Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares technique. In particular, the bioheat problem is solved by the method of lines based on an highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the regularized Gauss-Newton method coupled with a proper regularization parameter. The performance of the method on several test problems is illustrated numerically.