Abstract: In this paper a mathematical model of mass diffusion during the cryoprotectant addition for neural stem cell sphere is presented.The mass diffusion equation is established separately for intracellular and extracellular spaces but taking into account the mass exchange across the cell membrane.The volume change of cells in different positions is also simulated when cryoprotectant is added step by step.The factors affecting volume change are analyzed.Different procedures of addition are used to investigate osmotic damage.The results shows that change of DMSO in extracellular space,which can attain stable within 10 s near the surface and 15 s close to the center of the ball,is faster than that in the intracellular element.Decreasing L_p and increasing ω can greatly improve the volume change while the impact on the size of neural stem cell spheres is limit.The multi-steps addition procedures,which keep the same osmotic pressure difference in each step while gradually reduced time durations,should be chosen.In addition,four-step addition is better than other stepwise additions.An ideal continuous addition should combine with low concentration difference and short loading time,and convex curve addition patterns are preferred.

Key words: neural stem cell spheres, CPA addition model, factor analysis, osmotic damage

摘要： 建立了神经干细胞球的低温保护剂添加模型。通过计算研究了在保护剂添加过程中,神经球中不同位置的细胞体积变化情况,以及细胞内外浓度和细胞膜两侧浓差随时间和空间的变化情况;并分析了影响细胞体积变化的因素,利用该模型进行了保护剂添加程序的优化。结果表明细胞外的保护剂浓度变化较快,在球表面处不到10 s接近平衡,接近球中心处15 s后接近平衡;由于跨膜传质阻力的影响,胞内的保护剂浓度变化较为平缓。减小L_p和增大ω可以显著改善保护剂添加过程的细胞体积变化,神经球尺寸对细胞体积变化影响较小。添加高浓度保护剂时,可以采用等渗透压差、渗透时间间隔逐渐减小的分步添加方法,分步添加方法以四步法较好。理想的连续梯度添加方案应是低浓差和短添加时间的组合,凸曲线添加方案是一种合适的添加方法。

关键词: 神经干细胞球, 保护剂添加模型, 因素分析, 渗透损伤