Tear Film Group
This was the group
in Spring 2008. Back row, l to r: Toby, Rich and Pam.
Front row, l to r: Alfa, Kara and Usha.
Alfa had successfully defended his thesis that day.
Multiple Blink Cycles and the Tear Film
Overset Grids in 1D and 2D
Tear film evolution in 2D
Kara has also developed 2D models of the post-blink tear film using the Overture framework; Bill Henshaw (LLNL) is helping considerably with this effort. In the first case, we used lubrication equations for the tear film and the boundary conditions that specify the film thickness and the pressure at the boundary. This work is under revision for publication.
We have also implemented flux boundary conditions;
some preliminary work was presented in this talk at the 2008
APS DFD meeting and elsewhere. (These three movies were used for this talk:
thickness difference (27MB),
thickness difference (50MB),
and thickness difference (28MB).)
The image at left above is the flux direction vectors superimposed over magnitude of the flux;
darker indicates slower flow. Tear fluid is supplied from superior temporal location of the lacrimal
gland, and is extracted at the locations of the puncta which are near the nasal canthus (corner) at the left
end of the domain. The flux conditions are independent of time, which is an
initial model. (In a real blink, the supply and drainage of tear fluid are time dependent and are
closely related to lid motion.) Most of the flow is around the lid margins.
The image at right is the thickness distribution at time 10 when gravity is included
in the simulation. Maroon indicates greater than or equal to 3 microns; the dark blue is the minimum thickness.
The drooping area of maroon indicates a bulge in the meniscus outward from the lid margin.
For the flux boundary conditions we used, the fluid in the upper meniscus
can break through the black line if enough time is allowed between blinks.
This work with flux BCs specified is submitted for publication.
Capturing Eyelid Motion
Ms. Xiaolin Yang, an MS student in the Department of Computer and Information Sciences, who worked with Braun on capturing the lid motion during a blink automatically from high speed digital movies of blinks. The movies were made in the MEC Lab in the UD Department of Mathematical Sciences with the help of Dr. John Pelesko. She developed a code that could extract least squares polynomial fits from the blink movies using Sobel edge detection with some pre- and post-processing. That mathematical approximation that she generated of a blink has already been incorporated into our efforts to compute the tear film evolution in two dimensions. She worked with Braun in summer 2006 and January 2007. The code was developed in Matlab, and the code with some results will appear on this website in the near future.
Mr. Peter Ucciferro (a Quantitative Biology major) and Mr. Paul Parsons (a Physics major) were supported by an REU supplement for this NSF grant for the summer of 2007. They worked on evaluating and extending Xiaolin's algorithms for capturing and mathematically representing eyelid motion during a blink. Ucciferro and Parsons recorded some observations of blinks and extended the software for this aspect of the project. One aspect of their work was to use roifill to blur regions around the eye so that more blink movies could be used. They presented their results in an excellent joint presentation during the Departmental symposium on summer undergraduate research in August 2007.
Publicity