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Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley, CA 94720, United StatesChemical and Biomolecular Engineering Department, University of California, Berkeley, CA 94720, United StatesClinical Research Center, University of California, Berkeley, CA 94720, United States
Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley, CA 94720, United StatesChemical and Biomolecular Engineering Department, University of California, Berkeley, CA 94720, United States
To determine whether localized hyperosmotic spikes on the pre-lens tear film (PrLTF) due to tear break up results in hyperosmotic spikes on the ocular surface during soft-contact-lens (SCL) wear and whether wear of SCLs can protect the cornea against PrLTF osmotic spikes.
Two-dimensional transient diffusion of salt was incorporated into a computationally designed SCL, post-lens tear film (PoLTF), and ocular surface and solved numerically. Time-dependent localized hyperosmolarity spikes were introduced at the anterior surface of the SCL corresponding to those generated in the PrLTF. Salt spikes were followed in time until spikes penetrate through the lens into the PoLTF. Lens-salt diffusivities () were varied to assess their importance on salt migration from the PrLTF to the ocular surface. SCL and PoLTF initial conditions and the lens anterior-surface boundary condition were varied depending on the value of and on dry-eye symptomatology. Determined corneal surface osmolarities were translated into clinical pain scores.
For above about , it takes around 5–10 s for the PrLTF hyperosmotic break-up spikes to diffuse across the SCL and reach the corneal surface. Even if localized hyperosmotic spikes penetrate to the ocular surface, salt concentrations there are much lower than those in the progenitor PrLTF spikes. For less than , the SCL protects the cornea from hyperosmotic spikes for both normal and dry eyes. When localized corneal hyperosmolarity is converted into transient pain scores, pain thresholds are significantly lower than those for no-lens wear.
A cornea can be protected from localized PrLTF hyperosmolarity spikes with SCL wear. With regular blinking (e.g., less than 10 s), SCL wear shields the cornea from significant hyperosmotic pain. Decreasing increases that protection. Low- soft contact lenses can protect against hyperosmotic spikes and discomfort even during infrequent blinking (e.g., > 10 s).
]. The outermost layer of the tear film is comprised of a thin lipid layer, which retards the evaporation of the muco-aqueous layer that contains electrolytes, metabolites, and various antimicrobial compounds [
] showed that soft-contact-lens (SCL) wear can effectively mitigate hyperosmolarity in the post-lens tear film (PoLTF), which directly interfaces the ocular surface, and that PoLTF osmolarity is different from those of the meniscus and pre-lens tear film (PrLTF). The ability of a SCL to attenuate PoLTF osmolarity depends on lens-salt diffusivity (), lens-salt partition coefficient (), and lens thickness (). These three parameters regulate how much salt diffuses across the SCL from the PrLTF to the PoLTF. However, Kim et al. [
] found that physically acceptable ranges for and had a limited effect on PoLTF osmolarity. These authors stated that to minimize PoLTF hyperosmolarity, SCL should be designed with low values while not allowing lens adherence [
In addition to intrinsic SCL properties, lacrimal tear-production rate, evaporation rate, tear-drainage rate, and interblink period strongly affect PoLTF osmolarity as well. Interestingly, PoLTF osmolarity for dry-eye subjects (e.g., low tear production and/or high evaporation rates) with SCL wear can be reduced to osmolarity lower than that of the pre-corneal tear film of normal-eye subjects during no-lens wear by lowering [
] specified spatial average tear-compartment osmolarities and did not account for regional variance in tear evaporation rate within the PrLTF. Understanding both the spatial average osmolarity and the localized osmolarity is essential to quantify tear hyperosmolarity during SCL wear and how osmolarity affects corneal epithelial cells and lens-wear comfort.
Localized break-up regions are widely believed to be caused by localized lipid-layer thickness and/or composition variations resulting in different localized evaporation rates [
This work addresses the question of whether SCL can effectively attenuate PrLTF salinity spikes and protect the cornea from irritating salinity exposure. The proposed physical model assesses whether SCL wear can protect the PoLTF/cornea from localized PrLTF hyperosmotic break-up areas for normal and dry eyes. Calculated PoLTF osmolarities are then converted to dry-eye pain scores from Liu et al. [
]. Therefore, localized evaporation-driven osmolarity spikes in the PrLTF are anticipated to be similar to those on the pre-corneal tear film during no-lens wear. Fig. 1 provides a schematic of what is expected for PoLTF osmolarity when the SCL is permeable to aqueous salt and there is a localized break-up area in the PrLTF. Because the PoLTF is so thin compared to the SCL, once salt enters the PoLTF, contact with the cornea is essentially immediate.
