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- Title
Instantaneous closed loop control of the radiative transfer equations with applications in radiotherapy.
- Authors
Frank, M.; Herty, M.; Hinze, M.
- Abstract
In this paper we consider a time-dependent Boltzmann equation for particle transport in biological tissues, which can be used for radiation dose calculation. We assume that the dose should be delivered to a target volume which moves over time. We formulate this as an optimal control problem and derive closed-loop control laws for the dose delivery problem using boundary and distributed control. Optimality conditions are derived. For the construction of the closed-loop control laws we use an inexact variant of model predictive control called instantaneous control. We compare numerical results obtained with instantaneous control to those obtained by optimal open-loop control, and present numerical simulations in one and two spatial dimensions. This work could be applied to image-guided radiation therapy, where patient motion during treatment is one of the future challenges.
- Subjects
RADIATIVE transfer; RADIOTHERAPY; FIRST-order logic; FINITE element method; PHYSIOLOGICAL control systems; MATHEMATICAL analysis
- Publication
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2012, Vol 92, Issue 1, p8
- ISSN
0044-2267
- Publication type
Article
- DOI
10.1002/zamm.201000191