Estimation of the Size Distribution of Fibrillar Centres in Nucleoli-An Example of the "Swiss Cheese" Problem in Stereology

Abstract

The "Swiss cheese" problem in stereology is that variant of the classical corpuscle problem where the size distribution of randomly distributed spherical "holes" in an opaque medium is to be inferred from the size distribution of the circular holes observed in sections. In our electron microscopical studies of the neurons of the rat supraoptic nucleus, we encountered a Swiss cheese problem in connection with the size distribution of the fibrillar centres of the nucleoli. We found no practical examples in the literature, and attempts to obtain a Wicksell-type algorithm met with severe numerical instability problems. The present paper shows that the chi-distributions of Keiding, Jensen, and Ranek (1972, Biometrics 28, 813-829) may be used as the basis for a parametric maximum likelihood solution for the Swiss cheese problem. The concept of a capping angle (nonobservability of spheres cut at too acute an angle), also introduced by Keiding et al., carries over as well. The methods are illustrated on data from the mentioned experiment.