June 2013
Volume 54, Issue 15
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ARVO Annual Meeting Abstract  |   June 2013
Mathematical Modeling of Tear Break-up and Fluorescent Intensity
Richard Braun; Carolyn Begley; Adam Winkeler; Peter King-Smith; Javed Siddique
Author Affiliations & Notes
  • Richard Braun
    Dept of Mathematical Sciences, University of Delaware, Newark, DE
  • Carolyn Begley
    School of Optometry, Indiana University, Bloomington, IN
  • Adam Winkeler
    School of Optometry, Indiana University, Bloomington, IN
  • Peter King-Smith
    College of Optometry, The Ohio State University, Columbus, OH
  • Javed Siddique
    Dept of Mathematics, Pennsylvania State University, York, PA
  • Footnotes
    Commercial Relationships Richard Braun, None; Carolyn Begley, Santen, Inc. (C), ohnson & Johnson Vision Care, Inc. (C), ohnson & Johnson Vision Care, Inc. (F); Adam Winkeler, None; Peter King-Smith, None; Javed Siddique, None
  • Footnotes
    Support None
Investigative Ophthalmology & Visual Science June 2013, Vol.54, 949. doi:
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      Richard Braun, Carolyn Begley, Adam Winkeler, Peter King-Smith, Javed Siddique; Mathematical Modeling of Tear Break-up and Fluorescent Intensity. Invest. Ophthalmol. Vis. Sci. 2013;54(15):949.

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Abstract
 
Purpose
 

The local mechanisms involved in the formation and development of areas of tear breakup (TBU) remain poorly understood. The purpose of this project is to develop mathematical theory for variables of interest to compare with experimental images of TBU to better predict local fluctuations in tear film osmolarity and fluorescence (FL) during and following TBU.

 
Methods
 

Tear films of 10 subjects with a range of tear break-up times (3-45 sec) were simultaneously recorded at high resolution following the instillation of 2 microliters of 2% fluorescein. Using these images, which were aligned by the center of the pupil, as input, math models were solved for local changes tear film thickness (h), insoluble surfactant concentration (representing the lipid layer and affecting evaporation), as well as osmolarity (c) and FL (f) concentrations inside the tear film. FL concentration was converted to fluorescent intensity I using the expression involving h and the full range of f as described by Nichols et al (IOVS 2012;53:5426--32).

 
Results
 

Theoretical results show that elevated surfactant concentration or evaporation rate led to thinner regions where TBU first occurs. Figure 1 shows results for h, c & I (in the plots, x is location in space and t is time) with evaporation at 2.5 microns/min from the initially 2 micron film surface and osmosis from the cornea; a single breakup regions (blue) is shown. The model predicts locally elevated concentrations of osmolarity within areas of TBU (red). The model predicts the FL intensity patterns very similar to the computed thickness and the observed experimental results (Figure 2: color contour plot). For the rate of osmosis from the cornea in the displayed results, the osmolarity increases to 2.4x the isosmolar value, or 720 mOsm. The sensitive dependence of this result on the corneal permeability will be studied. Quenching of the FL is captured as well.

 
Conclusions
 

This model, which was developed using experimental data from subjects with a range of tear film instability, explains dynamics of areas of TBU and predicts local increases in osmolarity and the dynamics of fluorescent intensity in areas of TBU.

 
Figure 1. Thickness h, osmolarity c and intensity I at different times
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Figure 1. Thickness h, osmolarity c and intensity I at different times
 
Figure 1. Thickness h, osmolarity c and intensity I at different times
Figure 1. Thickness h, osmolarity c and intensity I at different times
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Figure 2. Color contour plots of h, c, f and I. Blue is smaller, red is larger. The thickness and intensity plots (left) are quite similar, as are the plots for osmolarity and fluorescein concentration (right).
View OriginalDownload Slide
 
Figure 2. Color contour plots of h, c, f and I. Blue is smaller, red is larger. The thickness and intensity plots (left) are quite similar, as are the plots for osmolarity and fluorescein concentration (right).
 
Figure 2. Color contour plots of h, c, f and I. Blue is smaller, red is larger. The thickness and intensity plots (left) are quite similar, as are the plots for osmolarity and fluorescein concentration (right).
Figure 2. Color contour plots of h, c, f and I. Blue is smaller, red is larger. The thickness and intensity plots (left) are quite similar, as are the plots for osmolarity and fluorescein concentration (right).
View OriginalDownload Slide
 
Keywords: 486 cornea: tears/tear film/dry eye  
© 2013, The Association for Research in Vision and Ophthalmology, Inc., all rights reserved. Permission to republish any abstract or part of an abstract in any form must be obtained in writing from the ARVO Office prior to publication.
Copyright © 2015 Association for Research in Vision and Ophthalmology.
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