Mathematical Models of the Tear Film

Braun, Richard; Driscoll, Tobin A.; Begley, Carolyn G.

doi:10.1007/978-3-030-25886-3_17

Cited by 9 publications

(7 citation statements)

References 114 publications

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“…Ordinary di erential equation (ODE) models have been designed to capture TF thinning while neglecting spatial variation; exact solutions exist for some cases. Braun et al 21 extended an ODE model without tangential flow from previous work 22 to include time-independent extensional, tangential fluid flow; a time-dependent version has recently been developed and is presented here. The tangential flow is divergent from the origin and can be considered with evaporative loss and osmotic supply.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Luke

Braun

Begley

2022

MAIO

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“…[67][68][69] Models for flow over the (2D) exposed ocular surface have been developed. [70][71][72][73][74][75] The 2D models capture a number of aspects of the overall flows, osmolarity, and FL imaging. Some 2D models may take into account the effect of blinking via timedependent flow boundary conditions with no lid motion, 76 or via lid motion with model problems plus simple boundary conditions, 73 but there is much room to develop blinking models.…”

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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“…Fluid-dynamical studies have the goal of predicting distributions of pressures and velocities characterizing the flow of a fluid in the tissue. In the eye, such studies have focused on the flow of blood, aqueous humor and tear film, with few contributions considering the dynamics of vitreous humor and cerebrospinal fluid, as reviewed in recent works (Arciero et al, 2019 ; Braun et al, 2019 ; Dvoriashyna et al, 2019 ; Repetto and Dvoriashyna, 2019 ; Sala et al, 2019b ).…”

Section: Overview Of Mechanism-driven Models Of the Eye And Their mentioning

confidence: 99%

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

et al. 2020

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Neurodegenerative disorders (NDD) such as Alzheimer's and Parkinson's diseases are significant causes of morbidity and mortality worldwide. The pathophysiology of NDD is still debated, and there is an urgent need to understand the mechanisms behind the onset and progression of these heterogenous diseases. The eye represents a unique window to the brain that can be easily assessed via non-invasive ocular imaging. As such, ocular measurements have been recently considered as potential sources of biomarkers for the early detection and management of NDD. However, the current use of ocular biomarkers in the clinical management of NDD patients is particularly challenging. Specifically, many ocular biomarkers are influenced by local and systemic factors that exhibit significant variation among individuals. In addition, there is a lack of methodology available for interpreting the outcomes of ocular examinations in NDD. Recently, mathematical modeling has emerged as an important tool capable of shedding light on the pathophysiology of multifactorial diseases and enhancing analysis and interpretation of clinical results. In this article, we review and discuss the clinical evidence of the relationship between NDD in the brain and in the eye and explore the potential use of mathematical modeling to facilitate NDD diagnosis and management based upon ocular biomarkers.

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Mathematical Models of the Tear Film

Cited by 9 publications

References 114 publications

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

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

Fitting ODE models of tear film breakup

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

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