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

Natalya Ki̇zi̇lova

doi:10.18186/thermal.653915

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.

Highlights

During the last decades different methods of phototherapy and photodynamic therapy based on the coherent optical radiation of low-level lasers (LLL) and non-coherent radiation of light-emitting diodes (LED) had been introduced, tested and approved for routine treatment purposes [1-3]
Other parameters are determined by the frequency of optical radiation and the chemical reactions induced by it
The typical dynamics of the temperature curves is similar to the skin, muscle and bone tissues with different rates of the temperature rise and relaxation determined by the thermal properties of the tissue

Summary

Introduction

During the last decades different methods of phototherapy and photodynamic therapy based on the coherent optical radiation of low-level lasers (LLL) and non-coherent radiation of light-emitting diodes (LED) had been introduced, tested and approved for routine treatment purposes [1-3]. The typical surface temperature T (t) curves for the heating and relaxation processes computed on the Pennes equation in this case can be found in Figure 2 that present the model validation curves.

Results

Conclusion