Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.