Computational Model of Oxygen Transport in Retina and Optic Nerve

Abstract

 

Purpose

 

In order to increase our understanding of oxygen saturation patterns observed in retinal vessels, we propose a computational model to describe oxygen transport and its dependence on local, systemic and extrinsic factors, such as vessel width, blood flow, illumination and oxygen supplementation.

 

Methods

 

A mathematical model of arteriole-venule pairs and surrounding tissue was developed. Coupled non-linear partial differential equations describing convection, diffusion and interaction of oxygen with hemoglobin and oxygen-consuming tissue are solved numerically. Taking into account non-uniform blood-flow and hematocrit profiles, longitudinal and radial oxygen saturation and partial pressure gradients are calculated. The results are compared with measurements obtained with the Oxymap retinal oximeter (Oxymap ehf., Reykjavik, Iceland), as well as with data previously published by researchers using other methods.

 

Results

 

Oxygen saturation gradients along major retinal vessels reflect oxygen consumption of perivascular tissue, with a smaller component due to countercurrent exchange between closely spaced vessels. Our model predicts longitudinal saturation gradients consistent with those measured in retinal oximetry. Oxygen penetrates by diffusion into a perivascular tissue layer comparable in thickness to the capillary-free zone. A gradient of 1 - 4 % in saturation is predicted in central retinal vessels along the optic nerve. The model predicts reduced oxygen saturation with decreased blood flow. It helps explain a distribution width of 5 - 10 % in saturation in short segments of retinal vessels and the variability in saturation observed between normal eyes. According to the model, the 3 % increase in retinal arteriolar saturation observed in darkness can be accounted for by increased blood flow in the dark. Diffusion currents of oxygen in vitreous close to major retinal arterioles are predicted to be approx. 10^-6 ml O₂/cm²/sec, compatible with previously published results, obtained with polarographic methods.

 

Conclusions

 

Our model predicts retinal vessel oxygen saturation patterns that are consistent with those observed in retinal oximetry and helps us gain a quantitative understanding of some aspects of oxygen transport in the retina and optic nerve.

 

 

Saturation profile in central retinal vessels along 10 mm in optic nerve

 

Keywords: 473 computational modeling • 688 retina • 635 oxygen