Research Papers

Thermodynamic Theory and Experimental Validation of a Multiphase Isochoric Freezing Process

[+] Author and Article Information
Matthew J. Powell-Palm

Department of Mechanical Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: mpowellp@berkeley.edu

Justin Aruda, Boris Rubinsky

Department of Mechanical Engineering,
University of California Berkeley,
Berkeley, CA 94720

1Corresponding author.

Manuscript received February 26, 2019; final manuscript received April 8, 2019; published online May 13, 2019. Assoc. Editor: Ram Devireddy.

J Biomech Eng 141(8), 081011 (May 13, 2019) (8 pages) Paper No: BIO-19-1106; doi: 10.1115/1.4043521 History: Received February 26, 2019; Revised April 08, 2019

Freezing of the aqueous solutions that comprise biological materials, such as isotonic physiological saline, results in the formation of ice crystals and the generation of a hypertonic solution, both of which prove deleterious to biological matter. The field of modern cryopreservation, or preservation of biological matter at subfreezing temperatures, emerged from the 1948 discovery that certain chemical additives such as glycerol, known as cryoprotectants, can protect cells from freeze-related damage by depressing the freezing point of water in solution. This gave rise to a slew of important medical applications, from the preservation of sperm and blood cells to the recent preservation of an entire liver, and current cryopreservation protocols thus rely heavily on the use of additive cryoprotectants. However, high concentrations of cryoprotectants themselves prove toxic to cells, and thus there is an ongoing effort to minimize cryoprotectant usage while maintaining protection from ice-related damage. Herein, we conceive from first principles a new, purely thermodynamic method to eliminate ice formation and hypertonicity during the freezing of a physiological solution: multiphase isochoric freezing. We develop a comprehensive thermodynamic model to predict the equilibrium behaviors of multiphase isochoric systems of arbitrary composition and validate these concepts experimentally in a simple device with no moving parts, providing a baseline from which to design tailored cryopreservation protocols using the multiphase isochoric technique.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Giwa, S. , Lewis, J. K. , Alvarez, L. , Langer, R. , Roth, A. E. , Church, G. M. , Markmann, J. F. , Sachs, D. H. , Chandraker, A. , Wertheim, J. A. , Rothblatt, M. , Boyden, E. S. , Eidbo, E. , Lee, W. P. A. , Pomahac, B. , Brandacher, G. , Weinstock, D. M. , Elliott, G. , Nelson, D. , Acker, J. P. , Uygun, K. , Schmalz, B. , Weegman, B. P. , Tocchio, A. , Fahy, G. M. , Storey, K. B. , Rubinsky, B. , Bischof, J. , Elliott, J. A. W. , Woodruff, T. K. , Morris, G. J. , Demirci, U. , Brockbank, K. G. M. , Woods, E. J. , Ben, R. N. , Baust, J. G. , Gao, D. , Fuller, B. , Rabin, Y. , Kravitz, D. C. , Taylor, M. J. , and Toner, M. , 2017, “ The Promise of Organ and Tissue Preservation to Transform Medicine,” Nat. Biotechnol., 35(6), pp. 530–542. [CrossRef] [PubMed]
Belzer, F. O. , and Southard, J. H. , 1988, “ Principles of Solid Organ Preservation by Cold Storage,” Transplantation, 45(4), pp. 673–676. [CrossRef] [PubMed]
Thomson, L. K. , Fleming, S. D., Aitken, R. J., De Iuliis, G. N., Zieschang, J. A., and Clark, A. M., 2009, “ Cryopreservation-Induced Human Sperm DNA Damage Is Predominantly Mediated by Oxidative Stress Rather Than Apoptosis,” Hum. Reprod., 24(9), pp. 2061–2070. [CrossRef] [PubMed]
Tatone, C. , Di Emidio, G. , Vento, M. , Ciriminna, R. , and Artini, P. G. , 2010, “ Cryopreservation and Oxidative Stress in Reproductive Cells,” Gynecol. Endocrinol., 26(8), pp. 563–567. [CrossRef] [PubMed]
Fuller, B. J. , Gower, J. D. , and Green, C. J. , 1988, “ Free Radical Damage and Organ Preservation: Fact or Fiction?: A Review of the Interrelationship Between Oxidative Stress Physiological Ion Disbalance,” Cryobiology, 25(5), pp. 377–393. [CrossRef] [PubMed]
Arav, A. , and Zvi, R. , 2008, “ Do Chilling Injury and Heat Stress Share the Same Mechanism of Injury in Oocytes?,” Mol. Cell. Endocrinol., 282(1–2), pp. 150–152. [CrossRef] [PubMed]
Fahy, G. M. , Wowk, B. , Wu, J. , Phan, J. , Rasch, C. , Chang, A. , and Zendejas, E. , 2004, “ Cryopreservation of Organs by Vitrification: Perspectives and Recent Advances,” Cryobiology, 48(2), pp. 157–178. [CrossRef] [PubMed]
Guan, N. , Blomsma, S. A. , Fahy, G. M. , Groothuis, G. M. M. , and de Graaf, I. A. M. , 2013, “ Analysis of Gene Expression Changes to Elucidate the Mechanism of Chilling Injury in Precision-Cut Liver Slices,” Toxicol. In Vitro, 27(2), pp. 890–899. [CrossRef] [PubMed]
Steif, P. S. , Palastro, M. C. , and Rabin, Y. , 2007, “ The Effect of Temperature Gradients on Stress Development During Cryopreservation Via Vitrification,” Cell Preserv. Technol., 5(2), pp. 104–115. [CrossRef] [PubMed]
