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Math Med Biol. 2016 Jun;33(2):123-57. doi: 10.1093/imammb/dqv013. Epub 2015 Apr 15.

Computed tear film and osmolarity dynamics on an eye-shaped domain.

Author information

1
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA.
2
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA rjbraun@udel.edu.
3
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
4
Lawrence Livermore National Laboratory, Box 808, L-422, Livermore, CA 94551-0808, USA.
5
College of Optometry, The Ohio State University, Columbus, OH 43218, USA.

Abstract

The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge-Kutta-Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink.

KEYWORDS:

composite overlapping grid; lubrication theory; osmolarity dynamics; tear film; thin film

PMID:
25883248
PMCID:
PMC5394582
DOI:
10.1093/imammb/dqv013
[Indexed for MEDLINE]
Free PMC Article