Dipartimento di Ingegneria Chimica e Materiali, Università degli Studi di Cagliari, Piazza d'Armi, 09123 Cagliari, Italy.
Cryobiology. 2011 Jun;62(3):218-31. doi: 10.1016/j.cryobiol.2011.03.006. Epub 2011 Apr 2.
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.
典型的细胞悬浮液冷冻保存的数学模型假设细胞外溶液中的冰和液态水之间存在热力学平衡。本工作通过引入无任何冷冻保护剂（CPA）时的动态细胞外冰形成（EIF）的种群平衡方法来研究该假设的有效性。种群平衡模型反映了悬浮溶液中的成核和扩散限制生长，其驱动力在相关相图中进行评估。细胞外隔室的这种种群平衡描述已与文献中最近提出的模型[Fadda 等人，AIChE Journal，56，2173-2185，（2010）]耦合，该模型能够定量描述和预测细胞内的内部冰形成（IIF）。细胞通过大小分布进行特征描述（即通过另一个种群平衡），从而克服了具有相同大小细胞的种群的经典观点。从细胞大小分布动力学方面比较系统行为，可以得出结论，细胞外隔室中热力学平衡的假设并不总是合理的。根据冷却速率，需要考虑 EIF 的动力学。
