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

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.