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

We consider an inverse problem arising in laser‐induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues are destroyed by coagulation. For the dosage planning, numerical simulations 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 in this paper. 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. Numerical implementations are presented to show the validity of the optimization schemes. Copyright © 2012 John Wiley & Sons, Ltd.