C L I N I C A L A N D E X P E R I M E N T A L OPTOMETRY ORIGINAL PAPER

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1 C L I N I C A L A N D E X P E R I M E N T A L Corneal oxygenation during contact lens wear Brennan OPTOMETRY ORIGINAL PAPER Corneal oxygenation during contact lens wear: comparison of diffusion and EOP-based flux models Clin Exp Optom 2005; 88: 2: Noel A Brennan MScOptom PhD FAAO FCLSA Brennan Consultants, Auburn Village, Victoria, Australia Submitted: 13 September 2004 Revised: 18 September 2004 Accepted for publication: 22 October 2004 Purpose: The aim of this study was to compare corneal oxygen flux values derived from an oxygen diffusion model, with estimates from a model in which equivalent oxygen percentage (EOP) values were substituted for the post-lens tear film oxygen tension in Fick s law. Methods: A previously described five-layer corneal oxygen diffusion model was found to artefactually allow theoretical oxygen consumption, when the predicted oxygen tension fell to zero. Consequently, an eight-layer diffusion model was constructed, with consumption set to zero at points within the cornea, where predicted oxygen tension falls to zero. Post-lens tear layer thickness was corrected to more contemporary estimates. The eight-layer and EOP-based anterior corneal oxygen flux estimates were compared across the range of commonly encountered contact lens Dk/t values. Results: The eight-layer model overcomes deficiencies in the five-layer model and provides predicted values that are remarkably similar to the EOP-based model. Open and closed eye anterior corneal oxygen flux in the absence of contact lens wear was estimated at 7.8 and 7.6 µl/cm 2 /hr for the open eye and 6.0 and 6.1 µl/cm 2 /hr for closed eye for the diffusion and EOP-based models, respectively. Conclusions: The diffusion model supports the EOP model in that there is minimal oxygen benefit to be gained by increasing Dk/t above the Holden-Mertz criteria of 24 and 87 x 10 9 (cm/sec)(ml0 2 /ml.mmhg) during open and closed eye wear, respectively. The eight-layer model is suitable for further definition of corneal oxygenation during contact lens wear. Key words: contact lenses, models, oxygenation, oxygen flux Hypoxia is responsible for a broad spectrum of corneal changes in response to contact lens wear. 1,2 Despite the importance of oxygen supply to corneal physiology, accurate quantification of oxygenation beneath a contact lens remains elusive. 3,4 Improved methods for describing the supply of oxygen to the cornea are desirable in the quest for enhanced safety of contact lenses, particularly with overnight wear. Oxygen flow through a contact lens can be investigated with the aid of basic diffusion equations, which have been welldefined in the engineering literature. 5 Diffusion of oxygen through a contact lens obeys Fick s Law, which states j = (P 1 - P 0 ) * Dk/t where j is the oxygen flux through the lens, P 1 and P 0 are the partial pressures of oxygen at the front and back surfaces of the lens, respectively and Dk/t is the oxygen transmissibility of the lens. 6 Direct calculation of flux is difficult because the oxygen tension P 0 under the contact lens is not easily measured. As a result, two indices have evolved for the practical assessment of corneal oxygenation: Dk/t, which is a physical property of a lens and can be 103

2 determined as a benchtop measurement 6 and equivalent oxygen percentage (EOP), which is an attempt to ascertain P 0 by comparing oxygen diffusion from a Clark polarographic oxygen sensor into the cornea following contact lens removal to the diffusion observed, when the cornea is exposed to gases of known oxygen tension. 7 Fatt 3 has explained the inadequacy of Dk/t and EOP to fully define corneal oxygenation. He claimed that Dk/t used by itself as a measure of lens performance has been a disappointment. It does not allow calculation of oxygen flux into the cornea and there is no way of knowing whether a given lens provides oxygenation of the cornea similar to oxygenation when no lens is present. The introduction in the late 1990s of high Dk materials for continuous wear has compounded the problem. While the relationship between Dk/t and corneal oxygen flux could be expected to be approximately linear for low Dk/t values [say under 50 x 10 9 (cm/sec)(ml0 2 / ml.mmhg)], this is not the case for higher Dk/t values. Dk/t alone does not provide sufficient information to gauge the relative oxygenation between different contact lens types on the eye. Fatt 3 also discounts the value of EOP measurement on the basis of theoretical rationale, reliability and difficulties of measurement. In 1999, Harvitt and Bonanno 8 published a model that addresses some of these problems. This work reassesses the oxygen diffusion profile models pioneered by Fatt 9,10 and Fatt, Freeman and Lin 11 incorporating a correction for oxygen consumption induced by corneal acidosis. Harvitt and Bonanno 8 used a five-layer mathematical model incorporating values they deemed to be the best available estimates for the various parameters used in the model. Although the authors did not present data for anterior corneal oxygen flux, it is relatively simple to calculate