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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