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A Mathematical Framework for Developing Freezing Protocols in the Cryopreservation of Cells
SIAM Journal on Applied Mathematics ( IF 1.9 ) Pub Date : 2020-03-03 , DOI: 10.1137/19m1275875
Mohit P. Dalwadi , Sarah L. Waters , Helen M. Byrne , Ian J. Hewitt

SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 657-689, January 2020.
When cooling cells to preserve them during cryopreservation, cooling too quickly results in the formation of lethal intracellular ice, while cooling too slowly amplifies the toxic effects of the cryoprotective agents (CPAs) added to slow down ice formation. We derive a mathematical model for cell cryopreservation to understand and quantify these observations. We assume that the system has a spherical geometry of three different regions: ice, extracellular liquid medium, and cell. The two interfacial boundaries separating the three regions can move and must be determined as part of the solution. The presence of CPA lowers the freezing point of the system, and the cell membrane moves due to the osmotic pressure difference across the membrane. We use a combination of numerical and asymptotic methods to determine how the temperature, the CPA concentration, and concentration of an ion species internal and external to the cell evolve during cooling for a range of cooling rates across different timescales. We introduce two metrics to characterize the cell damage caused by freezing, accounting for supercooling and CPA toxicity. Given cell properties and the operating protocol of the cryopreservation process, we show how the damage metrics can be used to predict an optimal cooling rate. Our asymptotic analysis provides a computationally efficient framework from which to determine this optimal rate.


中文翻译:

在细胞冷冻保存中开发冷冻方案的数学框架

SIAM应用数学杂志,第80卷,第2期,第657-689页,2020年1月。
当冷却细胞以在冷冻保存过程中保存它们时,过快的冷却会导致致命的细胞内冰的形成,而过慢的冷却则会放大添加的防冻剂(CPA)的毒性,从而减缓冰的形成。我们导出了细胞冷冻保存的数学模型,以了解和量化这些观察结果。我们假设系统具有三个不同区域的球形几何结构:冰,细胞外液体培养基和细胞。分隔三个区域的两个界面边界可以移动,并且必须确定为解决方案的一部分。CPA的存在会降低系统的凝固点,并且由于跨膜的渗透压差,细胞膜会移动。我们使用数值和渐近方法的组合来确定温度,CPA浓度以及电池内部和外部离子种类的浓度会在冷却期间以不同的时间范围内的一定冷却速率变化。我们介绍了两个指标来表征由冷冻引起的细胞损伤,这是过冷和CPA毒性的原因。在给定的细胞特性和冷冻保存过程的操作规程的基础上,我们展示了如何使用损伤指标来预测最佳冷却速率。我们的渐近分析提供了一个计算有效的框架,可以从中确定最佳速率。在给定的细胞特性和冷冻保存过程的操作规程的基础上,我们展示了如何使用损伤指标来预测最佳冷却速率。我们的渐近分析提供了一个计算有效的框架,可以从中确定最佳速率。在给定的细胞特性和冷冻保存过程的操作规程的基础上,我们展示了如何使用损伤指标来预测最佳冷却速率。我们的渐近分析提供了一个计算有效的框架,可以从中确定最佳速率。
更新日期:2020-03-03
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