation, severe mental retardation and lethal death. The childhood cancer excessive absolute risk was estimated using a linear no-threshold dose-response relationship. The risk would be 1.0 (95% CI: 0.6, 1.6) and 0.1 (95% CI: -0.01, 0.52) in 10(5) for the 9-month fetus for PBS with a prescribed dose of 52.2 Gy(RBE). The increased risks for PPT and photon therapy are about two and one orders of magnitude larger than that for PBS, respectively. We can conclude that a pregnant woman with a brain tumor could be treated with pencil beam scanning with acceptable risks to the fetus.

A framework for implementation of organ effect models in TOPAS with benchmarks extended to proton therapy.

The aim of this work was to develop a framework for modeling organ effects within TOPAS (TOol for PArticle Simulation), a wrapper of the Geant4 Monte Carlo toolkit that facilitates particle therapy simulation. The DICOM interface for TOPAS was extended to permit contour input, used to assign voxels to organs. The following dose response models were implemented: The Lyman-Kutcher-Burman model, the critical element model, the population based critical volume model, the parallel-serial model, a sigmoid-based model of Niemierko for normal tissue complication probability and tumor control probability (TCP), and a Poisson-based model for TCP. The framework allows easy manipulation of the parameters of these models and the implementation of other models. As part of the verification, results for the parallel-serial and Poisson model for x-ray irradiation of a water phantom were compared to data from the AAPM Task Group 166. When using the task group dose-volume histograms (DVHs), results were found to be sensitive to the number of points in the DVH, with differences up to 2.4%, some of which are attributable to differences between the implemented models. New results are given with the point spacing specified. When using Monte Carlo calculations with TOPAS, despite the relatively good match to the published DVHs, differences up to 9% were found for the parallel-serial model (for a maximum DVH difference of 2%) and up to 0.5% for the Poisson model (for a maximum DVH difference of 0.5%). However, differences of 74.5% (in Rectangle1), 34.8% (in PTV) and 52.1% (in Triangle) for the critical element, critical volume and the sigmoid-based models were found respectively. We propose a new benchmark for verification of organ effect models in proton therapy. The benchmark consists of customized structures in the spread out Bragg peak plateau, normal tissue, tumor, penumbra and in the distal region. The DVHs, DVH point spacing, and results of the organ effect models are provided. The models were used to calculate dose response for a Head and Neck patient to demonstrate functionality of the new framework and indicate the degree of variability between the models in proton therapy.

Experimental depth dose curves of a 67.5 MeV proton beam for benchmarking and validation of Monte Carlo simulation.

PURPOSE To measure depth dose curves for a 67.5 ± 0.1 MeV proton beam for benchmarking and validation of Monte Carlo simulation. METHODS Depth dose curves were measured in 2 beam lines. Protons in the raw beam line traversed a Ta scattering foil, 0.1016 or 0.381 mm thick, a secondary emission monitor comprised of thin Al foils, and a thin Kapton exit window. The beam energy and peak width and the composition and density of material traversed by the beam were known with sufficient accuracy to permit benchmark quality measurements. Diodes for charged particle dosimetry from two different manufacturers were used to scan the depth dose curves with 0.003 mm depth reproducibility in a water tank placed 300 mm from the exit window. Depth in water was determined with an uncertainty of 0.15 mm, including the uncertainty in the water equivalent depth of the sensitive volume of the detector. Parallel-plate chambers were used to verify the accuracy of the shape of the Bragg peak and the peak-to-plateau ratio measured with the diodes. The uncertainty in the measured peak-to-plateau ratio was 4%. Depth dose curves were also measured with a diode for a Bragg curve and treatment beam spread out Bragg peak (SOBP) on the beam line used for eye treatment. The measurements were compared to Monte Carlo simulation done with geant4 using topas. RESULTS The 80% dose at the distal side of the Bragg peak for the thinner foil was at 37.47 ± 0.11 mm (average of measurement with diodes from two different manufacturers), compared to the simulated value of 37.20 mm. The 80% dose for the thicker foil was at 35.08 ± 0.15 mm, compared to the simulated value of 34.90 mm. The measured peak-to-plateau ratio was within one standard deviation experimental uncertainty of the simulated result for the thinnest foil and two standard deviations for the thickest foil. It was necessary to include the collimation in the simulation, which had a more pronounced effect on the peak-to-plateau ratio for the thicker foil. The treatment beam, being unfocussed, had a broader Bragg peak than the raw beam. A 1.3 ± 0.1 MeV FWHM peak width in the energy distribution was used in the simulation to match the Bragg peak width. An additional 1.3-2.24 mm of water in the water column was required over the nominal values to match the measured depth penetration. CONCLUSIONS The proton Bragg curve measured for the 0.1016 mm thick Ta foil provided the most accurate benchmark, having a low contribution of proton scatter from upstream of the water tank. The accuracy was 0.15% in measured beam energy and 0.3% in measured depth penetration at the Bragg peak. The depth of the distal edge of the Bragg peak in the simulation fell short of measurement, suggesting that the mean ionization potential of water is 2-5 eV higher than the 78 eV used in the stopping power calculation for the simulation. The eye treatment beam line depth dose curves provide validation of Monte Carlo simulation of a Bragg curve and SOBP with 4%/2 mm accuracy.

Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio

Simulation of water radiolysis and the subsequent chemistry provides important information on the effect of ionizing radiation on biological material. The Geant4 Monte Carlo toolkit has added chemical processes via the Geant4-DNA project. The TOPAS tool simplifies the modeling of complex radiotherapy applications with Geant4 without requiring advanced computational skills, extending the pool of users. Thus, a new extension to TOPAS, TOPAS-nBio, is under development to facilitate the configuration of track-structure simulations as well as water radiolysis simulations with Geant4-DNA for radiobiological studies. In this work, radiolysis simulations were implemented in TOPAS-nBio. Users may now easily add chemical species and their reactions, and set parameters including branching ratios, dissociation schemes, diffusion coefficients, and reaction rates. In addition, parameters for the chemical stage were re-evaluated and updated from those used by default in Geant4-DNA to improve the accuracy of chemical yields. Simulation results of time-dependent and LET-dependent primary yields Gx (chemical species per 100 eV deposited) produced at neutral pH and 25 °C by short track-segments of charged particles were compared to published measurements. The LET range was 0.05-230 keV µm-1. The calculated Gx values for electrons satisfied the material balance equation within 0.3%, similar for protons albeit with long calculation time. A smaller geometry was used to speed up proton and alpha simulations, with an acceptable difference in the balance equation of 1.3%. Available experimental data of time-dependent G-values for [Formula: see text] agreed with simulated results within 7%  ±  8% over the entire time range; for [Formula: see text] over the full time range within 3%  ±  4%; for H2O2 from 49%  ±  7% at earliest stages and 3%  ±  12% at saturation. For the LET-dependent Gx, the mean ratios to the experimental data were 1.11  ±  0.98, 1.21  ±  1.11, 1.05  ±  0.52, 1.23  ±  0.59 and 1.49  ±  0.63 (1 standard deviation) for [Formula: see text], [Formula: see text], H2, H2O2 and [Formula: see text], respectively. In conclusion, radiolysis and subsequent chemistry with Geant4-DNA has been successfully incorporated in TOPAS-nBio. Results are in reasonable agreement with published measured and simulated data.

Geometrical structures for radiation biology research as implemented in the TOPAS-nBio toolkit

Computational simulations, such as Monte Carlo track structure simulations, offer a powerful tool for quantitatively investigating radiation interactions within cells. The modelling of the spatial distribution of energy deposition events as well as diffusion of chemical free radical species, within realistic biological geometries, can help provide a comprehensive understanding of the effects of radiation on cells. Track structure simulations, however, generally require advanced computing skills to implement. The TOPAS-nBio toolkit, an extension to TOPAS (TOol for PArticle Simulation), aims to provide users with a comprehensive framework for radiobiology simulations, without the need for advanced computing skills. This includes providing users with an extensive library of advanced, realistic, biological geometries ranging from the micrometer scale (e.g. cells and organelles) down to the nanometer scale (e.g. DNA molecules and proteins). Here we present the geometries available in TOPAS-nBio.

Flagged uniform particle splitting for variance reduction in proton and carbon ion track-structure simulations

Flagged uniform particle splitting was implemented with two methods to improve the computational efficiency of Monte Carlo track structure simulations with TOPAS-nBio by enhancing the production of secondary electrons in ionization events. In method 1 the Geant4 kernel was modified. In method 2 Geant4 was not modified. In both methods a unique flag number assigned to each new split electron was inherited by its progeny, permitting reclassification of the split events as if produced by independent histories. Computational efficiency and accuracy were evaluated for simulations of 0.5-20 MeV protons and 1-20 MeV u-1 carbon ions for three endpoints: (1) mean of the ionization cluster size distribution, (2) mean number of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) classified with DBSCAN, and (3) mean number of SSBs and DSBs classified with a geometry-based algorithm. For endpoint (1), simulation efficiency was 3 times lower when splitting electrons generated by direct ionization events of primary particles than when splitting electrons generated by the first ionization events of secondary electrons. The latter technique was selected for further investigation. The following results are for method 2, with relative efficiencies about 4.5 times lower for method 1. For endpoint (1), relative efficiency at 128 split electrons approached maximum, increasing with energy from 47.2  ±  0.2 to 66.9  ±  0.2 for protons, decreasing with energy from 51.3  ±  0.4 to 41.7  ±  0.2 for carbon. For endpoint (2), relative efficiency increased with energy, from 20.7  ±  0.1 to 50.2  ±  0.3 for protons, 15.6  ±  0.1 to 20.2  ±  0.1 for carbon. For endpoint (3) relative efficiency increased with energy, from 31.0  ±  0.2 to 58.2  ±  0.4 for protons, 23.9  ±  0.1 to 26.2  ±  0.2 for carbon. Simulation results with and without splitting agreed within 1% (2 standard deviations) for endpoints (1) and (2), within 2% (1 standard deviation) for endpoint (3). In conclusion, standard particle splitting variance reduction techniques can be successfully implemented in Monte Carlo track structure codes.

