Temperature Distributions for Regional Hypothermia Based on Nonlinear Bioheat Equation of Pennes Type: Dermis and Subcutaneous Tissues

Emmanuel Kengne, Ahmed Lakhssassi, Rémi Vaillancourt

Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada.
Laboratoire d’Ingénierie des Microsystèmes Avancés, Département d’Informatique et d’Ingénierie, Université du Québec en Outaouais, Succursale Hull, Gatineau, Canada.

DOI: 10.4236/am.2012.33035                

Abstract

We have used a nonlinear one-dimensional heat transfer model based on temperature-dependent blood perfusion to predict temperature distribution in dermis and subcutaneous tissues subjected to point heating sources. By using Jacobi elliptic functions, we have first found the analytic solution corresponding to the steady-state temperature distribution in the tissue. With the obtained analytic steady-state temperature, the effects of the thermal conductivity, the blood perfusion, the metabolic heat generation, and the coefficient of heat transfer on the temperature distribution in living tissues are numerically analyzed. Our results show that the derived analytic steady-state temperature is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to such applications as parameter measurement, temperature field reconstruction and clinical treatment.

Keywords

Regional Hypothermia; Dermis and Subcutaneous Tissues; Jacobi Elliptic Functions; Temperature-Dependent Blood Perfusion

Conflicts of Interest

The authors declare no conflicts of interest.

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