Birth and death simulation of human corneal endothelium cells
Abstract
The human corneal endothelium, the most posterior layer of the cornea, is a monolayer of flat cells that are perfectly joined and are essential for maintaining its transparency over time. Long considered to be non-regenerative in adults, several recent studies have nevertheless shown that some cells can proliferate in the periphery of the endothelium. At birth, the endothelial cell density (ECD, number of cells per unit area) is very high and the
endothelial mosaic consists of perfect hexagons. During life, some cells disappear, others divide and the mosaic reorganizes itself: its polymorphism and polymegethism increase. Thus, after 20 years, the central WFD decreases by 0.6% per year, remaining higher in the periphery. However, endothelial homeostasis remains poorly understood, in particular how new peripheral cells partially compensate for the disappearance of other more central cells. The cells form a regular pavement, which can be considered mathematically as a Voronoi pavement without holes. We simulated the organization and reorganization of the cells by means of a centered Voronoi diagram, which was created iteratively by moving the seeds of the diagram to the geometric center of the cells. The initialization of the seeds was done with a uniform distribution, and a few centering iterations were sufficient to have cells close to hexagons. Subsequently, we simulated the evolution through cycles of cell death/birth, followed by cell centering. This new simulation tool will allow us to test many hypotheses on the number and frequency of cellular events (mitosis and death) in order to elucidate endothelial pathophysiology.