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

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 to those states. We investigate a two-dimensional...

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Published inJournal of engineering mathematics Vol. 149; no. 1
Main Authors Chen, Qinying, Driscoll, Tobin A., Braun, R. J.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Collocation methods
Computational Mathematics and Numerical Analysis
Eye diseases
Film thickness
In vivo methods and tests
Independent variables
Inverse problems
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Proper Orthogonal Decomposition
Theoretical and Applied Mechanics
Thinning
Tear film
Dimension reduction
Lubrication theory
Proper orthogonal decomposition
Dry eye disease
Fluorescent imaging
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Summary: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 to those states. 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 between spots and streaks in 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.
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content type line 14
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-024-10407-6