Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population

Cryopreservation of biological material is a crucial step of tissue engineering, but biological material can be damaged by the cryopreservation process itself. Depending on some bio-physical properties that change from cell to cell lineages, an optimum cryopreservation protocol needs to be identified for any cell type to maximise post-thaw cell viability. Since a prohibitively large set of operating conditions has to be determined to avoid the principal origins of cell damage (i.e., ice formation and solution injuries), mathematical modelling represents a valuable alternative to experimental optimisation. The theoretical analysis traditionally adopted for the cryopreservation of a cell suspension addresses only a single, average cell size and ascribes the experimental evidence of different ice formation temperatures to statistical variations. In this chapter our efforts to develop a novel mathematical model based on the population balance approach that comprehensively takes into account the size distribution of a cell population are reviewed. According to this novel approach, a sound explanation for the experimental evidence of different ice formation temperatures may now be given by adopting a fully deterministic criterion based on the size distribution of the cell population. In this regard, the proposed model represents a clear novelty for the cryopreservation field and provides an original perspective to interpret system behaviour as experimentally measured so far. First our efforts to successfully validate the proposed model by comparison with suitable experimental data taken from the literature are reported. Then, in absence of suitable experimental data, the model is used to theoretically investigate system behaviour at various operating conditions. This is done both in absence or presence of a cryo-protectant agent, as well as when the extra-cellular ice is assumed to form under thermodynamic equilibrium or its dynamics is taken into account consistently by means of an additional population balance. More specifically, the effect of the cell size distribution on system behaviour when varying cooling rate and cryo-protectant content within practicable values for a standard cryopreservation protocol is investigated. It is demonstrated that, cell survival due to intra-cellular ice formation depends on the initial cell size distribution and its osmotic parameters. At practicable operating conditions in terms of cooling rate and cryo-protectant concentration, intra-cellular ice formation may be lethal for the fraction of larger size classes of the cell population whilst it may not reach a dangerous level for the intermediate size class cells and it will not even take place for the smaller ones.