Advertisement

Prevention of localized corneal hyperosmolarity spikes by soft-contact-lens wear

  • Young Hyun Kim
    Affiliations
    Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley, CA 94720, United States

    Chemical and Biomolecular Engineering Department, University of California, Berkeley, CA 94720, United States

    Clinical Research Center, University of California, Berkeley, CA 94720, United States
    Search for articles by this author
  • Meng C. Lin
    Affiliations
    Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley, CA 94720, United States

    Clinical Research Center, University of California, Berkeley, CA 94720, United States
    Search for articles by this author
  • Cheng-Chun Peng
    Affiliations
    CooperVision Inc., Pleasanton, CA 94588, United States
    Search for articles by this author
  • Clayton J. Radke
    Correspondence
    Corresponding author at: Department of Chemical and Biomolecular Engineering, University of California, 101E Gilman Hall, Berkeley, CA 94720, United States.
    Affiliations
    Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley, CA 94720, United States

    Chemical and Biomolecular Engineering Department, University of California, Berkeley, CA 94720, United States
    Search for articles by this author
Open AccessPublished:June 16, 2022DOI:https://doi.org/10.1016/j.clae.2022.101722

      Abstract

      Purpose

      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.

      Methods

      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 (Ds) 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 Ds and on dry-eye symptomatology. Determined corneal surface osmolarities were translated into clinical pain scores.

      Results

      For Ds above about 10-7cm2/s, 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 Ds less than 10-7cm2/s, 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.

      Conclusions

      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 Ds increases that protection. Low-Ds soft contact lenses can protect against hyperosmotic spikes and discomfort even during infrequent blinking (e.g., > 10 s).

