Analysis of thermal conductivity in living biological tissue with vascular network and convection

Abstract

Based on the blood circulatory system, a model is established for living biological tissue represented by a vascular network and surrounding tissue. In this paper, we analyze the heat transfer in living biological tissue and present an analytical model for the effective thermal conductivity of living biological tissue by taking into account the effects of geometric structures of branching vascular network and convection caused by blood flow. The proposed model is expressed as a function of the thermal conductivities of solid tissue matrix and blood, structural parameters of branching vascular network, porosity and properties of blood. It is found that the effective thermal conductivity of living biological tissue decreases with the increase of branching levels, length ratio and diameter ratio. It is also found that there exists a thermal conductivity ratio, at which the effective thermal conductivity is same for different porosities, below which the effective thermal conductivity increases with the increase of porosity, and above which the effective thermal conductivity decreases with the increase of porosity. A good agreement is obtained between the proposed model predictions and available experimental data for living tissue. The present results show that blood flow plays an important role in increasing the effective thermal conductivity, and the proposed model with blood flow is more reasonable and can reveal more physical mechanisms of heat transfer in living biological tissue.