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.
Author: | Dietmar Hömberg, Jijun Liu, Nataliya Togobytska |
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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 |