Certain forms of glaucoma are associated with displacement of the iris from its normal contour. We present here a mathematical model of the coupled aqueous humor–iris system that accounts for the contribution of aqueous humor flow and passive iris deformability to the iris contour. The aqueous humor is modeled as a Newtonian fluid, and the iris is modeled as a linear elastic solid. The resulting coupled equation set is solved by the finite element method with mesh motion in response to iris displacement accomplished by tracking a pseudo-solid overlying the aqueous humor. The model is used to predict the iris contour in healthy and diseased eyes. The results compare favorably with clinical observations, supporting the hypothesis that passive iris deformation can produce the iris contours observed using ultrasound biomicroscopy.
Issue Section:
Technical Papers
1.
Quigley
, H. A.
, 1996
, “Number of People With Glaucoma Worldwide
,” Br. J. Ophthamol.
, 80
, pp. 389
–393
.2.
Farrar
, S. M.
, and Shields
, M. B.
, 1993
, “Current Concepts in Pigmentary Glaucoma
,” Surv. Ophthalmol.
, 37
, pp. 233
–252
.3.
Tiedeman
, J. S.
, 1991
, “A Physical Analysis of the Factors That Determine the Contour of the Iris
,” Am. J. Ophthalmol.
, 111
, pp. 338
–343
.4.
Friedland
, A. B.
, 1978
, “A Hydrodynamic Model of Aqueous Flow in the Posterior Chamber of the Eye
,” Bull. Math. Biol.
, 40
, pp. 223
–235
.5.
Van Buskirk, E. M., 1997, “Anatomy,” Chandler and Grant’s Glaucoma, D. L. Epstein et al., eds., Williams & Wilkins, Baltimore, pp. 6–17.
6.
Cantrill
, H. L.
, and Pederson
, J. E.
, 1984
, “Experimental Retinal Detachment. VI. The Permeability of the Blood–Retinal Barrier
,” Pap. Proc. Annu. Meet. Am. Econ. Assoc.
, 102
, pp. 747
–751
.7.
Caprioli, J., 1992, “The Ciliary Epithelia and Aqueous Humor,” Adler’s Physiology of the Eye: Clinical Application, W. M. Hart, ed., Mosby-Year Book, St. Louis, pp. 228–247.
8.
Fontana
, S. T.
, and Brubaker
, R. F.
, 1980
, “Volume and Depth of the Anterior Chamber of the Normal Aging Human Eye
,” Pap. Proc. Annu. Meet. Am. Econ. Assoc.
, 98
, pp. 1803
–1808
.9.
Bartels, S. P., 1989, “Aqueous Humor Formation. Fluid Production by a Sodium Pump,” The Glaucomas, R. Ritch et al., eds., C. V. Mosby Company, St. Louis, pp. 199–218.
10.
Liebmann
, J. M.
, and Ritch
, R.
, 1996
, “Ultrasound Biomicroscopy of the Anterior Segment
,” J. Am. Optom. Assoc.
, 67
, pp. 469
–479
.11.
Pavlin
, C. J.
, Harasiewicz
, K.
, and Foster
, F. S.
, 1995
, “An Ultrasound Biomicroscopic Dark-Room Provocative Test
,” Ophthalmic Surg.
, 26
, pp. 253
–255
.12.
Karickhoff
, J. R.
, 1992
, “Pigmentary Dispersion Syndrome and Pigmentary Glaucoma: A New Mechanism Concept, A New Treatment, and A New Technique
,” Ophthalmic Surg.
, 23
, pp. 269
–277
.13.
Smith
, S. D.
, 1991
, “Measurement of the Rate of Aqueous Humor Flow
,” Yale J. Biol. Med.
, 64
, pp. 89
–102
.14.
McLaren
, J. W.
, Ziai
, N.
, and Brubaker
, R. F.
, 1993
, “A Simple Three-Compartment Model of Anterior Segment Kinetics
,” Exp. Eye Res.
, 56
, pp. 355
–366
.15.
Scott
, J. A.
, 1988
, “A Finite Element Model of Heat Transport in the Human Eye
,” Phys. Med. Biol.
, 33
, pp. 227
–241
.16.
Beswick
, J. A.
, and McCulloch
, C.
, 1956
, “Effect of Hyaluronidase on the Viscosity of the Aqueous Humour
,” Br. J. Ophthamol.
, 40
, pp. 545
–548
.17.
Gunzburger, M. D., 1989, Finite Element Methods for Viscous Incompressible Flows: A Guide to Theory, Practice, and Algorithms, Academic Press, Boston, pp. 269.
