Johnson-Mehl-Avrami Kinetics of Intracellular Ice Formation in Confluent Tissue Constructs

Abstract

In an effort to minimize the harmful effects of intracellular ice formation (IIF) during cryopreservation of confluent tissues, computer simulations based on Monte Carlo methods were performed to predict the probability of IIF in confluent monolayers during various freezing procedures. To overcome the prohibitive computational costs of such simulations for large tissues, the well-known Johnson-Mehl-Avrami (JMA) model of crystallization kinetics was implemented as a continuum approximation of IIF in tissues. This model, which describes nucleation, growth, and impingement of crystals in a supercooled melt, is analogous to the process of intracellular ice formation and propagation in biological tissues. Based on the work of Weinberg and Kapral (1989), the JMA model was modified to account for finite-size effects, and was shown to predict accurately the results of freezing simulations in 1-D tissue constructs, for various propagation rates and tissue sizes. An initial analysis of IIF kinetics in 2-D tissues is also presented. The probability of IIF in 2-D liver tissue was measured experimentally during freezing of HepG2 cells cultured in monolayers, and compared to Monte Carlo simulations and predictions of the continuum model. The Avrami coefficient and exponent for IIF in HepG2 tissue were estimated to be k = 0.19 and n = 0.45.