An analytical method to evaluate cooling rates during cryopreservation protocols for organs.

A simple, graphical procedure has been established to estimate the cooling rates at a specified location and temperature in a biological medium frozen by imposing a constant cooling rate at the outer surface. The graphical procedure also facilitates the determination of the outer surface temperature at the instant a given temperature has been attained in a specific location. The results obtained through a numerical study using finite elements can be applied to biological media with various chemical compositions including different concentrations of cryoprotective agents.