18.
Heys
, J.
, and Barocas
, V. H.
, 1999
, “Mechanical Characterization of the Bovine Iris
,” J. Biomech.
, 32
, pp. 999
–1003
.19.
Coleman, D. J., Lizzi, F. L., and Jack, R. L., 1977, Ultrasonography of the Eye and Orbit, Lea & Febiger, Philadelphia, p. 174.
20.
Thijssen
, J. M.
, 1993
, “The History of Ultrasound Techniques in Ophthalmology
,” Ultrasound Med. Biol.
, 19
, pp. 599
–618
.21.
Sokol
, J.
, Stegman
, Z.
, Liebmann
, J. M.
, and Ritch
, R.
, 1996
, “Location of the Iris Insertion in Pigment Dispersion Syndrome
,” Ophthalmology
, 103
, pp. 289
–293
.22.
Kaufman, P. L., 1989, “Pressure-Dependent Outflow,” The Glaucomas, R. Ritch et al., eds., C. V. Mosby Company, St. Louis, pp. 219–240.
23.
Johnson
, M. C.
, and Kamm
, R. D.
, 1983
, “The Role of Schlemm’s Canal in Aqueous Outflow From the Human Eye
,” Invest. Ophthalmol. Visual Sci.
, 24
, pp. 320
–325
.24.
Maurice
, D. M.
, 1987
, “Flow of Water Between Aqueous and Vitreous Compartments in the Rabbit Eye
,” Am. J. Physiol.
, 252
, pp. F104–F108
F104–F108
.25.
Araie
, M.
, Sugiura
, Y.
, Sakurai
, M.
, and Oshika
, T.
, 1991
, “Effect of Systemic Acetazolamide on the Fluid Movement Across the Aqueous–Vitreous Interface
,” Exp. Eye Res.
, 53
, pp. 285
–293
.26.
Epstein
, D. L.
, Hashimoto
, J. M.
, Anderson
, P. J.
, and Grant
, W. M.
, 1979
, “Experimental Perfusions Through the Anterior and Vitreous Chamber With Possible Relationships to Malignant Glaucoma
,” Am. J. Ophthalmol.
, 88
, pp. 1078
–1086
.27.
Brown
, J. D.
, and Brubaker
, R. F.
, 1989
, “A Study of the Relation Between Intraocular Pressure and Aqueous Humor Flow in the Pigment Dispersion Syndrome
,” Ophthalmology
, 96
, pp. 1468
–1470
.28.
Johnson, M., and Erickson, K., 2000, “Mechanisms and Routes of Aqueous Humor Drainage,” Glaucoma, D. M. Albert et al., eds., WB Saunders Co., Philadelphia, pp. 2577–2594.
29.
Roark, R. J., 1965, Formulas for Stress and Strain, McGraw-Hill, New York.
30.
Puslow
, P. P.
, and Karwatowski
, W. S. S.
, 1996
, “Ocular Elasticity
,” Ophthalmology
, 103
, pp. 1686
–1692
.31.
Smolek
, M. K.
, 1994
, “Holographic Interferometry of Intact and Radially Incised Human Eye-Bank Corneas
,” J. Cataract Refractive Surg.
, 20
, pp. 277
–286
.32.
Werff
, T. J. v. d.
, 1981
, “A New Single-Parameter Ocular Rigidity Function
,” Am. J. Ophthalmol.
, 92
, pp. 391
–395
.33.
Bryant
, M. R.
, and McDonnell
, P. J.
, 1996
, “Constitutive Laws for Biomechanical Modeling of Refractive Surgery
,” ASME J. Biomech. Eng.
, 118
, pp. 473
–481
.34.
Krag
, S.
, Olsen
, T.
, and Andreassen
, T. T.
, 1997
, “Biomechanical Characteristics of the Human Anterior Lens Capsule in Relation to Age
,” Invest. Ophthalmol. Visual Sci.
, 38
, pp. 357
–363
.35.
Pavlin
, C. J.
, Buys
, Y. M.
, and Pathmanathan
, T.
, 1998
, “Imaging Zonular Abnormalities Using Ultrasound Biomicroscopy
,” Pap. Proc. Annu. Meet. Am. Econ. Assoc.
, 116
, pp. 854
–857
.36.
Thompson, H. S., 1992, “The Pupil,” Adler’s Physiology of the Eye: Clinical Application, W. M. Hart, ed., Mosby Year Book, St. Louis, MO, pp. 412–441.
