Understanding the Values that Describe Oxygen Flux Through a Contact Lens
BY KENNETH A. LEBOW, OD, FAAO AND DAVID CAMPBELL-BURNS FC OPTOM,
FAAO, FACLP
JANUARY 1998
Oxygen permeability, oxygen transmissibility and equivalent oxygen percentage values can help you prescribe the most appropriate lenses for your patients, but only if you understand what they measure.
As contact lens practitioners, we aim to maintain corneal health when prescribing contact lenses. Oxygen flux to the corneal tissue is the single most important factor for determining corneal health, yet significant confusion exists in the literature regarding oxygen transmission characteristics of various contact lens materials and designs. Different measurement techniques can produce a wide variety of values for identical materials used by manufacturers to promote their products. Here we identify the variables that affect oxygen flow measurements and the clinical responses you can use to evaluate overall on-eye lens performance.
Oxygen Permeability
Oxygen permeability (Dk) is an intrinsic physical property of a material that describes in mathematical terms the rate of oxygen flow through that material. The diffusion coefficient of the material is "D"; "k" represents the solubility coefficient. Dk is exponentially dependent upon the water content rather than the chemical composition of the hydrogel material. The maximum limit for hydrogel materials is 80 Dk units.
Every material has a unique permeability that can be measured, but the actual numerical values obtained may be influenced by the measurement technique. Although a direct relationship does exist between water content and permeability, the values obtained are subject to a number of variables such as edge correction, boundary layer effect, electrode shape, temperature and inter-laboratory variation. Edge and boundary layer effects are the primary influences on the results, but the shape (curved or flat) of the electrode employed to measure Dk also plays a significant role. The boundary effect causes transmissibility and permeability to be underestimated, and the edge effect causes the opposite result. Thus, for a given 58 percent material, the published Dk value may vary between 22 and 35 Fatt units -- a 63 percent variation.
Oxygen Transmissibility
Oxygen transmissibility (Dk/l or Dk/t) describes a material's oxygen flux as it relates to a specific contact lens design made from that material. Contact lens thickness (l) is the key variable that differentiates contact lens transmissibility (Dk/l) from material permeability (Dk). Lens design variables such as refractive power, optic zone size, junction thickness, peripheral curve design and overall lens diameter influence contact lens thickness, so transmissibility values should be calculated based on central, zonal or harmonic mean lens thickness. To demonstrate this point, consider what happens in a prism ballasted toric hydrogel lens where the lens is thicker inferiorly. The corneal swelling response to varying transmissibility values across the contact lens surface produces localized areas of corneal edema that are almost totally dependent upon optical power, both sphere and prism.
Therefore, reporting Dk/l data using only nominal center thickness information can produce misleading values for oxygen transmissibility. Although this is especially true for low powered minus hydrogel lenses, transmissibility values for plus powered lenses may be more accurately stated using center thickness values only. Hence, within a range of contact lens parameters for a given material, some lenses will theoretically meet established criteria for extended wear, while others will be questionable for even daily wear. Figure 1 shows that although transmissibility through the center of the lens (Dk=27; -3.00D@0.06 ct) exceeds the criteria for safe daily wear, the increased thickness in the midperiphery could create an edematous environment. The same conclusion applies even if two materials with different water contents are used. While it is theoretically possible to design contact lenses of approximately the same transmissibility using materials with different permeabilities by adjusting the lens thickness, clinically significant variations can occur.
FIG. 1: The Dk/l through the midperiphery of this contact lens falls short of the criteria for safe daily wear, despite acceptable Dk/l values in the center.
Other key variables that influence actual on-eye transmissibility measurements include lens material, the temperature at which the measurement is taken, lens movement and, in hydrogel materials, water content and on-eye lens dehydration.
Transmissibility data is just as prone to variation and error as permeability data is because published values rarely state which lens thickness value is used for the calculation, i.e., center, zonal or harmonic mean thickness. The scale of these errors is considerable and can range from 23 to 36 Dk/l units for the same 58 percent lens design -- a 64 percent difference. The value obtained when the Dk is divided by the center thickness of a -3.00D lens is frequently used by the marketing departments of contact lens manufacturers to describe the performance of a particular lens design over the entire prescription range. If the eye derived its oxygen supply at the corneal apex only, this approach would be perfectly legitimate. Yet nothing could be further from the truth, particularly with minus lenses. A recent study by Efron and Fitzgerald has shown that lateral diffusion of oxygen in the cornea is minimal, indicating that only those Dk/l values derived for the whole lens, or at least for a sizeable zone, are of clinical significance. Therefore, when quoted values relate to the center only, it should be clearly presented in the literature.
Considering the ranges of values both Dk and Dk/l in combination, the disparity reaches alarming proportions. The variation for a given 58 percent material might be as shown in Table 1. Clinically, the difference between the two extremes of 47 and 21.5 represents the difference between safe daily wear and compromised extended wear. This explains why the correspondence columns of our clinical journals so often sparkle with claims and counter claims regarding the performance of a given lens design. Until manufacturers provide accurate, clinically relevant product information, this confusion about Dk and Dk/l will persist.
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*Data shown is for a standard spherical 58% lens with a specification of 8.5, 14.2, -3.00D.
Equivalent Oxygen Percentage
Equivalent oxygen percentage (EOP) describes oxygen flux through a contact lens as if the eye were responding to various amounts of atmospheric oxygen. This indirect measure of oxygen flow through a contact lens enables practitioners to relate mathematically derived data (Dk/l) with clinically observed levels of corneal edema. Since this measurement is taken directly from the cornea, it has the advantage of incorporating all of the factors that affect the cornea's response rather than just oxygen transmissibility through a contact lens.