Ehrlich, L. E. , Fahy, G. M. , Wowk, B. G. , Malen, J. A. , and Rabin, Y. , 2017, “ Thermal Analyses of a Human Kidney and a Rabbit Kidney During Cryopreservation by Vitrification,” ASME J. Biomech. Eng., 140(1), p. 011005. [CrossRef]
X, S. , 2008, “ Thermal Stresses From Large Volumetric Expansion During Freezing of Biomaterials,” ASME J. Biomech. Eng., 120(6), pp. 720–726.
Mazur, P. , 1984, “ Freezing of Living Cells: Mechanisms and Implications,” Am. J. Physiol., 247(3 Pt. 1), pp. C125–C142. [CrossRef] [PubMed]
Mazur, P. , 1970, “ Cryobiology: The Freezing of Biological Systems,” Science, 168(3934), pp. 939–949. [CrossRef] [PubMed]
Lovelock, J. E. , 1953, “ The Haemolysis of Human Red Blood-Cells by Freezing and Thawing,” Biochim. Biophys. Acta, 10, pp. 414–426. [CrossRef] [PubMed]
Ishiguro, H. , and Rubinsky, B. , 2011, “ Microscopic Behavior of Ice Crystals and Biological Cells During Directional Solidification of Solutions With Cells,” Trans. Jpn. Soc. Mech. Eng. Ser. B, 60(572), pp. 1349–1355. [CrossRef]
Ishiguro, H. , and Rubinsky, B. , 1994, “ Mechanical Interactions Between Ice Crystals and Red Blood Cells During Directional Solidification,” Cryobiology, 60(572), pp. 1349–1355.
Leibo, S. P. , McGrath, J. J. , and Cravalho, E. G. , 1978, “ Microscopic Observation of Intracellular Ice Formation in Unfertilized Mouse Ova as a Function of Cooling Rate,” Cryobiology, 15(3), pp. 257–271. [CrossRef] [PubMed]
Diller, K. R. , 1975, “ Intracellular Freezing: Effect of Extracellular Supercooling,” Cryobiology, 12(5), pp. 480–485. [CrossRef] [PubMed]
Smith, A. U. , and Polge, C. , 1950, “ Survival of Spermatozoa at Low Temperatures,” Nature, 166(4225), pp. 668–669. [CrossRef] [PubMed]
Polge, C. , Smith, A. U. , and Parkes, A. S. , 1949, “ Revival of Spermatozoa After Vitrification and Dehydration at Low Temperatures,” Nature, 164(4172), p. 666. [CrossRef] [PubMed]
Elliott, G. D. , Wang, S. , and Fuller, B. J. , 2017, “ Cryoprotectants: A Review of the Actions and Applications of Cryoprotective Solutes That Modulate Cell Recovery From Ultra-Low Temperatures,” Cryobiology, 76, pp. 74–91. [CrossRef] [PubMed]
Fahy, G. M. , 1986, “ The Relevance of Cryoprotectant ‘Toxicity’ to Cryobiology,” Cryobiology, 23(1), pp. 1–13. [CrossRef] [PubMed]
Finger, E. B. , and Bischof, J. C. , 2018, “ Cryopreservation by Vitrification: A Promising Approach for Transplant Organ Banking,” Curr. Opin. Organ Transplant., 23(3), pp. 353–360. [CrossRef] [PubMed]
Huang, H. , Yarmush, M. L. , and Usta, O. B. , 2018, “ Long-Term Deep-Supercooling of Large-Volume Water and Red Cell Suspensions Via Surface Sealing With Immiscible Liquids,” Nat. Commun., 9(1), p. 3201. [CrossRef] [PubMed]
Berendsen, T. A. , Bruinsma, B. G. , Puts, C. F. , Saeidi, N. , Usta, O. B. , Uygun, B. E. , Izamis, M. L. , Toner, M. , Yarmush, M. L. , and Uygun, K. , 2014, “ Supercooling Enables Long-Term Transplantation Survival Following 4 Days of Liver Preservation,” Nat. Med., 20(7), pp. 790–793. [CrossRef] [PubMed]
Taylor, M. J. , and Baicu, S. C. , 2010, “ Current State of Hypothermic Machine Perfusion Preservation of Organs: The Clinical Perspective,” Cryobiology, 60(3 Suppl.), pp. S20–S35. [CrossRef] [PubMed]
Rubinsky, B. , Perez, P. A. , and Carlson, M. E. , 2005, “ The Thermodynamic Principles of Isochoric Cryopreservation,” Cryobiology, 50(2), pp. 121–138. [CrossRef] [PubMed]
Preciado, J. A. , and Rubinsky, B. , 2010, “ Isochoric Preservation: A Novel Characterization Method,” Cryobiology, 60(1), pp. 23–29. [CrossRef] [PubMed]
Powell-Palm, M. J. , Zhang, Y. , Aruda, J. , and Rubinsky, B. , 2019, “ Isochoric Conditions Enable High Subfreezing Temperature Pancreatic Islet Preservation Without Osmotic Cryoprotective Agents,” Cryobiology, 86, pp. 130–133. [CrossRef] [PubMed]
Wan, L. , Powell-Palm, M. J., Lee, C., Gupta, A., Weegman, B. P., Clemens, M. G., and Rubinsky, B., 2018, “ Preservation of Rat Hearts in Subfreezing Temperature Isochoric Conditions to –8 ° C and 78 MPa,” Biochem. Biophys. Res. Commun., 496(3), pp. 852–857. [CrossRef] [PubMed]
Mikus, H. , Miller, A., Nastase, G., Serban, A., Shapira, M., and Rubinsky, B., 2016, “ The Nematode Caenorhabditis elegans Survives Subfreezing Temperatures in an Isochoric System,” Biochem. Biophys. Res. Commun., 477(3), pp. 401–405. [CrossRef] [PubMed]
Rubinsky, B. , and Pegg, D. E. , 1988, “ A Mathematical Model for the Freezing Process in Biological Tissue,” Proc. R. Soc. B Biol. Sci., 234(1276), pp. 343–358.
Pegg, D. E. , 2007, “ Principles of Cryopreservation,” Methods Mol. Biol., 368, pp. 39–57. [CrossRef] [PubMed]
Pegg, D. E. , 2015, “ Principles of Cryopreservation,” Cryopreserv. Free. Dry. Protoc., 1257, pp. 3–19.
Pegg, D. E. , and Diaper, M. P. , 1988, “ On the Mechanism of Injury to Slowly Frozen Erythrocytes,” Biophys. J., 54(3), pp. 471–488. [CrossRef] [PubMed]
Karlsson, J. O. M. , and Toner, M. , 1996, “ Long-Term Storage of Tissues by Cryopreservation: Critical Issues,” Biomaterials, 17(3), pp. 243–256. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 2

