Elastohydrodynamics of the Eyelid Wiper
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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.
KeywordsTear film Lubrication theory Dry eye Eyelid
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- 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
- 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
- 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
- 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
- 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
- Miller, D., 1967. Pressure of the lid on the eye. Arch. Ophthal. 78, 328–330. Google Scholar
- 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
- Remington, L.A., 2005. Clinical Anatomy of the Visual System. Elsevier, St. Louis. Google Scholar
- 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
- 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