Geometry, Energy and Sensitivity in Stochastic Proton Dynamics
This work provides improved numerical tools for proton therapy dose calculation, addressing the need for accurate and stable sensitivity estimates in treatment planning.
The authors develop numerical schemes and sensitivity methods for stochastic proton transport models, achieving strong order one convergence with a positivity-preserving logarithmic Milstein scheme and a Lie-group integrator for angular dynamics. Numerical experiments confirm expected convergence rates and stable dose sensitivity estimates.
We develop numerical schemes and sensitivity methods for stochastic models of proton transport that couple energy loss, range straggling and angular diffusion. For the energy equation we introduce a logarithmic Milstein scheme that guarantees positivity and achieves strong order one convergence. For the angular dynamics we construct a Lie-group integrator. The combined method maintains the natural geometric invariants of the system. We formulate dose deposition as a regularised path-dependent functional, obtaining a pathwise sensitivity estimator that is consistent and implementable. Numerical experiments confirm that the proposed schemes achieve the expected convergence rates and provide stable estimates of dose sensitivities.