directly from the simultaneous equations used to generate their oxygen profiles. In a different approach, I have substituted values of EOP derived for a range of lenses on human eyes for P 0 in Fick s law. 12 Using a mathematical technique to dampen instability of the model caused by small differences in oxygen tension across Endothelium Q 1 = A Stroma Figure 1. Illustration of the eight-layer oxygen diffusion model for cornea covered by a contact lens. The curves represent an approximate po 2 profile across the cornea for given scenarios. The layers are numbered sequentially from the endothelium and Q n is the consumption of the nth layer. A. po 2 is always > 0, so intra-corneal layer Q 0 for any n B. po 2 within the stroma and Q 3 C. po 2 within the stroma and epithelium, so Q 3 = Q 4 = Q 5 (The positions of the boundaries between layers 2 and 3, 3 and 4, and 5 and 6 are determined by iteration.) a lens of high Dk/t, I produced estimates of oxygen flux for open and closed eye conditions across the Dk/t range. In this paper, I compare the flux predictions made by the different approaches of the diffusion model and the EOP-based model, and explore the implications of these findings with respect to our understanding of corneal oxygenation during contact lens wear. Epithelium METHODS Tears Q 7 Endothelium Q 1 = Tears Q 7 B Stroma Epithelium Endothelium Q 1 = Tears Q 7 C Stroma Epithelium Contact lens Q 2 = 2.29 Q 3 = 2.29 Q 4 = 2.29 Q 5 = 25.9 Q 6 = 25.9 Q 8 = Contact lens Q 2 = 2.29 Q 3 Q 4 = 2.29 Q 5 = 25.9 Q 6 = 25.9 Q Contact lens Q 2 = 2.29 Q 3 Q 4 Q 5 Q 6 = 25.9 Q Anterior corneal oxygen flux was calculated for the five-layer model according to the technique described by Harvitt and Bonanno. 8 Values for the various parameters were taken from that paper, estimated from their graphs or calculated, if not explicitly provided. The one exception to this choice of values was the post-lens 104

3 Partial pressure of oxygen (mmhg) endothelium stroma epithelium contact lens b a (Microsoft Corporation, Redmond, WA, USA) to prevent the predicted oxygen tension becoming a negative value. Flux estimates for the EOP-based flux model were taken directly from my earlier paper. 12 The direct comparisons of this fluxbased model to the profile models were performed without correction for acidosis in the five- and eight-layer models. This approach was taken because EOP measurements are taken within five minutes of lens application and thus the measures would not be expected to be reflective of conditions under which acidosis occurs Figure 2. Examples of oxygen profiles comparing the five-layer model (broken lines) proposed by Harvitt and Bonanno 8 to the eight-layer model (unbroken lines), as developed in this study, for contact lenses with Dk/t of 6 (a) and 22 (b) under open eye conditions. The boundaries between the intra-stromal and intraepithelial layers, as determined by an iterative procedure, are shown (dotted lines). tear film thickness. Harvitt and Bonanno used a value of 45 µm for the thickness of this layer, which may occur with some steep rigid lenses but is unlikely with soft lenses. Recent estimates suggest that a post-lens tear layer thickness of two to 12 µm may be more appropriate for soft lenses The technique of Nichols and King- Smith 14 provides the most direct method for obtaining the post-lens tear film estimate. As the mean value that they found was at the low end of the range of estimates, I selected a value of three microns for the purpose of this paper. During this investigation it became apparent that the five-layer model foundered when predicted oxygen tension fell below zero within the cornea, to the extent that estimated total corneal oxygen consumption remained constant even when sections of the cornea became anoxic and the anterior corneal oxygen tension fell to zero. To prevent the model from yielding negative partial pressures, which do not Position (cm) 0.07 exist, Harvitt and Bonanno 8 set such values to zero, however, this treatment does not prevent consumption in the mathematical sense, in the region at which the predicted oxygen concentration is zero. The artefact affects derived estimates of overall oxygen consumption, flux into the cornea and indeed the profiles of oxygen tension. To compensate, I derived a new model using the same matrix principles as described by Harvitt and Bonanno 8 that allowed for zero oxygen consumption at regions of the cornea where oxygen pressure fell to zero. To achieve this, an eightlayer model was required. Figure 1 illustrates the principle of this model. The stroma is divided into three separate layers and the epithelium into two layers. The key to the model is that the consumption of layers 3, 4 and 5 can be set to zero as necessary. The position of the interface between the intrastromal and intraepithelial layers was determined by iteration using the Excel X Solver add-in RESULTS Figure 2 plots some predicted oxygen tension profiles demonstrating the differences between the five-layer and eightlayer models. For scenarios in which the oxygen falls to zero at some point within the cornea, the eight-layer model predicts greater oxygen concentrations across the corneal profile, a higher anterior