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A model of tear-film breakup with continuous mucin concentration and viscosity profiles

Published online by Cambridge University Press:  06 November 2018

Mohar Dey ,
Atul S. Vivek ,
Harish N. Dixit Open the ORCID record for Harish N. Dixit [Opens in a new window] ,
Ashutosh Richhariya  and
James J. Feng Open the ORCID record for James J. Feng [Opens in a new window]
Mohar Dey
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Atul S. Vivek
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, India
Harish N. Dixit
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, India
Ashutosh Richhariya
Affiliation:
L. V. Prasad Eye Institute, Hyderabad, Telangana 500034, India
James J. Feng*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
*
†Email address for correspondence: [email protected]
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Abstract

We propose an alternative to the prevailing framework for modelling tear-film breakup, which posits a layered structure with a mucus layer next to the cornea and an aqueous layer on top. Experimental evidence shows continuous variation of mucin concentration throughout the tear film, with no distinct boundary between the two layers. Thus, we consider a continuous-viscosity model that replaces the mucus and aqueous layers by a single liquid layer with continuous profiles of mucin concentration and viscosity, which are governed by advection–diffusion of mucin. The lipids coating the tear film are treated as insoluble surfactants as previously, and slip is allowed on the ocular surface. Using the thin-film approximation, we carry out linear stability analysis and nonlinear numerical simulations of tear-film breakup driven by van der Waals attraction. Results show that for the same average viscosity, having more viscous material near the ocular surface stabilizes the film and prolongs the breakup time. Compared with the layered models, the continuous-viscosity model predicts film breakup times that are in better agreement with experimental data. Finally, we also suggest a hydrodynamic explanation for how pathological loss of membrane-associated mucins may lead to faster breakup.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 352 - 376
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Copyright
© 2018 Cambridge University Press 

