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Identification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy

Please always quote using this URN:urn:nbn:de:0296-matheon-8041
  • We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissue is destroyed by coagulation. For the dosage planning numerical simulation plays an important role. To this end a crucial problem is to identify the thermal growth kinetics of the coagulated zone. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. The solution to this inverse problem is defined as the minimizer of a non-convex cost functional. The existence of the minimizer is proven. We derive the Gateaux derivative of the cost functional, which is based on the adjoint system, and use it for a numerical approximation of the optimal coefficient.

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Metadaten
Author:Dietmar Hömberg, Jijun Liu, Nataliya Togobytska
URN:urn:nbn:de:0296-matheon-8041
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/04/18
Release Date:2011/04/18
Tag:
Institute:Research Center Matheon
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R30 Inverse problems
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Fxx Coupling of solid mechanics with other effects / 74F05 Thermal effects
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] / 74N99 None of the above, but in this section
Preprint Number:774
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