To address whether localized salinity spikes on the cornea with SCL wear can be mitigated with low-SCL- materials, the original effort of Peng et al. [
] is extended to include a PrLTF, a lens, and a PoLTF. Localized salinity spikes are imposed at the PrLTF/lens interface (i.e., at the lens anterior surface) and traced numerically during interblinks of various duration. A series of values is tested for both normal and dry eyes. Both lateral and sagittal diffusion of salt through the lens and PoLTF are accounted for. The contact lens overlying the cornea is a translationally invariant rectangle of length 12 mm and height 130 µm. Since the effect of on PoLTF osmolarity is minimal for the typical range of SCLs, [
] was set as 130 μm. A similar rectangle represents the 3-µm thick PoLTF () between the lens and the cornea. The 2D coordinate system and boundary conditions are summarized in Fig. 2.
Salt transports across the lens and through the PoLTF according to Fick’s second law written as
respectively. Here, is the molar salt concentration in the lens per lens volume as a function of time, , and spatial coordinates and . is the lateral coordinate with locating the center of the lens and is the sagittal coordinate with demarking the PoLTF/cornea interface. is the PoLTF transient aqueous salt concentration, is the bulk water salt diffusivity [
] low , medium , and high are chosen to investigate the role of lens-salt diffusion rates in attenuating corneal salinity spikes. values chosen are within the range of those available for current commercial SCLs [
]. Eqs. ((1), (2)) each require four boundary conditions and an initial condition.
The boundary condition at the lens/PrLTF interface (i.e., at ) is local equilibrium given by Nernst’s law or
where and are the salt concentrations at the lens side and the PrLTF side of the lens/PrLTF interface, respectively. is set constant at 0.28 for all calculations since the range of for commercially available SCLs does not meaningfully affect the PoLTF osmolarity [
] assuming that tear break up over a SCL is of similar origin to that over the cornea (i.e., due to lipid layer break up and tear evaporation). To quantify the concentration distribution in Fig. 3 as a function of time and location, a Gaussian function was modified to match the results of Peng et al. [
where is the transient osmolarity peak height in Fig. 3 and illustrated in Fig. 4, quantifies the salt-osmolarity rise at the lens anterior surface outside the salt spike and depicted in Fig. 5, and is the Gaussian standard deviation set as 0.2 mm to match the pre-corneal tear-film osmolarity plot of Peng et al. [
]. is a constant listed below that shifts Fig. 3 in the sagittal direction so that matches the PrLTF osmolarity at the beginning of the periodic steady-state interblink for various lens and normal/dry eye results from Kim et al. [
], is different for each and for normal and dry eyes. Both terms on the right of Eq. (4) are divided by 2 because Eqs. ((1), (2)) solve for the salt molar concentration and not for osmolarity. For multi-spike analyses, two peaks are introduced at the PrLTF/SCL interface. The second Gaussian function is shifted laterally to the desired location. and values for the multi-spike analyses remain unchanged from those of the single-spike analyses.
At the PoLTF/lens interface (), local equilibrium salt partitioning
and continuity of salt flux (i.e., )
are imposed where and are the salt concentrations at the PoLTF side and lens side of the PoLTF/lens interface, respectively, and and are the salt fluxes at the PoLTF side and lens side of the PoLTF/lens interface, respectively. To simplify the analysis, no-flux boundary conditions are demanded at the lens and PoLTF edges () and at the PoLTF/cornea interface (). Thus, lateral salt exchange to the pre-conjunctival tear film/tear menisci or sagittal exchange to the corneal epithelium, respectively, are not accounted for [
]. Therefore, salt originating from the PrLTF accumulates within the PoLTF during the interblink period.
The initial condition for the SCL is adapted from the periodic steady-state salt-concentration profile in the SCL at the beginning of an interblink for normal and dry eyes and for low, medium, and high of Kim et al. [
] with a 130-μm , a 0.28 , and a blink pattern of 5 s. Since this initial condition is involved, feasibility was assessed for using a spatially averaged lens-salt concentration as the initial profile. This approximation resulted in PoLTF/cornea interface osmolarities differing by less than 0.5 mOsM for every time point when compared to the results from using the actual periodic salt-concentration profile as the initial condition. Therefore, the average lens-salt-concentration initial condition was implemented because it well reflects the actual initial lens-salt-concentration profile and it simplifies numerical analysis.
Finally, the initial condition for the PoLTF salt-concentration profile also is uniform and set as the calculated time-averaged periodic steady state PoLTF concentration from Kim et al. [
] with a 130-μm , a 0.28 , and a blink pattern of 5 s. Depending on the and normal/dry-eye condition being assessed, the initial conditions of the PoLTF and SCL are different. These changes, along with of Eq. (4), both given below assess osmolarity profiles of the PoLTF at the corneal surface for various lens and normal/dry eye combinations.
