A Numerical Study of a 3D Bioheat Transfer
Problem with Different Spatial Heating

Samir Karaa and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA
Fuqian Yang
Department of Chemical and Materials Engineering
University of Kentucky
Lexington, KY 40506-0046, USA


We develop numerical methods for the computer simulation and modeling of a three dimensional heat transfer problem in biological bodies. The technique is intended for the temperature predications and parameter measurements in thermal medical practices and for the studies of thermomechanical interaction of biological bodies at high temperature.

We examine a mathematical model based on the classical well-known Pennes equation for heat transfer in biological bodies. A finite difference discretization scheme is used to discretize the governing partial differential equation. A preconditioned iterative solver is employed to solve the resulting sparse linear system at each time step. Numerical results are obtained to demonstrate the efficacy of the proposed numerical methods.

Key words: bioheat transfer, hyperthermia, Pennes' equation, preconditioning

Mathematics Subject Classification: 90C10, 80A20, 65M06.

Download the compressed postscript file bioheat3d.ps, or the PDF file bioheat3d.pdf.
This paper has been accepted for publication in Mathematics and Computers in Simulation.

Technical Report 372-03, Department of Computer Science, University of Kentucky, Lexington, KY, 2003.

This research work was supported in part by the U.S. National Science Foundation under grants CCR-9988165, CCR-0092532, ACR-0202934, and ACR-0234270, by the U.S. Department of Energy Office of Science under grant DE-FG02-02ER45961, by the Kentucky Science & Engineering Foundation under grant KSEF-02-264-RED-002, and by the Japanese Research Organization for Information Science & Technology.