BIOHEAT EQUATION WITH FOURIER AND NON-FOURIER HEAT TRANSPORT LAWS: APPLICABILITY TO HEAT TRANSFER IN HUMAN TISSUES

Abstract

The paper is dedicated to mathematical problem formulations for the heat propagation in biological tissues based on the Fourier and non-Fourier laws at different boundary conditions. The heating of the tissues is provided by external heat sources like low intensity lasers or light-emitting diodes which are widely used in contemporary medical care. Numerical computations on the standard Pennes bioheat equation with Fourier heat conduction give the temperature curves for both heating and thermal relaxation processes that do not correspond to the in vivo measurement data on human skin tissue. It is shown the modified bioheat equation based on the Guyer-Krumhansl heat conduction with correct formulation of the boundary conditions produces realistic temperature curves when the distributed heat sources and sinks in the tissue are accounted for. The former corresponds to the metabolic heat and temperature dependent chemical reactions, while the latter is provided by the heat convection with blood microcirculation system. The proposed model gives realistic two time temperature curves. The perspective applications of the novel mathematical formulation are discussed.

Keywords

• Pennes Bioheat Equation,Non-Fourier Heat Transport Laws,Heat Transfer in Biological Tissues,Mathematical Modeling

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