In cryopreservation of cells, the bell-shaped cell survival curve with an optimal cooling rate is understood on the basis of two-factor hypothesis, i.e. extracellular freezing injury without intracellular freezing and intracellular freezing injuries. Mathematical description and prediction of the cell survival curve is one of important subjects in the area of cryobiology. The intracellular freezing injury was already modeled successfully and mathematically based on intracellular ice formation. In the present study, a mathematical model with reaction kinetic formulation was newly proposed and developed to describe the extracellular freezing injury, i.e. slow-freezing injury. A parameter study of model constants was performed to evaluate the cells survival rate as a function cooling rate. The model constants were also determined by inverse problem analysis based on the experiment with human erythrocytes and monocytes. The experiment and prediction by the model were compared on the cell survival curve. The result shows that the extracellular freezing-induced cell death is successfully described by the reaction kinetic mode in this study.
