Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model. (9th February 2016)

• Record Type: Journal Article
• Authors: Barnard, Richard C.; Frank, Martin; Krycki, Kai
• Is Part Of: Mathematical medicine and biology. Volume 34:Number 1(2017:Mar.)
• Page Start: 109
• Page End: 123
• Publication Date: 2016-02-09
• Subjects: sensitivity analysis -- adjoint method -- deterministic dose calculations -- radiotherapy simulation -- average deposition depth; Biomathematics -- Periodicals; Medicine -- Mathematics -- Periodicals; Medicine -- Periodicals; Biology -- Periodicals; Biomedical Research -- Periodicals; Models, Theoretical -- Periodicals; 570.15195
• DOI: 10.1093/imammb/dqv039
• Languages: English
• ISSNs: 1477-8599

Abstract

Abstract : 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 Harten-Lax-van 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. This in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present.