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Application of Different Variants of the BEM in Numerical Modeling of Bioheat Transfer Problems

Ewa Majchrzak*
* Institute of Computational Mechanics and Engineering, Silesian University of Technology, 44-100 Gliwice, Konarskiego 18a, Poland. Email: ewa.majchrzak@polsl.pl

Molecular & Cellular Biomechanics 2013, 10(3), 201-232. https://doi.org/10.3970/mcb.2013.010.201

Abstract

Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems are discussed. For the steady state problems and the vascular models the classical BEM algorithm and also the multiple reciprocity BEM are presented. For the transient problems connected with the heating of tissue, the various tissue models are considered for which the 1st scheme of the BEM, the BEM using discretization in time and the general BEM are applied. Examples of computations illustrate the possibilities of practical applications of boundary element method in the scope of bioheat transfer problems.

Keywords

bioheat transfer models, Pennes equation, Cattaneo-Vernotte equation, dual-phase lag equation, boundary element method, heating of tissue

Cite This Article

Majchrzak, E. (2013). Application of Different Variants of the BEM in Numerical Modeling of Bioheat Transfer Problems. Molecular & Cellular Biomechanics, 10(3), 201–232.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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