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OPTIMAL RADIOTHERAPY TREATMENT PLANNING GOVERNED BY KINETIC EQUATIONS

MARTIN FRANK

TU Kaiserslauten, Erwin-Schrödinger-Strasse, 67663 Kaiserslautern, Germany

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MICHAEL HERTY

RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

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, and

ALBERT N. SANDJO

RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

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https://doi.org/10.1142/S0218202510004386Cited by:18 (Source: Crossref)

Abstract

In this paper we study a problem in radiotherapy treatment planning. This problem is formulated as an optimization problem of a functional of the radiative flux. It is constrained by the condition that the radiative flux, which depends on position, energy and direction of the particles, is governed by a Boltzmann integro-differential equation. We show the existence, uniqueness and regularity of solutions to this constrained optimization problem in an appropriate function space. The main new difficulty is the treatment of the energy loss term. Furthermore, we characterize optimal controls by deriving first-order optimality conditions.

Keywords:

AMSC: 85A25, 76P05, 49J20, 92C50

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