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

Abstract

Purpose: Little quantitative or mechanistic information about tear film breakup can be determined directly via current imaging techniques. In this paper, we present simplified mathematical models based on two proposed mechanisms of tear film breakup: evaporation of water from the tear film and tangential fluid flow within the tear film. We use our models to determine whether one or a combination of the two mechanisms causes tear film breakup in a variety of instances. In this study, we estimate related breakup parameters that cannot currently be measured in breakup during subject trials, such as tear film osmolarity and thinning rates. The present study validates our procedure against previous work.Methods: Five ordinary differential equation models for tear film thinning were designed that model evaporation, osmosis, and various types of tangential flow. Eight tear film breakup instances occurring within a time interval of 1–8 s postblink of five healthy subjects thatwere 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 difference 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 tangential flow rate parameters. The smallest norm of the difference 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 tangential flow. Our optimal parameter values and thinning rate as well as tangential fluid flow profiles compare well with previous partial differential equation model results in most instances.Conclusion: Our fitting results suggest that a combination of tangential fluid flow 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 for wider usage.

Fitting ODE models of tear film breakup

“…79 In this work, we use local models for TBU involving tangential flow, evaporation, osmosis, and FL, but the models have been simplified to ODEs for the thickness, osmolarity, fluorescein, and FL intensity. 80 We find the optimal parameters for these models that make them as close as possible to FL intensity data extracted from video recordings of in vivo TFs. With those optimal parameters, we can infer which effects are most important in each TBU instance.…”

“…The principles of the Declaration of Helsinki were followed during data collection, and informed consent was obtained from all subjects. Data collection is described in a previous publication 19 and discussed in several papers, 19,51,[79][80][81] but will be summarized briefly here. Twenty-five subjects with no self-reported history of DED, ocular surface or systemic disease, or ocular surgery or medications affecting ocular sensation participated in the study.…”

“…The trials typically start with a FL concentration close to 0.2% (discussed more below), which is the so-called critical concentration where peak FL occurs for thin TFs. 83 The critical FL concentration may also be expressed as 0.0053 M. 80…”

“…We model TBU using a hierarchy of ODE models 74,80 represented as a system of non-dimensional equations:…”

“…We use f 0 as the ratio between non-dimensional osmolarity and FL concentration throughout the fit. The permeability parameter in Equation ( 1), P c , varies during the optimization as discussed in the previous section (see also Luke et al 80 ). We excluded any intensity time series that showed substantial, sustained brightening; while this may happen in vivo, 29 we aim to fit thinning and TBU processes.…”