Profs. Richard Braun (PI) and Tobin Driscoll (CoPI) have been awarded a three year NSF grant from the Division of Mathematical Sciences; the project is funded for about $444,000 from the Program in Mathematical Biology and the Cyber-enabled Discovery Initiative. The grant includes support for two graduate students and support to travel to meetings to disseminate the results.

The project will study dynamics of the thin liquid film that coats the front of the eye during and after each blink: the tear film. This thin layer is critical for clear vision and a healthy eye. The spreading and dynamics of the tear film will be studied with a hierarchy of new mathematical models and will develop new computational methods to solve them. There will be two thrusts for the project, with one involving stationary eye-shaped domains and the other on moving but simpler-shaped domains. Successful application of these methods will 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 will improve accepted mathematical models from our group 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, and the computational approaches benefit from continued collaboration with Lawrence Livermore National Laboratory.