Numerical solution of Eqs. ((1), (2)) is by finite-element analysis using Comsol Multiphysics 5.5 and requires amalgamation of Matlab R2019b (Mathworks, Natick, MA) to specify the PrLTF/SCL interface boundary conditions. Because the lens-anterior-surface concentration boundary condition in Fig. 3 covers the time period of 33 s [
] measured subject pain scores set between 0 and 10, with 0 reflecting no pain and 10 marking intolerable pain, upon direct instillation of hyperosmolar solutions onto the ocular surface. From those data, calculated peak lens-wear PoLTF osmolarities were converted into pain scores to reveal whether low- SCL wear can meaningfully mitigate dryness discomfort.
Figs. 6a-c present the calculated transient osmolarity of the PoLTF at the corneal surface for low, medium, and high , respectively, for normal eyes experiencing the localized osmolarity spike at the lens anterior surface. Note that the ordinate scales in each of these figures are different to allow visualization of the salt-concentration changes at the cornea. For Figs. 6a-c, α in Eq. (4) is 11, 9.5, and 9, respectively, to set the initial PrLTF osmolarity to be 311 mOsM, 309.5 mOsM, and 309 mOsM for low, medium, and high , respectively. Figs. 6b-c reveal that a salt spike at the lens anterior surface indeed penetrates through the lens to the corneal surface within an interblink. However, Fig. 6a reveals that the low- lens completely attenuates the PrLTF salt spike. Here, the osmolarity difference between any two chronological time points is ∼ 0.1 mOsM; peaks are too small to visualize even after 30 s of interblink.
Figs. 7a-c provide PoLTF osmolarity profiles for low, medium, and high values, respectively, for dry eyes. Again, the ordinate scales in each of these figures are different to allow visualization of the salt-concentration changes at the cornea. For Figs. 7a-c, α in Eq. (4) is 25, 20.5, and 20, respectively, to determine the initial PrLTF osmolarity as 325 mOsM, 320.5 mOsM, and 320 mOsM for low, medium, and high , respectively [
]. Similar to the normal eye, a low- lens eliminates the PrLTF salt spike at the corneal surface up to at least 30 s of interblink. Due to the higher initial PrLTF and PoLTF osmolarities than those of normal eyes, PoLTF osmolarity at the corneal surface is significantly higher for dry eyes than for normal eyes at early time. However, the difference between normal and dry eyes diminishes at later time. Similar to the normal eye, a low- lens completely attenuates the PrLTF salt spike at the corneal surface up to at least 30 s of interblink.
Fig. 8a compares PoLTF osmolarities at the corneal surface as a function of interblink time for the three lens values. 5–10 s is required for salt to diffuse through the lens and PoLTF to reach the corneal surface for values above about , albeit at much lower salt concentrations. Most importantly, Fig. 8a demonstrates that for values below about , SCL wear well protects against corneal hyperosmotic exposure for both normal and dry eyes. Fig. 8b converts the peak corneal salt concentrations in Fig. 8a to clinical pain scores ranging between 0 and 10 based on the results of Liu et al. [
]. Comparison with the no-lens pain scores shows that all three values produce significantly less hyperosmotic discomfort than that arising from no-lens wear.
Fig. 9 assesses the effect of a nearby osmolarity spike arising from multiple tear ruptures on the anterior lens surface within one interblink for normal eyes. Fig. 9a provides the PrLTF osmolarity profile when the spike apexes are 0.5 mm apart for a medium- lens. Corresponding PoLTF osmolarity at the corneal surface is provided in Fig. 9b. All parameters are identical to the analysis done for determining Fig. 6b. Due to the close proximity of the two peaks, the region between the peaks elevates in osmolarity for both PrLTF and PoLTF regions. Fig. 9c depicts the PrLTF osmolarity profile when the spike apexes are 2.0 mm apart with other controllable parameters identical to those in Fig. 6b and 9a. Corresponding PoLTF osmolarity at the corneal surface for Fig. 9c is provided in Fig. 9d. In this case, two peaks at the PrLTF act independently and do not influence each other. Although not explicitly shown here, results from Fig. 9a and 9b imply that larger break-up areas on the anterior lens surface results in larger high osmolarity regions in the PoLTF.
