A two-phase model for the aqueous outflow through the trabecular meshwork
Keywords:Aqueous Humor, Trabecular Meshwork, Uveal-Corneoscleral Meshwork, Juxtacanalicular Meshwork..
A two-phase steady-state model for the percolation of aqueous humor through the trabecular meshwork (TM) in eye has been developed. The model treats the meshwork as an annular porous cylinder comprised of two concentric rings that represent the uveal-corneoscleral meshwork and juxtacanalicular meshwork. Both the rings are assumed to be made up of homogeneous, isotropic, viscoelastic material swollen with continuously flowing aqueous humor through the tissue with different structural properties. The model incorporates a strain-dependent permeability function. An analytical solution to the mathematical model has been obtained and the expressions for the displacement and fluid pressure distributions have been derived. The computational results for the displacement in solid phase, the fluid pressure distribution and the dilatation of the ocular tissue material have been presented through the graphs. The effects of structural model parameters on the displacement and the dilatation have also been investigated.
R.J. Atkin and R.E. Craine, Continuum theories of mixtures: applications, Inst. Math. Appl. 17 (1976) 153.http://dx.doi.org/10.1093/imamat/17.2.153.
R. Avtar, R. Srivastava, Aqueous outflow in Schlemmâ€™s canal, Appl. Math. Comput. 174 (2006) 316-328.http://dx.doi.org/10.1016/j.amc.2005.04.081.
R. Avtar, R. Srivastava, Modelling aqueous humor outflow through trabecular meshwork, Appl. Math. Comput. 189 (2007) 734-745.http://dx.doi.org/10.1016/j.amc.2006.11.109.
R.M. Bowen, Theory of mixtures in Continuum Physics, A.C. Eringen (Ed), Vol. II, New York: Academic (1976).
P.A. Chandler, W.M. Grant, Glaucoma, second ed.,Lea &Febiger, Philadelphia, 1979, pp. 77-109.
C.R. Ethier, R.D. Kamm, B.A. Palaszewski, M.C. Johnson, T.M. Richardson, Calculations of flow resistance in the juxtacanalicular meshwork, Invest Ophthalmol. Vis. Sci. (1986) 27(12) 1741-1750.
C.R. Ethier, M. Johnson, J. Rubert, Ocular biomechanics and biotransport, Ann. Rev. Biomed. Eng. 6 (2004) 249-273.http://dx.doi.org/10.1146/annurev.bioeng.6.040803.140055.
W.M. Grant, Facility of flow through the trabecular meshwork, Arch. Ophthalmol. 54 (1955) 245-248.http://dx.doi.org/10.1001/archopht.1955.00930020251012.
W.M. Grant, Further studies on facility of flow through the trabecular meshwork, Arch. Ophthalmol. 60 (1958) 523-533.http://dx.doi.org/10.1001/archopht.1958.00940080541001.
M. Johnson, Modulation of outflow resistances by the pores of the inner wall endothelium, Invest. Ophth. Vis. Sci. 33 (5) (1992) 1670-1675.
D.E. Kenyon, Transient filtration in a porous cylinder, Appl. Mech. 43 (1976) 594-598.http://dx.doi.org/10.1115/1.3423938.
M. Klanchar, J.M. Tarball, Modelling water flow through arterial tissue, Bull. Math. Bio. 49 (1987) 651-669.http://dx.doi.org/10.1007/BF02481766.
W.M. Lai, V.C. Mow, Drag induced compression of articular cartilage during a permeation experiment, Biorheology 17 (1980) 111-123.
A. Llobet, X. Gasull, A. Gual, Understanding trabecular meshwork physiology: a key to the control of intraocular pressure, News Physiol. Sci. 18 (2003) 205-209.
W.K. McEwen, Application of Poiseuilleâ€™s law of aqueous outflow, Arch. Ophthalmol, 60 (1958) 290-307.http://dx.doi.org/10.1001/archopht.1958.00940080306017.
R.A. Moses, The effect of intraocular pressure on resistance of outflow, Surv. Ophthalmol. 22 (1977) 88-100.http://dx.doi.org/10.1016/0039-6257(77)90088-1.
R.A. Moses, Circumferential flow in Schlemmâ€™s Canal, Am. J. Ophthalmol. 88 (1979) 585-591.http://dx.doi.org/10.1016/0002-9394(79)90519-1.
R.A. Moses, Jr. Wj. Grodzki, EL. Etheridge, C.D. Wilson, Schlemmâ€™s canal: The effect of intraocular pressure, Invest. Ophthalmol Vis. Sci. Vol. 20(1) (1981) 61-68.
A.L. Rabenstain, Introduction to Ordinary Differential Equations, New York: Academic (1972).
A.J. Sit, Hydrodynamics of aqueous humor outflow, S.M. Thesis, Massachusetts Institute of technology, 1995.
A.J. Sit, H. Gong, R. Nathan, F.T. Freddo, R. Kamm, M. Johnson, The role of soluble proteins in generating aqueous outflow resistance in the bovine and human eye, Exp, Eye Res. 64 (1997) 813-821.http://dx.doi.org/10.1006/exer.1997.0276.
T. Seiler, J. Wollensak, The resistance of the trabecular meshwork to aqueous humor outflow, Graefes Arch. Clin. Exp. Ophthalmol. (1985) 223(2) 88-91.http://dx.doi.org/10.1007/BF02150951.
P.N. Tandon, R. Avtar, Biphasic model of the trabecular meshwork in the eye, Med. Biol. Eng. Comput. 29 (1991) 281-290.http://dx.doi.org/10.1007/BF02446710.