OPTIMAL TREATMENT PLANNING IN RADIOTHERAPY BASED ON BOLTZMANN TRANSPORT CALCULATIONS

Abstract

A Boltzmann transport model for dose calculation in radiation therapy is considered. We formulate an optimal control problem for the desired dose. We prove existence and uniqueness of a minimizer. Based on this model, we derive optimality conditions. The PN discretization in angle of the full model is considered. We show that the PN approximation of the optimality system is in fact the optimality system of the PN approximation, provided that, instead of the usually used Marshak boundary conditions, Mark's boundary conditions are used. Numerical results in one and two dimensions are presented.