Oxygen Flux : What’s it all about?

Noel Brennan Noel Brennan is director of Brennan Consultants Pty Ltd, an independent private research consulting company.  His principal research interest is the interaction between the eye and contact lenses and associated care products. Dr Brennan is an optometrist with both Masters and PhD degrees.  He was formerly an academic staff member at the University of Melbourne, reaching the level of Reader and Associate Professor.  As a Senior Fulbright alumnus, Dr Brennan studied with David Maurice at Stanford University. He also serves as a councillor of the International Society of Contact Lens Research.  He has lectured internationally and published extensively.

Although we all know that oxygen is key to maintaining corneal health during contact lens wear, not all agree on how much oxygen is needed, nor on how we can best assess the oxygen needs of our lens wearers.

At present, there is no reliable or clinically useful technique for measuring the amount of oxygen (Po) beneath a lens and practitioners rely on indirect measures such as equivalent oxygen percentage (EOP), where the flow of oxygen is estimated from measurement of the corneal oxygen uptake rate immediately after a lens is removed, or from models of oxygen consumption across the cornea, to predict oxygen flow to the eye during lens wear.

The first model of oxygen distribution across the cornea during contact lens wear was proposed by Hill and Fatt. This model is based on Fick’s Law of diffusion and states that the greater the difference in oxygen tension on either side of a lens, the greater the driving force across the lens, and that the greater the Dk/t, the more oxygen will flow. While several researchers agree that there is a ‘law of diminishing returns’ ie a level of Dk/t beyond which no further increases in oxygen flow (flux) will be gained, researchers do not agree what this level of Dk/t may be for daily and extended wear. More recently corneal oxygen consumption (%Q) has been proposed as an alternative method for predicting the oxygen needs of the cornea during lens wear.

In the following  editorial Noel Brennan explores the concept of corneal oxygen consumption.

Fatt commented in his 1996 paper that oxygen transmissibility (Dk/t) has been a ‘disappointment’, correctly pointing out that it fails to inform how much oxygen actually gets to the cornea, how one lens compares to another in terms of the amount of oxygen reaching the eye and how a given lens compares to the no-lens situation [1]. 

He advocated using flux as a better measure of corneal oxygenation and numerous authors have since made determinations of the relation between flux and lens Dk/t.  However, the anterior corneal oxygen flux, that is, the amount of oxygen that “reaches the eye” is not necessarily the amount of oxygen available for the cornea to metabolize.  What we desire to know is the amount of oxygen that the cornea consumes under a given scenario [2]. Since oxygen can also pass across the back surface of the cornea, the real amount of oxygen that the cornea uses will equal the net flux across both surfaces.

Corneal oxygen consumption can not currently be directly measured, so it is best determined using oxygen diffusion equations.  The features of such calculation are as follows:

• The mathematics tying these variables together comes from solid engineering background in the form of universally accepted diffusion theory - the diffusion theory itself will never be wrong, only the input parameters and handling of the equations may be inaccurate.
• Incorporation of the numerous contributory parameters, such as corneal and tear layer thickness and permeability, corneal layer consumption rates, and boundary conditions as well as contact lens Dk/t enables, in principle, comprehensive definition of oxygen use by the cornea.
• Oxygen diffusion equations enable not only total corneal oxygen consumption to be determined but also other parameters of interest, such as anterior corneal pO2, flux at both surfaces, partial pressure profiles, position of borders of regions within the corneal layers that are hypoxic and local oxygen consumption. 
• Expression of the approach in mathematical terms allows easy scrutiny of technique and assumptions by other researchers.  Empirical corroboration is also crucial, but is subject to methodological quirks of individual laboratories, which are often hidden until expensive replication of work is conducted.
• ‘What-if’ scenarios can be easily and cheaply created using diffusion theory by varying the input parameters to test theories and assess the reasonableness of experimental claims against other known aspects of corneal physiology.
• There is inherent uncertainty in some of the input parameters; these may vary further between individuals and indeed with oxygen concentration.  Such uncertainty can be controlled, in part, by calculating relative consumption estimates (%Q) and by tailoring theoretical development to established experimental results.
• The %Q paradigm can be plotted across the corneal profile to ascertain oxygen delivery beneath contact lenses in the corneal periphery.
• Hypoxic regions of the cornea can be quickly recognized as any part of the cornea at which %Q does not equal 100%.

Figure 1 graphs %Q vs Dk/t, as calculated according to a publication in Optometry and Vision Science last year [2].  One observes that oxygen consumption for the open eye is nearly linear with Dk/t for values under 18, but essentially flatlines above this value.  For the closed eye, the “law of diminishing returns” kicks in around a Dk/t value of 50, above which there are only marginal gains in net flux for increasing Dk/t values.  These estimates are supported by other work on diffusion theory [3-6], empirically derived EOP values [7-9], corneal swelling data [7] and flux measurements into the eye in the absence of a contact lens [10-13].

Figure 1: Percentage corneal oxygen consumption versus contact lens Dk/t relative to no-lens situation as predicted by oxygen diffusion theory [adapted from reference 2].

Critics of this work have generally argued that the amount of oxygen reaching the cornea is proportional to Dk/t- a scientifically implausible situation- and have failed to date to provide a specific alternative proposal relating corneal oxygenation to Dk/t.  In a new twist, Holden and co-workers claim that anterior corneal oxygen flux during open eye contact lens wear decreases above Dk/t values of around 90 [9].  Such a scenario is at least consistent with the proposition from oxygen diffusion equations that there is not a continual increase in oxygen reaching the cornea with increasing Dk/t.  Holden explains his new finding by theorizing that the cornea undergoes hypoxic stress at Dk/t values about and below 90, leading to greater demand by the tissue.  Research by Harvitt and Bonanno on increased oxygen consumption with corneal acidosis is not inconsistent with such thinking [3].  However, the empirical data is far from convincing.  And while such a mechanism is not impossible, the theory is unproven and unlikely in the quantitative terms suggested when compared to the large body of literature on bioenergetics and mitochondrial kinetics.

The problem with higher Dk materials is that they have tended to be accompanied by higher material modulus, potentially leading to a range of undesirable performance characteristics.  The true oxygen benefits to the cornea of increasing Dk/t need to be characterised so that clinicians can make informed choices to achieve the best balance of contact lens properties. While corneal oxygen supply is ultimately dependent on contact lens Dk/t, the nature of the relationship has proven to be sufficiently obscure that new metrics are required.  The %Q paradigm offers an attractive alternative, and future developments in the field are likely to refine rather than redefine such an index.

Corneal oxygen consumption

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2. Brennan NA. Beyond flux: total corneal oxygen consumption as an index of corneal oxygenation during contact lens wear.  Optom Vis Sci 2005
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