Numerical Solution of the Multidimensional Freezing Problem During Cryosurgery

[+] Author and Article Information
Y. Rabin

Department of Human Oncology, Allegheny University of the Health Sciences, Pittsburgh, PA 15212-4772

A. Shitzer

Department of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000 Israel

J Biomech Eng 120(1), 32-37 (Feb 01, 1998) (6 pages) doi:10.1115/1.2834304 History: Received June 25, 1995; Revised February 12, 1997; Online January 07, 2008


A multidimensional, finite difference numerical scheme for the freezing process of biological tissues during cryosurgery is presented, which is a modification of an earlier numerical solution for inanimate materials. The tissues are treated as nonideal materials, freezing over a temperature range and possessing temperature-dependent thermophysical properties, blood perfusion, and metabolic heat generation. The numerical scheme is based on the application of an effective specific heat, substituting the intrinsic property, to include the latent heat effect within the phase transition temperature range. Results of the numerical solution were verified against an existing exact solution of a one-dimensional inverse Stefan problem in Cartesian coordinates. Results were further validated against experimental data available from the literature. The utility of the numerical solution for the design and application of cryodevices is demonstrated by parametric studies of the freezing processes around spherical and cylindrical cryoprobes. The parameters studied are the cryoprobe cooling power and the dimensions of the frozen region. Results are calculated for typical thermophysical properties of soft biological tissues, for angioma and for water.

Copyright © 1998 by The American Society of Mechanical Engineers
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