Testing abnormality in the spatial arrangement of cells in the corneal endothelium using spatial point processes

The study of central corneal endothelium morphology is important in Ophthalmology. Some of the pathologies that could compromise endothelial cell morphology are trauma, cataract, surgery, use of contact lenses, corneal dystrophies or degenerations. The quantitative analysis of cell shape and cellular pattern is more sensitive in detecting subtle changes in endothelial morphology than cell density measurement or cell area analysis. In this paper, the morphology of the central cornea, the most important area from the point of view of vision, is studied through an associated bivariate spatial point pattern: the centroids of the cells and the triple points, that is, the points where three different cells converge. Nine different summary descriptors (widely used in the statistical analysis of spatial point patterns) have been used: the empty space distribution function; the nearest neighbour distribution function and Ripley's K-function for each type of point separately (centroids and triple points), plus the corresponding three versions of these functions in the bivariate case. A control sample with similar age and cell density and no known abnormality is associated to each patient. The above descriptors are calculated for the patient and the controls. Each descriptive of the patient is compared with the corresponding descriptors from the controls by means of a graphical analysis and a formal test. Some patients presenting different pathologies are analysed in detail. Endothelia considered morphologically abnormal by visual inspection, which were not detected by hexagonality or density analysis, could be distinguished from control endothelia by these new descriptors.