Where should the cooling rate be determined in an extended freezing sample?
Computer simulations have been performed to calculate the transient cooling and solidification process at different locations in a flat plate-shaped freezing container filled with isotonic solution (0.9 wt% NaCl in water). The one-dimensional model accounts for the influences of the external cooling conditions, the container wall, the freezing bag, and the nonplanar solidification of an aqueous solution. The cooling rate was found to increase within the sample from the portions adjacent to the inner surface of the bag toward the center. An important result for cryobiological experiments was the fact that the geometrical center of the sample, a commonly used location for the determination of cooling rate, is not representative for the entire volume of the sample. Even worse, the calculations have shown that the center is often the least representative place. As an alternative, the most suitable location for cooling rate measurements has been determined. With the assumed surface cooling and geometry conditions an optimum location at x/(d/2) approximately 2/3 (x is the space coordinate, originating at the inner surface of the freezing bag; d is the sample thickness) has been calculated, i.e., a distance of one-third away from the center and two-thirds from the inside surface of the sample container. Admitting a 50% range of variation, the cooling rate measured at this point represents at least 80% of the entire sample volume. The survival signature, i.e., the functional dependence of cell survival from cooling rate (determined at a single location), for a fictitious cell kind is also influenced by the location of temperature determination: the "optimum" cooling rate seems to be shifted, and the shape of the signature is changed depending on the location where the cooling rate is determined.