Mathematical Modelling of Intraretinal Oxygen Partial Pressure

Abstract

Purpose: The aim of our present work is to develop a simple steady state model for intraretinal oxygen partial pressure distribution and to investigate the effect of various model parameters on the partial pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model for intraretinal oxygen partial pressure distribution was developed using Fick's law of diffusion, Michaelis-Menten kinetics, and oxygen delivery in the inner retina. The system of non-linear differential equations was solved numerically using Runge-kutta Nystroms method. Result: The model predicts that a decrease in the blood flow rate reduces the partial pressure of oxygen in adapted conditions of light and darkness. It was also observed that the partial pressure of oxygen was higher in adapted light conditions than in adapted dark conditions. Conclusion: The partial pressure of oxygen observed in different layers of the retina was reduced by a decrease in the blood flow rate in the inner retina. The pressure becomes minimum when there is no blood flow in the inner retina. This minimum pressure may fall below the critical level of oxygen partial pressure and affect the retinal function. In order to restore normal retinal function, extreme hyperoxia may assist to make the choroid capable of supplying oxygen to the whole retina during total retinal artery occlusion.