Mathematical modelling and simulation of heat transfer in Biological tissue

Abstract

Mathematical study of heat transfer in living biological tissue is a burning research area. Mathematical models on biological real phenomenon such as tumor, cancer and others malignant diseases in human body is very complicated task for researchers. Need of applied mathematics for the formulation of mathematical models of biological problems,its mathematical analysis and computer simulation is very helpful for treatment with high accuracy. In this work, mathematical models involving with phase-lag-phenomenon newlineoccur in numerous important area of medical sciences, thermal therapy treatment and also in bioengineering. Because the devices most often used for the generation heat inside tissues involved either electromagnetic radiation, e,g. radiofrequency and microwave, or newlineultrasound, electrical engineers have entered in this field of research. newlineThe thesis consists of seven chapters, begin with introduction, and deals with mathematical modeling, computer simulation, fundamental definition, the literature review, basic equations related to other chapters with analytical and latest hybrid numerical methods which are used as solution tools in this work. However, each chapter also contains newlinebrief introduction of the reserach work carried out in the respective chapter. newlineIn second chapter, the temperature distribution in a biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions are studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bioheat transfer in biological tissues. The analytical newlinesolution is obtained for all the three models using Laplace transform technique and results are compared.