A mathematical model describing the thermomechanical interactions in biological bodies at high temperature is proposed by treating the soft tissue in biological bodies as a thermoporoelastic media. The heat transfer and elastic deformation in soft tissues are examined based on the Pennes bioheat transfer equation and the modified Duhamel-Neuman equations. The three dimensional governing equations based on the proposed model is discretized using a 19 point finite difference scheme. The resulting large sparse linear system is solved by a preconditioned Krylov subspace method. Numerical simulations show that the proposed model works well in the test situations and the proposed numerical techniques are efficient.

Mathematics Subject Classification:

Technical Report 391-04, Department of Computer Science, University of Kentucky, Lexington, KY, 2004.

This research work was supported in part by NSF under grants CCR-9988165, CCR-0092532, ACR-0202934, ACR-0234270, in part by DOE under grant DE-FG02-02ER45961, in part by Kentucky Science & Engineering Foundation under grant KSEF-02-264-RED-002, and in part by the University of Kentucky Research Committee.