Bulletin of Mathematical Biology

, Volume 81, Issue 1, pp 39–80 | Cite as

Dynamics of Fluorescent Imaging for Rapid Tear Thinning

  • L. ZhongEmail author
  • R. J. Braun
  • C. G. Begley
  • P. E. King-Smith
Original Article


A previous mathematical model has successfully simulated the rapid tear thinning caused by glob (thicker lipid) in the lipid layer. It captured a fast spreading of polar lipid and a corresponding strong tangential flow in the aqueous layer. With the simulated strong tangential flow, we now extend the model by adding equations for conservation of solutes, for osmolarity and fluorescein, in order to study their dynamics. We then compare our computed results for the resulting intensity distribution with fluorescence experiments on the tear film. We conclude that in rapid thinning, the fluorescent intensity can linearly approximate the tear film thickness well, when the initial fluorescein concentration is small. Thus, a dilute fluorescein is recommended for visualizing the rapid tear thinning during fluorescent imaging.


Tear film Marangoni effect Dry eye Fluorescent imaging 



This work is funded by NSF Grant 1412085 (Braun), NIH Grant 1R01EY021794 (Begley), and NEI Grant R01EY017951 (King-Smith).


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.School of OptometryIndiana UniversityBloomingtonUSA
  3. 3.College of OptometryThe Ohio State UniversityColumbusUSA

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