Mechanistic determination of tear film thinning via fitting simplified models to tear breakup

Abstract

Purpose: To determine whether evaporation, tangential flow, or a combination of the two cause tear film breakup in a variety of instances; to estimate related breakup parameters that cannot be measured in breakup during subject trials; and to validate our procedure against previous work. Methods: Five ordinary di erential equation models for tear film thinning were designed that model evaporation, osmosis, and various types of flow. Eight tear film breakup instances of five healthy subjects that were identified in fluorescence images in previous work were fit with these five models. The fitting procedure used a nonlinear least squares optimization that minimized the di erence of the computed theoretical fluorescent intensity from the models and the experimental fluorescent intensity from the images. The optimization was conducted over the evaporation rate and up to three flow rate parameters. The smallest norm of the di erence was determined to correspond to the model that best explained the tear film dynamics. Results: All of the breakup instances were best fit by models with time-dependent flow. Our optimal parameter values and thinning rate and fluid flow profiles compare well with previous partial di erential equation model results in most instances. Conclusion: Our fitting procedure suggests that the combination of the Marangoni effect and evaporation cause most of the breakup instances. Comparison with results from previous work suggests that the simplified models can capture the essential tear film dynamics in most cases, thereby validating this procedure as one that could be used on many other instances.