A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy

TL;DR

This paper introduces a stabilised finite element method for proton transport in tissue that guarantees non-negative fluence and dose calculations, improving reliability and accuracy in proton therapy treatment planning.

Contribution

It presents a novel positivity-preserving finite element framework with proven convergence, enhancing dose computation accuracy in proton therapy.

Findings

Guarantees non-negative dose and fluence on coarse meshes

Achieves optimal convergence rates in error estimates

Validated through numerical benchmarks

Abstract

We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees non-negative fluence and dose, even on coarse meshes. This enables reliable computation of clinically relevant quantities for treatment planning. We derive a priori error estimates demonstrating optimal convergence rates and validate the method through numerical benchmarks. The proposed framework provides a robust, accurate and efficient tool for advancing proton beam therapy.