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TECHNICAL PAPERS

Effect of Microscale Mass Transport and Phase Change on Numerical Prediction of Freezing in Biological Tissues

[+] Author and Article Information
Ramachandra V. Devireddy

Materials Research Science and Engineering Center, Department of Chemical Engineering, University of Minnesota, Minneapolis, MN 55455

David J. Smith, John C. Bischof

Bioheat and Mass Transfer Laboratory, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

J. Heat Transfer 124(2), 365-374 (Oct 22, 2001) (10 pages) doi:10.1115/1.1445134 History: Received May 04, 2001; Revised October 22, 2001
Copyright © 2002 by ASME
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References

Figures

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A schematic depiction (flow chart) of the source term matching algorithm used in the coupled thermal/biophysical model
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The Krogh cylinder used to describe cellular-level geometry in the tissue medium. The values of the cylinder dimensions ΔX,rvo, and l used in the solution of Eqs. (1) to (14) are shown in Table 2 for both the rat liver and AT-1 tumor tissue system. The lower part of the figure schematically depicts the biophysical processes (dehydration and intracellular ice formation, IIF) that occur during freezing inside the tissue as a function of cooling rate. In the light micrographs shown the optically dense or “dark” spaces represent the “cell space” while the optically transparent or “white” spaces represent “ice” in the tissue. The scale bar in the micrographs represents 20 μm.
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Predicted interface propagation in rat liver tissue under (a) cryopreservation and (b) cryosurgery conditions. The cooling conditions are described in Table 4. Microscale freezing model predictions are given by the dotted line (- - - -), and enthalpy method model predictions are given by the solid line (—). Time (secs) is shown on the x-axis while the distance from the cooling surface (m) is shown on the y-axis.
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Predicted interface propagation in AT-1 tumor tissue under (a) cryopreservation and (b) cryosurgery conditions. The cooling conditions are described in Table 4. Microscale freezing model predictions are given by the dotted line (- - - -), and enthalpy method model predictions are given by the solid line (–). Time (secs) is shown on the x-axis while the distance from the cooling surface (m) is shown on the y-axis.
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Predicted thermal history at various locations (as indicated) under (a) cryopreservation and (b) cryosurgery conditions (the results are essentially identical for both rat liver and AT-1 tumor tissue). The cooling conditions are described in Table 4. Microscale freezing model predictions are given by the dotted line (- - - -), and enthalpy method model predictions are given by the solid line (–). Time (secs) is shown on the x-axis while the temperature (°C) is shown on the y-axis.
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Predicted isotherms under (a) cryopreservation and (b) cryosurgery conditions (the isotherms are essentially identical for both rat liver and AT-1 tumor tissue). The cooling conditions are described in Table 4. In Fig. (a) the contours from left to right represent isotherms of 203 to 273 K, in increments of 10 K, respectively. In Fig. (b) the lines from left to right represent isotherms of 133 to 303 K, in increments of 10 K. The distance from the cooling surface (m) is shown on the x-axis while time (secs) is shown on the y-axis.
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(a) Predicted unfrozen fractions and the probability of intracellular ice formation, and (b) PIF under cryosurgery conditions in the rat liver (solid lines,–) and AT-1 tumor tissue (dotted lines,- - - -). The cooling conditions are described in Table 4. Note that the “stepped” behavior of the contours is not intrinsic to the tissue freezing process and is caused by the computational limitation of generating and plotting data at discrete intervals. In Fig. 7(a) the region to the left of the inner contours is essentially frozen (i.e., 99 percent frozen) and the region to the right of the right contours is essentially unfrozen (i.e., 99 percent unfrozen) while the region between the contours represents the “mushy” or partially frozen region. In Fig. 7(b) as in Fig. 7(a) the region to the left of the inner contour represents the freezing domain with 99 percent PIF and the region to the right of the outer contour represents the freezing domain with 1 percent PIF. The distance from the cooling surface (m) is shown on the x-axis while time (secs) is shown on the y-axis.
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(a) Predicted volumetric shrinkage response and the probability of intracellular ice formation, and (b) PIF under cryosurgery conditions in the rat liver (solid lines,–) and AT-1 tumor tissue (dashed-dotted lines,[[dot_dash_line]]), at 4 different locations within the tissue. The cooling conditions are described in Table 4. In Fig. 8, the lines from left to right are at 0.1 mm, 6 mm, 12 mm, and 16 mm from the cooling surface, respectively. The distance from the cooling surface (m) is shown on the x-axis while time (secs) is shown on the y-axis.

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