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

TL;DR

This paper develops a numerical method using a Fokker-Planck model and adjoint sensitivities to analyze how electron dose calculations in radiotherapy depend on stopping power and transport coefficients, especially at lower beam energies.

Contribution

It introduces a novel approach combining Fokker-Planck approximation and adjoint methods for sensitivity analysis in radiotherapy dose calculations.

Findings

Sensitivity increases as beam energy decreases.

Method verified against finite difference approximations.

Numerical results demonstrate the impact of transport coefficients.

Abstract

In this paper we study the sensitivities of electron dose calculations with respect to the stopping power and the 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 HLL 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 transport coefficients, demonstrating the increasing relative sensitivities as beam energy decreases.