Tear Film Dynamics and Imaging in Tear Break-up

Abstract

 

Purpose

 

The purpose of this project is to use mathematical models to visualize tear film (TF) flows and match them with detailed tear break up (TBU) imaging methods using fluorescence (FL). We determine the correspondence between FI images for different kinds of TBU (circular spots and linear grooves) and compute local changes in tear film osmolarity (c) and FL during and after TBU.

 

Methods

 

Math models were solved for local changes tear film thickness (h), osmolarity and FL (f) concentrations inside the tear film for localized breakup. FL concentration was converted to FL intensity I for the thinning TF depending on h and the full range of f as described by Braun et al (IOVS 2014; 55:1133-1142).

 

Results

 

The computed c from the model recovers locally elevated osmolarity c within areas of TBU as in, e.g., Peng et al (ACIS 2014; 206:250-264) but extends those results significantly. The model identifies a critical hole size L=[σ/(µv)]^1/4d, depending on the surface tension σ, the viscosity µ, the evaporation (thinning) rate v and the characteristic TF thickness d. For hole radii r_w≥L, the TBU area occurs in the same time d/v and with the same elevated c as for a flat film. For r_w <L, the time to TBU is increased due to inward surface tension driven flow and the maximum c is decreased due to (outward) diffusion. The model predicts elevated f as well but its smaller diffusion rate makes it more susceptible to transport by TF flow. As a result, f increases much more than c, yielding FL intensity distributions that are narrower than h distributions, particularly for r_w <L. The computed FL intensity patterns are very important for properly interpreting TBU with FL imaging and we quantify this for different initial values of f.

 

Conclusions

 

The model explains why small enough holes in the lipid layer do not lead to TBU, and quantifies FL imaging vs. TF thickness dynamics in TBU areas. The model is closely compared with experimental data, matches well with in vivo observations and is instrumental in understanding TF and TBU dynamics.  

 

TBU time (TBUT, relative to d/v) as a function of hole radius r_w (relative to L) for different peak thinning rates with background 1micron/min rate. Fixed thinning rate distributions are roughly piecewise constant (dashed) and Gaussian (solid). TBUT increases dramatically for r_w <L.