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.