Abstract: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… Show more
“…79 In this work, we use local models for TBU involving tangential flow, evaporation, osmosis, and FL, but the models have been simplified to ODEs for the thickness, osmolarity, fluorescein, and FL intensity. 80 We find the optimal parameters for these models that make them as close as possible to FL intensity data extracted from video recordings of in vivo TFs. With those optimal parameters, we can infer which effects are most important in each TBU instance.…”
Section: Mathematical Modelsmentioning
confidence: 99%
“…The principles of the Declaration of Helsinki were followed during data collection, and informed consent was obtained from all subjects. Data collection is described in a previous publication 19 and discussed in several papers, 19,51,[79][80][81] but will be summarized briefly here. Twenty-five subjects with no self-reported history of DED, ocular surface or systemic disease, or ocular surgery or medications affecting ocular sensation participated in the study.…”
Section: Fluorescence Imagingmentioning
confidence: 99%
“…The trials typically start with a FL concentration close to 0.2% (discussed more below), which is the so-called critical concentration where peak FL occurs for thin TFs. 83 The critical FL concentration may also be expressed as 0.0053 M. 80…”
Section: Fluorescence Imagingmentioning
confidence: 99%
“…We model TBU using a hierarchy of ODE models 74,80 represented as a system of non-dimensional equations:…”
Section: Modelsmentioning
confidence: 99%
“…We use f 0 as the ratio between non-dimensional osmolarity and FL concentration throughout the fit. The permeability parameter in Equation ( 1), P c , varies during the optimization as discussed in the previous section (see also Luke et al 80 ). We excluded any intensity time series that showed substantial, sustained brightening; while this may happen in vivo, 29 we aim to fit thinning and TBU processes.…”
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.
“…79 In this work, we use local models for TBU involving tangential flow, evaporation, osmosis, and FL, but the models have been simplified to ODEs for the thickness, osmolarity, fluorescein, and FL intensity. 80 We find the optimal parameters for these models that make them as close as possible to FL intensity data extracted from video recordings of in vivo TFs. With those optimal parameters, we can infer which effects are most important in each TBU instance.…”
Section: Mathematical Modelsmentioning
confidence: 99%
“…The principles of the Declaration of Helsinki were followed during data collection, and informed consent was obtained from all subjects. Data collection is described in a previous publication 19 and discussed in several papers, 19,51,[79][80][81] but will be summarized briefly here. Twenty-five subjects with no self-reported history of DED, ocular surface or systemic disease, or ocular surgery or medications affecting ocular sensation participated in the study.…”
Section: Fluorescence Imagingmentioning
confidence: 99%
“…The trials typically start with a FL concentration close to 0.2% (discussed more below), which is the so-called critical concentration where peak FL occurs for thin TFs. 83 The critical FL concentration may also be expressed as 0.0053 M. 80…”
Section: Fluorescence Imagingmentioning
confidence: 99%
“…We model TBU using a hierarchy of ODE models 74,80 represented as a system of non-dimensional equations:…”
Section: Modelsmentioning
confidence: 99%
“…We use f 0 as the ratio between non-dimensional osmolarity and FL concentration throughout the fit. The permeability parameter in Equation ( 1), P c , varies during the optimization as discussed in the previous section (see also Luke et al 80 ). We excluded any intensity time series that showed substantial, sustained brightening; while this may happen in vivo, 29 we aim to fit thinning and TBU processes.…”
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.
This paper discusses the spreading of gel-based ophthalmic formulation on the cornea surface assumed to be flat. We show that gel-based formulations exhibit rheological behaviors that the Herschel–Bulkley model can describe. The continuity and momentum equations are solved numerically using the monofluid formulation and the volume-of-fluid (VOF) method. We investigated the influence of the rheological properties, namely the consistency, the yield stress, and the flow behavior index, on the spreading of a gel-based artificial tear over the cornea surface. We propose optimal values of these properties for efficient gel-based artificial tears.
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