Methods for the study of cellular sociology: Voronoi diagrams and parametrization of the spatial relationships

In order to study cellular sociology, a model of parametrization and quantitation of cellular population topographies is developed here. This approach is based on space partition constructed from the set of points locating the position of cells. This spatial partition from Voronoi paving is considered to be a set of individual forms which permits calculation of three parameters which are characteristic of the population topography, (i) RFav, the average roundness factor of those forms, (ii) RFH, a measure of the roundness factor homogeneity and (iii) AD, a measure of their area heterogeneity (also called area disorder). A characterization of the space defined by the three parameters, is obtained by simulation of spatial perturbations of various theoretical populations. These theoretical populations have been subjected to factors such as aggregation and randomization of positions by an increase of spatial degrees of freedom. The use of a diagram involving RFav, RFH and AD turns out to be a powerful tool for the determination of the intrinsic disorder of a cellular population. Furthermore, it makes it possible to determine for a given set of cells, a model including its nearest homogeneous set, and the intrinsic disorder to which it refers. Finally, this model appears to be a useful way to quantify topographies and study order and disorder in many point sets by a simple reading in the parametric space defined by RFav, RFH and AD.