Parallel Computer Simulations of Heat Transfer in Biological Tissues

Abstract

Parallel computer simulation of heat transfer in parts of the human body is described. Realistic geometric models and tissues with different thermodynamic properties are analyzed. The principal steps of the computer simulations, including mathematical and geometric modeling, domain discretization, numerical solution, validation of simulated results, and visualization, are described. An explicit finite difference method for the inhomogeneous computational domain has been developed and tested on the diffusion equation. The bio-heat equation, which incorporates heat conduction, heat transfer between blood and tissues and heat production by metabolism, was used in our analysis. Because of significant calculation complexity, a parallel simulation code was also implemented.Domain decomposition and communication with messages have been selected in the parallel implementation of the explicit finite difference method. Mapping of the computational domain on the parallel computer was addressed, followed by theoretical performance analysis of the proposed parallel algorithm. The implementation of all simulation steps is shown in detail for the simulation of the steady-state temperature and its evolution in time for a human knee exposed to external conditions and to topical cooling. The results have been validated by experimental measurements. Execution time was measured on a computing cluster with different numbers of processors and compared with theoretical expectations. It is shown that parallel computer simulations can be of great use in medicine, either for planning surgery or for evaluating doctrines of medical treatment. The chapter concludes with a summary of the results and a list of relevant references from the research field.