KAUST Grant NumberKUK-C1-013-04
Online Publication Date2010-06-17
Print Publication Date2011-06
Permanent link to this recordhttp://hdl.handle.net/10754/599905
MetadataShow full item record
AbstractIn 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. © 2010 Society for Mathematical Biology.
CitationAydemir E, Breward CJW, Witelski TP (2010) The Effect of Polar Lipids on Tear Film Dynamics. Bull Math Biol 73: 1171–1201. Available: http://dx.doi.org/10.1007/s11538-010-9555-y.
SponsorsThe authors are particularly grateful for extensive dialogue with Prof. Colin Please,useful comments by Dr. Jim Oliver, and for the support and insight provided by their experimental collab-orators, Prof. Anthony Bron and Dr. John Tiffany. This work was partly funded by an EPSRC-funded MScstudentship, is also partially based on work supported by award number KUK-C1-013-04 made by KingAbdullah University of Science and Technology and by NSF DMS CAREER grant 0239125.
JournalBulletin of Mathematical Biology
CollectionsPublications Acknowledging KAUST Support
- The influence of a lipid reservoir on the tear film formation.
- Authors: Maki KL, Braun RJ, Barron GA
- Issue date: 2020 Sep 10
- Dynamics of tear film deposition and draining.
- Authors: Jones MB, Please CP, McElwain DL, Fulford GR, Roberts AP, Collins MJ
- Issue date: 2005 Sep
- Insertion of tear proteins into a meibomian lipids film.
- Authors: Miano F, Calcara M, Millar TJ, Enea V
- Issue date: 2005 Jul 25
- A mathematical model for ocular tear and solute balance.
- Authors: Zhu H, Chauhan A
- Issue date: 2005 Oct
- Tear film dynamics on an eye-shaped domain I: pressure boundary conditions.
- Authors: Maki KL, Braun RJ, Henshaw WD, King-Smith PE
- Issue date: 2010 Sep