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 P N discretization in angle of the full model is considered. We show that the P N approximation of the optimality system is in fact the optimality system of the P N approximation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)