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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.

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Figures

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. 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. 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).

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