      Keywords

      1. Introduction

      The human ocular surface is coated by a thin tear film that keeps the ocular surface lubricated, hydrated, and protected against infection [
      • Fleiszig S.M.J.
      • McNamara N.A.
      • Evans D.J.
      The tear film and defense against infection.
      ,
      • Willcox M.D.P.
      • Argüeso P.
      • Georgiev G.A.
      • Holopainen J.M.
      • Laurie G.W.
      • Millar T.J.
      • et al.
      TFOS DEWS II tear film report.
      ]. 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 [
      • Willcox M.D.P.
      • Argüeso P.
      • Georgiev G.A.
      • Holopainen J.M.
      • Laurie G.W.
      • Millar T.J.
      • et al.
      TFOS DEWS II tear film report.
      ,
      • Peng C.-C.
      • Cerretani C.
      • Li Y.
      • Bowers S.
      • Shahsavarani S.
      • Lin M.C.
      • et al.
      Flow evaporimeter to assess evaporative resistance of human tear-film lipid layer.
      ]. Between the muco-aqueous layer and the ocular surface is the glycocalyx adlayer that engenders corneal wetting and promotes the epithelial barrier function of the ocular-surface [
      • Argüeso P.
      • Guzman-Aranguez A.
      • Mantelli F.
      • Cao Z.
      • Ricciuto J.
      • Panjwani N.
      Association of cell surface mucins with galectin-3 contributes to the ocular surface epithelial barrier.
      ].
      During an interblink, evaporation of the muco-aqueous layer results in periodic increased tear-film osmolarity [
      • Tomlinson A.
      • Khanal S.
      Assessment of tear film dynamics: Quantification approach.
      ,
      • Cerretani C.F.
      • Radke C.J.
      Tear dynamics in healthy and dry eyes.
      ]. Tear evaporation rate depends on the lipid-layer thickness and composition [
      • King-Smith P.E.
      • Reuter K.S.
      • Braun R.J.
      • Nichols J.J.
      • Nichols K.K.
      Tear film breakup and structure studied by simultaneous video recording of fluorescence and tear film lipid layer images.
      ,
      • Svitova T.F.
      • Lin M.C.
      Evaporation retardation by model tear-lipid films: The roles of film aging, compositions and interfacial rheological properties.
      ,
      • Kim Y.H.
      • Graham A.D.
      • Li W.
      • Dursch T.J.
      • Radke C.J.
      • Lin M.C.
      Effect of tear lipid-layer thickness on tear-film evaporation and tear properties.
      ]. When a suboptimal lipid layer allows excess tear evaporation, tear becomes hyperosmotic causing deleterious effects on the corneal epithelia [
      • Gilbard J.P.
      • Carter J.B.
      • Sang D.N.
      • Refojo M.F.
      • Hanninen L.A.
      • Kenyon K.R.
      Morphologic effect of hyperosmolarity on rabbit corneal epithelium.
      ,
      • Gilbard J.P.
      Tear film osmolarity and keratoconjunctivitis sicca.
      ,
      • Gilbard J.P.
      • Rossi S.R.
      • Gray K.L.
      • Hanninen L.A.
      • Kenyon K.R.
      Tear film osmolarity and ocular surface disease in two rabbit models for keratoconjunctivitis sicca.
      ,
      • Guzmán M.
      • Miglio M.
      • Keitelman I.
      • Shiromizu C.M.
      • Sabbione F.
      • Fuentes F.
      • et al.
      Transient tear hyperosmolarity disrupts the neuroimmune homeostasis of the ocular surface and facilitates dry eye onset.
      ,
      • Hirata H.
      • Oshinsky M.
      • Fried N.
      Short exposure to intense tear hyperosmolarity leads to functional alterations of the corneal nerves involved in tearing and/or ocular pain: Implications for dry eye disease.
      ,
      • Hirata H.
      • Rosenblatt M.I.
      Hyperosmolar tears enhance cooling sensitivity of the corneal nerves in rats: Possible neural basis for cold-induced dry eye pain.
      ,
      • Hirata H.
      • Mizerska K.
      • Marfurt C.F.
      • Rosenblatt M.I.
      Hyperosmolar tears induce functional and structural alterations of corneal nerves: Electrophysiological and anatomical evidence toward neurotoxicity.
      ] and triggering dry-eye symptoms [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ]. Tear osmolarity is significantly higher in the ocular-surface tear film than in the tear meniscus [
      • Cerretani C.F.
      • Radke C.J.
      Tear dynamics in healthy and dry eyes.
      ,
      • Bron A.J.
      • Tiffany J.M.
      • Yokoi N.
      • Gouveia S.M.
      Using osmolarity to diagnose dry eye: A compartmental hypothesis and review of our assumptions.
      ,
      • Gaffney E.A.
      • Tiffany J.M.
      • Yokoi N.
      • Bron A.J.
      A mass and solute balance model for tear volume and osmolarity in the normal and the dry eye.
      ], where osmolarity is typically measured [
      • Amparo F.
      • Jin Y.
      • Hamrah P.
      • Schaumberg D.A.
      • Dana R.
      What is the value of incorporating tear osmolarity measurement in assessing patient response to therapy in dry eye disease?.
      ,
      • Farris R.L.
      Tear osmolarity variation in the dry eye.
      ,
      • Farris R.L.
      • Stuchell R.N.
      • Mandel I.D.
      Basal and reflex human tear analysis. I. Physical measurements: Osmolarity, basal volumes, and reflex flow rate.
      ,
      • Farris R.L.
      • Gilbard J.P.
      • Stuchell R.N.
      • Mandel I.D.
      Diagnostic tests in keratoconjunctivitis sicca.
      ,
      • Gilbard J.P.
      Human tear film electrolyte concentrations in health and dry eye disease.
      ,
      • Gilbard J.P.
      • Farris R.L.
      • Santamaria J.
      Osmolarity of tear micro volumes in keratoconjunctivitis sicca.
      ,
      • Mathers W.D.
      • Lane J.A.
      • Sutphin J.E.
      • Zimmerman M.B.
      Model for ocular tear film function.
      ,
      • Mishima S.
      • Kubota Z.
      • Farris R.L.
      The tear flow dynamics in normal and in keratoconjunctivitis sicca cases.
      ,
      • Ogasawara K.
      • Tsuru T.
      • Mitsubayashi K.
      • Karube I.
      Electrical conductivity of tear fluid in healthy persons and keratoconjunctivitis sicca patients measured by a flexible conductimetric sensor.
      ,
      • Tomlinson A.
      • Khanal S.
      • Ramaesh K.
      • Diaper C.
      • McFadyen A.
      Tear film osmolarity: Determination of a referent for dry eye diagnosis.
      ,
      • Yeh T.N.
      • Graham A.D.
      • Lin M.C.
      Relationships among tear film stability, osmolarity, and dryness symptoms.
      ].
      Recently, Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] 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 (Ds), lens-salt partition coefficient (ks), and lens thickness (hlens). These three parameters regulate how much salt diffuses across the SCL from the PrLTF to the PoLTF. However, Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] found that physically acceptable ranges for ks and hlens had a limited effect on PoLTF osmolarity. These authors stated that to minimize PoLTF hyperosmolarity, SCL should be designed with low Ds values while not allowing lens adherence [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ,
      • Cerretani C.
      • Peng C.C.
      • Chauhan A.
      • Radke C.J.
      Aqueous salt transport through soft contact lenses: An osmotic-withdrawal mechanism for prevention of adherence.
      ,

      Nicolson P, Baron R, Charbrereck P, et al. Extended wear ophthalmic lens. US Patent 5, 965,631. 1999:1-37.

