Skip Navigation


Mathematical Medicine and Biology Advance Access originally published online on July 14, 2008
Mathematical Medicine and Biology 2008 25(3):187-214; doi:10.1093/imammb/dqn013
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
25/3/187    most recent
dqn013v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Maki, K. L.
Right arrow Articles by King-Smith, P. E.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Maki, K. L.
Right arrow Articles by King-Smith, P. E.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

An overset grid method for the study of reflex tearing

K. L. Maki, R. J. Braun{dagger} and T. A. Driscoll

Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA

P. E. King-Smith

College of Optometry, The Ohio State University, Columbus, OH 43218, USA

{dagger} Email: braun{at}math.udel.edu

Received on February 19, 2008. Revised on May 29, 2008. Accepted on May 30, 2008.

We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper and lower eyelids to capture localized capillary thinning referred to as ‘black lines’ and a Cartesian grid covers the remaining domain. Numerical studies are performed on a non-linear test problem to confirm the accuracy and convergence of the scheme. The computations on the tear film model show qualitative agreement with in vivo tear film thickness measurements. Furthermore, the role of the black lines in the presence of tear supply from the lid margins, reflex tearing, was found to be more subtle than a barrier to tear fluid flow between the anterior of the eye and the meniscus at the lid margin. During reflex tearing, tears may flow through the region normally containing the black line and drift down over the cornea under the influence of gravity.

Keywords: tear film; reflex tearing; black line; overset grid; lubrication theory


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.