Parameter Estimation for Evaporation-Driven Tear Film Thinning

Luke, Rayanne A; Braun, Richard; Driscoll, Tobin A.; Begley, Carolyn G.; Awisi-Gyau, Deborah

doi:10.1007/s11538-020-00745-8

Cited by 11 publications

(36 citation statements)

References 90 publications

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“…Data was taken from 25 normal, healthy subjects in a study conducted at Indiana University, 44 as discussed in previous papers. 20,25 Approval was received from the Biomedical Institutional Review Board of Indiana University, Declaration of Helsinki principles were followed during data collection, and informed consent was obtained from all subjects. Subjects were seated behind a slit lamp biomicroscope and 2% sodium fluorescein solution was instilled in the patient's eye.…”

Section: Fl Imagesmentioning

confidence: 99%

“…Our single-variable ODE models are designed to capture the key ingredients in thinning in order to distinguish which is the dominant mechanism causing thinning: evaporation, outward tangential flow, or a combination of the two. Evaporationdominated thinning is characterized by inward tangential flow, if any, 25 while Marangoni flow is characterized by strong outward tangential flow that decreases in strength as the trial progresses. 20 There is a hierarchy of ODE models we explore; we derive the most complicated version here.…”

Section: Governing Dimensional Equationsmentioning

confidence: 99%

“…Winter et al 23 (PDE model) and Braun 24 (ODE model) included van der Waals forces to stop thinning with a zero permeability condition at the tear/cornea interface; such terms and forces are omitted from the models in this work. Luke et al 25 fit TBU data with ODE models with evaporation, with or without osmosis, but without tangential flow. Neither the PDE nor ODE model gave the best fit for all of the TBU instances.…”

Section: Introductionmentioning

confidence: 99%

“…[31][32][33] Dry eye measurements in the same location can reach 316-360 mOsmol/L 26,32,34,35 but estimates for the TF over the cornea reach 900 mOsmol/L or higher. 17,25,30,36 High levels of TF osmolarity are associated with pain, inflammation, and cellular changes. [36][37][38] In support of these potentially high levels of TF osmolarity over the cornea, mathematical models without spatial variation have estimated peak osmolarities up to ten times the isotonic concentration.…”

Section: Introductionmentioning

confidence: 99%

“…43 In Braun et al, 18 both peak and background evaporation rates in TBU instances, as well as the width of the evaporation distribution, were studied parametrically. Subsequently, parameter estimation schemes were developed in Luke et al 20,25 for fitting PDE models to experimental FL intensity distributions. They found evaporation rates ranging from -4.91 to 36.9 µm/min (the lower bound indicating thickening) and overall TF thinning rates ranging from 1.85 to 23.5 µm/min.…”

Section: Introductionmentioning

confidence: 99%

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Mechanistic determination of tear film thinning via fitting simplified models to tear breakup

Luke

Braun

Begley

2022

MAIO

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Purpose: Little quantitative or mechanistic information about tear film breakup can be determined directly via current imaging techniques. In this paper, we present simplified mathematical models based on two proposed mechanisms of tear film breakup: evaporation of water from the tear film and tangential fluid flow within the tear film. We use our models to determine whether one or a combination of the two mechanisms causes tear film breakup in a variety of instances. In this study, we estimate related breakup parameters that cannot currently be measured in breakup during subject trials, such as tear film osmolarity and thinning rates. The present study validates our procedure against previous work.Methods: Five ordinary differential equation models for tear film thinning were designed that model evaporation, osmosis, and various types of tangential flow. Eight tear film breakup instances occurring within a time interval of 1–8 s postblink of five healthy subjects thatwere identified in fluorescence images in previous work were fit with these five models. The fitting procedure used a nonlinear least squares optimization that minimized the difference of the computed theoretical fluorescent intensity from the models and the experimental fluorescent intensity from the images. The optimization was conducted over the evaporation rate and up to three tangential flow rate parameters. The smallest norm of the difference was determined to correspond to the model that best explained the tear film dynamics.Results: All of the breakup instances were best fit by models with time-dependent tangential flow. Our optimal parameter values and thinning rate as well as tangential fluid flow profiles compare well with previous partial differential equation model results in most instances.Conclusion: Our fitting results suggest that a combination of tangential fluid flow and evaporation cause most of the breakup instances. Comparison with results from previous work suggests that the simplified models can capture the essential tear film dynamics in most cases, thereby validating this procedure for wider usage.

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Section: Fl Imagesmentioning

confidence: 99%

Section: Governing Dimensional Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mechanistic determination of tear film thinning via fitting simplified models to tear breakup

Luke

Braun

Begley

2022

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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