46. Modelling the Cryopreservation Process: the Effect of the Cell Size Distribution

Cryopreservation modelling starts from the pioneering work by Mazur in 1963. Later in the nineties continuous improvements led to a complete physico-chemical theory describing IIF, where the water transport model is coupled to the classical nucleation theory of ice nucleation and diffusion limited crystal growth. Following the developed theoretical approach, the PIIF has been defined to allow the comparison of model results with typical experimental data obtained through cryo-microscopy. Since this, researchers have been operating in a cul-de-sac, being unable or even uninterested to overcome the predictive limitations that this theoretical approach shows. Above all, the PIIF adopted so far is strictly valid only for the case of a single ice nucleus per cell and growing extremely fast. Moreover, since in this theoretical approach all the cells in a population are assumed of the same average size, resorting to the “sporadic nucleation” of identical cells (i.e. stochastic criterion) is mandatory to explain the experimental evidence that cells subjected to the same freezing cycle show different IIF temperatures. On the other hand, it is well known that even a purified population of cells does not comprise cells of identical size. Needless to say that, larger cells are characterised by a smaller surface-to-volume ratio than smaller cells. As such, larger cells are expected to lose less water via osmosis. Therefore, at any cooling rate, the largest cells of a population are expected to reach the super-cooled conditions earlier than the smallest. Following these considerations, in this work a size distributed cell population has been taken into account through a Population Balance approach, and the “sporadic nucleation” has been dropped in favour of a fully deterministic criterion: differences in cell volumes are now invoked to explain the experimental evidence that cells subjected to the same freezing cycle show different IIF temperatures. Accordingly, a new general definition of PIIF has been provided, able to take into account not only the ice nucleation but also the ice crystal growth of an unlimited number of ice nuclei per cell. Experimental validation of this novel modelling approach has been provided by comparisons with suitable experimental data taken from the literature regarding rat hepatocytes. The new definition of PIIF appears to be far more consistent with the experimental measurements than the previous theoretical interpretations. In addition, the novel modelling approach has provided an original and more sound explanation for well-known experimental evidences. In particular, while the stochastic model for a population of identical cells needs to invoke two different ice nucleation mechanisms (namely SCN and VCN, surface and volume catalysed nucleation mechanisms) in order to describe the experimental evidence of the so called “break point for IIF incidence”, the novel deterministic model is able to describe such experimental behaviour by considering only one heterogeneous nucleation mechanism of IIF taking place in a population of differently sized cells. The Fondazione Banco di Sardegna, Italy, and The Sardinia Regional Government are gratefully acknowledged for the financial support.