Bio-Heat Diffusion under Local Thermal Non-Equilibrium Conditions using Dual-Phase Lag-based Green’s functions

The two-equation model for porous media based on local thermal non-equilibrium between the fluid and solid phases is analyzed in order to describe the rapid heating of living biological tissues during hyperthermia therapy. Analytical solutions for this type of problem are not well documented in the specialized literature. Once it is proven that the two-step model leads to the dual-phase lag bio-heat diffusive equation, the bio-heat term is cancelled out from the same equation by using an appropriate transformation of the dependent variable. Then, an exact analytical temperature solution for both tissue and blood phases can be derived by applying the dual-phase lag Green’s function solution equation; where the blood temperature is somewhat of neglected in the specialized literature. The calculated temperature for finite and regular tissues is in the form of a Fourier-series solution and is valid at both small and large times. Applications of the solutions are presented that focus on the effects of thermal therapy by laser irradiation of perfuse, highly absorbent tissues. Temperature profiles for both solid and fluid phases are shown and discussed. In particular, the plotted data in the figures clearly show blood temperature delays as suggested by the time delay parameter between the phases.