Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

TL;DR

This paper introduces a new deterministic PDE model for electron dose calculation in radiotherapy, offering an alternative to Monte Carlo and semi-empirical methods, with a novel numerical scheme ensuring accurate property preservation.

Contribution

It derives a macroscopic PDE model based on radiative transfer equations with an angular closure, and develops a new HLLC scheme for its numerical solution.

Findings

Model is exact in free-streaming and isotropic regimes

Numerical scheme preserves key properties of solutions

Test cases demonstrate model's accuracy and potential

Abstract

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.