We study tear film dynamics with evaporation on a wettable eye-shaped ocular surface using a lubrication model. The mathematical model has a time-dependent flux boundary condition that models the cycles of tear fluid supply and drainage; it mimics blinks on a stationary eye-shaped domain. We generate computational grids and solve the nonlinear governing equations using the OVERTURE computational framework. In vivo experimental results using fluorescent imaging are used to visualize the influx and redistribution of tears for an open eye. Results from the numerical simulations are compared with the experiment. The model captures the flow around the meniscus and other dynamic features of human tear film observed in vivo.
REFERENCES
1.
F. J.
Holly
and M. A.
Lemp
, “Tear physiology and dry eyes
,” Rev. Surv. Ophthalmol.
22
, 69
–87
(1977
).2.
M. A.
Lemp
, “The definition and classification of dry eye disease: Report of the definition and classification subcommittee of the international dry eye workshop
,” Ocul. Surf.
5
, 75
–92
(2007
).3.
Anonymous
, “Report of the International Dry Eye WorkShop (DEWS)
,” Ocul. Surf.
5
, 65
–204
(2007
).4.
M. E.
Johnson
and P. J.
Murphy
, “Changes in the tear film and ocular surface from dry eye syndrome
,” Prog. Ret. Eye Res.
23
, 449
–474
(2004
).5.
M. S.
Norn
, “Semiquantitative interference study of the fatty layer of precorneal film
,” Acta Ophthalmol.
57
, 766
–774
(1979
).6.
F. J.
Holly
, “Formation and rupture of the tear film
,” Exp. Eye Res.
15
, 515
–525
(1973
).7.
A. J.
Bron
, J. M.
Tiffany
, S. M.
Gouveia
, N.
Yokoi
, and L. W.
Voon
, “Functional aspects of the tear film lipid layer
,” Exp. Eye Res.
78
, 347
–360
(2004
).8.
I. K.
Gipson
, “Distribution of mucins at the ocular surface
,” Exp. Eye Res.
78
, 379
–388
(2004
).9.
B.
Govindarajan
and I. K.
Gipson
, “Membrane-tethered mucins have multiple functions on the ocular surface
,” Exp. Eye Res.
90
, 655
–693
(2010
).10.
P. E.
King-Smith
, B. A.
Fink
, R. M.
Hill
, K. W.
Koelling
, and J. M.
Tiffany
, “The thickness of the tear film
,” Curr. Eye. Res.
29
, 357
–368
(2004
).11.
P. E.
King-Smith
, J. J.
Nichols
, K. K.
Nichols
, and R. J.
Braun
, “A high resolution microscope for imaging the lipid layer of the tear film
,” Ocul. Surf.
9
(4
), 197
–211
(2011
).12.
S.
Mishima
, A.
Gasset
, S. D.
Klyce
, and J. L.
Baum
, “Determination of tear volume and tear flow
,” Invest. Ophthalmol. Visual Sci.
5
, 264
–276
(1966
).13.
M. G.
Doane
, “Blinking and the mechanics of the lacrimal drainage system
,” Ophthalmology
88
, 844
–851
(1981
).14.
H.
Zhu
and A.
Chauhan
, “A mathematical model for tear drainage through the canaliculi
,” Curr. Eye Res.
30
, 621
–630
(2005
).15.
S.
Mishima
and D. M.
Maurice
, “The oily layer of the tear film and evaporation from the corneal surface
,” Exp. Eye Res.
1
, 39
–45
(1961
).16.
A.
Tomlinson
, M. G.
Doane
, and A.
McFadyen
, “Inputs and outputs of the lacrimal system: Review of production and evaporative loss
,” Ocul. Surf.
7
, 186
–198
(2009
).17.
S. H.
Kimball
, P. E.
King-Smith
, and J. J.
Nichols
, “Evidence for the major contribution of evaporation to tear film thinning between blinks
,” Invest. Opthalmol. Visual Sci.
51
, 6294
–6297
(2010
).18.
M. G.
Doane
, “An instrument for in vivo tear film interferometry
,” Optom. Vis. Sci.
66
, 383
–388
(1989
).19.
P. E.
King-Smith
, B. A.
Fink
, J. J.
Nichols
, K. K.
Nichols
, R. J.
Braun
, and G. B.
McFadden
, “The contribution of lipid layer movement to tear film thinning and breakup
,” Invest. Ophthalmol. Visual Sci.
50
, 2747
–2756
(2009
).20.
J.
Wang
, D.
Fonn
, T. L.
Simpson
, and L.
Jones
, “Precorneal and pre- and postlens tear film thickness measured indirectly with optical coherence tomography
,” Invest. Ophthalmol. Visual Sci.
44
, 2524
–2528
(2003
).21.
W. W.
Harrison
, C. G.
