Numerical Simulation Of Mass Transfer During The Cryoprotectant Diffusion Of Neural Stem Cell Sphere

The transplant of neural stem cells has excellent future for healing some neurodegenerative diseases and tissue defects. The cryopreservation of NSCs play significant role in tissue repair and medical treating. Because that the NSCs always grow in term of sphere, it is more effective to preserve the neural stem cell sphere than the cell solution. In this article, we try to give a mathematical review for the process of cryo-protectant diffusion in neural stem cell sphere, in order to optimize this process and rise the percent of survival cell.In this paper a level construction model based on the model of nutrients transport in tissue is developed. The distribution of cell on each level has been given. Combining with the cross membrane transport process, based on the diffusion of inner and extra space, the continuity equation has been proposed. And then by the volume controlling method, combined with C language program, the differential equations is solved and the curve for distribution of cryo-protectant in neural stem cell sphere is finally got. After this, according to this model, a more complicated mathematical model based on the volume changing for the diffusion of cryo-protectant has been established. This model combine with the changes in cell wall and cytoplasm of the separation process for cryo-protectant transport, and has clear statement for distribution of concentration and cell volume.From the result we can see that, the inner and extra concentration and concentration difference is smaller for the neural stem cell sphere with diameter of 200μm. Although it is weaker for the diffusive and toxicity damage, the concentration of cryo-protectant is not sufficient. So all of these factors should be considered when choosing the diameter of neural stem cell sphere. It has been reported that cryopreservation of the sphere with diameter of 80-100μm can get the best result. At the same time the diffusive coefficient do not has obvious influence on the concentration and concentration difference, and higher permeability for membrane can effectively increase the driving force of mass transfer and decrease the concentration difference. Using cryo-protectant in high concentration will bring high concentration difference and conducing cryo-protectant in low temperature can increase the concentration difference in contrast with conducing in normal temperature because the cross membrane transport will be slow down. Studies have shown that high hydraulic pressure can cause cell damage, and in relative to other cryo-protectant, DMSO has more obvious injure. So increasing the diffusive coefficient, enhancing the cross membrane transport of DMSO, and using a step-conduction methods for cryo-protectant in high concentration can effectively retard the damage caused by membrane permeability.