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References

Albertsmeyer, A.-C., Kakkassery, V., Spurr-Michaud, S., Beeks, O. & Gipson, I. K. 2010 Effect of pro-inflammatory mediators on membrane-associated mucins expressed by human ocular surface epithelial cells. Exp. Eye Res. 90 (3), 444–451.Google Scholar
Bandyopadhyay, D. & Sharma, A. 2006 Nonlinear instabilities and pathways of rupture in thin liquid bilayers. J. Chem. Phys. 125, 054711.Google Scholar
Berger, R. & Corrsin, S. 1974 A surface tension gradient mechanism for driving the pre-corneal tear film after a blink. J. Biomech. 7, 225–238.Google Scholar
Braun, R. & King-Smith, P. E. 2007 Model problems for the tear film in a blink cycle: single equation models. J. Fluid Mech. 586, 465–490.Google Scholar
Braun, R. J. 2012 Dynamics of tear films. Annu. Rev. Fluid Mech. 44, 267–297.Google Scholar
Braun, R. J., Driscoll, T. A., Begley, C. G., King-Smith, P. E. & Siddique, J. I. 2018 On tear film breakup (TBU): dynamics and imaging. Math. Med. Biol. 35, 145–180.Google Scholar
Braun, R. J., Usha, R., McFadden, G. B., Driscoll, T. A., Cook, L. P. & King-Smith, P. E. 2012 Thin film dynamics on a prolate spheroid with application to the cornea. J. Engng Maths 73, 121–138.Google Scholar
Bron, A. J., Argüeso, P., Irkec, M. & Bright, F. V. 2015 Clinical staining of the ocular surface: mechanisms and interpretations. Prog. Retin. Eye Res. 44, 36–61.Google Scholar
Bron, A. J., Tiffany, J. M., Gouveia, S. M., Yokoi, N. & Voon, L. W. 2004 Functional aspects of the tear film lipid layer. Exp. Eye Res. 78, 347–360.Google Scholar
Bruna, M. & Breward, C. J. W. 2014 The infuence of non-polar lipids on tear fillm dynamics. J. Fluid Mech. 746, 565–605.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 464–494.Google Scholar
Celli, J., Gregor, B., Turner, B., Afdhal, N. H., Bansil, R. & Erramilli, S. 2005 Viscoelastic properties and dynamics of porcine gastric mucin. Biomacromolecules 6, 1329–1333.Google Scholar
Chen, H. B., Yamabayashi, S., Tanaka, Y., Ohno, S. & Tsukahara, S. 1997 Structure and composition of rat precorneal tear film: a study by an in vitro cryofixation. Invest. Ophthalmol. Vis. Sci. 38, 381–387.Google Scholar
Cho, P. & Douthwaite, W. 1992 Tear breakup time and the effect of lifting the eyelid during its measurement. Clin. Exp. Optom. 75, 231–235.Google Scholar
Craig, J. & Tomlinson, A. 1997 Importance of the tear film lipid layer in human tear film stability and evaporation. Optom. Vis. Sci. 33, 8–13.Google Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.Google Scholar
De Wit, A., Gallez, D. & Christov, C. I. 1994 Nonlinear evolution equations for thin liquid films with insoluble surfactants. Phys. Fluids 6, 3256–3266.Google Scholar
Deng, Q., Braun, R. J. & Driscoll, T. A. 2014 Heat transfer and tear film dynamics over multiple blink cycles. Phys. Fluids 26, 071901.Google Scholar
Dohlman, C. H., Friend, J., Kalevar, V., Yagoda, D. & Balazs, E. 1976 The glycoprotein (mucus) content of tears from normals and dry eye patients. Exp. Eye Res. 22, 359–365.Google Scholar
Ern, P., Charru, F. & Luchini, P. 2003 Stability analysis of a shear flow with strongly stratified viscosity. J. Fluid Mech. 496, 295–312.Google Scholar
Ghosh, S., Usha, R. & Sahu, K. C. 2014 Linear stability analysis of miscible two-fluid flow in a channel with velocity slip at the walls. Phys. Fluids 26, 014107.Google Scholar
Gipson, I. K. 2004 Distribution of mucins at the ocular surface. Exp. Eye Res. 78, 379–388.Google Scholar
Govindarajan, B. & Gipson, I. K. 2010 Membrane-tethered mucins have multiple functions on the ocular surface. Exp. Eye Res. 90, 655–663.Google Scholar
Gribbon, P. & Hardingham, T. E. 1998 Macromolecular diffusion of biological polymers measured by confocal fluorescence recovery after photobleaching. Biophys. J. 75, 1032–1039.Google Scholar
Heryudono, A., Braun, R. J., Driscoll, T. A., Maki, K. L., Cook, L. P. & King-Smith, P. E. 2007 Single-equation models for the tear film in a blink cycle: realistic lid motion. Math. Med. Biol. 24, 347–377.Google Scholar
Hodges, R. R. & Dartt, D. A. 2013 Tear film mucins: front line defenders of the ocular surface; comparison with airway and gastrointestinal tract mucins. Exp. Eye Res. 117, 62–78.Google Scholar
Holly, F. J. & Lemp, M. A. 1977 Tear physiology and dry eyes. Surv. Ophthalmol. 22, 69–87.Google Scholar
Inatomi, T., Spurr-Michaud, S., Tisdle, A. S., Zhan, Q., Feldman, S. T. & Gipson, I. K. 1996 Expression of secretory mucin genes by human conjunctival epithelia. Invest. Ophthalmol. Vis. Sci. 37, 1684–1692.Google Scholar
Jones, M. B., Please, C. P., McElwain, D. L., Fulford, G. R., Roberts, A. P. & Collins, M. J. 2005 Dynamics of tear film deposition and draining. Math. Med. Biol. 22, 265–288.Google Scholar
Jossic, L., Lefevre, P., Loubens, C., Magnin, A. & Corre, C. 2009 The fluid mechanics of shear-thinning tear substitutes. J. Non-Newtonian Fluid Mech. 161, 1–9.Google Scholar
King-Smith, P. E., Begley, C. G. & Braun, R. J. 2018 Mechanisms, imaging and structure of tear film breakup. Ocul. Surf. 16, 4–30.Google Scholar
Korb, D. R., Greiner, J. V. & Herman, J. 2001 Comparison of fluorescein break-up time measurement reproducibility using standard fluorescein strips versus the dry eye test (DET) method. Cornea 20, 811–815.Google Scholar
Lemp, M. A. & Hamill, J. R. 1973 Factors affecting tear film breakup in normal eyes. Arch. Ophthalmol. 89, 103–105.Google Scholar