      ].
      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 Ds [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ]. However, the analysis of Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] only considered a uniform tear evaporation rate across the whole PrLTF. In other words, Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] 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 [
      • King-Smith P.E.
      • Reuter K.S.
      • Braun R.J.
      • Nichols J.J.
      • Nichols K.K.
      Tear film breakup and structure studied by simultaneous video recording of fluorescence and tear film lipid layer images.
      ,
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ]. This hypothesis is supported by faster cooling of localized break-up areas in the pre-corneal tear film (PrCTF) that correlates directly with fluorescein break-up areas [
      • Li W.
      • Graham A.D.
      • Selvin S.
      • Lin M.C.
      Ocular surface cooling corresponds to tear film thinning and breakup.
      ]. Osmolarity of localized break-up areas in the PrCTF can reach 600–800 milliOsmolar (mOsM) during a 10-s interblink period [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ,
      • Braun R.J.
      • King-Smith P.E.
      • Begley C.G.
      • Li L.
      • Gewecke N.R.
      Dynamics and function of the tear film in relation to the blink cycle.
      ], which is approximately 2 to 2.5 times the osmolarity of the spatial average PrCTF [
      • Cerretani C.F.
      • Radke C.J.
      Tear dynamics in healthy and dry eyes.
      ]. Localized PrLTF salt spikes therefore expose epithelial cells to much higher salinities and hence to higher pain thresholds [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ]. Similar to the PrCTF during no-lens wear [
      • Abelson M.B.
      • Ousler G.W.
      • Nally L.A.
      • Welch D.
      • Krenzer K.
      Alternative Reference Values for Tear Film Break up Time in Normal and Dry Eye Populations.
      ], localized tear break-up areas exhibiting high evaporation rates also occur on the PrLTF during SCL wear [
      • Graham A.D.
      • Lin M.C.
      The relationship of pre-corneal to pre-contact lens non-invasive tear breakup time.
      ]. However, because of minimal mixing of the PrLTF with the PoLTF [
      • McNamara N.A.
      • Polse K.A.
      • Brand R.J.
      • Graham A.D.
      • Chan J.S.
      • McKenney C.D.
      Tear mixing under a soft contact lens: Effects of lens diameter.
      ], salt concentration spikes at the anterior lens surface must first diffuse through the SCL to reach the cornea [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ].
      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. [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ] to predict if SCLs with low Ds can protect wearers from salinity-induced dryness discomfort.

      2. Methods

      Although break-up areas cannot be visualized with fluorescein dye during SCL wear, non-invasive tear break-up analysis using concentric ring patterns confirms that the PrLTF exhibits tear break up [
      • Graham A.D.
      • Lin M.C.
      The relationship of pre-corneal to pre-contact lens non-invasive tear breakup time.
      ,
      • Montani G.
      • Martino M.
      Tear film characteristics during wear of daily disposable contact lenses.
      ]. 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.
      Figure thumbnail gr1
      Fig. 1Schematic salinity spike in the pre-lens tear film and the post-lens tear film due to localized pre-lens tear-film break up. Figure is not to scale.
      To address whether localized salinity spikes on the cornea with SCL wear can be mitigated with low-SCL-Ds materials, the original effort of Peng et al. [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ] 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 Ds 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 hlens on PoLTF osmolarity is minimal for the typical hlens range of SCLs, [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] hlens was set as 130 μm. A similar rectangle represents the 3-µm thick PoLTF (hPoLTF) between the lens and the cornea. The 2D coordinate system and boundary conditions are summarized in Fig. 2.
      Figure thumbnail gr2
      Fig. 2Schematic of the translationally invariant calculation domain and the requisite boundary conditions in the z direction. For convenience, the no-flux boundary conditions are not shown at the domain ends (in the x direction). Figure is not to scale.
      Salt transports across the lens and through the PoLTF according to Fick’s second law written as
      clenst-Ds2clensx2+2clensz2=0SCLhPoLTFzhPoLTF+hSCL
      (1)


      and
      ct-D2cx2+2cz2=0PoLTF0zhPoLTF
      (2)


      respectively. Here, clens(t,x,z) is the molar salt concentration in the lens per lens volume as a function of time, t, and spatial coordinates x and z. x is the lateral coordinate with x=0 locating the center of the lens and z is the sagittal coordinate with z=0 demarking the PoLTF/cornea interface. c(t,x,z) is the PoLTF transient aqueous salt concentration, D(=1.5×10-5cm2/s) is the bulk water salt diffusivity [
      • Newman J.S.
      • Thomas-Alyea K.E.
      Electrochemical Systems.
      ], and Ds is the salt diffusivity in the contact lens. The 2D geometry in Eqs. ((1), (2)) accounts for both lateral and sagittal salt transport. Consistent with Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] low Ds(=2.8×10-8cm2/s), medium Ds(=1.1×10-6cm2/s), and high Ds(=6.0×10-6cm2/s) are chosen to investigate the role of lens-salt diffusion rates in attenuating corneal salinity spikes. Ds values chosen are within the range of those available for current commercial SCLs [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ,
      • Guan L.
      • Jiménez M.E.G.
      • Walowski C.
      • Boushehri A.
      • Prausnitz J.M.
      • Radke C.J.
      Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses.
      ,
      • Mann A.
      • Sáez-Martinez V.
      • Lydon F.
      • Tighe B.
      Investigating the permeation properties of contact lenses and its influence on tear electrolyte composition.
      ]. Because ks ranges of hydrogel and silicone-hydrogel lenses are well understood, [
      • Guan L.
      • Jiménez M.E.G.
      • Walowski C.
      • Boushehri A.
      • Prausnitz J.M.
      • Radke C.J.
      Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses.
      ,
      • Peng C.C.
      • Chauhan A.
      Ion transport in silicone hydrogel contact lenses.
      ] Ds values used here were either calculated from the lens-salt permeability values measured by Mann et al. [
      • Mann A.
      • Sáez-Martinez V.
      • Lydon F.
      • Tighe B.
      Investigating the permeation properties of contact lenses and its influence on tear electrolyte composition.
      ] or taken directly from the measured values of Guan et al. [
      • Guan L.
      • Jiménez M.E.G.
      • Walowski C.
      • Boushehri A.
      • Prausnitz J.M.
      • Radke C.J.
      Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses.
      ]. Ds values of commercially available SCLs lie somewhere between the low and high Ds values illustrated here [
      • Guan L.
      • Jiménez M.E.G.
      • Walowski C.
      • Boushehri A.
      • Prausnitz J.M.
      • Radke C.J.
      Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses.
      ,
      • Mann A.
      • Sáez-Martinez V.
      • Lydon F.
      • Tighe B.
      Investigating the permeation properties of contact lenses and its influence on tear electrolyte composition.
      ]. Eqs. ((1), (2)) each require four boundary conditions and an initial condition.
      The boundary condition at the lens/PrLTF interface (i.e., at z=hPoLTF+hlens) is local equilibrium given by Nernst’s law or
      kscPrLTF=clensz=hPoLTF+hlens
      (3)


