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Richard J Braun, Rayanne A Luke, Alexandra Manchel, Deborah Awisi-Gyau, Carolyn G Begley; Fitting Simple Models of Tear Break Up (TBU) to Fluorescence Data. Invest. Ophthalmol. Vis. Sci. 2020;61(7):353.
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© ARVO (1962-2015); The Authors (2016-present)
Simplified mathematical models for TBU dynamics and its fluorescent (FL) imaging are developed and fit to in vivo data in the center of TBU instances. The models capture some essential dynamics of some common types of TBU. Etiologies of TBU include evaporation driven (Type I; Fig 1a) and divergent flow driven (Type II; Fig 1b); a mix of these two appears to occur in vivo (Type III, or mixed-mechanism). The models used here were Type III. These models aim to aid understanding of TBU visualization.
Ordinary differential equation (ODE) models are derived for the tear film thickness h(t), osmolarity c(t) and FL concentration f(t), where t is time. In each case, the ODEs are solved for using a custom Matlab code; solute concentrations are computed from solute mass conservation. FL intensity I(t) is computed as described by Nichols et al (IOVS 2012, 53:5426). In vivo FL intensity is from 25 normal subjects, with 10 trials in each of 2 visits. Individual instances of TBU were selected for simple shapes (spots or streaks). The parameters for evaporation rate and time-dependent tangential flow were determined by nonlinear least squares fits to the central values of the selected TBU instances.
For the Type III model used here, all three of divergent flow, evaporation and osmosis are active. The FL intensity from the math models is consistent with experimental results when time is not too large. The models can capture the steady, roughly linear decrease often interpreted as evaporative thinning (a in Fig. 2), and in some cases can capture the time-dependent tangential flow that may be into or out of the center of TBU (b in Fig. 2).
Simple models of TBU can capture dynamics of evaporation, osmosis, divergent flow, and imaging. The models can be designed to allow tangential flow that may change with time as in experiments. Challenges remain for fitting for some instances of TBU in which fitting of more complicated partial differential equations provide more information and a better fit. Numerically computed fitting criteria may aid model selection in some cases.
This is a 2020 ARVO Annual Meeting abstract.
Fig 1: Sketches of (a) Type I and (b) Type II TBU.
Fig 2: Sample results for I(t) from the ODE models and from in vivo central TBU measurements in two instances of TBU from normal tear films. (a) Evaporation is moderately fast and flow is divergent. (b) Evaporation is fast and tangential flow is initially convergent and then divergent.
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