Chapter 4 - Analytical Bioheat Transfer: Solution Development of the Pennes’ Model

Abstract

This chapter considers the analytic solution to the simple and sometimes controversial Penne’s bioheat equation. The Penne's representation of the influence of blood perfusion is often used as a first attempt at modeling heat transfer in living tissue. Exact solutions for the bioheat equation are developed in various geometries. The focus of the solution development presented here is to capitalize on existing published solutions of pure heat conduction. It is shown that the integral solution of the transient heat conduction problem may be easily manipulated in order to arrive at the solution to the corresponding bioheat problem. Furthermore, the Green’s function of the heat conduction problem may be similarly modified in order to arrive at the Green’s function of the corresponding bioheat problem. Because the analytic solutions of the heat conduction problem have been archived for various geometries and boundary condition types, this manipulation provides an efficient means to arrive at the analytic solution of the bioheat problem.