Researcher(s)
- Jordan Photis, Applied Mathematics, University of Delaware
Faculty Mentor(s)
- Richard Braun, Mathematical Sciences, University of Delaware
Abstract
The tear film (TF) is a thin fluid layer of the eye which has the purpose of protecting and nourishing the eye. As the TF thins over time, an instance of tear film breakup (TBU) eventually occurs. TBU causes irritation in the eye until one blinks which restores the TF. Some eye irritation may be normal, but an excessive frequency and amount of TBU can be a sign of dry eye disease, a problem affecting millions of people. One way to understand dry eye disease is to measure what happens when TBU occurs; however, there is currently no way to directly measure TF quantities during TBU. One solution is to create mathematical models to replicate what happens within the TF during TBU. This project develops a simple model that governs the aqueous and lipid layers of the TF as well as the cornea and TF temperatures. A system of differential equations (DEs) governs the TF thickness, and the osmolarity and fluorescein concentrations; they include the effects of divergent flow, evaporation, osmosis and fluorescence. Those DEs are combined with a partial differential equation governing the temperature of a model cornea and the TF surface. A realistic model of evaporation of water from the TF is part of the model as well. We solve the discretized differential-algebraic equations simultaneously using MATLAB’s ode15s to find a numerical solution. The model can closely approximate data measured in vivo for TF temperature and fluorescent intensity. The flow and evaporation parameters have a strong effect on TF variables, while the convective cooling rate has the strongest effect on the temperature at the TF surface. The model is able to fit TF data from various data sets with similar success when compared to other models. The model can likely give valuable information about data from some instances; however, more trials are needed to confirm how widely the models can be applied.