Liu, H., Begley, C., Chen, M., Bradley, A., Bonanno, J., McNamara, N. A., Nelson, J. D. & Simpson, T. 2009 A link between tear instability and hyperosmolarity in dry eye. Invest. Ophthalmol. Vis. Sci. 50, 3671–3679.Google Scholar
Mantelli, F. & Argueso, P. 2008 Functions of ocular surface mucins in health and disease. Curr. Opin. Allergy Clin. Immunol. 8, 477–483.Google Scholar
Matar, O. 2002 Nonlinear evolution of thin free viscous films in the presence of soluble surfactant. Phys. Fluids 14, 4216–4234.Google Scholar
McCulley, J. P. & Shine, W. 1997 A compositional based model for the tear film lipid layer. Trans. Am. Ophthalmol. Soc. 95, 79–93.Google Scholar
Mengher, L. S., Bron, A. J., Tonge, S. R. & Gilbert, D. J. 1985 A non-invasive instrument for clinical assessment of the precorneal tear film stability. Curr. Eye Res. 4, 1–7.Google Scholar
Nagyová, B. & Tiffany, J. M. 1999 Components responsible for the surface tension of human tears. Curr. Eye Res. 19, 4–11.Google Scholar
Norn, M. S. 1969 Desiccation of the precorneal film. Part I. Corneal wetting-time. Acta Ophthalmol. 47, 865–880.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.Google Scholar
Peng, C. C., Cerretani, C., Braun, R. J. & Radke, C. J. 2014 Evaporation-driven instability of the precorneal tear film. Adv. Colloid Interface Sci. 206, 250–264.Google Scholar
Pototsky, A., Bestehorn, M., Merkt, D. & Thiele, U. 2004 Alternative pathways of dewetting for a thin liquid two-layer film. Phys. Rev. E 70 (2), 025201.Google Scholar
Prydal, J. I. & Campbell, F. W. 1992 Study of precorneal tear film thickness and structure by interferometry and confocal microscopy. Invest. Ophthalmol. Vis. Sci. 33, 1996–2005.Google Scholar
Ruckenstein, E. & Jain, R. K. 1974 Spontaneous rupture of thin liquid films. J. Chem. Soc., Faraday Trans. 2 70, 132–147.Google Scholar
Selinger, D. S., Selinger, R. C. & Reed, W. P. 1979 Resistance to infection of the external eye: the role of tears. Surv. Ophthalmol. 24, 33–38.Google Scholar
Sharma, A. 1998 Acid–base interactions in the cornea-tear film system: surface chemistry of corneal wetting, cleaning, lubrication, hydration and defense. J. Dispersion Sci. Technol. 19, 1031–1068.Google Scholar
Sharma, A., Khanna, R. & Reiter, G. 1999 A thin film analog of the corneal mucus layer of the tear film: an enigmatic long range non-classical DLVO interaction in the breakup of thin polymer films. Colloids Surf. B 14, 223–235.Google Scholar
Sharma, A. & Ruckenstein, E. 1985 Mechanism of tear film rupture and formation of dry spots on cornea. J. Colloid Interface Sci. 106, 12–27.Google Scholar
Sharma, A. & Ruckenstein, E. 1986a An analytical nonlinear theory of thin film rupture and its application to wetting films. J. Colloid Interface Sci. 113, 456–479.Google Scholar
Sharma, A. & Ruckenstein, E. 1986b The role of lipid abnormalities, aqueous and mucus deficiencies in the tear film breakup, and implications for tear substitutes and contact lens tolerance. J. Colloid Interface Sci. 111, 8–34.Google Scholar
Siddique, J. I. & Braun, R. J. 2015 Tear film dynamics with evaporation, osmolarity and surfactant transport. Appl. Math. Model. 39, 255–269.Google Scholar
Stevenson, W., Chauhan, S. K. & Dana, R. 2012 Dry eye disease: an immune-mediated ocular surface disorder. Arch. Ophthalmol. 130, 90–100.Google Scholar
Sullivan, B. D., Crews, L. A., Sonmez, B., de la Paz, M. F., Comert, E., Charoenrook, V., de Araujo, A. L., Pepose, J. S., Berg, M. S., Kosheleff, V. P. & Lemp, M. A. 2012 Clinical utility of objective tests for dry eye disease: variability over time and implications for clinical trials and disease management. Cornea 31, 1000–1008.Google Scholar
Sweeney, D. F., Millar, T. J. & Raju, S. R. 2013 Tear film stability: a review. Exp. Eye Res. 117, 28–38.Google Scholar
Tiffany, J. M. 1991 The viscosity of human tears. Intl Ophthalmol. 15, 371–376.Google Scholar
Usha, R., Tammisola, O. & Govindarajan, R. 2013 Linear stability of miscible two-fluid flow down an incline. Phys. Fluids 25, 104102.Google Scholar
Vanley, G. T., Irving, B. A., Leopold, H. & Gregg, T. H. 1977 Interpretation of tear film break-up. Arch. Ophthalmol. 95, 207–209.Google Scholar
William, M. B. & Davis, S. H. 1982 Nonlinear theory of film rupture. J. Colloid Interface Sci. 90, 220–228.Google Scholar
Winter, K. N., Anderson, D. M. & Braun, R. J. 2010 A model for wetting and evaporation of a post-blink precorneal tear film. Math. Med. Biol. 27, 211.Google Scholar
Yañez-Soto, B., Mannis, M. J., Schwab, I. R., Li, J. Y., Leonard, B. C., Abbott, N. L. & Murphy, C. J. 2014 Interfacial phenomena and the ocular surface. Ocul. Surf. 12, 178–201.Google Scholar
Yokoi, N., Georgiev, G., Kato, H., Komuro, A., Sonomura, Y., Sotozono, C., Tsubota, K. & Kinoshita, S. 2017 Classification of fluorescein breakup patterns: a novel method of differential diagnosis for dry eye. Am. J. Ophthalmol. 180, 72–85.Google Scholar
Zhang, Y. L., Craster, R. V. & Matar, O. K. 2003a Analysis of tear film rupture: effect of non-Newtonian rheology. J. Colloid Interface Sci. 262, 130–148.Google Scholar
Zhang, Y. L., Craster, R. V. & Matar, O. K. 2003b Surfactant driven flows overlying a hydrophobic epithelium: film rupture in the presence of slip. J. Colloid Interface Sci. 264, 160–175.Google Scholar
Zhang, Y. L., Craster, R. V. & Matar, O. K. 2004 Rupture analysis of the corneal mucus layer of the tear film. Mol. Simul. 30, 167–172.Google Scholar
Zhong, L., Ketelaar, C. F., Braun, R. J., Begley, C. G. & King-Smith, P. E. 2018 Mathematical modelling of glob-driven tear film breakup. Math. Med. Biol. doi:10.1093/imammb/dqx021.Google Scholar