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Bulletin of Mathematical Biology

, Volume 70, Issue 2, pp 323–343 | Cite as

Elastohydrodynamics of the Eyelid Wiper

  • M. B. JonesEmail author
  • G. R. Fulford
  • C. P. Please
  • D. L. S. McElwain
  • M. J. Collins
Original Article

Abstract

This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface. For the lubrication film to be effective, it is required that the orientation of the eyelid wiper changes between the opening and closing phases of a blink. In order to model this, the hydrodynamic model is coupled with an elastic mattress model for the soft tissue of the eyelid wiper and ocular surface. This leads to a one-dimensional non-linear partial differential equation governing the fluid pressure in the lubrication film. In order to solve the differential equation, a loading condition or constraint equation must be specified. The resulting system is then solved numerically. The model allows predictions of the tear film flux from under the upper eyelid, as well as normal and shear stresses acting on the ocular surface. These factors are important in relation to dry eye syndrome, deformation of the cornea and contact lens design. It is found that the pressure and shear stress under the eyelid act across a length of approximately 0.1 mm which is consistent with clinical observations. It order to achieve a flow of tears from under the upper eyelid during a blink, the model requires that the normal force the eyelid applies to the ocular surface during the closing phase of the blink is significantly higher than during the opening phase of the blink.

Keywords

Tear film Lubrication theory Dry eye Eyelid 

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References

  1. Agache, P.G., Monneur, C., Leveque, J.L., Rigal, J.D., 1980. Mechanical properties and Young’s modulus of human skin in vivo. Arch. Dermatol. Res. 269, 221–232. CrossRefGoogle Scholar
  2. Anderson, K., El-Sheikh, A., Newson, T., 2004. Application of structural analysis to the mechanical behaviour of the cornea. J. Roy. Soc. Interface 1, 3–15. CrossRefGoogle Scholar
  3. Bissett, E.J., 1989. The line contact problem of elastohydrodynamic lubrication. I. Asymptotic structure for low speeds. Proc. Roy. Soc. Lond. A 424, 393–407. zbMATHMathSciNetGoogle Scholar
  4. Bron, A.J., Tripathi, R.C., Tripathi, B.J., Wolff, E., 1997. Wolff’s Anatomy of the Eye and Orbit, 8th edn. Chapman & Hall Medical, London. Google Scholar
  5. Buehren, T., Collins, M.J., Carney, L.G., 2003. Corneal aberrations and reading. Optom. Vis. Sci. 80(2), 159–166. CrossRefGoogle Scholar
  6. Chauhan, A., Radke, C.J., 2002. Settling and deformation of a thin elastic shell on a thin fluid layer lying on a solid surface. J. Colloid Interface Sci. 245, 187–197. CrossRefGoogle Scholar
  7. Collins, M.J., Buehren, T., Bece, A., Voetz, S.C., 2006. Corneal optics after reading, microscopy and computer work. Acta Ophthalmol. Scand. 84, 216–224. CrossRefGoogle Scholar
  8. Doughty, M.J., 2001. In consideration of three types of spontaneous eyeblink activity in normal humans: during reading and VDT use, in primary gaze and while in conversation. Optom. Vis. Sci. 78, 712–725. CrossRefGoogle Scholar
  9. Doughty, M.J., Bergmanson, J.P., 2003. New insights into the surface cells and glands of the conjunctiva and their relevance to the tear film. Optometry 74(8), 485–500. Google Scholar
  10. Doughty, M.J., Naase, T., Donald, C., Hamilton, L., Button, N.F., 2004. Visualisation of ‘Marx’s line’ along the marginal eyelid conjunctiva of human subjects with lissamine green dye. Ophthal. Physiol. Opt. 24, 1–7. CrossRefGoogle Scholar