      where cPrLTF and clens are the salt concentrations at the lens side and the PrLTF side of the lens/PrLTF interface, respectively. ks is set constant at 0.28 for all calculations since the range of ks for commercially available SCLs does not meaningfully affect the PoLTF osmolarity [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ,
      • Guan L.
      • Jiménez M.E.G.
      • Walowski C.
      • Boushehri A.
      • Prausnitz J.M.
      • Radke C.J.
      Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses.
      ,
      • Peng C.C.
      • Chauhan A.
      Ion transport in silicone hydrogel contact lenses.
      ].
      The imposed transient PrLTF/lens interface salt-spike concentration, cPrLTF, is that in Fig. 3 obtained from Peng et al. [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ] 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. [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ] for the PrCTF or
      cPrLTF=c(t,x,z=hPoLTF+hlens)=cAt-cB(t)2exp-x22σ2+cBt+α2
      (4)


      where cAt is the transient osmolarity peak height in Fig. 3 and illustrated in Fig. 4, cBt quantifies the salt-osmolarity rise at the lens anterior surface outside the salt spike and depicted in Fig. 5, and σ is the Gaussian standard deviation set as 0.2 mm to match the pre-corneal tear-film osmolarity plot of Peng et al. [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ]. α is a constant listed below that shifts Fig. 3 in the sagittal direction so that c(t=0,x,z=hPoLTF+hlens) matches the PrLTF osmolarity at the beginning of the periodic steady-state interblink for various lens Ds and normal/dry eye results from Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ]. Since the periodic steady-state osmolarity of the PrLTF upon eye opening varies depending on the Ds value and on dry-eye symptomatology [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ], α is different for each Ds 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. σ and α values for the multi-spike analyses remain unchanged from those of the single-spike analyses.
      Figure thumbnail gr3
      Fig. 3Pre-corneal tear-film osmolarity spike arising from pre-corneal tear-film break up. Adopted as pre-lens tear-film osmolarity. Reprinted with permission from Peng et al.
      [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ]
      . Copyright (2014) Elsevier B.V.
      Figure thumbnail gr4
      Fig. 4Fitting of peak osmolarity in the break-up area, cAt in Eq. from . Peak osmolarity data of Peng et al.
      [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ]
      are given as solid squares. The dashed line is a best fit of the data to the quadratic equation listed in the figure.
      Figure thumbnail gr5
      Fig. 5Fit of non-tear break-up area osmolarity, cBt in Eq. from . Calculated osmolarities of non-tear break-up area of Peng et al.
      [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ]
      are given as solid squares. The dashed line is a best fit of the data to the linear equation listed in the figure.
      At the PoLTF/lens interface (z=hPoLTF), local equilibrium salt partitioning
      kscPoLTF=clensz=hPoLTF
      (5)


      and continuity of salt flux (i.e., Jlens=JPoLTF)
      -DSclensz=-Dczz=hPoLTF
      (6)


      are imposed where cPoLTF and clens are the salt concentrations at the PoLTF side and lens side of the PoLTF/lens interface, respectively, and JPoLTF and Jlens 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 (x=±6mm) and at the PoLTF/cornea interface (z=0). Thus, lateral salt exchange to the pre-conjunctival tear film/tear menisci or sagittal exchange to the corneal epithelium, respectively, are not accounted for [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ]. 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 (i.e.,att=0) for normal and dry eyes and for low, medium, and high Ds of Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] with a 130-μm hlens, a 0.28 ks, 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. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] with a 130-μm hlens, a 0.28 ks, and a blink pattern of 5 s. Depending on the Ds and normal/dry-eye condition being assessed, the initial conditions of the PoLTF and SCL are different. These changes, along with α of Eq. (4), both given below assess osmolarity profiles of the PoLTF at the corneal surface for various lens Ds 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 [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ], the analysis provided here extends out to 30 s.
      In a small sample-size clinical study, Liu et al. [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ] 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-Ds SCL wear can meaningfully mitigate dryness discomfort.

