S. Weinbaum, L. M. Jiji and D. E. Lemons, “Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part I: Anatomical Foundation and Model Conceptualization,” Journal of Biomechanical Engineering, Vol. 106, No. 4, 1984, pp. 321330. doi:10.1115/1.3138501

has been cited by the following article:

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

  AUTHORS: Emmanuel Kengne, Ahmed Lakhssassi, Rémi Vaillancourt

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

  JOURNAL NAME: Applied Mathematics, Vol.3 No.3, March 27, 2012

  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.