Mathematical modelling of cellular osmotic responses to low temperatures is being increasingly used to overcome obstacles in the successful cryopreservation of cells and tissues. Current cryobiological models often contain simplifying assumptions regarding the solution behaviour of the complicated, multisolute intra- and extra-cellular solutions. In order to obtain more accurate predictions of cryobiological outcomes, equations derived from thermodynamic principles that more accurately describe the biological solution behaviour could be used to greatly advance the design of novel cryopreservation protocols. The general hypothesis of this thesis is that the application of the multisolute osmotic virial equation, with mixing rules derived from thermodynamic first principles, to solutions of interest in cryobiology will result in more accurate predictions of the multisolute solution behaviour, which will lead to improved cryobiological modelling and increased understanding of cellular responses to cryopreservation. Specifically, this thesis demonstrates that the osmotic virial coefficients, obtained from single-solute solution data, can be used in the multisolute osmotic virial equation to accurately predict the multisolute solution behaviour, without the need to fit multisolute solution data. The form of the multisolute osmotic virial equation proposed in this thesis was used to predict the solution behaviour of a range of multisolute solutions of interest in cryobiology. The equation commonly used in cryobiology to describe cellular osmotic equilibrium is based on ideal, dilute solution assumptions. In this thesis, a non-ideal osmotic equilibrium equation was derived and, combined with the multisolute osmotic virial equation, used to more accurately predict the osmotic equilibrium of human erythrocytes. The improved equations proposed in this thesis were combined with experimental measurements of the incidence of intracellular ice formation in order to further the understanding of the role of several important cryobiological parameters on the formation of intracellular ice. This thesis work has significantly contributed to the field of cryobiology by substantially improving the accuracy of two key equations used in the modelling of cellular osmotic responses to cryopreservation. The combination of accurate mathematical modelling and results from experiments will allow increased understanding of cellular responses to cryopreservation, leading to the design of novel cryopreservation protocols. / Chemical Engineering and Medical Sciences

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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.