      3. Results

      Figs. 6a-c present the calculated transient osmolarity of the PoLTF at the corneal surface for low, medium, and high Ds, 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 Ds, 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-Ds 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.
      Figure thumbnail gr6
      Fig. 6Salinity-spike growth kinetics due to local tear-film rupture at the lens anterior surface in for normal eyes. (a) transient post-lens tear-film osmolarity profiles for low-lens-salt diffusivity (Ds=2.8×10-8cm2/s), (b) medium-lens-salt diffusivity (Ds=1.1×10-6cm2/s), and (c) high-lens-salt diffusivity (Ds=6.0×10-6cm2/s). Different ordinate scales are adopted in each graph. The PrLTF salinity spike penetrates through to the PoLTF/corneal interface for (b) and (c) but not (a).
      Figs. 7a-c provide PoLTF osmolarity profiles for low, medium, and high Ds 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 Ds, respectively [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ]. Similar to the normal eye, a low-Ds 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-Ds lens completely attenuates the PrLTF salt spike at the corneal surface up to at least 30 s of interblink.
      Figure thumbnail gr7
      Fig. 7Salinity-spike growth kinetics due to local tear-film rupture at the lens anterior surface in for dry eyes. (a) transient post-lens tear-film osmolarity profiles for low-lens-salt diffusivity (Ds=2.8×10-8cm2/s), (b) medium-lens-salt diffusivity (Ds=1.1×10-6cm2/s), and (c) high-lens-salt diffusivity (Ds=6.0×10-6cm2/s). Different ordinate scales are adopted in each graph. The PrLTF salinity spike penetrates through to the PoLTF/corneal interface for (b) and (c) but not for (a).
      Fig. 8a compares PoLTF osmolarities at the corneal surface as a function of interblink time for the three lens Ds values. 5–10 s is required for salt to diffuse through the lens and PoLTF to reach the corneal surface for Ds values above about 10-7cm2/s, albeit at much lower salt concentrations. Most importantly, Fig. 8a demonstrates that for Ds values below about 10-7cm2/s, 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. [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ]. Comparison with the no-lens pain scores shows that all three Ds values produce significantly less hyperosmotic discomfort than that arising from no-lens wear.
      Figure thumbnail gr8
      Fig. 8(a) Peak transient ocular-surface osmolarity with lens wear as a function of interblink time. (b) Clinical pain score as a function of interblink time. Clinical pain scores were determined from osmolarity values of (a) and the results of Liu et al.
      [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ]
      . Salt diffusivities are given as: low Ds=2.8×10-8cm2/s (blue line), medium Ds=1.1×10-6cm2/s (red line), and high Ds=6.0×10-6cm2/s (black line). No-lens wear peak osmolarity from is shown as a yellow line.
      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-Ds 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.
      Figure thumbnail gr9
      Fig. 9Salinity-spike growth kinetics due to local tear-film rupture at the lens anterior surface. (a) two spikes at the lens anterior surface with peaks separated by 0.5 mm; (b) corresponding post-lens tear-film osmolarity at the corneal interface; (c) two spikes at the lens anterior surface with peaks separated by 2.0 mm; (d) corresponding PoLTF osmolarity at the corneal interface. (a) and (c) have different y-axis scales than do (b) and (d).

      4. Discussion

      Fig. 6, Fig. 7, Fig. 8a clearly demonstrate that low-Ds 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-Ds 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 [
      • Zhang J.
      • Begley C.G.
      • Situ P.
      • Simpson T.
      • Liu H.
      A link between tear breakup and symptoms of ocular irritation.
      ]. 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 Ds 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 Ds; 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 Ds, 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).
      Following the work of Peng et al. [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ] 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 [
      • Guillon M.
      • Maissa C.
      Contact lens wear affects tear film evaporation.
      ] 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 [
      • Graham A.D.
      • Lin M.C.
      The relationship of pre-corneal to pre-contact lens non-invasive tear breakup time.
      ]. Both the results of Peng et al. [
      • Peng C.C.
      • Cerretani C.F.
      • Braun R.J.
      • Radke C.J.
      Evaporation-driven instability of the precorneal tear film.
      ] 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 [
      • Zhang J.
      • Begley C.G.
      • Situ P.
      • Simpson T.
      • Liu H.
      A link between tear breakup and symptoms of ocular irritation.
      ,
      • Ding J.E.
      • Kim Y.H.
      • Yi S.M.
      • Graham A.D.
      • Li W.
      • Lin M.C.
      Ocular surface cooling rate associated with tear film characteristics and the maximum interblink period.
      ]. Since osmotic initial conditions for PoLTF, PrLTF, and the SCL are those of Kim et al. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ], 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. [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ] were utilized. A limitation of this conversion is that the hyperosmolarity of localized break-up spots were analyzed in this work whereas Liu et al. [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ] administered saline to the entire ocular surface. Because there are ∼ 7,000 nociceptors per square millimeter [
      • Müller L.J.
      • Marfurt C.F.
      • Kruse F.
      • Tervo T.M.T.
      Corneal nerves: Structure, contents and function.
      ] and approximately 70% of those are polymodal and sensitive to osmolarity [
      • Maharaj R.L.
      In vivo ocular surface osmolarity in a dry eye population.
      ,
      • Rosenthal P.
      • Borsook D.
      The Corneal pain system. Part I: The missing piece of the dry eye puzzle.
      ], it is likely that localized hyperosmotic spikes also trigger pain. Another limitation to utilizing the results of Liu et al. [
      • Liu H.
      • Begley C.
      • Chen M.
      • Bradley A.
      • Bonanno J.
      • McNamara N.A.
      • et al.
      A link between tear instability and hyperosmolarity in dry eye.
      ] 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 Ds values studied protects the corneal surface against random hyperosmotic spikes. Only the lowest Ds 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. [
      • Kim Y.H.
      • Nguyen T.
      • Lin M.C.
      • Peng C.C.
      • Radke C.J.
      Protection against corneal hyperosmolarity with soft-contact-lens wear.
      ] 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.