WE-H-BRA-04: Biological Geometries for the Monte Carlo Simulation Toolkit TOPASNBio

PURPOSE New advances in radiation therapy are most likely to come from the complex interface of physics, chemistry and biology. Computational simulations offer a powerful tool for quantitatively investigating radiation interactions with biological tissue and can thus help bridge the gap between physics and biology. The aim of TOPAS-nBio is to provide a comprehensive tool to generate advanced radiobiology simulations. METHODS TOPAS wraps and extends the Geant4 Monte Carlo (MC) simulation toolkit. TOPAS-nBio is an extension to TOPAS which utilizes the physics processes in Geant4-DNA to model biological damage from very low energy secondary electrons. Specialized cell, organelle and molecular geometries were designed for the toolkit. RESULTS TOPAS-nBio gives the user the capability of simulating biological geometries, ranging from the micron-scale (e.g. cells and organelles) to complex nano-scale geometries (e.g. DNA and proteins). The user interacts with TOPAS-nBio through easy-to-use input parameter files. For example, in a simple cell simulation the user can specify the cell type and size as well as the type, number and size of included organelles. For more detailed nuclear simulations, the user can specify chromosome territories containing chromatin fiber loops, the later comprised of nucleosomes on a double helix. The chromatin fibers can be arranged in simple rigid geometries or within factual globules, mimicking realistic chromosome territories. TOPAS-nBio also provides users with the capability of reading protein data bank 3D structural files to simulate radiation damage to proteins or nucleic acids e.g. histones or RNA. TOPAS-nBio has been validated by comparing results to other track structure simulation software and published experimental measurements. CONCLUSION TOPAS-nBio provides users with a comprehensive MC simulation tool for radiobiological simulations, giving users without advanced programming skills the ability to design and run complex simulations.

SU-E-T-466: Implementation of An Extension Module for Dose Response Models in the TOPAS Monte Carlo Toolkit

Purpose: To develop and verify an extension to TOPAS for calculation of dose response models (TCP/NTCP). TOPAS wraps and extends Geant4. Methods: The TOPAS DICOM interface was extended to include structure contours, for subsequent calculation of DVH’s and TCP/NTCP. The following dose response models were implemented: Lyman-Kutcher-Burman (LKB), critical element (CE), population based critical volume (CV), parallel-serials, a sigmoid-based model of Niemierko for NTCP and TCP, and a Poisson-based model for TCP. For verification, results for the parallel-serial and Poisson models, with 6 MV x-ray dose distributions calculated with TOPAS and Pinnacle v9.2, were compared to data from the benchmark configuration of the AAPM Task Group 166 (TG166). We provide a benchmark configuration suitable for proton therapy along with results for the implementation of the Niemierko, CV and CE models. Results: The maximum difference in DVH calculated with Pinnacle and TOPAS was 2%. Differences between TG166 data and Monte Carlo calculations of up to 4.2%±6.1% were found for the parallel-serial model and up to 1.0%±0.7% for the Poisson model (including the uncertainty due to lack of knowledge of the point spacing in TG166). For CE, CV and Niemierko models, the discrepancies between the Pinnacle and TOPAS results are 74.5%, 34.8% and 52.1% when using 29.7 cGy point spacing, the differences being highly sensitive to dose spacing. On the other hand, with our proposed benchmark configuration, the largest differences were 12.05%±0.38%, 3.74%±1.6%, 1.57%±4.9% and 1.97%±4.6% for the CE, CV, Niemierko and LKB models, respectively. Conclusion: Several dose response models were successfully implemented with the extension module. Reference data was calculated for future benchmarking. Dose response calculated for the different models varied much more widely for the TG166 benchmark than for the proposed benchmark, which had much lower sensitivity to the choice of DVH dose points. This work was supported by National Cancer Institute Grant R01CA140735