(582h) Oxygen Diffusion and Reaction in the Human Cornea

Diffusion of oxygen from the ambient air into the cornea is critical to maintaining the health of the human eye. Eye diseases, dysfunctions, and prolonged contact-lens wear can compromise oxygen diffusion that is critical to the metabolic reactions in the cornea. Measuring the properties of the cornea that are critical to maintaining good eye health and treating eye conditions is challenging owing to the thinness (~500 μm) of the cornea and maintaining its transparency. An innovative technique developed by Bonanno and co-workers [1] [2] involves placing on the eye a contact lens whose inner surface is coated with a photosensitive dye that responds to the oxygen tension (partial pressure). This technique permits determining the oxygen tension at the interface between the cornea and the contact lens and has provided the defining data set used by researchers in the field of ophthalmology. Since the thickness and oxygen transmissivity of the contact lens are known, the measured oxygen tension at the cornea/lens interface and the known oxygen tension at the cornea/air interface permit determining the oxygen mass-transfer flux into the cornea. A mathematical model for the oxygen diffusion and reaction within the cornea can then be developed from which one or more of the unknown corneal properties can be extracted via numerical optimization methods. Several prior studies have used this procedure to extract parameters such as the oxygen consumption rate, the oxygen diffusion coefficient, and the oxygen solubility in the cornea. However, the values of the extracted parameters vary considerably. Moreover, the oxygen diffusion coefficient determined in prior studies was found to be larger than the diffusion coefficient of oxygen in pure water. This is problematic since the cornea consists of ~78% water, the remaining component being collagen fibrils in which oxygen is nearly insoluble. Hence, some researchers [3] [4] have suggested that the diffusion coefficient is not constant within the cornea. Although a few prior studies have allowed for a different constant diffusion coefficient in the three main layers of the cornea [5] [6] [7], prior modeling studies have not incorporated any functional dependence of the oxygen diffusion coefficient on the oxygen tension.

The present study allows for the dependence of the oxygen diffusion coefficient D (cm²/s) on the oxygen tension given by the following functional form:

D = α exp(βP)

Where P is the oxygen tension (mm Hg), and α (cm²/s) and β (mm Hg)^‒1 are parameters that can be obtained by fitting a model for the diffusion-reaction process to the data for the oxygen tension at the cornea/lens interface. This functional form is suggested by the prior study of Del Castillo and co-workers [3] who found that the “constant” diffusion coefficient determined from fitting their model to the data of Bonanno and co-workers was strongly dependent on the oxygen tension at the cornea/lens interface and increased markedly at an oxygen tension ~90 mm Hg.

An analytical solution for the steady state diffusion and reaction of oxygen in the human cornea was obtained that permits putting narrow bounds on the oxygen consumption rate, thereby eliminating the need to extract this parameter from the data for the oxygen tension at the cornea/lens interface. Sensitivity and propagation-of-error analyses were done to determine how the error in the measured oxygen tension at the cornea/lens interface affects the magnitude of the parameters extracted from models fit to these data. The estimated average error of 2.4% in the measured oxygen tension at the cornea/lens interface was found to cause errors of 36% to 40% in the extracted parameters α and β that translate to an error of as much as 69% in the diffusion coefficient predicted by the above equation.

The solid line in Fig. 1 shows the diffusion coefficient predicted by the above equation as a function of the oxygen tension in the human cornea. The predicted diffusion coefficient is less than the diffusion coefficient of oxygen in pure water that is shown by the short-dashed line within the lower error bound that is shown by the long-dashed line. The straight-line asymptotes at very low and very high oxygen tensions intersect at an oxygen tension of 88.2 mm Hg that agrees well with the work of Del Castillo and co-workers [3] who identified an intersection point of ~90 mm Hg that they interpreted as arising from a kinetic transition owing to metabolic reactions occurring in the Krebs cycle and other corneal reactions.

The predicted oxygen tension profiles in the human cornea for the seven contact lenses considered in this study are shown in Fig. 2. The two N&D lenses with the highest transmissibility coefficients show the highest oxygen tension, whereas the Advanced contact lens with the lowest transmissibility coefficient shows the lowest oxygen tension as would be expected. However, an unexpected result is that the lenses with the lowest transmissibility coefficients show regions within the cornea wherein all the oxygen is depleted.

To determine the effect of assuming a constant diffusion coefficient, the diffusion coefficient given by the above equation was averaged across the thickness of the cornea and used to determine the oxygen tension profiles shown in Fig. 3. In marked contrast with the predictions shown in Fig. 2, no regions are predicted in Fig. 3 within which all the oxygen is depleted. This underscores the importance of allowing for the oxygen dependence of the diffusion coefficient. The implication of this is that the metabolic reactions in the cornea that are driven by oxygen will be impacted but might not be predicted if the oxygen dependence of the diffusion coefficient is not considered.

[1] Bonanno, J. A., Stickel, T., Nguyen, T., Biehl, T., Carter, D., Benjamin, W. J., Soni, P. S., Estimation of human corneal oxygen consumption by noninvasive measurement of tear oxygen tension while wearing hydrogel lenses. Invest. Ophthalmol. Vis. Sci. 2002, 43, 371–376.

[2] Bonanno, J. A., Clark, C., Pruitt, J., Alvord, L., Tear oxygen under hydrogel and silicone hydrogel contact lenses in humans. Optometry and Vision Science 2009, 86, E936–E942.

[3] Del Castillo, L. F., Ramírez‐Calderón, J. G., Del Castillo, R. M., Aguilella‐Arzo, M., Compañ, V., Corneal relaxation time estimation as a function of tear oxygen tension in human cornea during contact lens wear. J Biomed Mater Res 2020, 108, 14–21.

[4] Daneh-Dezfuli, A., Zarei, M. R., Jalalvand, M., Bahoosh, R., Simulation of time-fractional oxygen diffusion in cornea coated by contact-lens. Mech Time-Depend Mater 2023, 27, 1225–1235.

[5] Chhabra, M., Prausnitz, J. M., Radke, C. J., Modeling corneal metabolism and oxygen transport during contact lens wear. Optometry and Vision Science 2009, 86, 454–466.

[6] Moreno, V. C., Aguilella-Arzo, M., Del Castillo, R. M. del, Espinos, F. J., Del Castillo, L. F. , A refined model on flow and oxygen consumption in the human cornea depending on the oxygen tension at the interface cornea/post lens tear film during contact lens wear. J. Optom. 2022, 15, 160–174.

[7] Aguilella-Arzo, M., Compan, V., A three-dimensional model to describe complete human corneal oxygenation during contact lens wear. J. Biomed. Mater. Res. Part B 2023, 111, 610–621.