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 Lp 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.