Modeling Tear Film Dynamics

University Of Delaware, Newark DE

Investigators

Abstract

The spreading and dynamics of the tear film will be studied with a hierarchy of computational models. The starting point is a single liquid layer governed by two partial differential equations (PDEs), one for the tear film thickness and one for the tear film osmolarity. The project progresses to models with additional PDEs involving surfactant transport and multiple liquid layers as well. More detailed understanding of evaporation and lipid layer dynamics, especially as applied to tear film breakup and osmolarity variation, will emerge from this work. Two methods will be used in the computational approaches to these problems. For eye-shaped domains, an overset grid method via the Overture framework from Lawrence Livermore National Laboratory provides much of the software capability needed to manage complex boundaries; some solvers specific to the tear film problems have been and are developed at Delaware. For simpler geometries, the investigators use spectral and adaptive radial basis function (RBF) methods to take advantage of a grid free approach near small regions of rapid variation in some of the problems. Successful application of these methods bring new capabilities for understanding tear film dynamics. New understanding of tear film dynamics would benefit a large number of people. As of 1998, up to ten million Americans required use of artificial tear preparations; nearly 5 million Americans age 50 or older suffer from moderate to severe dry eye symptoms. This project improves accepted mathematical models to include more physiologically important effects, particularly osmolarity, the combined concentration of certain salts and sugars in the tear film. Osmolarity is suspected by physicians of being crucial in the development of dry eye, and the model yields new insights into tear film and osmolarity dynamics. The project benefits from synergy in the intensive collaboration with optometrists at the Ohio State University. This vital collaboration allows the research team to understand and interpret the computationally-generated results and make close comparisons with images and videos obtained through experiments. The computational approaches benefit from continued collaboration with Lawrence Livermore National Laboratory. Dissemination of results are joint with between the mathematicians and their optometrist collaborators in both the applied-mathematical and biomedical communities; results are presented at major major scientific meetings in mathematics, fluid-dynamics, and eye-related fields. As part of reaching these goals, graduate students are trained in multidisciplinary applications of mathematical modeling and computational mathematics.