  11. Ehrmann, K., Francis, I., Stapleton, F., 2001. A novel instrument to quantify the tension of upper and lower eyelids. Cont. Lens Ant. Eye 24, 65–72. CrossRefGoogle Scholar
  12. Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M., Rossi, F., 2005. GNU Scientific Library: Reference Manual. Network Theory Limited, Bristol. Google Scholar
  13. Hjortdal, J.O., 1996. Regional elastic performance of the human cornea. J. Biomech. 29(7), 931–942. CrossRefGoogle Scholar
  14. Hughes, C., Hamilton, L., Doughty, M.J., 2003. A quantitative assessment of the location and width of Marx’s line along the marginal zone of the human eyelid. Opt. Vis. Sci. 80(8), 564–572. CrossRefGoogle Scholar
  15. Johnson, L., 1985. Contact Mechanics. Cambridge University Press, Cambridge. zbMATHGoogle Scholar
  16. Jones, M.B., McElwain, D.L.S., Fulford, G.R., Collins, M.J., Roberts, A.P., 2006. The effect of the lipid layer on tear film behaviour. Bull. Math. Biol. 68, 1–27. CrossRefMathSciNetGoogle Scholar
  17. Jones, M.B., Please, C.P., McElwain, D.L.S., Fulford, G.R., Roberts, A.P., Collins, M.J., 2005. Dynamics of tear film deposition and draining. Math. Med. Biol. 22, 265–288. zbMATHCrossRefGoogle Scholar
  18. Korb, D.R., Herman, J.P., Greiner, J.V., Scaffidi, R.C., Finnemore, V.M., Exford, J.M., Blackie, C.A., Douglass, T., 2005. Lid wiper epitheliopathy and dry eye symptoms. Eye Contact Lens 31(1), 2–8. CrossRefGoogle Scholar
  19. Lydon, D., Tait, A., 1988. Lid pressure: its measurement and probable effects on the shape and form of the cornea-rigid contact lens system. J. BCLA 11(1), 11–22. Google Scholar
  20. Mathers, W.D., Daley, T.E., 1996. Tear flow and evaporation in patients with and without dry eye. Ophthalmol. 103(4), 664–669. Google Scholar
  21. Miller, D., 1967. Pressure of the lid on the eye. Arch. Ophthal. 78, 328–330. Google Scholar
  22. Mishima, S., Gasset, A., Klyce, S.D., Baum, J.L., 1966. Determination of tear volume and tear flow. Invest. Ophthalmol. 5(3), 264–275. Google Scholar
  23. Nagyova, B., Tiffany, J.M., 1999. Components responsible for the surface tension of human tears. Curr. Eye Res. 19, 4–11. CrossRefGoogle Scholar
  24. Remington, L.A., 2005. Clinical Anatomy of the Visual System. Elsevier, St. Louis. Google Scholar
  25. Ren, H., Wilson, G., 1997. The effect of a shear force on the cell shedding rate of the corneal epithelium. Acta Ophthalmol. Scand. 75, 383–387. Google Scholar
  26. Skotheim, J.M., Mahadevan, L., 2005. Soft lubrication: the elastohydrodynamics of nonconforming and conforming contacts. Phys. Fluids 17, 092101(23). CrossRefMathSciNetGoogle Scholar
  27. Tripathi, B.J., Tripathi, R.C., Borisuth, N.S.C., 1994. Microscopic anatomy and ultrastructure of the cornea, conjunctiva and lids. In: M. Ruben, M. Guillon (Eds.), Contact Lens Practice. Chapman & Hall, London, pp. 211–223, Chap. 12. Google Scholar
  28. Woo, S., Kobayashi, A., Lawrence, C., Schlegel, W., 1972. Nonlinear material properties of intact cornea and sclera. Exp. Eye Res. 14, 29–39. CrossRefGoogle Scholar
  29. Yokoi, N., Bron, A.J., Tiffany, J.M., Brown, N.A.P., Hsuan, J.D., Fowler, C., 1999. Reflective meniscometry: a non-invasive method to measure tear meniscus curvature. Br. J. Ophthalmol. 83, 92–97. CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2007

Authors and Affiliations

  • M. B. Jones
    • 1
    Email author
  • G. R. Fulford
    • 1
  • C. P. Please
    • 2
  • D. L. S. McElwain
    • 1
  • M. J. Collins
    • 3
  1. 1.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia
  2. 2.School of MathematicsUniversity of SouthamptonSouthamptonUK
  3. 3.School of OptometryQueensland University of TechnologyBrisbaneAustralia

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