Parameter Estimation for Tear Film Breakup Dynamics

Abstract

Purpose : Many parameters associated with evaporation-driven tear film breakup (TBU) affect tear film (TF) thickness and fluorescent (FL) intensity distributions over time; directly measured values or ranges during TBU for some parameters are not available. We conduct parameter estimation by fitting mathematical models for TBU and the computed FL intensity to experimental intensity data gathered in vivo.

Methods : We used computer simulated data with added noise to validate parameter estimation via least squares minimization of the difference between data and computed answers using the Levenberg-Marquardt method. Theoretical intensity dependent on thickness and FL concentration was based on Nichols et al (2012, IOVS, 53:5426). Models for circular (spot) or linear (streak) TBU have been solved. After verifying the method, we fit FL intensity data recorded from normal subjects’ TFs. The initial FL concentration was estimated (Wu et al, IOVS 2015, 56:4211). Subject data extracted along a line at each time level was used to optimize five parameters: peak (v_max) and background (v_min) thinning rates, evaporation width (r_w), initial FL concentration (f₀) and initial TF thickness (h₀).

Results : For a range of subject trials, our fits are robust and the optimal values fall within accepted experimental ranges. The optimal f₀ is often close to the critical FL concentration peak but lower than the experimental value, which may lead to an h₀ lower than our characteristic value. For TBU fits we attempted, the optimal v_max falls within the range of experimental values (Nichols et al, IOVS 2005, 46:2353). This justifies our selection of relatively slow TBU cases for fitting. Our fits are improved by aligning the minimum intensity of each time level, disregarding time levels before thinning begins, and leveling tilt across the TBU. An example fit is shown.

Conclusions : Our model yields parameters for selected evaporative instances of TBU that fall within expected ranges for variables that cannot be measured in vivo during TBU. This method makes it possible to estimate parameters in a variety of TBU instances, which may lead to better understanding of dry eye.

This abstract was presented at the 2019 ARVO Annual Meeting, held in Vancouver, Canada, April 28 - May 2, 2019.

 

Spot TBU intensity as a function of radius r is fit with an axisymmetric model for FL intensity. Optimal parameter values are v_max = 6.17 mm/min, v_min = 1.37 mm/min, r_w = 0.455 mm, f₀ = 0.183%, and h₀ = 2.65 mm.