A mathematical model, the membranes and devices based upon that model to optimize protocols for the addition or removal of cryoprotectant to or from biological cells, and a method to observe the biological cells and obtain the data to implement the models. This disclosure describes the use of four equations to predict optimal protocols to add or remove cryoprotectant to or from biological cells. The equations particularly require experimentally found data, specific to cell-type and species, regarding the osmotic tolerance of the cells, where osmotic tolerance refers to the cells ability to shrink or swell to various changes in osmolality without injury. The equations further require the cryoprotectant permeability coefficient and the water permeability coefficient of the particular cells' plasma membrane. These coefficients are found with experimental data of the knetic volume change of the cell-type to a known concentration and temperature of cryoprotectant, and one method is particularly presented as to how this data may be obtained. Also disclosed are particularly preferred methods and devices to add or remove cryoprotectant to or from these cells based upon these equations.