Sensitivity analysis for dose deposition in radiotherapy via a Fokker–Planck model

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.

Effects of tumour heterogeneous properties on modelling the transport of radiative particles

“…In order to simplify models for dose calculation while increasing accuracy, a lot of studies have focused on the use of deterministic dose calculation models as an alternative method to Monte Carlo approach that is widely used in RT clinical treatment planning. 18,[45][46][47] More specifically, the studies have focused on directly modelling the transport of radiative particles (electrons, photons, etc.) through the use of BTEs 48,49 and in addition approximating their solutions as accurately as possible.…”