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

Ben S. Ashby; Abdalaziz Hamdan; Tristan Pryer

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arXiv · 2506.01105

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

Ben S. Ashby·Abdalaziz Hamdan·Tristan Pryer

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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.

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Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer. 2025-06-01. A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy. https://arxiv.org/abs/2506.01105

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