0
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
Your Session has timed out. Please sign back in to continue.

References

Gage,  A. A., and Baust,  J. 1998, “Mechanism of Tissue Injury in Cryosurgery,” Cryobiology, 37, pp. 171–186.
Nerem,  R. M. 2000, “Tissue Engineering: Confronting the Transplantation Crisis,” Proc. Instn. Mech. Engrs., 214, (Part H), pp. 95–99.
Mazur,  P. 1984, “Freezing of Living Cells: Mechanisms and Implications,” (review), Am. J. Physiol., 143, pp. C125–C142.
Budman,  H., Shitzer,  A., and Del Giudice,  S. 1986, “Investigation of Temperature Fields Around Embedded Cryoprobes,” ASME J. Biomech. Eng., 108, pp. 42–48.
Keanini,  R. G., and Rubinsky,  B. 1992, “Optimization of Multiprobe Cryosurgery,” ASME J. Heat Transfer , 114, pp. 796–801.
Bischof,  J. C., and Rubinsky,  B. 1993, “Microscale Heat and Mass Transfer of Vascular and Intracellular Freezing in the Liver,” ASME J. Heat Transfer 115, pp. 1029–1035.
Rabin,  Y., and Shitzer,  A. 1998, “Numerical Solution of the Multidimensional Freezing Problem During Cryosurgery,” ASME J. Biomech. Eng., 120, pp. 32–37.
Lunardini, V., 1981, “Finite Difference Methods for Freezing and Thawing,” in Heat Transfer in Cold Climates, Van Nostrand Reinhold, Co., New York.
Alexiades, V., and Solomon, A. D., 1993, Mathematical Modeling of Melting and Freezing Processes, Hemisphere Publishing Corp., Washington.
Ozisik, M. N., 1994, Finite Difference Methods in Heat Transfer, CRC Press, Boca Raton, FL.
Hayes,  L. J., and Diller,  K. R. 1983, “Implementation of Phase Change in Numerical Models of Heat Transfer,” Journal Energy Research Technology, 105, pp. 431–435.
Hayes,  L. J., Diller,  K. R., Chang,  H.-J., and Lee,  H. S. 1988, “Prediction of Local Cooling Rates and Cell Survival During the Freezing of a Cylindrical Specimen,” Cryobiology, 25, pp. 67–82.
Rubinsky,  B., and Pegg,  D. E., 1988, “A mathematical model for the freezing process in biological tissue,” Proc. Phys. Soc. London, Sect. B, 234, pp. 343–358.
Toner,  M., Cravalho,  E. G., and Karel,  M. 1990, “Thermodynamics and Kinetics of Intracellular Ice Formation During Freezing of Biological Cells,” J. Appl. Phys., 67, pp. 1582–1593.
Hayes, L. J., Diller, K. R., and Chang, H. J., 1986, “A Robust Numerical Method for Latent Heat Release During Phase Change,” Advances in Heat and Mass Transfer in Biotechnology, HTD-Vol. 62, pp. 63–69.
Pitt,  R. E. 1990, “Cryobiological Implications of Different Methods of Calculating the Chemical Potential of Water in Partially Frozen Suspending Media,” Cryo-Letters, 11, pp. 227–240.
Mazur,  P. 1963, “Kinetics of Water Loss From Cells at Subzero Temperatures and the Likelihood of Intracellular Freezing,” J. Gen. Physiol., 47, pp. 347–369.
Levin,  R. L., Cravalho,  E. G., and Huggins,  C. E. 1976, “A Membrane Model Describing the Effect of Temperature on the Water Conductivity of Erythrocyte Membranes at Subzero Temperatures,” Cryobiology, 13, pp. 415–429.
Toner, M., 1993, “Nucleation of Ice Crystals Inside Biological Cells,” in Advances In Low-Temperature Biology, P. Steponkus ed., JAI Press, London, pp. 1–52.
Toner,  M., Tompkins,  R. G., Cravalho,  E. G., and Yarmush,  M. L. 1992, “Transport Phenomena During Freezing of Isolated Hepatocytes,” AIChE J., 38, pp. 1512–1522.
Smith, D. J., Devireddy, R. V., and Bischof, J. C., 1999, “Prediction of Thermal History and Interface Propagation During Freezing in Biological Systems—Latent Heat and Temperature-Dependent Property Effects,” Proc. 5th ASME/JSME Thermal Eng. Joint Conf., San Diego CA. CD-ROM Publication, (http://www.me.umn.edu/divisions/tht/bhmt/publications/pdf/ASMEJSME-freezing.pdf).
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Co., New York.
Pazhayannur,  P. V., and Bischof,  J. C. 1997, “Measurement and Simulation of Water Transport During Freezing in Mammalian Liver Tissue,” ASME J. Biomech. Eng., 119, pp. 269–277.
Devireddy,  R. V., and Bischof,  J. C. 1998, “Measurement of Water Transport During Freezing in Mammalian Liver Tissue: Part II—The Use of Differential Scanning Calorimetry,” ASME J. Biomech. Eng., 120, pp. 559–569.
Devireddy, R. V., Bischof, J. C., Leo, P. H., and Lowengrub, J. S., 2000, “Measurement and Modeling of Latent Heat Release During Freezing of Aqueous Solutions in a Small Container,” Advances in Heat and Mass Transfer in Biotechnology, HTD-Vol. 368/BED-Vol. 47, pp. 23–31.
Fennema, O. R., Powrie, W. D., and Marth, E. H., 1973, Low-Temperature Preservation of Foods and Living Matter, Marcel Dekker, Inc., New York.
Devireddy,  R. V., Smith,  D. J., and Bischof,  J. C. 1999, “Mass Transfer During Freezing in Rat Prostate Tumor Tissue,” AIChE J., 45, No. 3, pp. 639–654.
Schulte, M. G., 1996, “The Effects of Varying Concentrations of DMSO on the Biophysical Parameters of Isolated Mammalian Cells During Freezing in the Presence of Extracellular Ice,” M.S. thesis, University of Minnesota, Minneapolis, MN.
Smith, D. J., Josephson, S. S., and Bischof, J. C., 1997, “A Model of Cryosurgical Destruction in AT-1 Prostate Tumor Based on Cellular Damage Mechanisms,” Advances in Heat and Mass Transfer in Biotechnology, HTD-Vol. 355, pp. 149–150.

Figures

Grahic Jump Location
A schematic depiction (flow chart) of the source term matching algorithm used in the coupled thermal/biophysical model
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
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.
Grahic Jump Location
(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.
Grahic Jump Location
(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.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In