A mathematical model of in situ freezing in liquid nitrogen

Abstract

In situ freezing is a procedure, typically applied in neuroscience, to halt metabolism and diffusion. However, the freezing process is not instantaneous, and the regional concentrations of a compound under study may change before the tissue is completely frozen. Knowing the local freezing time, metabolic rate and the diffusion coefficient of the compound of interest, it should be possible to reconstruct the spatial concentration profile prevailing before the object was placed in the cryogen. A mathematical model for calculating the temperature changes at different depths in rabbit and rat heads cooled in liquid nitrogen has been developed. By comparing with experimental results it has been found that the mathematical model can be used for prediction of the local freezing time with a small error.