Optimal treatment planning governed by kinetic equations

Details Optimal treatment planning governed by kinetic equations Optimal treatment planning governed by kinetic equations

2009-04-06

arxiv.org/abs/0904.0740v1

Mathematics

Optimization and Control

15 pages, 1 figure

Scientific paper

In this paper we study a problem in radiotherapy treatment planning, where the evolution of the radiation field is governed by a deterministic Boltzmann transport equation. We show existence, uniqueness and regularity of solutions to an optimal dose distribution problem constrained by the Boltzmann Continuous Slowing-Down equation in an appropriate function space. The main new difficulty is the treatment of the stopping power term. Furthermore, we characterize optimal controls for problems governed by this transport equation.

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