BB2: Tear film dynamics

Project completed June 30, 2012

Background

The first optical element of the eye is the cornea, which is essential for image formation. Damage to the cornea may cause loss of vision and even blindness. The exposed cornea and adjacent conjunctiva are covered by a protective tear film. The tear film consists of a surface lipid layer and a deeper aqueous layer. The lipid is spread onto the tear film with each blink. It serves to lower the surface tension of the tear film and is critical to retard evaporation from the eye. Dysfunction of the aqueous or lipid layers of the tear film, such as a decrease in aqueous tear production or a defective tear film lipid layer, give rise to a symptomatic, disabling condition of the ocular surface called dry eye. Dry eye’s prevalence worldwide is between 12 and 30%. In each case, evaporation leads to tear hyperosmolarity (an increase in concentration of solutes) which can damage the surface of the eye.

The biophysical factors that dictate dysfunction of the tear film are poorly understood and are difficult to investigate experimentally, highlighting the need for mathematical modelling in this field. Researchers at the Oxford Centre for Collaborative Applied Mathematics (OCCAM) exploit tear film observations in order to develop and validate the current model of the tear film. 

Techniques and Challenges

Particular challenges for modelling the tear film are the blinking eyelid and free surface of the tear film, because the domain is moving. The full hydrodynamic, three-dimensional model is too complicated to be solved numerically. Based on the lubrication approximation, the researchers derived a simplified model that comprises a system of one-dimensional, nonlinear, coupled partial differential equations (PDEs) tracking the depth of the aqueous layer of the tear film, the concentration of the polar lipid, and the concentration of physiological solutes contained in the aqueous layer.

Results

Observations: This work explored the behaviour of osmolarity and lipids within the ocular surface fluid during a blink–interblink cycle. In particular, the researchers observed osmolar heterogeneity across the ocular surface, and that measurements of solute concentrations within the lower meniscus need not reflect those in the upper meniscus (see Figure 1). In addition, polar lipid profiles were predicted to be very heterogeneous, with a thin layer forming across the tear film together with reservoirs at the menisci during the up-blink, subsequently followed by polar lipid transport from the reservoirs onto the central film during the interblink.

Diffusion was predicted to be insufficient in preventing relative hyperosmolarity at the so-called black lines (regions of very thin tear film). This was especially true when considering dry eye conditions. In addition, eyeball motions, such as the look-down vertical saccadic motions, can ameliorate lower meniscus black line osmolarity.

Finally, it was observed that without evaporative retardation, high black line osmolarities would emerge at extremely thin tear film depths. Thus, evaporative retardation is likely to play an important role in limiting ocular hyperosmolarity and resulting surface damage at the black lines.

Model: The model is limited to the use of the lubrication approximation, which is not guaranteed to be uniformly valid a priori throughout the tear meniscus. However, resolving tear film behaviour within the meniscus and especially its apices is required to characterise the flow dynamics where the tear film is especially thin and thus most susceptible to evaporatively-induced hyperosmolarity and subsequent epithelial damage. The accuracy of the model was explored by explicit comparisons with the 2D Navier–Stokes model (only the aqueous component of the tear film was considered). Results demonstrated that the lubrication model is qualitatively accurate except in the vicinity of the eyelids. In particular, and in contrast to lubrication theory, the solution of the full Navier–Stokes equations predicts a distinct absence of fluid flow, and thus an absence of convective mixing, in the region adjacent to the tear film contact line. These observations not only support emergent hypotheses concerning the formation of Marx’s line (a region of epithelial cell staining adjacent to the contact line on the eyelid), but also enhance the understanding of the pathophysiological consequences of the flow profile near the tear film contact line.

The Future

Further detailed studies of the lubrication model, incorporating non-polar lipids and the influence of lipids on evaporation, will enable comparison with observations of the combined polar and non-polar lipid layer behaviours near the lower lid margins, as well as an in-depth exploration of the evaporative barrier role of lipids.

A clear extension of the 2D Navier–Stokes model is the inclusion of evaporation and lipid dynamics together with solute transport to further investigate the Marx’s line hyperosmolar hypothesis.

Initial results of the tear film experimental modelling using a ‘mechanical eye’ look very promising. Further experimental studies could explain in vivo observations, showing that after the upper eyelid has stopped moving, the non-polar lipid layer continues to move upwards over the tear film surface.

Related Publications

[12/51] Zubkov V.S., Breward C.J.W., Gaffney E.A.: Meniscal tear film fluid dynamics near Marx’s line

[11/43] Zubkov V.S., Breward C.J.W., Gaffney E.A.: Coupling fluid and solute dynamics within the ocular surface tear film: a modelling study of black line osmolarity, Bulletin of Mathematical Biology

[09/24] Aydemir E., Breward C.J.W., Witelski T.P.: The effect of polar lipids on tear film dynamics, Bulletin of Mathematical Biology

[09/01] 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, Progress in Retinal and Eye Research