Ice Crystal Growth during the Rapid Freezing of Tissues

This paper contains a few comments on the physical analysis of the factors controlling the rate of cooling, and the relation of the rate of cooling to ice crystal formation which has been carried out in connection with the electron microscopic work described by Dr. C-ersh at this conference. Of the many factors which influence the rate of cooling, by far the most important is the size of the sample. The necessity for cutting small pieces to minimize ice crystal artefact has been realized since the introduction of freezing as a method of histological fixation (1, 2), but until we examined the problem mathematically before starting to cut these extremely small pieces, we did not appreciate just how small was small. The essential point brought olat by computation was that if anything approaching ideal cooling (that is, cooling in which the surface of the sample is maintained at the temperature of the body of the coolant) could be achieved, the cooling rate would be inversely proportional to the square of the least linear dimension. This is illustrated in Fig. 1. Thus a cube 0.1 ram. on edge might be expected to cool 100 times faster than one 1.0 ram. on edge. The conditions of heat transfer at the surface are important in determining for how small a sample ideal cooling can be approximated. Experimentally recorded cooling curves of thin copper slabs cooled in liquid propane, isopentane, and liquid nitrogen are compared in Fig. 2. For such a system cooling is limited only by surface transfer. Propane clearly gives somewhat better surface transfer than isopentane and both are better by an order of magnitude than liquid nitrogen. Detailed analysis shows that the assumption of ideal cooling is not valid (even when cooling in liquid propane) for pieces of tissue in which the least linear dimension is less than about 1.0 ram. For smaller pieces cooling rate is still size-dependent, but more nearly proportional to the inverse first power than to the inverse square of the least linear dimension. The relation between cooling rates and crystallization phenomena was more difficult to determine. Some previous attempts we had made to get a relation between ice crystal size and cooling rate had yielded essentially random results (3). At first the electron microscopic observations were equally puzzling. Either almost no apparent crystallization or complete crystallization into fairly large 45