A model of tear-film breakup with continuous mucin concentration and viscosity profiles – CORRIGENDUM

Dey, Mohar; Vivek, Atul S; Dixit, Harish N.; Richhariya, Ashutosh; Feng, James J.

doi:10.1017/jfm.2020.138

Cited by 4 publications

(1 citation statement)

References 4 publications

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“…Effects added to this type of model include Marangoni effects, 45 evaporation, 46 van der Waals wetting terms, 47 and curvature of the ocular surface. 48 Local models for TF thinning and TBU include those which have been studied for the following effects: evaporation to air and osmosis from corneal surface 49 and with FL; 50 Marangoni effects; 51 a non-polar lipid layer (LL); 52,53 dewetting of the ocular surface from long-range van der Waals forces; 54,55 and dewetting of the ocular surface with mucin-dependent viscosity 56,57 and membrane-associated mucins. 58 Some models for TBU are discussed in more detail below.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Fitting ODE models of tear film breakup

Driscoll,

Braun,

Luke

et al. 2023

MAIO

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Purpose: Several elements are developed to quantitatively determine the contribution of different physical and chemical effects to tear breakup (TBU) in subjects with no self-reported history of dry eye (DED) or other ocular surface disease. Fluorescence (FL) imaging is employed to visualize the tear film (TF) and to determine TF thinning and potential TBU. Methods: An automated system using a convolutional neural network that was trained and tested on more than 50,000 images from FL imaging experiments was deployed. The trained system could identify multiple TBU instances in each trial. Once identified, extracted FL intensity data was fit by mathematical models that included tangential flow along the eye, evaporation, osmosis, and FL intensity of emission from the TF. The mathematical models consisted of systems of ordinary differential equations for the aqueous layer thickness, osmolarity, and the FL concentration; they are a local approximation to TF thinning and/or TBU dynamics. FL intensity was computed using the resulting thickness and FL concentration. Optimizing the fit of the models to the FL intensity data determined the mechanism(s) driving each instance of TBU and produced an estimate of the osmolarity within TBU. Results: Initial estimates for FL concentration and initial TF thickness agree well with prior results. Fits were produced for N = 467 instances of potential TBU from 15 non-DED subjects. The results showed a distribution of causes of TBU in these healthy subjects, as reflected by estimated flow and evaporation rates, which appear to agree well with previously published data. Final osmolarity depended strongly on the TBU mechanism, generally increasing with evaporation rate but complicated by the dependence on flow. Conclusion: The method has the potential to classify TBU instances based on the mechanism and dynamics, and to estimate the final osmolarity at the TBU locus. The results suggest that it might be possible to classify individual subjects and provide a baseline for comparison and potential classification of DED subjects.

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Section: Mathematical Modelsmentioning

confidence: 99%

Fitting ODE models of tear film breakup

Driscoll,

Braun,

Luke

et al. 2023

MAIO

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On modeling tear breakup dynamics with a nematic lipid layer

Taranchuk,

Braun

2024

J Eng Math

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One of the main roles of the lipid layer (LL) of the tear film (TF) is to help prevent evaporation of the aqueous layer (AL). The LL thickness, composition, and structure all contribute to its barrier function. It is believed that the lipid layer is primarily nonpolar with a layer of polar lipids at the LL/AL interface. There is evidence that the nonpolar region of the LL may have liquid crystalline characteristics. We investigate the structure and function of the LL via a model of the tear film with two layers, using extensional flow of a nematic liquid crystal for the LL and shear-dominated flow of a Newtonian AL. Evaporation is taken into account and is affected by the LL thickness, internal arrangement of its rod-like molecules, and external conditions. We conduct a detailed parameter study with a focus on the evaporative resistance parameter, the Marangoni number, and primary liquid crystal parameters including the Leslie viscosities and director angle. This new model responds similarly to previous Newtonian models in some respects; however, incorporating internal structure via the orientation of the liquid crystal molecules affects both evaporation and flow. As a result, we see new effects on TF dynamics and breakup.

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