Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Models for Dynamics of the Human Tear Film R.J. Braun 1 , K.L ˙ Maki 2 , A. Heryudono 3 , T.A. Driscoll 1 , L.P . Cook 1 , . Ucciferro 1 , P .E. King-Smith 4 , W.D. Henshaw 5 , G.B. McFadden 6 , P R. Usha 7 , D.M. Anderson 8 and K.N. Winter 8 1 Mathematical Sciences, U of Delaware; 2 IMA, University of Minnesota; 3 Math, UMass Dartmouth; 4 College of Optometry, The Ohio State University; 5 CASC, LLNL; 6 MCSD, NIST; 7 IIT Madras, India; 8 Mathematical Sciences, George Mason U Supported by the NSF
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Outline Motivation Is tear film a complex fluid? (Modeling) Deciding from 1D models 1D results Goal: Quantify tear film Corneal substrate Blinks and partial blinks dynamics! Reflex tearing Evaporation and conjoining pressure 2D computations – none today Summary and Future Directions
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Why Study Human Tear Film? Normal tear film dynamics: Much to understand and quantify! Dry eye syndrome: Common abnormality from insufficient or malfunctioning tear film causing disruption. Prevalence: An estimated 10% - 15% of Americans over the age of 65 have one or more symptoms of dry eye syndrome ∗ . Symptoms: Burning/stinging; Blurred vision Irritation/redness; Dry sensation Foreign body or “gritty" sensation; Tearing Impact: Negative impact on, e.g., reading and driving from dry eye syndrome**. *Stein et al. 1997; DEWS Report, 2007. **Miljanovic et al. 2007.
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film A multilayer structure playing a vital role in health and function of the eye. (M): A possible mucus film, if separate from aqueous debatable. A: Aqueous layer, primarily water (est. up to 98 % ). L: Lipid layer, polar surfactants at the A/L Typical thickness of each layer in interface. microns.
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film What’s in there? Properties? Mucins: Shear thinning: Tiffany 16 known mucins, most in aqueous layer (1991), Pandit et al (1999) 3 transmembrane at corneal surface Not elastic: Tiffany (1994) Aqueous: gave inconclusive evidence Salts for it more than proteins Surface tension: 45mN/m, mucins Tiffany and coworkers Lipid layer: insoluble in aqueous (1999); need proteins and polar: sphingolipids, phospholipids lipids to get this value nonpolar: waxes, cholesterol esters
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film What’s in there? Properties? Mucins: Shear thinning: Tiffany 16 known mucins, most in aqueous layer (1991), Pandit et al (1999) 3 transmembrane at corneal surface Not elastic: Tiffany (1994) Aqueous: gave inconclusive evidence Salts for it more than proteins Surface tension: 45mN/m, mucins Tiffany and coworkers Lipid layer: insoluble in aqueous (1999); need proteins and polar: sphingolipids, phospholipids lipids to get this value nonpolar: waxes, cholesterol esters
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film What’s in there? Properties? Mucins: Shear thinning: Tiffany 16 known mucins, most in aqueous layer (1991), Pandit et al (1999) 3 transmembrane at corneal surface Not elastic: Tiffany (1994) Aqueous: gave inconclusive evidence Salts for it more than proteins Surface tension: 45mN/m, mucins Tiffany and coworkers Lipid layer: insoluble in aqueous (1999); need proteins and polar: sphingolipids, phospholipids lipids to get this value nonpolar: waxes, cholesterol esters
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film What’s in there? Properties? Mucins: Shear thinning: Tiffany 16 known mucins, most in aqueous layer (1991), Pandit et al (1999) 3 transmembrane at corneal surface Not elastic: Tiffany (1994) Aqueous: gave inconclusive evidence Salts for it more than proteins Surface tension: 45mN/m, mucins Tiffany and coworkers Lipid layer: insoluble in aqueous (1999); need proteins and polar: sphingolipids, phospholipids lipids to get this value nonpolar: waxes, cholesterol esters
