Accurate prediction of Purkinje cell number from cerebellar weight can be achieved with the fractionator.

Purkinje cell nucleoli are used as counting units in order to obtain unbiased (fractionator) estimates of the number, N, of Purkinje neurons in adult mammalian cerebella of known weight, W. Regression analysis is then employed to establish the nature of the relationship between logN and logW. The linear regression equation defines an allometric relation that is employed to predict number in cerebella of known weight from other mammals. Predicted numbers are tested against empirical estimates. For 19 cerebella ranging in weight from 0.2 g (rat) to 113 g (human), the allometric relation between Purkinje cell number and organ weight was determined. By using this relation, the mean complement in three rabbit cerebella (average weight, 0.87 g) is predicted to be 0.63 million. This figure is confirmed by fractionator estimates made on the same three brains. The cat cerebellum should contain about 1.5-2.0 million Purkinje cells. An estimate of 1.2-1.3 million cells is to be found in the literature. Including rabbit cerebella in a refined equation yields the following relation: N = 686000W(0.695). With this refined equation, further predictions are made about the numbers likely to be found in the cerebella of the dog, goat, pig, ox, and horse. The numbers predicted for these animals must await experimental verification, but they are entirely consistent with previous suggestions that neuronal packing densities decrease with increasing brain size.