Diffusion controlled ice growth with soft impingement inside biological cells during freezing

An iterative method has been proposed to determine the relationship between the temperature depression of intracellular ice formation (IIF) and the equilibrium melting point depression for initial cryoprotective agent (CPA) concentrations larger than 1.5M. Using the iterative method coupling with a water transport model for freezing induced cell dehydration and intracellular ice growth, the temperature of IIF has been determined. The new model of temperature of IIF has been applied to predict nucleation parameters at various temperature and initial CPA concentrations according to Karlsson's approach. A geometrical model of soft impingement proposed by Bruna has been incorporated into Karlsson's diffusion limited crystal growth model to include the effect of soft impingement. The new crystal growth model has been verified by a comparison between the predicted critical cooling rates for vitrification with the reported values in literature. With the new crystal growth model, it has been found that the limiting value of the crystallized volume fraction increases as cooling progresses and decreases as the initial CPA concentration increases. A comparison of simulated crystallized volume fractions when soft impingement, hard impingement and no corrections are used has also been made and the result shows that soft impingement could not be omitted in the prediction of intracellular ice formation and growth, especially when the final crystallized volume fraction is larger than 0.1.