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film What’s in there? Properties? Mucins: Shear thinning: Tiffany 16 known mucins, most in aqueous layer (1991), Pandit et al (1999) 3 transmembrane at corneal surface Not elastic: Tiffany (1994) Aqueous: gave inconclusive evidence Salts for it more than proteins Surface tension: 45mN/m, mucins Tiffany and coworkers Lipid layer: insoluble in aqueous (1999); need proteins and polar: sphingolipids, phospholipids lipids to get this value nonpolar: waxes, cholesterol esters
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? What is Human Tear Film? Tear film What’s in there? Properties? Mucins: Shear thinning: Tiffany 16 known mucins, most in aqueous layer (1991), Pandit et al (1999) 3 transmembrane at corneal surface Not elastic: Tiffany (1994) Aqueous: gave inconclusive evidence Salts for it more than proteins Surface tension: 45mN/m, mucins Tiffany and coworkers Lipid layer: insoluble in aqueous (1999); need proteins and polar: sphingolipids, phospholipids lipids to get this value nonpolar: waxes, cholesterol esters
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Overview of the Dynamics Tear film supply and drainage Lacrimal gland: The lacrimal gland supplies new tear fluid during a blink cycle. Meibomian glands: The meibomian gland supplies lipids from lid edges. Punctal drainage: Removes excess fluid starting at the halfway open Image from Wikipedia. position of the lids. Typical blink cycle Upstroke/Formation: Opening of lids, 0.1758s. Interblink/Relaxation: Lids remain open, 5s (wide variation). Downstroke: Closing of lids, 0.0821s.
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Characteristics of the Human Tear Film Characteristic tear film thickness In the middle of the cornea, 3 − 5 µ m. Upper and lower menisci Volume: Contain an estimated 73% of exposed tear film volume (experimental range 2 . 45 − 4 . 0 µ l). Tear meniscus height (TMH): 181 − 336 µ m in expt. Tear meniscus width (TMW): 48 − 66 µ m in expt. Tear meniscus radius of curvature (TMC): 127 − 351 µ m in expt. Image from Jones et al. 2005. From Wang et al. 2006.
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Prior work: tear film dynamics Upward post-blink motion: Marangoni effect Berger and Corrsin (74), Owens and Philips (01), King-Smith et al (04,05) Post-blink relaxation (Newtonian) Wong et al (96), Sharma et al (98), Miller et al (02) Braun and Fitt (03), Winter et al (09): evaporation Post-blink relaxation, substrate (non-Newtonian) Gorla and Gorla (04), Braun et al (09) Tear film formation and relaxation Wong et al (96), Jones et al (05,06), Jossic et al (09, non-Newt) Blink Cycles Braun and King-Smith (07), Heryudono et al (07) (today) Reflex tearing: Maki et al (08) (today) 2D numerics with Pressure bcs or flux bcs Maki et al (09)
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Prior work: tear film dynamics Upward post-blink motion: Marangoni effect Berger and Corrsin (74), Owens and Philips (01), King-Smith et al (04,05) Post-blink relaxation (Newtonian) Wong et al (96), Sharma et al (98), Miller et al (02) Braun and Fitt (03), Winter et al (09): evaporation Post-blink relaxation, substrate (non-Newtonian) Gorla and Gorla (04), Braun et al (09) Tear film formation and relaxation Wong et al (96), Jones et al (05,06), Jossic et al (09, non-Newt) Blink Cycles Braun and King-Smith (07), Heryudono et al (07) (today) Reflex tearing: Maki et al (08) (today) 2D numerics with Pressure bcs or flux bcs Maki et al (09)
Tear Film Corneal shape Blink Cycles Reflex Tearing vdW wetting The End? Prior work: tear film dynamics Upward post-blink motion: Marangoni effect Berger and Corrsin (74), Owens and Philips (01), King-Smith et al (04,05) Post-blink relaxation (Newtonian) Wong et al (96), Sharma et al (98), Miller et al (02) Braun and Fitt (03), Winter et al (09): evaporation Post-blink relaxation, substrate (non-Newtonian) Gorla and Gorla (04), Braun et al (09) Tear film formation and relaxation Wong et al (96), Jones et al (05,06), Jossic et al (09, non-Newt) Blink Cycles Braun and King-Smith (07), Heryudono et al (07) (today) Reflex tearing: Maki et al (08) (today) 2D numerics with Pressure bcs or flux bcs Maki et al (09)
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