Oxygen transfer in the human cornea: Sensitivity and error-propagation analyses incorporating an oxygen-tension-dependent diffusion coefficient.

Eye diseases and prolonged contact-lens wear can decrease the corneal oxygen diffusion that is essential to metabolic reactions in the human eye. Measuring oxygen diffusion in the cornea is challenging because it is thin (∼500 μm) and its viability must be maintained. An innovative in vivo technique involves placing a contact lens on the corneal surface and its tear film. The inner surface of the contact lens is coated with a photosensitive dye that responds to the oxygen tension by phosphorescence quenching. Corneal properties such as the oxygen diffusion coefficient, maximum oxygen-consumption rate, and oxygen solubility can be extracted from the measured oxygen tension and contact-lens properties via a model for the diffusion process. Considerable variability is observed in the extracted properties that emanates from the model assumptions and uncertainties in extracting the properties. Prior studies suggest the diffusion coefficient depends on the oxygen tension, although a constant value has been assumed in the cornea or in its individual layers. This paper considers an oxygen-tension-dependent diffusion coefficient and puts narrow bounds on the maximum oxygen-consumption rate, thereby reducing the corneal properties that must be extracted. Scaling analysis indicates that the oxygen-tension dependence of the diffusion coefficient can never be neglected. A significant result is that the sensitivity and error-propagation analyses indicate that a small error in the measured oxygen tension can translate into large errors in the extracted properties. A measurement error of 2.6 % in the oxygen tension at the cornea/lens interface translates into an error of 76 % in the diffusion coefficient determined from the extracted parameters. This could be reduced considerably by eliminating the sample error via replicate experiments on the same contact lens and by developing improved and new analytical techniques for reducing the uncertainty in the input parameters used in the model for the diffusion process.