Identification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy
- Hömberg, Dietmar
- Liu, Jijun
- Togobytska, Nataliya
2010 Mathematics Subject Classification
- 35R30 74F05 74N99
- Inverse problem, nonlinear equation, optimal control, iteration scheme, coupled system, numerics
We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning numerical simulation play 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 nonconvex 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.
- Math. Methods Appl. Sci., 35 (2012) pp. 497--509.