Measuring the spatial homogeneity in corneal endotheliums by means of a randomization test

Abstract

Quantification of regularity of cell sizes and the spatial arrangement of cells in corneal endotheliums becomes of a great importance associated to stress situations such as cataract surgery, corneal transplantation or implantation of intra-ocular lenses. A new index of regularity of the spatial distribution of cell sizes in corneal endotheliums is proposed. The corneal endothelium is described by means of a spatial marked point pattern (the cell centroids marked with the cell areas). The hypothesis of no dependency between mark and locations is tested by a Monte Carlo test. The new index is the p-value of the test validating the hypothesis. Pairs of endotheliums from different eyes of the same person are compared in terms of the traditional measures (density, hexagonality and coefficient of variation) and the new index. Results show how the index proposed can discriminate subtle morphological changes that cannot be detected by the commonly used indices.