ON OPTIMAL TREATMENT PLANNING IN RADIOTHERAPY GOVERNED BY TRANSPORT EQUATIONS

Abstract

This paper is devoted to the study of optimal control problems arising in radiotherapy planning problems. The distribution of the radiative intensity in the patient's body is described by a Boltzmann-integro differential equation with position, angular and energy-dependent scattering and absorption coefficients and an energy loss term. The presented discussion is the last in the series of Refs. 13 and 14 discussing radiotherapy problems using the Boltzmann transport equation. We show the existence, uniqueness and regularity of an optimal control using evolution group theory. We extend existing results in order to treat the important case of energy-dependent scattering coefficients.