Mathematical Model of Oxygen Transport in Cornea

The aim of present work is the development of a quasi-steady state model for the time course concentration profile describing the oxygen diffusion and consumption in a multilayered corneal tissue and investigation of the effect of various model parameters on the oxygen concentration for open and closed eyes. A simple mathematical model for the oxygen transport in multilayered corneal tissue was developed using Fick’s law of diffusion, Michaelis-Menten kinetics of metabolism. A Crank-Nicolson finite difference scheme of the equation describing the oxygen diffusion and consumption was written, in which spatial diffusive terms of the equation 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-Nicholson finite differences schemes was solved by the Thomas Algorithm in which successive improve approximate results are obtained.