Models for Interaction of the Tear Film with the Corneal and Conjunctival Epithelia

Abstract

 

Purpose

 

Evaporation has been shown to be an important factor in the dynamics of the tear film (TF). The increased osmolarity from evaporation affects the underlying epithelium. We construct a mathematical model for the TF thickness (h), osmolarity (c) and the thicknesses of the underlying epithelia (hi) for both the cornea and the conjunctiva. The osmolarity in the TF and the epithelial cells is computed over many blink cycles for different interblink times.

 

Methods

 

Equations similar to those of Levin and Verkman for the epithelial layer thicknesses are coupled to equations for the TF thickness and osmolarity. Water transport is by osmosis through the cells to the TF; this is assumed to be the only interaction between each of the cells and with the TF. Seven epithelial cells of varying initial thickness represent the corneal epithelium (CoE; see Figure 1); four cells of different sizes represent the conjunctival epithelium (CjE). The TF thinning rate is specified by the parameters to match observed rates; permeability of cell boundaries is chosen to fit permeability values deduced from thinning rate measurements (previously described). The TF thickness was deduced from fluorescence imaging in the quenching regime from 15 subjects who kept the eye open for 60s. The system of ordinary differential equations is solved by custom MATLAB programs.

 

Results

 

For single interblinks of 6s or 30s with an initial 2.5 micron/min thinning rate, the change in osmolarity in the tear film is relatively small because osmosis is slow through the cells. For many blink cycles, with 6s interblinks, the osmolarity remains low in both the CoE and CjE. For many 30s interblinks in sequence and 2.5 micron/min, the TF osmolarity rises to 394 mOsm, and to 356 mOsm in the first cell layer of the CoE. In the CjE with an initial thinning rate of 1.4 micron/min (from measured rate), the TF increases to 334 mOsm, and the first cell rises to 323 mOsm. Cells beneath the first layer rose to smaller values. These osmolarity values do not correspond to tear breakup: they are spot values after a fixed repeated interblink interval.

 

Conclusions

 

The model can predict the osmolarities in the TF, CoE and CjE , for different thinning rates. The cornea is exposed to higher osmolarities than the conjunctiva for the same initial thinning rate.

 

 

Figure 1. A schematic of the model. Evaporation from the top of tear film drives osmolarity changes.

 

Keywords: 486 cornea: tears/tear film/dry eye • 482 cornea: epithelium • 474 conjunctiva