Hypoxic stress units (HSU), another measure used to classify the physiological response to contact lens wear, are derived from EOP data. Also called oxygen shortfall units (OSU), this analysis is based on a relative scale of 100 steps where a value of 0 HSUs represents the normal, non-contact lens wearing oxygen uptake rate of the cornea and 100 represents corneal oxygen demand with a non-moving PMMA contact lens. A relatively linear relationship exists between low-to-moderate Dk lenses and the number of HSUs they create for the cornea.
Oxygen delivery to the cornea is not a linear function of Dk/l, and oxygen transmissibility measurements are inherently limited when describing physiological corneal performance. Therefore, Biological Oxygen Apparent Transmissibility (BOAT) can be used to provide more information about these two functions. When selecting a contact lens, you can minimize isolated areas of epithelial edema by choosing a lens in which that portion with the lowest Dk/l (i.e., the thickest portion) supplies an adequate oxygen supply to the epithelium. Selecting a lens with the highest harmonic average transmissibility can help control overall corneal swelling. Ultimately, good on-eye contact lens performance is a function of adequate amounts of oxygen based upon appropriate patient wearing schedules.
EOP is clinically more relevant than oxygen transmissibility for evaluating patient response to contact lens wear, but it is probably the value most misunderstood by practitioners. EOP measures the actual oxygen concentration at the corneal surface during lens wear, but unlike Dk/l, it involves a new variable -- individual patient response.
The relationship between corneal swelling and EOP during lens wear is significantly different from the relationship between corneal swelling and oxygen concentration after exposure to gas mixtures. This results in vastly different calculated values necessary to avoid corneal swelling (18.0% for EOP vs. 10.9% for gas mixtures). Because this variable is so uniquely subjective, the potential for inconsistency in measurements is also quite significant. Hough's contact lens analysis software (CLAS) allows us to illustrate this high level of variability while comparing the various published models for EOP calculation (Table 2). Note that a high order of inter-subject variability exists within each methodology as well as high order error in the measurements themselves. Figure 2 shows the EOP profile of a lens with approximately 6.5% EOP transmission using the Ang & Efron criteria. However, Figure 3 with the same lens parameters demonstrates approximately 10% EOP transmission when the Holden & Mertz criteria are used.
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FIG.2: This lens has an EOP transmission of approximately 6.5% using Ang & Efron criteria. |
FIG.3: This is the same lens as in FIG. 2 showing a 10% EOP transmission value when Holden & Mertz criteria are used. |
The spread of 6.24% to 19.51% EOP units, representing a 313% difference in measurements, discourages a better appreciation of the value of this most fundamental measurement. This analysis presumes that a lens with Dk/l of 28 could exhibit an EOP performance that ranges from barely satisfying the criteria of minimally safe daily wear to being more than acceptable as an ideal extended wear lens.
While many factors influence the swelling response of the cornea, practitioners are primarily concerned with providing sufficient oxygen flux through a contact lens to avoid clinically detectable levels of edema. Key descriptors such as daily wear with edema, healthy daily wear, extended wear with edema and ideal extended wear set the clinically acceptable boundaries for the cornea's response to oxygen deprivation (Table 3).
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Conclusion
Practitioners originally fitting PMMA contact lenses were primarily concerned with achieving a successful fit that ensured pump-oxygenated tears under the lens surface. As our understanding of corneal physiology evolved and it became apparent that corneal oxygen level was a key factor in fitting success, practitioners and manufacturers alike raced to develop lenses that provided greater amounts of oxygen to the cornea. While our understanding of how oxygen deprivation affects the cornea is vital to the success of contact lens fitting, even today a significant amount of confusion exists about oxygen flux through and corneal performance under a contact lens.
It's important for us to understand key corneal requirements for oxygen and how these factors relate to the development of edema, as well as how various polymers or lens designs influence oxygen flux and hence corneal physiology. We should be cautious of published data that, when incorrectly interpreted, could lead to the divergence shown in the previous tables. Moreover, understanding how variations in measurements affect actual oxygen performance will help avoid fitting disasters (Table 4).
Potential Sources of Measurement Errors
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Remember that Dk data provides information only about intrinsic material characteristics unrelated to actual contact lens design. While Dk/l more accurately describes actual contact lens performance, the clinician may not be fully aware of the number of potential sources of error within these apparently definite numbers. EOP measurements most accurately reflect the on-eye clinical lens performance, but they are also prone to extreme variations since they include tear-pumping mechanisms and unique individual characteristics that may influence corneal physiology.
Finally, manufacturers have the responsibility of accurately presenting vital oxygen transmissibility data in a precise and consistent manner. With regard to Dk measurements, the use of specific subscripts indicating whether the measurement was taken with an edge correction (Dk(ec)) or boundary layer technique (Dk(bl)) is vital information the manufacturer should provide. Also, the use of appropriate subscripts depicting zonal (Dk/l(zonal)), average, i.e., harmonic thickness (Dk/l(ave)) or center thickness (Dk/l(ct)) values when describing oxygen transmissibility are vital to a better understanding of clinical results and will help foster more consistent comparisons within the industry. Even with EOP measurements, notations regarding the various authors' approaches toward measurements would be helpful to avoid the large discrepancies we highlight in this article.
Perhaps every contact lens parameter offered by a manufacturer could be labeled with appropriate transmissibility information and potential EOP values in addition to standard fitting parameters such as base curve and lens diameter. In this way, practitioners would not only be able to select specific fitting relationships, but they'd also be able to change materials more logically to satisfy unique physiological criteria. CLS
References are available upon request to the editors at Contact Lens Spectrum. To receive references via fax, call (800) 239-4684 and request document #32.
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