Evaporation-driven tear film thinning and breakup in two space dimensions

TL;DR

This paper models how evaporation patterns influence tear film thinning and breakup in two dimensions, revealing complex dynamics and offering computational speedups for future clinical applications.

Contribution

It introduces a 2D model of tear film breakup influenced by evaporation, showing continuous shape variation and implementing a proper orthogonal decomposition for faster simulations.

Findings

TBU dynamics are not simple superpositions of 1D solutions.

TBU shape varies continuously from spots to streaks based on evaporation profile.

Proper orthogonal decomposition significantly accelerates computations.

Abstract

Evaporation profiles have a strong effect on tear film thinning and breakup (TBU), a key factor in dry eye disease (DED). In experiments, TBU is typically seen to occur in patterns that locally can be circular (spot), linear (streak), or intermediate . We investigate a two-dimensional (2D) model of localized TBU using a Fourier spectral collocation method to observe how the evaporation distribution affects the resulting dynamics of tear film thickness and osmolarity, among other variables. We find that the dynamics are not simply an addition of individual 1D solutions of independent TBU events, and we show how the TBU quantities of interest vary continuously from spots to streaks for the shape of the evaporation distribution. We also find a significant speedup by using a proper orthogonal decomposition to reduce the dimension of the numerical system. The speedup will be especially useful for future applications of the model to inverse problems, allowing the clinical observation at scale of quantities that are thought to be important to DED but not directly measurable in vivo within TBU locales.