      References

        • Fleiszig S.M.J.
        • McNamara N.A.
        • Evans D.J.
        The tear film and defense against infection.
        in: Sullivan D.A. Stern M.E. Dartt D.A. Sullivan R.M. Bromberg B.B. Lacrimal Gland, Tear Film, and Dry Eye Syndromes 3. Springer, 2002: 523-530https://doi.org/10.1007/978-1-4615-0717-8_74
        • Willcox M.D.P.
        • Argüeso P.
        • Georgiev G.A.
        • Holopainen J.M.
        • Laurie G.W.
        • Millar T.J.
        • et al.
        TFOS DEWS II tear film report.
        Ocul Surf. 2017; 15: 366-403https://doi.org/10.1016/j.jtos.2017.03.006
        • Peng C.-C.
        • Cerretani C.
        • Li Y.
        • Bowers S.
        • Shahsavarani S.
        • Lin M.C.
        • et al.
        Flow evaporimeter to assess evaporative resistance of human tear-film lipid layer.
        Ind Eng Chem Res. 2014; 53: 18130-18139https://doi.org/10.1021/ie5030497
        • Argüeso P.
        • Guzman-Aranguez A.
        • Mantelli F.
        • Cao Z.
        • Ricciuto J.
        • Panjwani N.
        Association of cell surface mucins with galectin-3 contributes to the ocular surface epithelial barrier.
        J Biol Chem. 2009; 284: 23037-23045https://doi.org/10.1074/jbc.M109.033332
        • Tomlinson A.
        • Khanal S.
        Assessment of tear film dynamics: Quantification approach.
        Ocul Surf. 2005; 3: 81-95https://doi.org/10.1016/S1542-0124(12)70157-X
        • Cerretani C.F.
        • Radke C.J.
        Tear dynamics in healthy and dry eyes.
        Curr Eye Res. 2014; 39: 580-595https://doi.org/10.3109/02713683.2013.859274
        • King-Smith P.E.
        • Reuter K.S.
        • Braun R.J.
        • Nichols J.J.
        • Nichols K.K.
        Tear film breakup and structure studied by simultaneous video recording of fluorescence and tear film lipid layer images.
        Invest Ophthalmol Vis Sci. 2013; 54: 4900-4909https://doi.org/10.1167/iovs.13-11878
        • Svitova T.F.
        • Lin M.C.
        Evaporation retardation by model tear-lipid films: The roles of film aging, compositions and interfacial rheological properties.
        Colloids Surf B. 2021; 197111392https://doi.org/10.1016/j.colsurfb.2020.111392
        • Kim Y.H.
        • Graham A.D.
        • Li W.
        • Dursch T.J.
        • Radke C.J.
        • Lin M.C.
        Effect of tear lipid-layer thickness on tear-film evaporation and tear properties.
        American Academy of Optometry Annual Meeting Poster Session. 2021 (215076)
        • Gilbard J.P.
        • Carter J.B.
        • Sang D.N.
        • Refojo M.F.
        • Hanninen L.A.
        • Kenyon K.R.
        Morphologic effect of hyperosmolarity on rabbit corneal epithelium.
        Ophthalmology. 1984; 91: 1205-1212https://doi.org/10.1016/S0161-6420(84)34163-X
        • Gilbard J.P.
        Tear film osmolarity and keratoconjunctivitis sicca.
        CLAO J. 1985; 11: 243-250
        • Gilbard J.P.
        • Rossi S.R.
        • Gray K.L.
        • Hanninen L.A.
        • Kenyon K.R.
        Tear film osmolarity and ocular surface disease in two rabbit models for keratoconjunctivitis sicca.
        Invest Ophthalmol Vis Sci. 1988; 29: 374-378
        • Guzmán M.
        • Miglio M.
        • Keitelman I.
        • Shiromizu C.M.
        • Sabbione F.
        • Fuentes F.
        • et al.
        Transient tear hyperosmolarity disrupts the neuroimmune homeostasis of the ocular surface and facilitates dry eye onset.
        Immunology. 2020; 161: 148-161https://doi.org/10.1111/imm.13243
        • Hirata H.
        • Oshinsky M.
        • Fried N.
        Short exposure to intense tear hyperosmolarity leads to functional alterations of the corneal nerves involved in tearing and/or ocular pain: Implications for dry eye disease.
        Invest Ophthalmol Vis Sci. 2013; 54: 2193
        • Hirata H.
        • Rosenblatt M.I.
        Hyperosmolar tears enhance cooling sensitivity of the corneal nerves in rats: Possible neural basis for cold-induced dry eye pain.
        Invest Ophthalmol Vis Sci. 2014; 55: 5821-5833https://doi.org/10.1167/iovs.14-14642
        • Hirata H.
        • Mizerska K.
