The Thermodynamics of Water Transport From Biological Cells During Freezing

A thermodynamic model for the freezing of biological cells has been developed and has been applied to human erythrocytes. Analytical expressions describing the dynamics of water loss during the several stages of the freezing process have been derived from a cell modeled as an open system surrounded by a membrane permeable to water only. The permeability of the membrane to water is the most significant cell parameter in this process and in the present model, and is assumed to be a function of the temperature and osmolality of the extracellular solution. The resulting set of differential equations describing the cell freezing process is solved numerically for various cooling rates. For cooling rates less than 3000 K/min, erythrocytes lose 95 percent of their intracellular water before the eutectic temperature is reached. For cooling rates greater than 3000 K/min, the fraction of intracellular water remaining at the eutectic temperature is a strong function of cooling rate. The effect of supercooling of the extracellular solution on the kinetics of the cell water loss is also analyzed. As a consequence of the supercooling, the volume of water present intracellularly at a given temperature is substantially greater than when no supercooling occurs. This condition favors intracellular ice formation and is consistent with experimental observations in this laboratory.