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Title: SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

Abstract

Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from themore » numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)« less

Authors:
;  [1];  [2]
  1. Shanghai Jiao Tong University, Shanghai, Shanghai (China)
  2. Massachusetts General Hospital, Boston, MA (United States)
Publication Date:
OSTI Identifier:
22545157
Resource Type:
Journal Article
Resource Relation:
Journal Name: Medical Physics; Journal Volume: 42; Journal Issue: 6; Other Information: (c) 2015 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
60 APPLIED LIFE SCIENCES; ACCURACY; ANIMAL TISSUES; BENCHMARKS; BREMSSTRAHLUNG; CHARGED PARTICLES; COMPTON EFFECT; DOSIMETRY; FINITE ELEMENT METHOD; FOKKER-PLANCK EQUATION; GALLIUM OXIDES; MONTE CARLO METHOD; PAIR PRODUCTION; RADIATION DOSES

Citation Formats

Hong, X, Gao, H, and Paganetti, H. SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation. United States: N. p., 2015. Web. doi:10.1118/1.4924383.
Hong, X, Gao, H, & Paganetti, H. SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation. United States. doi:10.1118/1.4924383.
Hong, X, Gao, H, and Paganetti, H. Mon . "SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation". United States. doi:10.1118/1.4924383.
@article{osti_22545157,
title = {SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation},
author = {Hong, X and Gao, H and Paganetti, H},
abstractNote = {Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)},
doi = {10.1118/1.4924383},
journal = {Medical Physics},
number = 6,
volume = 42,
place = {United States},
year = {Mon Jun 15 00:00:00 EDT 2015},
month = {Mon Jun 15 00:00:00 EDT 2015}
}
  • Purpose: To investigate the dosimetric impact of the heterogeneity dose calculation Acuros (Transpire Inc., Gig Harbor, WA), a grid-based Boltzmann equation solver (GBBS), for brachytherapy in a cohort of cervical cancer patients. Methods and Materials: The impact of heterogeneities was retrospectively assessed in treatment plans for 26 patients who had previously received {sup 192}Ir intracavitary brachytherapy for cervical cancer with computed tomography (CT)/magnetic resonance-compatible tandems and unshielded colpostats. The GBBS models sources, patient boundaries, applicators, and tissue heterogeneities. Multiple GBBS calculations were performed with and without solid model applicator, with and without overriding the patient contour to 1 g/cm{sup 3}more » muscle, and with and without overriding contrast materials to muscle or 2.25 g/cm{sup 3} bone. Impact of source and boundary modeling, applicator, tissue heterogeneities, and sensitivity of CT-to-material mapping of contrast were derived from the multiple calculations. American Association of Physicists in Medicine Task Group 43 (TG-43) guidelines and the GBBS were compared for the following clinical dosimetric parameters: Manchester points A and B, International Commission on Radiation Units and Measurements (ICRU) report 38 rectal and bladder points, three and nine o'clock, and {sub D2cm3} to the bladder, rectum, and sigmoid. Results: Points A and B, D{sub 2} cm{sup 3} bladder, ICRU bladder, and three and nine o'clock were within 5% of TG-43 for all GBBS calculations. The source and boundary and applicator account for most of the differences between the GBBS and TG-43 guidelines. The D{sub 2cm3} rectum (n = 3), D{sub 2cm3} sigmoid (n = 1), and ICRU rectum (n = 6) had differences of >5% from TG-43 for the worst case incorrect mapping of contrast to bone. Clinical dosimetric parameters were within 5% of TG-43 when rectal and balloon contrast were mapped to bone and radiopaque packing was not overridden. Conclusions: The GBBS has minimal impact on clinical parameters for this cohort of patients with unshielded applicators. The incorrect mapping of rectal and balloon contrast does not have a significant impact on clinical parameters. Rectal parameters may be sensitive to the mapping of radiopaque packing.« less
  • Purpose: The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC. Methods: Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantagemore » in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward-peaking scattering. To be compatible with image-guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver. Results: The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document. Conclusion: We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.« less
  • Purpose: To use the Attila deterministic solver as a supplement to Monte Carlo for calculating out-of-field organ dose in support of epidemiological studies looking at the risks of second cancers. Supplemental dosimetry tools are needed to speed up dose calculations for studies involving large-scale patient cohorts. Methods: Attila is a multi-group discrete ordinates code which can solve the 3D photon-electron coupled linear Boltzmann radiation transport equation on a finite-element mesh. Dose is computed by multiplying the calculated particle flux in each mesh element by a medium-specific energy deposition cross-section. The out-of-field dosimetry capability of Attila is investigated by comparing averagemore » organ dose to that which is calculated by Monte Carlo simulation. The test scenario consists of a 6 MV external beam treatment of a female patient with a tumor in the left breast. The patient is simulated by a whole-body adult reference female computational phantom. Monte Carlo simulations were performed using MCNP6 and XVMC. Attila can export a tetrahedral mesh for MCNP6, allowing for a direct comparison between the two codes. The Attila and Monte Carlo methods were also compared in terms of calculation speed and complexity of simulation setup. A key perquisite for this work was the modeling of a Varian Clinac 2100 linear accelerator. Results: The solid mesh of the torso part of the adult female phantom for the Attila calculation was prepared using the CAD software SpaceClaim. Preliminary calculations suggest that Attila is a user-friendly software which shows great promise for our intended application. Computational performance is related to the number of tetrahedral elements included in the Attila calculation. Conclusion: Attila is being explored as a supplement to the conventional Monte Carlo radiation transport approach for performing retrospective patient dosimetry. The goal is for the dosimetry to be sufficiently accurate for use in retrospective epidemiological investigations.« less
  • No abstract prepared.
  • An approximate two-dimensional solver of the nonlinear Fokker-Planck-Landau collision operator has been developed using the assumption that the particle probability distribution function is independent of gyroangle in the limit of strong magnetic field. The isotropic one-dimensional scheme developed for nonlinear Fokker-Planck-Landau equation by Buet and Cordier [J. Comput. Phys. 179, 43 (2002)] and for linear Fokker-Planck-Landau equation by Chang and Cooper [J. Comput. Phys. 6, 1 (1970)] have been modified and extended to two-dimensional nonlinear equation. In addition, a method is suggested to apply the new velocity-grid based collision solver to Lagrangian particle-in-cell simulation by adjusting the weights of markermore » particles and is applied to a five dimensional particle-in-cell code to calculate the neoclassical ion thermal conductivity in a tokamak plasma. Error verifications show practical aspects of the present scheme for both grid-based and particle-based kinetic codes.« less