Fig. 6, Fig. 7, Fig. 8a clearly demonstrate that low- SCLs can protect the cornea against localized hyperosmotic spikes formed in the PrLTF due to localized tear break up and elevated evaporation. Even for medium- and high- SCLs, osmotic peaks are significantly smaller than those of the PrCTF summarized in Fig. 8a. Localized peak salt concentrations when translated into clinical pain scores in Fig. 8b, strikingly confirm that SCL wear mitigates discomfort induced by corneal hyperosmolarity. Even for dry eyes, correlated pain scores greater than unity are not achieved until after 10 s into an interblink, a time longer than most human interblinks. These results suggest why SCL wear allows longer maximum interblink intervals than those without lens wear when subjects are asked to keep their eyes open for as long as possible [
]. Wear of a SCL protects the cornea from localized osmolarity spikes as long as lens wearers blink frequently. However, if lens wearers blink infrequently, which is typically the case when the lens wearers are reading, watching TV, or working on a computer, corneas are more likely exposed to localized hyperosmotic spikes on the ocular surface. To ensure that the cornea is protected from localized osmolarity spikes, lens can be lowered, as demonstrated in Figs. 6a and 7a.
Interestingly, osmotic spikes at the ocular surface for normal and dry eyes during SCL wear are not significantly different for a given ; the difference further diminishes as eyes are open longer. The reason why the difference between normal and dry eyes diminishes at later times is the larger osmolarity difference between the PrLTF and the PoLTF resulting in a greater salt flux from the PrLTF to the PoLTF for dry eyes than for normal eyes. If the interblink period is set to even longer times (e.g., to min), normal and dry-eye osmolarities eventually merge. Because pain scores for normal and dry eyes in Fig. 8b differ minimally for a given , lens-wear discomfort due to localized hyperosmotic tear spikes is likely not influenced by lens wearers’ baseline dry-eye symptomatology.
The single-spike analyses in Fig. 6, Fig. 7 show the behavior of one PrLTF osmotic spike on the ocular surface during lens wear. With actual lens wear, multiple spikes are expected across the lens surface and, therefore, across the ocular surface. Fig. 9 shows that when tear break-up ruptures occur close to one another (e.g., peak-to-peak distance of 0.5 mm), there is a reinforcing influence (e.g., Figs. 9a and 9b) on the osmolarity. These results are expected because two small nearby tear break-up areas can combine into a one large rupture area during a prolonged interblink period. Meanwhile, when tear ruptures are located far away from each other (e.g., peak-to-peak distance of 2.0 mm), osmolarity of the isolated break-up areas are independent of one another (e.g., Figs. 9c and 9d).
] break-up areas in the PrLTF were initiated from a depleted lipid layer and, therefore, have high localized evaporation rates. Such tear ruptures have the same localized evaporation and localized osmotic increase rates for both normal and dry eyes. This assumption is reasonable since inadequate lipid regions likely exhibit localized evaporation rates of water regardless of the subjects’ dry-eye symptomatology. Thus, whole-eye tear evaporation rates during SCL wear [
] is due to the size and number of break-up spots on the lens and to the exposed ocular surface area. There is, however, a possibility that localized tear ruptures exhibit different evaporation rates for normal and dry eyes requiring further investigation.
This work assumes that the PrLTF-osmolarity increase due to localized tear break up are the same as the pre-corneal tear-film osmolarity increase due to localized break-up areas during no-lens wear. In reality, non-invasive tear break-up times for SCL wear is faster than that for no-lens wear [
] and here assume that localized break-up occurs immediately upon lid opening. Further, zero salt flux was imposed between the PoLTF and the cornea. Taking these effects together means that this work provides a worst possible scenario for localized hyperosmolarity in the PoLTF during SCL wear.
The mathematical analysis presented is equivalent to the maximum interblink period stress test conducted clinically [
], calculated results demand that localized PrLTF spikes happen randomly over the SCL surface. If, however, certain areas of the lens surface are more prone to tear rupture, then the localized hyperosmotic peaks may be even more saline than calculations here indicate. Further investigation is needed to elucidate PrLTF break-up patterns.
To convert determined localized hyperosmolarity results to pain scores, the clinical results of Liu et al. [
] is the small 5-subject size of their clinical study.
This work focuses on lens-wear irritation associated with hyperosmolarity. With SCL wear, however, there are multiple factors (e.g., lid-wiper epitheliopathy, blurry vision, lens edge, SCL surface dehydration, and lack of clear visual acuity) that can result in lens-wear discomfort. Nevertheless, SCL wear with all values studied protects the corneal surface against random hyperosmotic spikes. Only the lowest lens considered provides complete osmotic protection. Localized osmotic protection persists even when the interblink period is 30 s for both normal and dry eyes. Results of Kim et al. [
] and the calculations here confirm that SCL wear can protect the cornea both from spatial average hyperosmolarity and from localized hyperosmotic spikes.
5. Grant/financial support
Roberta J. Smith Foundation (MCL), CooperVision Inc. (MCL, C-CP, CJR).
Declaration of Competing Interest
Cheng-Chun Peng is an employee of CooperVision Inc. Remaining authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.