To theoretically predict the optimal protocol for cryopreservation of biological cells, a model for intracellular ice formation and its growth in a ternary solution of both temperature and concentration varying was developed. The modified water transport equation developed by us in 2006, ice nucleation, and the diffusion-limited ice growth theory were coupled to constitute this model. Typical cryopreservation processes for mouse oocytes being frozen in glycerol-water-NaCl ternary solutions were simulated. The finally crystallized volume fraction, together with the finally normalized intracellular water volume, as a function of both initial glycerol concentration and cooling rate was predicted by the model. Simulation results indicated that, (i) the normalized intracellular water volume decreased with the increase of initial glycerol concentration. (ii) the crystallized volume fraction decreased linearly with the increase of initial glycerol concentration at higher cooling rates, and first increased and then decreased with the increase of the cooling rate: (a) the critical cooling rate, i.e., the minimum cooling rate necessary to vitrify intracellular solution, decreased from 1.25×10¹³ ℃/min to 20 ℃/min along with the increase of the concentration of glycerol from 0 to 7.4 mol• L^－1, and (b) for initial glycerol concentration higher than 7.4 mol•L^－1, any cooling rate could vitrify intracellular solution. This model provides a theoretical method for prediction of the optimal protocol for cryopreservation of biological cells by seeking a combined region from the two dimensional figure of initial glycerol concentration versus cooling rate.

Key words: intracellular ice, vitrification, cryoprotective agent, critical cooling rate