Begley
, H.
Liu
, M.
Chen
, M.
Garcia
, and J. A.
Smith
, “Menisci and fullness of the blink in dry eye
,” Optom. Vis. Sci.
85
, 706
–714
(2008
).22.
P. E.
King-Smith
, P.
Ramamoorthy
, R. J.
Braun
, and J. J.
Nichols
, “Tear film images and breakup analyzed using fluorescent quenching
,” Invest. Ophthalmol. Visual Sci.
54
, 6003
–6011
(2013
).23.
D. M.
Maurice
, “The dynamics and drainage of tears
,” Int. Ophthalmol. Clin.
13
, 103
–116
(1973
).24.
J. R.
Lakowicz
, Principal of Fluorescence Spectroscopy
, 3rd ed. (Springer
, New York
, 2006
).25.
W. R. S.
Webber
and D. P.
Jones
, “Continuous fluorophotometric method measuring tear turnover rate in humans and analysis of factors affecting accuracy
,” Med. Biol. Eng. Comput.
24
, 386
–392
(1986
).26.
J. J.
Nichols
, P. E.
King-Smith
, E. A.
Hinel
, M.
Thangavelu
, and K. K.
Nichols
, “The use of fluorescent quenching in studying the contribution of evaporation to tear thinning
,” Invest. Ophthalmol. Visual Sci.
53
, 5426
–5432
(2012
).27.
R. J.
Braun
, N.
Gewwecke
, C. G.
Begley
, P. E.
King-Smith
, and J. I.
Siddique
, “A model for tear film thinning with osmolarity and fluorescein
,” Invest. Ophthalmol. Visual Sci.
55
, 1133
–1142
(2014
).28.
J. E.
McDonald
and S.
Brubaker
, “Meniscus-induced thinning of tear films
,” Am. J. Ophthalmol.
72
, 139
–146
(1971
).29.
K. L.
Miller
, K. A.
Polse
, and C. J.
Radke
, “Black line formation and the “perched” human tear film
,” Curr. Eye Res.
25
, 155
–162
(2002
).30.
R. J.
Braun
, “Dynamics of the tear film
,” Annu. Rev. Fluid Mech.
44
, 267
–297
(2012
).31.
R. E.
Berger
and S.
Corrsin
, “A surface tension gradient mechanism for driving the pre-corneal tear film after a blink
,” J. Biomech.
7
, 225
–228
(1974
).32.
R. J.
Braun
, R.
Usha
, G. B.
McFadden
, T. A.
Driscoll
, L. P.
Cook
, and P. E.
King-Smith
, “Thin film dynamics on a prolate spheroid with application to the cornea
,” J. Eng. Math.
73
, 121
–138
(2012
).33.
H.
Wong
, I.
Fatt
, and C. J.
Radke
, “Deposition and thinning of the human tear film
,” J. Colloid Interface Sci.
184
, 44
–51
(1996
).34.
R. J.
Braun
and A. D.
Fitt
, “Modeling the drainage of the precorneal tear film after a blink
,” Math. Med. Biol.
20
, 1
–28
(2003
).35.
A.
Sharma
, S.
Tiwari
, R.
Khanna
, and J. M.
Tiffany
, “Hydrodynamics of meniscus-induced thinning of the tear film
,” in Advances in Experimental Medicine and Biology
, Lacrimal Gland, Tear Film, and Dry Eye Syndromes 2
Vol. 438
, edited by D. A.
Sullivan
, D. A.
Dartt
, and M. A.
Meneray
(Springer
, Berlin
, 1998
), pp. 425
–431
.36.
K. N.
Winter
, D. M.
Anderson
, and R. J.
Braun
, “A model for wetting and evaporation of a post-blink precorneal tear film
,” Math. Med. Biol.
27
, 211
–225
(2010
).37.
L.
Li
and R. J.
Braun
, “A model for the human tear film with heating from within the eye
,” Phys. Fluids
24
, 062103
(2012
).38.
M. B.
Jones
, C. P.
Please
, D. L. S.
McElwain
, G. R.
Fulford
, A. P.
Roberts
, and M. J.
Collins
, “Dynamics of tear film deposition and drainage
,” Math. Med. Biol.
22
, 265
–288
(2005
).39.
M. B.
Jones
, D. L. S.
McElwain
, G. R.
Fulford
, M. J.
Collins
, and A. P.
Roberts
, “The effect of the lipid layer on tear film behavior
,” Bull. Math. Biol.
68
, 1355
–1381
(2006
).40.
R. J.
Braun
and P. E.
King-Smith
, “Model problems for the tear film in a blink cycle: Single equation models
,” J. Fluid Mech.
586
, 465
–490
(2007
).41.
A.
Heryudono
, R. J.
Braun
, T. A.
