Kinetics of corneal epithelial maintenance and graft loss. A population balance model

Abstract

We use a population balance model to study the mechanism and the rate of centripetal migration of epithelial cells, renewal of the corneal epithelial population by the cell derived from (progeny of) the limbal stem cells and the kinetics of the replacement of the donor corneal epithelium. The epithelial mass is constant under the normal circumstances and therefore the rate of cellular entry due to centripetal motion and mitosis into any epithelial volume must equal the cell loss from the same volume. The magnitude of the centripetal velocity and the rate of replacement of the donor tissue following keratoplasty are shown to depend only on the following directly quantifiable factors--the difference in the mitotic rates of the corneal and limbal epithelia and the radii of these two epithelia. The a priori model predictions are found to be in very good agreement with the observed centripetal velocities and the rate of corneal graft replacement. The model provides an independent support for the hypothesis that the stem cells for the corneal epithelium are located in the limbus and are responsible for a slow replenishment of the corneal epithelial cell. The model suggests some factors that diminish the centripetal supply of cells and thus provides insights into the pathogenesis of persistent corneal defects and delayed reepithelialization of defects and grafts. The model is suitable for interpreting and quantitatively correlating the influence of some epithelial alterations and drugs on the centripetal supply of epithelial cells.