title: Computed tear film and osmolarity dynamics on an eye-shaped domain.
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.
authors.affiliation: Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA.
authors.forename: Longfei
authors.initials: L
authors.lastname: Li
authors.affiliation: Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA rjbraun@udel.edu.
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Braun
authors.affiliation: Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA.
authors.forename: Tobin A
authors.initials: TA
authors.lastname: Driscoll
authors.affiliation: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
authors.forename: William D
authors.initials: WD
authors.lastname: Henshaw
authors.affiliation: Lawrence Livermore National Laboratory, Box 808, L-422, Livermore, CA 94551-0808, USA.
authors.forename: Jeffrey W
authors.initials: JW
authors.lastname: Banks
authors.affiliation: College of Optometry, The Ohio State University, Columbus, OH 43218, USA.
authors.forename: P Ewen
authors.initials: PE
authors.lastname: King-Smith
mesh_terms: D005123:Eye; D006801:Humans; D008153:Lubrication; D008962:Models, Theoretical; D009994:Osmolar Concentration; D013666:Tears
keywords: composite overlapping grid; lubrication theory; osmolarity dynamics; tear film; thin film