Models for Tear Film Structure, Dynamics and Parameter Identification

University Of Delaware, Newark DE

Investigators

Abstract

In 2008, nearly 5 million Americans age 50 or older suffered from moderate to severe dry eye, and it is thought that dysfunction of the tear film plays a major role in this condition. This project will develop mathematical models that explain how parts of the tear film function, and the principal investigators will work closely with leading optometrists to achieve this goal. One main thrust of the project will use mathematical models as a way to identify the conditions when the tear film fails, which is often called tear breakup. Computer-generated answers to models that simulate tear breakup can be used to determine local quantities in that cannot be measured experimentally; these quantities are crucial to understanding the mechanisms behind tear breakup and the causes for some instances of dry eye. The other main thrust will use two-layer fluid models to understand the function of the layer much better than is currently known. The lipid layer floats atop an aqueous layer; the lipid layer is a more complex fluid than water, and the aqueous layer can be assumed to act like water. New, more complex models for the floating lipid layer will be developed: the lipid layer will be treated as a so-called liquid crystal. We will solve models for the two layers together and compare them to experimental results. We expect to explain some lipid layer patterns seen experimentally on the eye, and we will solve new mathematical problems to obtain these explanations. Both thrusts of the project will advance our understanding of the tear film and dry eye, as well as advance applied mathematics. The award will provide graduate student training through research. The PIs will investigate the dynamics of thin fluid film models that may be applied to the tear film on the human eye. The two-layer film there has an oily lipid layer floating atop an aqueous layer. There is growing evidence that the floating lipid layer is a liquid crystal in many instances. However, there are essentially no models derived or solved for such two-layer films. In the first main thrust of the project, we propose to develop fundamental models for nematic and smectic A liquid crystals floating on water. In the second main thrust of the project, we also develop parameter identification methods for tear film models through a sequence of problems that will ultimately lead to identifying physical processes responsible for observed physiological tear breakup in the tear film. The project will draw upon the thin liquid film and liquid crystal literature, solve new models for these films, and prove the effectiveness of parameter identification methods on noisy data generated computationally. The project will also involve optometrists to test the theories on observed data. The PIs will combine modeling, analytical and computational approaches, together with experimental data from our collaborators, to advance understanding of two-layer films composed of liquid crystals floating on Newtonian fluids (water). Deriving these complex models and solving them on stationary and moving domains are substantial mathematical challenges. For example, the PIs are unaware of any extensional flow thin film models for smectic A liquid crystals; we will derive and solve models for both free and floating extensional layers. Applying parameter identification approaches to determine parameters on noisy test data for a hierarchy of film models will enable identification of parameters in these complex fluid systems. Beyond significant results in dynamics of complex fluids, the results of the project will enable ocular surface researchers to better understand thin film dynamics and the function of the tear film. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.