Speaker: Richard J. Braun, University of Delaware

Title: Models for Formation and Drainage of the Human Tear Film

Abstract: Every time one blinks, a tear film is left on the front of the eye. After a brief introduction to the structure of the tear film and the physiology of the anterior eye, recent models for the tear film formation and evolution over one or more blink cycles will be discussed. In these models, lubrication theory is used to derive fourth order nonlinear partial differential equations for the tear film thickness; two different limits of the physiological situation are studied which result in a single PDE. The equations are solved on a moving domain using a modified spectral method. We solve for tear film formation corresponding to eyelid upstroke, subsequent relaxation corresponding to an open eye, and the downstroke of the eyelid to begin the blink cycle again. Results are found for both full and partial blinks. Quantitative comparison with in vivo tear film thickness measurements for half blinks will be made; the results are encouraging. For full blinks, the solutions are periodic, while for half blinks are not; in between there is a transition between periodic and non-periodic behavior. Computational results show that if the eyelids close to about 1/8 of the fully open width, that is enough to fully refresh the tear film. We conclude with future directions in this area.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491