Fractal Study Of Heat Transport Properties For Biological Porous Media

With the development and progress of science and technology as well as modern medical treatment, the biological heat transport research has received widespread attention in the fields of biological science and medicine, such as hyperthermia, cryosurgery, organ transplantation frozen storage, biological tissue cutting and welding, disease diagnosis, food preservation and thermal comfort analysis etc. Study of biological heat transport has become one of the hot topics in the international academic circles. A large number of stu-dies have shown that the transport channels in biological porous media such as vascular, bronchial and botanical trees are statistically self-similar, the microstructures of transport systems have fractal characteristics in the range of a certain scale, and can be described by fractal-like tree branching network. So the fractal geometry theory can be used to study the heat transport properties for biological porous media. In this dissertation, the author mainly studies the heat transport properties for biological porous media consisting of vas-cular tree(s) and surrounding tissue. It is expected that this study is of great scientific and practical importance to understand and reveal the heat transport properties and mechanism of biological tissue as well as clinical applications.This paper consists of six chapters. In the first chapter, the research background, theoretical research and practical application of heat transport in biological porous media are reviewed, and fractal-like tree branching network and fractal geometry theory are in-troduced briefly. In the second chapter, based on the diameter of mother channels of vas-cular trees follows the fractal scaling law, the heat conduction characteristics of biological porous media consisting of randomly distributed vascular trees and surrounding tissue are analyzed, and a fractal model for the effective thermal conductivity of biological media filled with randomly distributed vascular trees is developed. A fair agreement between the model predictions and reported experimental data for dead tissue is found. In addition, the quantitative relationship between effective thermal conductivity and structural parameters of vascular tree is also analyzed. In the third chapter, considering the influence of the blood flow, a fractal analytical expression for the effective thermal conductivity of living biological tissue filled with randomly distributed vascular trees is derived based on the fractal theory, and the effects of structural parameters of vascular tree and blood flow on the effective thermal conductivity of living biological tissue are discussed in detail. The present model predictions are well agreed with reported experimental data for living tissue, and higher than reported experimental data for dead tissue and the model predictions without blood flow. In the fourth chapter, based on the blood circulatory system, a model of living biological tissue represented by a vascular network and surrounding tissue is es-tablished. According to the Fourier’s law and thermal-electrical analogy principle, the analytical expressions for the effective thermal conductivities for death tissue (without blood flow) and living tissue (with blood flow) are put forward. In the fifth chapter, the radial heat conduction characteristics of biological porous media consisting of vascular trees and surrounding tissue matrix are analyzed, and the distribution function for effective thermal conductivity of radial heat flow in biological media is derived. In the sixth chapter, we summarize the main contents and innovation of the present work, and the future study of the heat transport properties of biological porous media based on fractal theory is pros-pected.