Micro-scale Bio-Heat Diffusion using Green’s functions

The two-step mathematical model for heterogeneous media based on local thermal non-equilibrium (LTNE) is investigated in order to describe the rapid heating of living and perfused biological tissues that occurs during thermal therapy. Neither the numerical solutions nor the analytical solutions for this type of problem are well documented in the literature. This work uses a finite series solution that is valid at both small and large times to prepare a Green’s function (GF) solution. Once it is proven that the two-step model leads to the dual phase lag (DPL) bio-heat diffusive equation, the determination of the DPL-based Green’s functions in finite and regular tissues is the primary objective. Another objective is to present the related dual phase lag Green’s function solution equation (DPL-GFSE). Once the DPL Green’s functions and DPL-GFSE are known, one can produce exact analytical temperature solutions for different biological applications. Applications of the solutions are presented that focus on the effects of thermal therapy by laser irradiation of perfuse, highly absorbent tissue.