Identification of the thermo-physical properties of a stratified tissue. Adiabatic hypodermic wall

Biological living tissues possess thermophysical properties that are difficult to measure directly and their estimation is very important in order to decide the appropriate treatment procedure (e.g. place of inoculation and appropriate amount of drug dosage) in case an abnormality is detected. In the present paper, we numerically investigate, for the first time, the determination of several thermo-physical blood-tissue properties of a one-dimensional, multi-layered biological skin tissue subjected to external heating. In contrast to the usual parabolic model that assumes infinitely fast propagation of the heat signal, in the present paper, the bio-heat transfer in such a biological body is mathematically modelled by a hyperbolic partial differential equation, which takes into account that the thermal wave speed is finite. On the skin surface a convective boundary condition holds taking into account the heat exchange with the environment, whilst on the most inner wall of the tissue an adiabatic boundary condition applies. Then, in this framework, the piecewise constant thermo-physical properties of interest given by the thermal conductivity, heat capacity and blood perfusion rate are accurately and stably reconstructed from non-intrusive temperature measurements on the inner and outer boundaries of the multi-layered tissue by minimizing a weighted nonlinear least-squares objective function.