Time-dependent perfusion coefficient estimation in a bioheat transfer problem

We consider the estimation of the time-dependent blood perfusion coefficient in the Pennes bioheat equation with Ionkin-type nonlocal boundary and integral energy over-determination conditions. In contrast to several methods that transform the original problem into an inverse source problem and then estimate the perfusion coefficient through numerical differentiation, we propose an alternative method in which the coefficient is estimated directly through a nonlinear minimization technique. In the method, the bioheat equation is solved by the method of lines based on a highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the Levenberg-Marquardt method with the discrepancy principle as stopping rule. Numerical examples are presented to verify the accuracy and stability of the solution.