A Three Level Finite Difference Scheme for Solving the Pennes' Bioheat Transfer in a Triple-Layered Skin Structure

Weizhong Dai and Raja Nassar
Department of Mathematics and Statistics
Louisiana Tech University
Ruston, LA 71272, USA

and

Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Abstract

In this study, we develop a three-level finite difference scheme for solving a 1D Pennes' bioheat transfer equation in a triple-layered skin structure. A convergence theorem is obtained by the discrete energy method, implying that the scheme is unconditionally stable. Numerical results for thermal analysis of a skin composed of epidermis, dermis and subcutaneous layers are obtained.

Key words: finite difference; convergence; stability; bioheat transfer equation

Mathematics Subject Classification:

Download the compressed postscript file bioheat1.ps.gz, or the PDF file bioheat1.pdf.gz.
Technical Report 343-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

The research work of Jun Zhang was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.

The authors would like to thank Dr. Sherwood W. Samn at the Brooks Air Force Research Laboratory for a few discussions concerning the bioheat modelings.