Analytical Solutions to 3-D Bioheat Transfer Problems with or without Phase Change

Abstract

Theoretical analysis on the bioheat transfer process has been an extremely important issue in a wide variety of bioengineering situations such as cancer hyperthermia, burn injury evaluation, brain hypothermia, disease diagnostics, thermal comfort analysis, cryosurgery and cryopreservation etc. In this chapter, the theoretical strategies towards exactly solving the three-dimensional (3-D) bioheat transfer problems for both cases with and without phase change were systematically illustrated based on the authors’ previous works. Typical closed form analytical solutions to the hyperthermia bioheat transfer problems with space or transient heating on skin surface or inside biological bodies were summarized. In addition, exact solutions to the 3-D temperature transients of tissues under various phase change processes such as cryopreservation of biomaterials or cryosurgery of living tissues subject to freezing by a single or multiple cryoprobes were also outlined. Such solution is comprehensive enough by taking full account of many different factors such as generalized initial and boundary conditions, blood perfusion heat transfer, volumetric heating of hyperthermia apparatus or heat sink of cryoprobes etc. For illustrating the applications of the present methods, part of the solutions were adopted to analyze the selected bioheat transfer problems. The versatility of these theoretical approaches to tackle more complex issues was also discussed. The obtained solutions are expected to serve as the basic foundation for theoretically analyzing bioheat transfer problems.