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The effect of polar lipids on tear film dynamics.

Publication ,  Journal Article
Aydemir, E; Breward, CJW; Witelski, TP
Published in: Bulletin of mathematical biology
June 2011

In this paper, we present a mathematical model describing the effect of polar lipids, excreted by glands in the eyelid and present on the surface of the tear film, on the evolution of a pre-corneal tear film. We aim to explain the interesting experimentally observed phenomenon that the tear film continues to move upward even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled non-linear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that increasing the concentration of the lipid increases the flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system.

Duke Scholars

Published In

Bulletin of mathematical biology

DOI

EISSN

1522-9602

ISSN

0092-8240

Publication Date

June 2011

Volume

73

Issue

6

Start / End Page

1171 / 1201

Related Subject Headings

  • Tears
  • Surface Tension
  • Models, Biological
  • Lipids
  • Humans
  • Computer Simulation
  • Bioinformatics
  • 49 Mathematical sciences
  • 31 Biological sciences
  • 06 Biological Sciences
 

Citation

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Aydemir, E., Breward, C. J. W., & Witelski, T. P. (2011). The effect of polar lipids on tear film dynamics. Bulletin of Mathematical Biology, 73(6), 1171–1201. https://doi.org/10.1007/s11538-010-9555-y
Aydemir, E., C. J. W. Breward, and T. P. Witelski. “The effect of polar lipids on tear film dynamics.Bulletin of Mathematical Biology 73, no. 6 (June 2011): 1171–1201. https://doi.org/10.1007/s11538-010-9555-y.
Aydemir E, Breward CJW, Witelski TP. The effect of polar lipids on tear film dynamics. Bulletin of mathematical biology. 2011 Jun;73(6):1171–201.
Aydemir, E., et al. “The effect of polar lipids on tear film dynamics.Bulletin of Mathematical Biology, vol. 73, no. 6, June 2011, pp. 1171–201. Epmc, doi:10.1007/s11538-010-9555-y.
Aydemir E, Breward CJW, Witelski TP. The effect of polar lipids on tear film dynamics. Bulletin of mathematical biology. 2011 Jun;73(6):1171–1201.
Journal cover image

Published In

Bulletin of mathematical biology

DOI

EISSN

1522-9602

ISSN

0092-8240

Publication Date

June 2011

Volume

73

Issue

6

Start / End Page

1171 / 1201

Related Subject Headings

  • Tears
  • Surface Tension
  • Models, Biological
  • Lipids
  • Humans
  • Computer Simulation
  • Bioinformatics
  • 49 Mathematical sciences
  • 31 Biological sciences
  • 06 Biological Sciences