Application of cluster analysis for characterization of spatial distribution of particles by stereological methods

A method for the detection and characterization of clusters of particles observed in section with the electron microscope is presented. Cluster analysis is performed by the division method described by Berthet et al. (1976). Starting from a single cluster, profiles from each electron micrograph are successively classified in sets containing an increasing number of clusters. The decrease in the mean free distance, lambda, between profiles in the clusters, is used for terminating the subdivision procedure. The function relating the mean free distance with the number of clusters is evaluated in each subdivision set. The actual number of clusters is selected on the basis of the slope of that function, at a point where lambda has a value close to the average profile diameter. The method assumes a convex shape for the clusters; the salient feature is that it provides a physical delineation of clusters in the section. Hence, an evaluation of some characteristics of clusters in the three-dimensional sample may be obtained by using standard stereological procedures. Characterization of the volume to which the individual particles of a population are eventually restricted can as a result be performed. Practical problems in the acquisition of the data needed for cluster analysis are discussed and a system using for that purpose a Quantimet 720 image analyser in a basic configuration, connected on line with a PDP 11/10 minicomputer, is presented. Application of the method is illustrated by the analysis of lysosomes in cultured hepatoma (HTC) cells, at the end of mitosis and during the S phase. Cluster analysis shows that in cells actively synthesizing DNA they are grouped in clusters representing 5.7% of the cellular volume. Moreover, the average number of particles per cluster falls from a minimum of thirteen at mitosis to only six at the S phase.