A stereological method for the analysis of cellular lesions in tissue sections using three-dimensional cellular automata

A simple three-dimensional cellular automaton with random asynchrone single-site updates is used to simulate the spatial aggregation of cells into cell clusters resembling enzyme altered liver lesions. Realizations of these clusters are used to facilitate the computation of the stereological transformation coefficients, which are neeeded to link the two-dimensional number and size distributions of transections (sections through the clusters) to the three-dimensional number and size distributions of the cell clusters. The approach follows closely the one developed by De Gunst and Luebeck but is more general. It enables us to compute the maximum likelihood estimates of the three-dimensional number and size distributions of the clusters with only weak assumptions on their shape and maximum size. The proposed method is tested by analysis of simulated section data which were generated by the cellular automaton in conjuction with a parametric growth model which provides the size and number distribution of three-dimensional clusters as a function of time. These data are evaluated via maximum likelihood for investigation and the distribution of the model parameter estimators. A discretized version of the Wicksell transformation, which assumes that the transections are spherically shaped, is introduced and used for comparison. Finally, as an example of the proposed method, we present an analysis of foci data from an initiation promotion experiment where foci sizes were ascertained in terms of the number of visible stained cell nuclei.