Determination of a time-dependent coefficient in the bioheat equation

• An inverse problem of determining the time-dependent perfusion coefficient is investigated.
• The boundary element method is combined with either Tikhonov׳s regularization or smoothing splines.
• Numerical results illustrate that the methods proposed provide stable and accurate solutions.

In this paper, the identification of the time-dependent blood perfusion coefficient in the bioheat equation is considered as an inverse heat source problem with nonlocal boundary and integral energy over-determination conditions. The boundary element method (BEM) based on using the fundamental solution for the heat equation is employed, together with either the second-order Tikhonov regularization combined with finite differences, or with a smoothing spline regularization technique for computing the first-order derivative of a noisy function. A couple of benchmark numerical examples are presented to verify the accuracy and stability of the solution.