Fitting ODE models of tear film breakup

Abstract

Purpose: Several elements are developed to quantitatively determine the contribution of different physical and chemical effects to tear breakup (TBU) in subjects with no self-reported history of dry eye (DED) or other ocular surface disease. Fluorescence (FL) imaging is employed to visualize the tear film (TF) and to determine TF thinning and potential TBU. Methods: An automated system using a convolutional neural network that was trained and tested on more than 50,000 images from FL imaging experiments was deployed. The trained system could identify multiple TBU instances in each trial. Once identified, extracted FL intensity data was fit by mathematical models that included tangential flow along the eye, evaporation, osmosis, and FL intensity of emission from the TF. The mathematical models consisted of systems of ordinary differential equations for the aqueous layer thickness, osmolarity, and the FL concentration; they are a local approximation to TF thinning and/or TBU dynamics. FL intensity was computed using the resulting thickness and FL concentration. Optimizing the fit of the models to the FL intensity data determined the mechanism(s) driving each instance of TBU and produced an estimate of the osmolarity within TBU. Results: Initial estimates for FL concentration and initial TF thickness agree well with prior results. Fits were produced for N = 467 instances of potential TBU from 15 non-DED subjects. The results showed a distribution of causes of TBU in these healthy subjects, as reflected by estimated flow and evaporation rates, which appear to agree well with previously published data. Final osmolarity depended strongly on the TBU mechanism, generally increasing with evaporation rate but complicated by the dependence on flow. Conclusion: The method has the potential to classify TBU instances based on the mechanism and dynamics, and to estimate the final osmolarity at the TBU locus. The results suggest that it might be possible to classify individual subjects and provide a baseline for comparison and potential classification of DED subjects.