        • Marfurt C.F.
        • Rosenblatt M.I.
        Hyperosmolar tears induce functional and structural alterations of corneal nerves: Electrophysiological and anatomical evidence toward neurotoxicity.
        Invest Ophthalmol Vis Sci. 2015; 56: 8125-8140https://doi.org/10.1167/iovs.15-18383
        • Liu H.
        • Begley C.
        • Chen M.
        • Bradley A.
        • Bonanno J.
        • McNamara N.A.
        • et al.
        A link between tear instability and hyperosmolarity in dry eye.
        Invest Ophthalmol Vis Sci. 2009; 50: 3671-3679https://doi.org/10.1167/iovs.08-2689
        • Bron A.J.
        • Tiffany J.M.
        • Yokoi N.
        • Gouveia S.M.
        Using osmolarity to diagnose dry eye: A compartmental hypothesis and review of our assumptions.
        Adv Exp Med Biol. 2002; 506: 1087-1095
        • Gaffney E.A.
        • Tiffany J.M.
        • Yokoi N.
        • Bron A.J.
        A mass and solute balance model for tear volume and osmolarity in the normal and the dry eye.
        Prog Retin Eye Res. 2010; 29: 59-78https://doi.org/10.1016/j.preteyeres.2009.11.002
        • Amparo F.
        • Jin Y.
        • Hamrah P.
        • Schaumberg D.A.
        • Dana R.
        What is the value of incorporating tear osmolarity measurement in assessing patient response to therapy in dry eye disease?.
        Am J Ophthalmol. 2014; 157: 69-77.e2https://doi.org/10.1016/j.ajo.2013.07.019
        • Farris R.L.
        Tear osmolarity variation in the dry eye.
        Trans Am Ophthalmol Soc. 1986; 84: 250-268
        • Farris R.L.
        • Stuchell R.N.
        • Mandel I.D.
        Basal and reflex human tear analysis. I. Physical measurements: Osmolarity, basal volumes, and reflex flow rate.
        Ophthalmology. 1981; 88: 852-857
        • Farris R.L.
        • Gilbard J.P.
        • Stuchell R.N.
        • Mandel I.D.
        Diagnostic tests in keratoconjunctivitis sicca.
        CLAO J. 1983; 9: 23-28
        • Gilbard J.P.
        Human tear film electrolyte concentrations in health and dry eye disease.
        Int Ophthalmol Clin. 1994; 34: 27-36
        • Gilbard J.P.
        • Farris R.L.
        • Santamaria J.
        Osmolarity of tear micro volumes in keratoconjunctivitis sicca.
        Arch Ophthalmol. 1978; 96: 677-681
        • Mathers W.D.
        • Lane J.A.
        • Sutphin J.E.
        • Zimmerman M.B.
        Model for ocular tear film function.
        Cornea. 1996; 15: 110-119
        • Mishima S.
        • Kubota Z.
        • Farris R.L.
        The tear flow dynamics in normal and in keratoconjunctivitis sicca cases.
        Excerpta Medica. 1971; : 1801-1805
        • Ogasawara K.
        • Tsuru T.
        • Mitsubayashi K.
        • Karube I.
        Electrical conductivity of tear fluid in healthy persons and keratoconjunctivitis sicca patients measured by a flexible conductimetric sensor.
        Graefes Arch Clin Exp Ophthalmol. 1996; 234: 542-546https://doi.org/10.1007/BF00448797
        • Tomlinson A.
        • Khanal S.
        • Ramaesh K.
        • Diaper C.
        • McFadyen A.
        Tear film osmolarity: Determination of a referent for dry eye diagnosis.
        Invest Ophthalmol Vis Sci. 2006; 47: 4309-4315
        • Yeh T.N.
        • Graham A.D.
        • Lin M.C.
        Relationships among tear film stability, osmolarity, and dryness symptoms.
        Optom Vis Sci. 2015; 92: e264-e272https://doi.org/10.1097/OPX.0000000000000649
        • Kim Y.H.
        • Nguyen T.
        • Lin M.C.
        • Peng C.C.
        • Radke C.J.
        Protection against corneal hyperosmolarity with soft-contact-lens wear.
        Prog Retin Eye Res. 2022; 87101012https://doi.org/10.1016/j.preteyeres.2021.101012
        • Cerretani C.
        • Peng C.C.
        • Chauhan A.
        • Radke C.J.
        Aqueous salt transport through soft contact lenses: An osmotic-withdrawal mechanism for prevention of adherence.
        Cont Lens Anterior Eye. 2012; 35: 260-265https://doi.org/10.1016/j.clae.2012.07.003
      1. Nicolson P, Baron R, Charbrereck P, et al. Extended wear ophthalmic lens. US Patent 5, 965,631. 1999:1-37.

