WIAS Preprint No. 1600, (2011)

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



Authors

  • Hömberg, Dietmar
  • Liu, Jijun
  • Togobytska, Nataliya

2010 Mathematics Subject Classification

  • 35R30 74F05 74N99

Keywords

  • Inverse problem, nonlinear equation, optimal control, iteration scheme, coupled system, numerics

Abstract

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.

Appeared in

  • Math. Methods Appl. Sci., 35 (2012) pp. 497--509.

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