A Simplified Procedure to Determine the Optimal Rate of Freezing Biological Systems

Abstract

The effect of several cell-level parameters on the predicted optimal cooling rate Bopt of an arbitrary biological system has been studied using a well-defined water transport model. An extensive investigation of the water transport model revealed three key cell level parameters: reference permeability of the membrane to water Lpg, apparent activation energy ELp, and the ratio of the available surface area for water transport to the initial volume of intracellular water (SA∕WV). We defined Bopt as the “highest” cooling rate at which a predefined percent of the initial water volume is trapped inside the cell (values ranging from 5% to 80%) at a predefined end temperature (values ranging from −5°C to −40°C). Irrespective of the choice of the percent of initial water volume trapped and the end temperature, an exact and linear relationship exists between Lpg,SA∕WV, and Bopt. However, a nonlinear and inverse relationship is found between ELp and Bopt. Remarkably, for a variety of biological systems a comparison of the published experimentally determined values of Bopt agreed quite closely with numerically predicted Bopt values when the model assumed 5% of initial water is trapped inside the cell at a temperature of −15°C. This close agreement between the experimental and model predicted optimal cooling rates is used to develop a generic optimal cooling rate chart and a generic optimal cooling rate equation that greatly simplifies the prediction of the optimal rate of freezing of biological systems.