A novel Boltzmann equation solver for calculation of dose and fluence spectra distributions for proton beam therapy

Oleg N Vassiliev; Radhe Mohan

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arXiv · 2512.24514

A novel Boltzmann equation solver for calculation of dose and fluence spectra distributions for proton beam therapy

Oleg N Vassiliev·Radhe Mohan

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Abstract

The claim that Monte Carlo is the most accurate method is a case of misattributed credit. This claim is based on experience with advanced systems MCNPX, Geant4 and EGS. These systems achieve remarkable performance because they use most accurate physics, not because they use random numbers. The latter simplifies algorithms, but contaminates the solution with random noise. Currently prevalent fast Monte Carlo algorithms retain this worst part while achieving high computing speed at the expense of the best part- accurate physics. We employ an opposite strategy. We develop a Boltzmann solver for protons that retains unchanged the physics of most advanced Monte Carlo systems. We eliminate random noise, because our solution method is deterministic. Our method is also applicable to heavier ions, helium and carbon, for example. Results of the study provide a foundation for achieving a high computing speed with uncompromised accuracy in proton treatment planning systems.

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Oleg N Vassiliev, Radhe Mohan. 2025-12-30. A novel Boltzmann equation solver for calculation of dose and fluence spectra distributions for proton beam therapy. https://arxiv.org/abs/2512.24514

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