Optimal radiotherapy treatment planning using minimum entropy models

TL;DR

This paper develops an optimal radiotherapy treatment planning approach using a time-dependent Boltzmann model and minimum entropy approximation, enabling precise dose control and tumor cell survival minimization.

Contribution

It introduces a novel application of minimum entropy models to radiotherapy planning with detailed optimality systems and numerical validation.

Findings

Effective dose deviation minimization demonstrated

Tumor cell survival reduction achieved

Minimum entropy approximation proved advantageous

Abstract

We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative particles with tissue. This model allows for the modeling of inhomogeneities in the body and allows for anisotropic sources modeling distributed radiation---as in brachytherapy---and external beam sources---as in teletherapy. We study two optimization problems: minimizing the deviation from a spatially-dependent prescribed dose through a quadratic tracking functional; and minimizing the survival of tumor cells through the use of the linear-quadratic model of radiobiological cell response. For each problem, we derive the optimality systems. In order to solve the state and adjoint equations, we use the minimum entropy approximation; the advantages of this method are discussed. Numerical results are then presented.