Models of the tear film interaction with the ocular surface
Date
2013-05
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
Mathematical models that connect the tear lm with the underlying epithelia of the
cornea and conjunctiva were developed. The tear lm is assumed to be a spatially uniform
evaporating aqueous layer with a concentration variable representing the osmolarity in the
tear lm. In the rst model, the underlying epithelia are approximated as in Levin and
Verkmann [6], with a few layers of cells of varying thickness that are linked via osmosis
between each of the cells and with the tear lm. Loss of water due to evaporation from the
tear lm causes increased osmolarity there, leading to osmotic
ow from the epithelium to
the tear lm, and between the epithelial cells. The parameters are set by comparison with
thinning rate measurements from human subjects in vivo. In those experiments, 5%
uores-
cein solution is instilled in the tear lm, and the thickness of the tear lm is deduced from
subsequent intensity measurements in the concentrated
ourescein regime. These measure-
ments were used to calibrate the model parameters for osmosis. A second model is proposed
that includes the molecules involved in metabolism in the epithelial cell of the cornea. This
model is based on the Leung et al model [3]. The proposed model includes di erential and
algebraic equations to represent the concentrations of the metabolites in the cells and their
e ects over time. Both models are used to predict tear lm thickness and osmolarity, as well
as epithelial cell layer thicknesses and osmolarities. The rst model predicts thickness and
osmolarity changes for single interblinks and for extended periods of many blink cycles with
constant interblink duration. Cumulative e ects from multiple blink cycles are seen that are
signi cantly more than for single interblinks. We interpret the results in light of biochemical
response and the rate of progression of apoptosis in squamous cells.