Mathematical models and numerical methods for human tear film dynamics

Abstract

The human tear film is a multilayer thin film that spreads on the ocular surface. It is essential for clear vision and eye health. This thesis studies dynamics of the human tear film using methods of mathematical modeling and scientific computing. The underlying goal of this work is to theoretically explain phenomena that are observed in vivo, to provide predictions that are yet to be verified by any experiments, and to develop computational approaches to solve the model equations. In this thesis, we formulate three mathematical models that emphasize various physical aspects of tear film dynamics, as well as the associated thermal and osmolarity (the concentration of ions in the tear film) dynamics. We also conduct preliminary numerical study of a hybrid time stepping scheme that is used for solving a coupled system of tear film and osmolarity.