Driscoll
, L. P.
Cook
, K. L.
Maki
, and P. E.
King-Smith
, “Single-equation models for the tear film in a blink cycle: Realistic lid motion
,” Math. Med. Biol.
24
, 347
–377
(2007
).42.
V. S.
Zubkov
, C. J.
Breward
, and E. A.
Gaffney
, “Coupling fluid and solute dynamics within the ocular surface tear film: A modelling study of black line osmolarity
,” Bull. Math. Biol.
74
, 2062
–2093
(2012
).43.
N.
Efron
, G.
Young
, and N. A.
Brennan
, “Ocular surface temperature
,” Curr. Eye Res.
8
, 901
–906
(1989
).44.
K. L.
Maki
, R. J.
Braun
, W. D.
Henshaw
, and P. E.
King-Smith
, “Tear film dynamics on an eye-shaped domain I: Pressure boundary conditions
,” Math. Med. Biol.
27
, 227
–254
(2010
).45.
K. L.
Maki
, R. J.
Braun
, P.
Ucciferro
, W. D.
Henshaw
, and P. E.
King-Smith
, “Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions
,” J. Fluid Mech.
647
, 361
–390
(2010
).46.
P. E.
King-Smith
, B. A.
Fink
, N.
Fogt
, K. K.
Nichols
, R. M.
Hill
, and G. S.
Wilson
, “The thickness of the human precorneal tear film: Evidence from reflection spectra
,” Invest. Ophthalmol. Visual Sci.
41
, 3348
–3359
(2000
).47.
K. L.
Maki
, R. J.
Braun
, T. A.
Driscoll
, and P. E.
King-Smith
, “An overset grid method for the study of reflex tearing
,” Math. Med. Biol.
25
, 187
–214
(2008
).48.
V. S.
Ajaev
and G. M.
Homsy
, “Steady vapor bubbles in rectangular microchannels
,” J. Colloid Interface Sci.
240
, 259
–271
(2001
).49.
H.
Owens
and J.
Phillips
, “Spread of the tears after a blink: Velocity and stabilization time in healthy eyes
,” Cornea
20
, 484
–487
(2001
).50.
John M.
Tiffany
, “The viscosity of human tears
,” Int. Ophthalmol.
15
, 371
–376
(1991
).51.
B.
Nagyová
and J. M.
Tiffany
, “Components of tears responsible for surface tension
,” Curr. Eye Res.
19
, 4
–11
(1999
).52.
T. R.
Golding
, A. S.
Bruce
, and J. C.
Mainstone
, “Relationship between tear-meniscus parameters and tear-film breakup
,” Cornea
16
, 649
–661
(1997
).53.
W. D.
Mathers
and T. E.
Daley
, “Tear flow and evaporation in patients with and without dry eye
,” Ophthalmol.
103
, 664
–669
(1996
).54.
G.
Chesshire
and W. D.
Henshaw
, “Composite overlapping meshes for the solution of partial differential equations
,” J. Comput. Phys.
90
, 1
–64
(1990
).55.
W. D.
Henshaw
, “Ogen: The overture overlapping grid generator
,” Technical Report UCRL-MA-132237, Lawrence Livermore National Laboratory
, 2002
.56.
K. E.
Brenan
, S. L.
Campbell
, and L. R.
Petzold
, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations
(SIAM
, Philadelphia
, 1996
).57.
K. L.
Maki
, “Computational solutions of linear systems and models of the human tear film
,” Ph.D. thesis (University of Delaware
, 2009
).58.
P. E.
King-Smith
, J. J.
Nichols
, K. K.
Nichols
, B. A.
Fink
, and R. J.
Braun
, “Contributions of evaporation and other mechanisms to tear film thinning and breakup
,” Optom. Vis. Sci.
85
, 623
–630
(2008
).59.
J. J.
Nichols
, G. L.
Mitchell
, and P. E.
King-Smith
, “Thinning rate of the precorneal and prelens tear films
,” Invest. Ophthalmol. Visual Sci.
46
, 2353
–2361
(2005
).60.
D. T.
Liu
, M. A.
Di Pascuale
, J.
Sawai
, Y. Y.
Gao
, and S. C.
Tseng
, “Tear film dynamics in floppy eyelid syndrome
,” Invest. Ophthalmol. Visual Sci.
46
, 1188
–1194
(2005
).61.
M. A.
Lemp
, A. J.
Bron
, C.
Baudoin
, J. M.
Benítez Del Castillo
, D.
Geffen
, G. N.
Foulks
, J.
Tauber
, J. S.
Pepose
, and B. D.
Sullivan
, “Tear osmolarity in the diagnosis and management of dry eye disease
,” Am. J. Ophthalmol.
151
, 792
–798
(2011
).© 2014 AIP Publishing LLC.
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