corneal oxygen tension but lower anterior corneal oxygen flux values. Figure 3 plots calculated flux versus Dk/t for the five-layer model without compensation for altered consumption of the layers induced by acidosis and EOP models. It is immediately noticeable that the values correspond very well for the five-layer and EOP-based models, although there is some departure below a Dk/t of 100 x 10 9 (cm/sec)(ml0 2 /ml.mmhg) for the closed eye situation. It is at these transmissibility values that the consumption artefact of the five-layer model becomes manifest. Open eye anterior corneal oxygen flux, in the absence of contact lens wear, was estimated at 7.8 and 7.5 µl/cm 2 /hr for the diffusion and EOP-based models, respectively. For closed eye conditions in the absence of lens wear, the model predicted anterior corneal oxygen flux of 5.8 and 6.1 µl/cm 2 /hr for the diffusion and EOP-based models, respectively. The data for the five-layer model was truncated at lower Dk/t values as the oxygen tension is predicted to fall to zero at the anterior corneal boundary; it follows that the flux into the cornea must be zero in this case. Use of the eight-layer model corrects for 105

4 9 9 Anterior corneal oxygen flux (µl/cm 2.hr) open eye closed eye Anterior corneal oxygen flux (µl/cm 2.hr) open eye closed eye Dk/t x 10-9 (cm/sec)(mlo 2 /ml.mmhg) Dk/t x 10-9 (cm/sec)(mlo 2 /ml.mmhg) Figure 3. Comparison of anterior corneal oxygen flux predicted by the five-layer Harvitt-Bonanno model 8 (broken line) and the EOP-based model 12 (unbroken line) for open and closed eye conditions. Acidosis correction is not included. Figure 4. Comparison of the anterior corneal oxygen flux predicted by the eight-layer model developed in this study (broken line) and the EOP-based model 12 (unbroken line) for open and closed eye conditions. Acidosis correction is not included. Dk/t This study Compan et al 16 Huang et al 17 8-layer model EOP model Open eye Closed eye Table 1. Estimates from various studies of anterior corneal oxygen flux (µl/cm 2.hr) versus Dk/t for lenses representative of those commercially available the discrepancy of the five-layer model and yields predicted values that match the EOP-based model remarkably well (Figure 4). Flux estimates in the absence of contact lens wear are the same as for the five-layer model, as the eight-layer model corrects for the scenario when predicted oxygen tension falls to zero within the cornea and this occurs with wear of contact lenses with lower Dk/t values. DISCUSSION Two other studies have recently provided estimates of anterior corneal oxygen flux during contact lens wear. 16,17 Table 1 shows flux for Dk/t values representative of commercially available contact lenses derived from these studies and from both models used in this paper. In general, the numbers are close across the studies with the similar trend of diminishing returns in flux for increasing Dk/t. Both of the studies 16,17 used a methodology proposed by Fatt and Ruben, 18 based around the concept of biological oxygen apparent transmissibility (BOAT). The BOAT model is basically a simplified version of the diffusion model used here, except that the cornea is approximated as a single rather than eightlayer, system. Limitations of the single layer model may explain the deviations between the various models. The predicted values of anterior corneal oxygen flux at infinite Dk/t are consistent with many previously derived empirical values from normal human eyes in the absence of contact lens wear. 4 The similarity of the values from these studies is not absolute proof that any of the models are correct, and recent empirical estimates of anterior corneal oxygen tension by Bonanno and co-workers 19 using an oxygen sensitive phosphorescent dye are not consistent with the anterior corneal flux values predicted here. Further research is necessary to reconcile these differences. Holden and Mertz 20 determined critical Dk/t values of 24 and 87 x 10 9 (cm/sec) 106

5 (ml0 2 /ml.mmhg) to avoid increases in corneal thickness characteristic of open and closed eye conditions, respectively. The models here support these criteria, predicting that anterior corneal oxygen flux is approximately 90 per cent of maximum at these Dk/t values. Furthermore, they support Fatt s argument 3 that Dk/t provides a poor linear comparator with oneye oxygen performance of contact lenses; large changes in Dk/t above these values produce minimal change in anterior corneal oxygen flux for the given conditions. Fatt s further criticism of the Dk/t concept, that it fails to indicate how closely the oxygen consumption beneath a contact lens matches that when no lens is in place, is also resolved by use of these flux models. As anterior corneal oxygen flux is the volume of oxygen crossing the tear-epithelial interface per unit time, this parameter is of greater value in investigating the hypoxic consequences of contact lens wear than, say, anterior corneal oxygen tension or the Dk/t of the contact lens. It should be borne in mind that flux is not the ultimate determinant of corneal oxygenation. When the anterior flux is high, oxygen may flow through the cornea and into the anterior chamber. When the anterior oxygen supply decreases and flux into the cornea falls, the posterior region of the cornea may derive its oxygen from the anterior chamber. All of the cornea may remain fully oxygenated in both of these scenarios, yet the anterior flux values are different. Further exploration of corneal oxygenation during contact lens wear should investigate methods for describing the total corneal consumption and this will be the subject of a forthcoming paper. The similarity of the estimates of oxygen flux between these models is striking but, in large part, may be coincidental. The values for parameters used in the oxygen profile models were based largely on the values used by Harvitt and Bonanno. 