Abstract: A mathematical model, and membranes and devices based upon that model, to optimize protocols for the addition or removal of cryoprotectant to or from biological cells. 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.

Abstract: A mathematical model, and membranes and devices based upon that model, to optimize protocols for the addition or removal of cryoprotectant to or from biological cells. 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.

Abstract: A mathematical model to optimize protocols for the addition or removal of cryoprotectant to or from sperm cells. This disclosure describes the use of four equations to predict optimal protocols to add or remove cryoprotectant to or from sperm cells. The equations particularly require experimentally found date, specific to a species of sperm, regarding the osmotic tolerance of sperm cells, where osmotic tolerance refers to the sperm 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 sperm cells' plasma membrane. Also disclosed are two particularly preferred methods to add or remove cryoprotectant to or from sperm. These preferred methods are Fixed-Volume-Step addition/removal of cryoprotectant or Fixed-Molarity-Step addition/removal of cryoprotectant.