37.
Ren
, H.
, and Wilson
, G.
, 1997
, “The Effect of a Shear Force on the Cell Shedding Rate of the Corneal Epithelium
,” Acta Ophthalmol. Scand.
, 75
, pp. 383
–387
.38.
Hart, W. M., 1992, “The Eyelids,” Adler’s Physiology of the Eye: Clinical Application, W. M. Hart, ed., Mosby-Year Book, St. Louis, pp. 1–17.
39.
Percicot
, C. L.
, Schnell
, C. R.
, Debon
, C.
, and Hariton
, C.
, 1996
, “Continuous Intraocular Pressure Measurement by Telemetry in Alpha-Chymotrypsin-Induced Glaucoma Model in the Rabbit: Effects of Timolol, Dorzolamide, and Epinephrine
,” J. Pharmacol. Toxicol. Methods
, 36
, pp. 223
–228
.40.
Collins
, C. C.
, 1967
, “Miniature Passive Pressure Transsensor for Implanting in the Eye
,” IEEE Trans. Biomed. Eng.
, 14
, pp. 74
–83
.41.
Allingham, R. R., 1997, “Glaucoma Due to Intraocular Inflammation,” Chandler and Grant’s Glaucoma, D. L. Epstein et al., eds., Williams & Wilkins, Baltimore, pp. 375–394.
42.
Sackinger
, P. A.
, Schunk
, P. R.
, and Rao
, R. R.
, 1996
, “A Newton–Raphson Pseudo-Solid Domain Mapping Technique for Free and Moving Boundary Problems: A Finite Element Implementation
,” J. Comput. Phys.
, 125
, pp. 83
–103
.43.
Saad
, Y.
, and Schultz
, M. H.
, 1986
, “GMRES: A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems
,” SIAM J. Sci. Comput. (USA)
, 7
, pp. 856
–869
.44.
Pavlin
, C. J.
, and Foster
, F. S.
, 1998
, “Ultrasound Biomicroscopy: High-Frequency Ultrasound Imaging of the Eye at Microscopic Resolution
,” Radiol. Clin. North Am.
, 36
, pp. 1047
–1058
.45.
Marchini
, G.
, Pagliarusco
, A.
, Toscano
, A.
, Tosi
, R.
, Brunelli
, C.
, and Bonomi
, L.
, 1998
, “Ultrasound Biomicroscopic and Conventional Ultrasonographic Study of Ocular Dimensions in Primary Angle-closure Glaucoma
,” Ophthalmology
, 105
, pp. 2091
–2098
.46.
Liebmann
, J.
, Tello
, C.
, Chew
, S.
, Cohen
, H.
, and Ritch
, R.
, 1995
, “Prevention of Blinking Alters Iris Configuration in Pigment Dispersion Syndrome and in Normal Eyes
,” Ophthalmology
, 102
, pp. 446
–455
.47.
Epstein, D. L., 1997, “Practical Aqueous Humor Dynamics,” Chandler and Grant’s Glaucoma, D. L. Epstein et al., eds., Williams & Wilkins, Baltimore, Maryland, pp. 18–24.
48.
Woo
, E. K.
, Pavlin
, C. J.
, Slomovic
, A.
, Taback
, N.
, and Buys
, Y. M.
, 1999
, “Ultrasound Biomicroscopic Quantitative Analysis of Light-Dark Changes Associated With Pupillary Block
,” Am. J. Ophthalmol.
, 127
, pp. 43
–47
.49.
Lagendijk
, J. J. W.
, 1982
, “A Mathematical Model to Calculate Temperature Distributions in Human and Rabbit Eyes During Hyperthermic Treatment
,” Phys. Med. Biol.
, 27
, pp. 1301
–1311
.50.
Liebmann
, J. M.
, and Ritch
, R.
, 1996
, “Laser Iridotomy
,” Ophthalmic Surg. Lasers
, 27
, pp. 209
–221
.51.
Downey
, D. B.
, Nicolle
, D. A.
, Levin
, M. F.
, and Fenster
, A.
, 1996
, “Three-Dimensional Ultrasound Imaging of the Eye
,” Eye
, 10
, pp. 75
–81
.52.
Bellezza
, A. J.
, Hart
, R. T.
, and Burgoyne
, C. F.
, 2000
, “The Optic Nerve Head as a Biomechanical Structure: Initial Finite Element Modeling
,” Invest. Ophthalmol. Visual Sci.
, 41
, pp. 2991
–3000
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