Estimation of Time-dependent Surface Heat Flux in a Nonlinear Inverse Bio-heat Transfer Problem

This study deals with the solution of an inverse problem in a living tissue to estimate the time-dependent heat flux. The thermal properties such as thermal conductivity, blood perfusion and metabolic heat generation are considered temperature dependent. The Pennes bioheat model is applied to simulate thermal behavior. The Sequential Function Specification Method (SFSM) and Conjugate Gradient Method (CGM) with adjoint problem are applied to obtain the unknown surface heat flux. Two examples are considered to examine the accuracy and ability of the inverse analysis. A comparison of two methods in the solution of the nonlinear inverse bioheat transfer problem is done. Results confirm the accuracy of both methods in estimating unknown surface heat flux for exact data. The effects of measurement error, initial guess and measurement location upon the precision of the estimated results are evaluated. Results demonstrate that the accuracy of conjugate gradient method is more than the sequential method .However, in both methods; the precision of the inverse solutions decrease by increasing measurement error. Results show the time-dependent surface heat flux can be obtained by any arbitrary initial guess. In addition, the conjugate gradient method is more sensitive to measurement location than the sequential method.