Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model
In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (P _{N}) and an HartenLaxvan Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose deposition depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.
 Authors:

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 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 RWTH Aachen Univ., Aachen (Germany)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Mathematical Medicine and Biology
 Additional Journal Information:
 Journal Name: Mathematical Medicine and Biology; Journal ID: ISSN 14778599
 Publisher:
 Institute of Mathematics and its Applications (IMA)
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 59 BASIC BIOLOGICAL SCIENCES; radiotherapy simulation; sensitivity analysis; FokkerPlanck; adjoint method; deterministic dose calculations; average deposition depth
 OSTI Identifier:
 1267026
Barnard, Richard C., Frank, Martin, and Krycki, Kai. Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model. United States: N. p.,
Web. doi:10.1093/imammb/dqv039.
Barnard, Richard C., Frank, Martin, & Krycki, Kai. Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model. United States. doi:10.1093/imammb/dqv039.
Barnard, Richard C., Frank, Martin, and Krycki, Kai. 2016.
"Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model". United States.
doi:10.1093/imammb/dqv039. https://www.osti.gov/servlets/purl/1267026.
@article{osti_1267026,
title = {Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model},
author = {Barnard, Richard C. and Frank, Martin and Krycki, Kai},
abstractNote = {In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker–Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker–Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (PN) and an HartenLaxvan Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose deposition depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. In conclusion, this in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.},
doi = {10.1093/imammb/dqv039},
journal = {Mathematical Medicine and Biology},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {2}
}