A Mathematical Model to Solve Bio-Heat Transfer Problems through a Bio-Heat Transfer Equation with Quadratic Temperature-Dependent Blood Perfusion under a Constant Spatial Heating on Skin Surface

Emmanuel Kengne, Idir Mellal, Mariem Ben Hamouda, Ahmed Lakhssassi

Department of Computer Science and Engineering, University of Quebec at Outaouais, Gatineau, Canada.

DOI: 10.4236/jbise.2014.79071                

Abstract

We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.

Keywords

Bio-Heat Transfer Problems, Pennes Bio-Heat Model, Temperature-Dependent Blood Perfusion, Thermal Therapy, Extended Mapping Method

Conflicts of Interest

The authors declare no conflicts of interest.

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