A finite element and order of magnitude analysis of cryosurgery in the lung

Cryosurgical freezing of dense lung tumors within healthy lung tissue is investigated using numerical and order-of-magnitude analyses. The numerical model indicates that the freezing front accelerates as it leaves the tumor and enters the surrounding healthy, low density lung tissue, a prediction co...

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Bibliographic Details
Published in:International communications in heat and mass transfer 1999, Vol.26 (1), p.1-12
Main Authors: Schweikert, Robert J., Keanini, Russell G.
Format: Article
Language:English
Subjects:
Approximation theory
Biological and medical sciences
Finite element method
Freezing
Mathematical models
Medical sciences
Oncology
Physiological models
Pulmonary diseases
Surgery (general aspects). Transplantations, organ and tissue grafts. Graft diseases
Technology. Biomaterials. Equipments
Tissue
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Summary:Cryosurgical freezing of dense lung tumors within healthy lung tissue is investigated using numerical and order-of-magnitude analyses. The numerical model indicates that the freezing front accelerates as it leaves the tumor and enters the surrounding healthy, low density lung tissue, a prediction confirming the earlier analytical work of Bischof, Bastacky and Rubinsky [1]. Order-of-magnitude arguments are used to explain this somewhat counter-intuitive result as well as the qualitative features exhibited by the numerical freezing simulation. In particular, scaling arguments lead to three important findings : i.) The ratio of freezing front speeds in tumorous and healthy tissue is inversely proportional to the ratio of corresponding tissue densities. Thus, as predicted by the numerical simulation, the freezing front travels faster in healthy tissue. ii.) In either tissue, the speed of a radially propagating freezing front varies approximately as 1/r, where r is the instantaneous front radius. Thus, the front decelerates as it grows radially. iii.) Approximate closed form expressions can be derived to estimate the time-varying freezing front location in either tissue type.
ISSN:0735-1933
1879-0178
DOI:10.1016/S0735-1933(98)00116-X