        • Peng C.C.
        • Cerretani C.F.
        • Braun R.J.
        • Radke C.J.
        Evaporation-driven instability of the precorneal tear film.
        Adv Colloid Interfac. 2014; 206: 250-264https://doi.org/10.1016/j.cis.2013.06.001
        • Li W.
        • Graham A.D.
        • Selvin S.
        • Lin M.C.
        Ocular surface cooling corresponds to tear film thinning and breakup.
        Optom Vis Sci. 2015; 92: e248-e256https://doi.org/10.1097/OPX.0000000000000672
        • Braun R.J.
        • King-Smith P.E.
        • Begley C.G.
        • Li L.
        • Gewecke N.R.
        Dynamics and function of the tear film in relation to the blink cycle.
        Prog Retin Eye Res. 2015; 45: 132-164https://doi.org/10.1016/j.preteyeres.2014.11.001
        • Abelson M.B.
        • Ousler G.W.
        • Nally L.A.
        • Welch D.
        • Krenzer K.
        Alternative Reference Values for Tear Film Break up Time in Normal and Dry Eye Populations.
        in: Sullivan D.A. Stern M.E. Tsubota K. Dartt D.A. Sullivan R.M. Bromberg B.B. Lacrimal Gland, Tear Film, and Dry Eye Syndromes 3. Springer, 2002
        • Graham A.D.
        • Lin M.C.
        The relationship of pre-corneal to pre-contact lens non-invasive tear breakup time.
        PLoS One. 2021; 16e0247877https://doi.org/10.1371/journal.pone.0247877
        • McNamara N.A.
        • Polse K.A.
        • Brand R.J.
        • Graham A.D.
        • Chan J.S.
        • McKenney C.D.
        Tear mixing under a soft contact lens: Effects of lens diameter.
        Am J Ophthalmol. 1999; 127: 659-665https://doi.org/10.1016/S0002-9394(99)00051-3
        • Montani G.
        • Martino M.
        Tear film characteristics during wear of daily disposable contact lenses.
        Clin Ophthalmol. 2020; 14: 1521-1531https://doi.org/10.2147/OPTH.S242422
        • Newman J.S.
        • Thomas-Alyea K.E.
        Electrochemical Systems.
        3rd ed. John Wiley & Sons Inc, 2004: 611-634
        • Guan L.
        • Jiménez M.E.G.
        • Walowski C.
        • Boushehri A.
        • Prausnitz J.M.
        • Radke C.J.
        Permeability and partition coefficient of aqueous sodium chloride in soft contact lenses.
        J Appl Polym Sci. 2011; 122: 1457-1471https://doi.org/10.1002/app.33336
        • Mann A.
        • Sáez-Martinez V.
        • Lydon F.
        • Tighe B.
        Investigating the permeation properties of contact lenses and its influence on tear electrolyte composition.
        J Biomed Mater Res B. 2019; 107: 1997-2005https://doi.org/10.1002/jbm.b.34291
        • Peng C.C.
        • Chauhan A.
        Ion transport in silicone hydrogel contact lenses.
        J Membr Sci. 2012; 399–400: 95-105https://doi.org/10.1016/j.memsci.2012.01.039
        • Zhang J.
        • Begley C.G.
        • Situ P.
        • Simpson T.
        • Liu H.
        A link between tear breakup and symptoms of ocular irritation.
        Ocul Surf. 2017; 15: 696-703https://doi.org/10.1016/j.jtos.2017.03.001
        • Guillon M.
        • Maissa C.
        Contact lens wear affects tear film evaporation.
        Eye Contact Lens. 2008; 34: 326-330https://doi.org/10.1097/icl.0b013e31818c5d00
        • Ding J.E.
        • Kim Y.H.
        • Yi S.M.
        • Graham A.D.
        • Li W.
        • Lin M.C.
        Ocular surface cooling rate associated with tear film characteristics and the maximum interblink period.
        Sci Rep. 2021; 11: 15030https://doi.org/10.1038/s41598-021-94568-9
        • Müller L.J.
        • Marfurt C.F.
        • Kruse F.
        • Tervo T.M.T.
        Corneal nerves: Structure, contents and function.
        Exp Eye Res. 2003; 76: 521-542https://doi.org/10.1016/S0014-4835(03)00050-2
        • Maharaj R.L.
        In vivo ocular surface osmolarity in a dry eye population.
        Clin Refract Optom. 2017; 28: 3-6
        • Rosenthal P.
        • Borsook D.
        The Corneal pain system. Part I: The missing piece of the dry eye puzzle.
        Ocul Surf. 2012; 10: 2-14https://doi.org/10.1016/j.jtos.2012.01.002