8 Variation in estimates of layer thickness, baseline layer oxygen consumption or changes in consumption under different environmental stresses produce different results. Harvitt and Bonanno 8 used estimates for epithelial and total corneal thickness of approximately 40 and 495 µm, respectively. Other measures suggest human corneal epithelial thickness averages at least 50 µm and possibly 60 µm Recently, Doughty and Zaman 28 performed a metaanalysis of pachymetry studies and determined a mean total corneal thickness of 534 µm. Incorporation of these larger thickness estimates at constant volumetric consumption rates leads to higher estimates of anterior corneal oxygen flux, higher total corneal oxygen consumption and lower partial pressure of oxygen through the corneal profile. The eight-layer model is sensitive to changes in consumption rate assigned to the various corneal layers. The phosphorescent dye estimates of anterior corneal oxygen tension by Bonanno and co-workers 19 would be consistent with consumption rates over three times greater for open eye conditions and over six times greater for closed eye conditions. Under such circumstances, large sections of the stroma would be anoxic during eye closure in the absence of contact lens wear and inclusion of contact lenses in the model would exacerbate the predicted effect. Importantly, increases in consumption of this order of magnitude do not strongly impact on the finding presented here that there are minimal differences in anterior corneal oxygen flux for large changes in Dk/t above Dk/t values of 24 and 87 x 10 9 (cm/sec)(ml0 2 / ml.mmhg) for open and closed eye, respectively (unpublished data). As well as some uncertainty in the baseline consumption rate, temporary changes in oxygen consumption may result from environmental stresses. Hypoxia may lead to stromal acidosis which has been associated with increased oxygen consumption in mouse cornea in vitro. 29 This leads to a paradoxical effect in which anterior oxygen flux peaks in the Dk/t range of 20 to 70 and 50 to 100 x 10 9 (cm/sec)(ml0 2 / ml.mmhg) for open and closed eye respectively (unpublished data). In the eight-layer model presented here, the influence of acidosis was not included, primarily because measurements used in the EOP model represent a short-term phenomenon and acidosis is unlikely over this time. Indeed, the time course of acidotic increase in oxygen consumption is uncertain. Some investigators have reported a reduced anterior corneal oxygen flux following a longer term period of contact lens wear, 30,31 which would appear to be inconsistent with the findings of Harvitt and Bonanno. 29 Further, it has been reported that in human eyes there is a decrease in corneal oxygen uptake in response to tear film acidosis. 32 Other factors, which might influence corneal layer consumption rates, such as injury, neural activity and diurnal variation, also warrant further investigation. There is evidence of a range of adaptive mechanisms during hypoxia in eukaryotic cells 33 and specifically in the cornea. 34 The eight-layer model developed here assumes a dualistic nature of corneal cellular responses to hypoxia, in that oxygen consumption is either at a normal rate or zero. The assumption is based on evidence from other mammalian cells that maintain oxygen consumption at a consistent rate when oxygen tension is above approximately one millimetre of mercury at the mitochondria. 35 When the oxygen tension falls below this amount, consumption will fall rapidly towards zero, as oxygen tension approaches zero. Theoretical examination of the diffusion model suggests that it is robust for considerable departure of corneal cells from this threshold for constant oxygen consumption (unpublished data). Indeed, the eight-layer model offers a preferred paradigm for further investigation of corneal oxygenation. It is more versatile than the EOP-based model, it incorporates advances since the development of the earlier models of Fatt and coworkers, 9,33,34 corrects the consumption artifact of the Harvitt-Bonanno model 8 and is more comprehensive than the single layer models. 16,17 In summary, oxygen flux models based on oxygen diffusion profiles and EOP provide highly comparable results. While there are many aspects of corneal oxygenation during contact lens wear still to be fully defined, the data presented in this paper support the concept of Fatt that Dk/t is an inadequate descriptor of corneal 107

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