Abstract
The non-steady nonlinear thermal diffusion proceeding during the biological tissue freezing process is analyzed. The spherical cryoprobe is taken into account and its geometry determines the details of mathematical description of the process considered. In order to solve the problem discussed, the boundary element method and the approach called the artificial heat source method is used. The numerical experiments allow to determine the dependence between the depth of frozen region (the kinetics of ice ball generation) and the parameters of cryoprobe (the surface temperature and cryoprobe radius).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Budman, H., Shitzer, A. and Dayan, J. (1995) Analysis of the inverse problem of freezing and thawing of a binary solution during cryosurgical processes, Journal of Biomechanical Engineering, 117, 193–202.
Comini, G. and Del Giudice, L. (1976) Thermal aspects of cryosurgery, Journal of Heat Transfer, Transactions of the ASME, 543–549.
Idelsohn, S.R., Storti, M.A. and Crivelli, L.A. (1994) Numerical methods in phase change problems, Archives of Computational Methods in Engineering, 1, 49–74.
Mochnacki, B. and Suchy, J.S. (1995) Numerical Methods in Computations of Foundry Processes, PFTA, Cracow.
Majchrzak, E. (1998) Solution of non-steady thermal diffusion problem in spherical domains using the boundary element method, Publ. of the Sil. Techn. Univ., 7, 1998.
Mochnacki, B. (1996) Application of the BEM for numerical modelling of continuous casting, Computational Mechanics, 18, 1, 62–71.
Mochnacki, B. and Suchy, J.S. (1997) Numerical modelling of solidification: the concept of problem linearization, AFS Transactions, 96–11, 203–209.
Majchrzak, E. and Mochnacki, B. (1996) The BEM application for numerical solution of non-steady and nonlinear thermal diffusion problems, Computer Assisted Mechanics and Engineering Sciences, 3, 327–346.
Brinck, H. and Werner, J. (1994) Estimation of the Thermal Effect of Blood Flow in a Branching Countercurrent Network Using a Three Dimensional Vascular Model, Journal of Biomechanical Engineering, Transactions of the ASME, 116, 324–330.
Brebbia, C.A., Telles J.C.F. and Wrobel, L.C. (1984) Boundary Element Techniques, Springer-Verlag, Berlin & New York.
Majchrzak, E. and Mochnacki, B. (1995) Application of the BEM in the thermal theory of foundry, Engineering Analysis with Boundary Elements, 16, 99–121.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Majchrzak, E., Dziewonski, M. (2001). Numerical Analysis of Biological Tissue Freezing Process. In: Burczynski, T. (eds) IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9793-7_16
Download citation
DOI: https://doi.org/10.1007/978-94-015-9793-7_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5737-2
Online ISBN: 978-94-015-9793-7
eBook Packages: Springer Book Archive