A comprehensive study of the effective thermal conductivity of living biological tissue with randomly distributed vascular trees

The biological tissue can be treated as a porous medium consisting of randomly distributed vascular trees and solid tissue matrix. In this paper, taking into account the effects of geometric structures of vascular trees and blood flow, a fractal model for the effective thermal conductivity of living biological tissue is derived based on the assumptions that the mother channel diameters of vascular trees follow the fractal scaling law. The proposed model is expressed as a function of the thermal conductivities of solid tissue matrix and blood, structural parameters of vascular trees, porosity and properties of blood. It is found that the effective thermal conductivity of living biological tissue increases with the increase of branching levels m, length ratio α, decreases with the increase of diameter ratio β, and there exists a thermal conductivity ratio, at which the effective thermal conductivity is same for different porosities ɛ, below which the effective thermal conductivity increases with the increase of porosity ɛ, and above which the effective thermal conductivity decreases with the increase of porosity ɛ. A good agreement is obtained between the proposed model predictions and available experimental data for living tissue. The 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.