Multiphase isochoric freezing. (a) Pressure–temperature diagram depicting the equilibrium states occupied by a system consisting of two distinct aqueous phases, one internal to and one external to the mass-impermeable boundary Γ. The system will follow three distinct paths as temperature decreases, presented conceptually in schematics (b)–(d): On path 1 (b), only the internal phase forms ice. This path is identical to the liquidus curve of the phase diagram of the internal phase. Path 2 (c) covers the temperature range between the temperature at which the internal phase has frozen completely and the pressure-adjusted freezing point of the external phase. On path 3 (d), the external phase also forms ice. This phase represents a pressure-adjusted liquidus curve for the external phase.

Grahic Jump Location
Fig. 1

Single-phase isochoric freezing. (a) Schematic of an experimental isochoric chamber, loaded with a single homogeneous solution. Cross-sectional view depicts the two-phase liquid–solid equilibrium characteristic of isochoric freezing. (b) Phase diagram of pure water. The equilibrium states of an isochoric system occupy the labeled liquidus curve between ice-1 h and water between 0 °C and the triple point of water, ice-1 h, and ice III. (c) Ice percentage versus temperature for a generic series of solutions of varying solute concentration in an isochoric system. As the solute concentration increases, the freezing point of the solution will decrease and the ice percentage curve will shift deeper in temperature.

Grahic Jump Location
Fig. 3

Experimental results (markers) and theoretical predictions (curves) for a multiphase isochoric system employing an external phase of 2 M glycerol and 0.9% physiological saline and an internal phase of pure water. Each column represents a different internal phase volume (indicated at the top of the column as a percentage of the total system volume), and rows (a)–(c) present: (a) pressure data (measured directly). The theoretical internal phase liquidus line (blue) is extended over the entire temperature range for easy reference to single-phase isochoric behavior. (b) Ice percentage data (calculated from pressure data). (c) Percent increase in concentration (calculated from pressure data).

Grahic Jump Location
Fig. 4

Comparison of thermodynamic behaviors between single-phase isochoric and isobaric systems and a multiphase isochoric system. (a) Comparison of the concentration increase experienced in a solution of 2 M glycerol and 0.9% saline in an isobaric, single-phase isochoric, and multiphase isochoric system. (b) Calculated freezing point curves for various solutions of interest to cryopreservation in a multiphase isochoric system, as a function of internal water phase volume. The freezing points of the solutions in a single-phase isochoric system can be found intersecting the y-axis (at 0% internal water volume).



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