Mathematical models of the spatial distribution of retinal oxygen tension and consumption, including changes upon illumination

Abstract

To better understand oxygen utilization by the retina, a mathematical model of oxygen diffusion and consumption in the cat outer, avascular retina was developed by analyzing previously recorded profiles of oxygen tension (PO₂) as a function of retinal depth. Simple diffusion modelling of the oxygen distribution through the outer retina is possible because the PO₂ depends only on diffusion from the choroidal and retinal circulations and on consumption within the tissue. Several different models were evaluated in order to determine the best one from the standpoints of their ability to represent the data and to agree with physiological reality. For the steady state one-dimensional diffusion model adopted (the special three-layer diffusion model), oxygen consumption was constant through the middle layer and zero in the layers near the choroid and near the inner retina. On the average, the oxygen consuming layer, as found by nonlinear regression for each profile, extended from about 75% to 85% of the retinal depth from the vitreous. This is a narrow band through the mid-region of the photoreceptors. Oxygen consumption of the entire avascular retina, determined from fitting eight PO₂ profiles measured in light-adapted retinas, averaged 2.7 ml O₂(STP)/(100 g tissue · min), while the value determined from fitting thirty-two PO₂ profiles measured in dark-adapted retinas averaged 4.4 ml O₂(STP)/(100 g tissue · min). Consumption in the light was thus only 60% of that in the dark. This suggests that the outer retina is at greater risk of hypoxic injury in the dark than in the light, a fuinding of considerable clinical significance.