English

Optimal treatment planning governed by kinetic equations

Optimization and Control 2012-05-07 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0904.0740,
  title  = {Optimal treatment planning governed by kinetic equations},
  author = {Martin Frank and Michael Herty and Albert N. Sandjo},
  journal= {arXiv preprint arXiv:0904.0740},
  year   = {2012}
}

Comments

15 pages, 1 figure

R2 v1 2026-06-21T12:48:14.115Z