Mathematical analysis of corneal oxygenation

Abstract

Purpose: To develop a quasi steady state model for the time course concentration profile describing the oxygen diffusion and consumption in a multilayered corneal tissue and investigate the effect of various model parameters on the oxygen concentration for open and closed eyes. Method: A simple mathematical model for the oxygen transport in multilayered corneal tissue was developed using Fick’s law of diffusion and Michaelis-Menten kinetics of metabolism. A Crank-Nicoloson finite difference scheme of the equation describing the oxygen diffusion and consumption was written, in which spatial diffusive terms were approximated by central differences while the temporal terms were approximated by average of forward and backward time differences. A system of linear equations obtained from the Crank-Nicholoson finite differences schemes was solved by the Thomos Algorithm. Result: The model predict that oxygen tension without contact lens for an open and closed eye increases along the distance from the aqueous side in each of the layers and the partial pressure gradient in the stroma is higher than that in the epithelium and endothelium layers. It is also observed that the oxygen tension with contact lens in the steady and transient stares, in case of low oxygen permeability of lens decreases along the distance from the aqueous side to the stroma, whereas, at higher oxygen permeability of the lens it increases along the distance for open and closed eyes. Conclusion: Oxygen tension as observed in the cornea of an open eye with or without contact lens is higher than that in closed eye. Also at a high oxygen permeability of contact lens enhance the oxygen tension significantly than that of low oxygen permeability. Keywords: Oxygen transport, finite difference, metabolism, oxygen consumption, pressure gradient.