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Cryobiology. 2011 Jun;62(3):218-31. doi: 10.1016/j.cryobiol.2011.03.006. Epub 2011 Apr 2.

The effect of EIF dynamics on the cryopreservation process of a size distributed cell population.

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Dipartimento di Ingegneria Chimica e Materiali, Università degli Studi di Cagliari, Piazza d'Armi, 09123 Cagliari, Italy.


Typical mathematical modeling of cryopreservation of cell suspensions assumes a thermodynamic equilibrium between the ice and liquid water in the extracellular solution. This work investigates the validity of this assumption by introducing a population balance approach for dynamic extracellular ice formation (EIF) in the absence of any cryo-protectant agent (CPA). The population balance model reflects nucleation and diffusion-limited growth in the suspending solution whose driving forces are evaluated in the relevant phase diagram. This population balance description of the extracellular compartment has been coupled to a model recently proposed in the literature [Fadda et al., AIChE Journal, 56, 2173-2185, (2010)], which is capable of quantitatively describing and predicting internal ice formation (IIF) inside the cells. The cells are characterized by a size distribution (i.e. through another population balance), thus overcoming the classic view of a population of identically sized cells. From the comparison of the system behavior in terms of the dynamics of the cell size distribution it can be concluded that the assumption of a thermodynamic equilibrium in the extracellular compartment is not always justified. Depending on the cooling rate, the dynamics of EIF needs to be considered.

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