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OPTIMAL TREATMENT PLANNING IN RADIOTHERAPY BASED ON BOLTZMANN TRANSPORT CALCULATIONS

MARTIN FRANK

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

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MICHAEL HERTY

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

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MATTHIAS SCHÄFER

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

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https://doi.org/10.1142/S0218202508002784Cited by:19 (Source: Crossref)

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, 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.

Keywords:

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

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