Optimal treatment planning in radiotherapy based on Boltzmann transport equations

Abstract

We look at the optimization of radiotherapy treatment planning. By using a deterministic model of dose deposition in tissue derived from the Boltzmann transport equations, we can improve on the accuracy of existing models near tissue inhomogeneities while also making use of adjoint calculus for developing necessary conditions for optimality. We describe the relevant model and consider the planning problem in an optimal control framework. Two versions of the problem are discussed, optimality conditions are derived, and numerical methods are described. Numerical examples are presented.