Vladimir Zubkov

2. The Human Tear Film Modelling. OCCAM PDRA Project

tear film modelling

Team leaders: Dr Breward and Dr Gaffney.

Collaborators: Professor Bron, Ophthalmology, Oxford; Dr Tiffany, Ophthalmological Biophysics, Oxford; Professor Please, Mathematics, Southampton; and Professor Braun, Mathematics, Delaware.


The first optical element of the eye is the cornea, essential to for image formation and hence for sight. Damage may cause loss of vision and even blindness. The exposed cornea and adjacent conjunctiva are covered by a protective tear film in the waking state, which prevents desiccation of the surface epithelia by evaporation. The tear film consists of a deeper aqueous layer containing numerous physiological salts and a surface lipid layer. Dysfunction of the aqueous or lipid layers of the tear film give rise to a symptomatic, disabling condition of the ocular surface called dry eye whose prevalence worldwide is between and 12-30%. In the case of dry eye evaporation leads to tear hyperosmolarity, which damages the surface epithelium.


We have formulated and explored a model describing the spatial distribution of tear film osmolarity across the ocular surface of a human eye during one blink cycle, incorporating detailed fluid and solute dynamics. Based on the lubrication approximation, our model comprises three coupled partial differential equations tracking the thickness of the aqueous layer of the tear film, the concentration of the polar lipid and the concentration of physiological salts contained in the aqueous layer. The coupling between these equations is nonlinear. We have also assessed the accuracy of the lubrication tear film model results by explicit comparisons with the numerical solution of 2D Navier-Stokes model.


More generally these studies are motivated by characterizing the influence of natural and artificial lipid dynamics on the tear film behaviour and also understanding the spatial distribution of hyperosmolar ocular surface damage and its correlation with standard diagnostic indices, such as tear meniscus curvature.


More details can be found at here.


tear film modelling

References:

V.S. Zubkov, C.J.W. Breward, E.A. Gaffney, Meniscal tear film fluid dynamics near Marx’s line, submitted to Bulletin of Mathematical Biology.

V.S. Zubkov, C.J.W. Breward, E.A. Gaffney, Coupling fluid and solute dynamics within the ocular surface tear film: A modelling study of black line osmolarity, Bulletin of Mathematical Biology, to appear.