BB2: Tear film dynamics

The dynamics of tear films on human eyes are of particular interest to ophthalmologists due to the increasing incidence of dry-eye disease. This may be caused by decreased tear production or increased tear-film evaporation and it is often exacerbated or induced by environmental conditions.  Besides including symptoms of discomfort and visual disturbance, it is associated with tear film instability which can cause damage the ocular surface. It is normally treated using self-administered artificial tears.  

The tear film is a vital biofluid that protects and lubricates the eye's surface. It comprises three layers. Close to the eye surface, there is a very thin mucus layer. Above this is an aqueous layer that provides the majority of the tear-film volume which is capped by a lipid layer containing both polar and nonpolar lipids (which are present in the ratio f about 1:10). Both components are important for the evolution of the tear film: polar lipids reside at the interface between the aqueous and nonpolar lipid layers and reduce the interface tension, while the nonpolar lipids prevent evaporation of the aqueous layer.

The tear film is spread over the surface of the eye by blinking. Between blinks, the tear film thins by evaporation and by drainage into the menisci at the eyelids, and the concentration of salts in the tear fluid increases. Ocular surface damage is known to be caused by an abnormal increase in the concentration of salts within the tear film. However, solute concentrations can only be routinely measured within the fluid menisci residing near the eyelids. Hence, a theoretical relationship between the solute concentration measured in the menisci and the actual concentration in the tear film is crucial to understanding the damage caused by dry eye.

Our primary interests are in examining the effects of the lipid components on the evolution of the tear film during blinking and on the concentration of salts in the tear film over several blinks. In particular, we would like to understand experimental evidence that shows, after the upper eyelid has stopped moving, that the non-polar lipid layer continues to move upwards over the tear film surface. The behaviour of the film during the mechanics of a blink cycle may be crucial in predicting the occurrence of dry-eye and determining the salt concentration.

Our initial model comprises a system of partial differential equations governing the fluid dynamics of the aqueous layer, the concentration of polar lipid, and the fluid dynamics of the nonpolar lipid. The coupling between these equations is nonlinear and leads to interesting regimes. The model is able to capture the nonpolar lipid behaviour following a blink.

Our key challenges are to consider:

• an asymptotic decomposition of the domain, to enhance the predictive power of the model;
• the incorporation of evaporation into the model, and the coupling of evaporation with the thickness of the nonpolar lipid layer;
• the description of the motion of a triple point (between air, nonpolar lipid and water), if one develops;
• the incorporation of a more realistic constitutive relationship for the nonpolar lipid;
• the extension of the model to incorporate the tear film and solute behaviour on a timescale which encompasses numerous blink cycles;
• the examination of how interventions such as the introduction of artificial tears mediate against abnormal increases in salt concentration.

In addition to the immediate consequences and value of such a model to ophthalmology, the mathematical model can be applied to study the behaviour of fluid films in many other biological and industrial contexts, including mucus layers in the lungs, the use of detergents to aid in mechanical clean-up processes of liquid pollutants, and in oil recovery. The project has overlap with the OCCAM project on ionic surfactants, and with projects in OCIAM on thin films and adsorption at interfaces.

The team meets from 1300-1430 on the last Monday of every month.

Selected references:

Aydemir, Breward and Witelski, The effect of polar lipids on tear film dynamics, submitted to Bull Math Biol. Gaffney, Tiffany, Yokoi, Bron, A Mass and Solute Balance Model for Tear Volume and Osmolarity in The Normal And The Dry Eye, submitted to Progress in Retinal and Eye Research.