Heat Transfer during Cryopreservation

  • Boris Rubinsky
Conference paper
Part of the NATO ASI Series book series (NSSA, volume 147)


One of the technical difficulties encountered by surgeons in organ transplantation is caused by the shortage of available organs and the need for a close donor-recipient interaction in terms of time and the compatibility of the organ. A possible solution for these difficulties is to establish an organ bank, similar to the existing blood banks, in which organs with different immunological properties could be stored for longer periods of time. Cryopreservation, a method for storing organs at low temperatures, below freezing, appears to be promising.


Heat Transfer Cool Rate Phase Transition Temperature Directional Solidification Biological Organ 


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  1. 1.
    H.S. Garslaw and J.C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, Oxford (1973).Google Scholar
  2. 2.
    V.J. Lunardini, “Heat Transfer in Cold Climates,” Van Nostrand Reinhold Co., New York (1981).Google Scholar
  3. 3.
    C. Polge, A.V. Smith, A. Parkes, Revival of spermatozoa after vitrification and dehydration at low temperatures, Nature. 164:666 (1949).PubMedCrossRefGoogle Scholar
  4. 4.
    P. Mazur, Physical and chemical basis for injury in single-celled micro-organisms subjected to freezing and thawing, in “Cryobiology”, Meryman, H.T., Ed., Academic Press, London, 1966.Google Scholar
  5. 5.
    B. Rubinsky, M. Ikeda, A cryomicroscope using directional solidification for the controlled freezing of biological material, Cryobiology. 22:55 (1985).CrossRefGoogle Scholar
  6. 6.
    H.C. Flemings, “Solidification Processes,” McGraw-Hill, New York (1974).Google Scholar
  7. 7.
    H.G. O’Callahan, “Analysis of the Mass Transport During the Freezing of Biomaterials,” Ph.D. Thesis, M.I.T. (1978).Google Scholar
  8. 8.
    M.L. Shepard, C.S. Goldston, F.H. Cocks, The H20-NaCl-glycerol phase diagram and its application to cryobiology, Cryobiology. 13:9 (1976).PubMedCrossRefGoogle Scholar
  9. 9.
    B. Rubinsky, “A Study of Cryopreservation Protocols for Biological Organs,” Ph.D. Thesis, M.I.T. (1980).Google Scholar
  10. 10.
    B. Rubinsky, E.G. Cravalho, An analytical method to evaluate cooling rates during cryopreservation protocols for organs, Cryobiology. 21:303 (1984).PubMedCrossRefGoogle Scholar
  11. 11.
    “Summary of the panel discussions symposium on freezing rates,” Cryobiology. 2:210 (1966).Google Scholar
  12. 12.
    D.G. Wilson, A.D. Solomon, P.T. Boggs, “Moving Boundary Problems,” Academic Press Inc., New York (1978).Google Scholar
  13. 13.
    B. Rubinsky, E.G. Cravalho, The determination of the thermal history in a one-dimensional freezing system by a perturbation method, Trans. ASME Journal of Heat Transfer. 100:326 (1979).CrossRefGoogle Scholar
  14. 14.
    J. Yoo, B. Rubinsky, Numerical computations using finite elements for the moving interface in heat transfer problems with phase transformation, Numerical Heat Transfer. 6:1209 (1983).CrossRefGoogle Scholar
  15. 15.
    H.L. Tsai, B. Rubinskly, A front tracking finite element study on the morphological stability of a planar interface during transient solidification processes, J. Crystal Growth. 69:29 (1984).CrossRefGoogle Scholar
  16. 16.
    J. Yoo, B. Rubinsky, A finite element method for the study of solidification processes in the presence of natural convection, Int. J. for Num. Meth. in Eng. 23:1785 (1986).CrossRefGoogle Scholar
  17. 17.
    I.A. Jacobsen, D.E. Pegg, Cryopreservation of organs: A review, Cryobiology. 21:377 (1984).PubMedCrossRefGoogle Scholar
  18. 18.
    B. Rubinsky, E.G. Cravalho, Analysis for the temperature distribution during the thawing of a frozen biological organ, A.I.Ch.E., Symposium Series, 75:81–88 (1979).Google Scholar
  19. 19.
    B. Rubinsky, A. Shitzer, Analytical solutions of the heat equation involving a moving boundary with application to the change of phase problem (the inverse Stefan problem), Trans ASME J. of Heat Transfer. 99:300 (1978).CrossRefGoogle Scholar
  20. 20.
    B. Rubinsky, A. Shitzer, Analysis of a Stefan-like problem in a biological issue around a cryosurgical probe, Trans. ASME, J. of Heat Transfer. 97:514 (1976).CrossRefGoogle Scholar
  21. 21.
    M.A. Katz, B. Rubinsky, An inverse finite element technique to determine the change of phase location in one-dimensional melting problem, Num. Heat Transfer. 7:269 (1984).Google Scholar
  22. 22.
    Y.F. Hsu, B. Rubinsky, K. Mahin, An inverse finite element method for the analysis of stationary arc welding processes, J. of Heat Transfer, ASME Trans. 108:734 (1986).CrossRefGoogle Scholar
  23. 23.
    M.M. Chen, K.R. Holmes, Microvascular contributions in tissue heat transfer, Annals of the New York Academy of Science. 335:137 (1980).CrossRefGoogle Scholar
  24. 24.
    S. Weinbaum, L.M. Jiji, A new simplified bioheat equation for the effect of blood flow on local average tissue temperature, J. of Biomechanical Eng., ASME Trans. 107:131 (1985).CrossRefGoogle Scholar
  25. 25.
    R.L. Whitman, “Rheology of Circulation,” Pergamon Press, London, England (1968).Google Scholar
  26. 26.
    A.C. Burton, “Physiology and Biophysics of the Circulation,” Year Book Medical Publishers, Chicago, IL (1972).Google Scholar
  27. 27.
    F.P. Incropera, P.P. DeWitt, “Fundamentals of Heat Transfer,” John Wiley and Sons, NY (1981).Google Scholar
  28. 28.
    K.R. Diller, E.G. Cravalho, An experimental study of freezing and thawing processes in biological materials, Cryobiology, 7:191–199, (1971).CrossRefGoogle Scholar
  29. 29.
    P. Motta, Masaki Muto, Tsuneo Fujita, The Liver; An Atlas of Scanning Electron Microscopy, Igaku-Shoin Ltd. N.Y., Tokyo (First Edition, 1978).Google Scholar
  30. 1.
    B. Rubinsky and M. Ikeda, A crymicroscope using directional solidification for the controlled freezing of biological material, Cryobiology 22:55 (1985).CrossRefGoogle Scholar
  31. 2.
    M.W. Chaw and B. Rubinsky, Cryomicroscopic observations on directional solidification in onion cells, Cryobiology 22:392 (1985).CrossRefGoogle Scholar
  32. 3.
    C.V. Lusena, Ice propagation in glycerol solutions at temperatures below −40°C, Ann. N.Y. Acad. Sci. 85:541 (1960).PubMedCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Boris Rubinsky
    • 1
  1. 1.Department of Mechanical EngineerinUniversity of CaliforniaBerkeleyUSA

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