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Review of applied mathematical models for describing the behaviour of aqueous humor in eye structures

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.
Rocznik
Strony
757--772
Opis fizyczny
Bibliogr. 22 poz., rys., tab., wykr.
Twórcy
autor
  • WS-SPZOZ Zgorzelec, Opthalmological Ward Lubańska St. 11-12, 59-900 Zgorzelec, POLAND
autor
  • University of Zielona Góra, Department of Mechanics Szafrana St. 2, 65-516 Zielona Góra, POLAND
Bibliografia
  • [1] Amiri A. and Vafai K. (1994): Analysis of dispersion effects and non- thermal equilibrium, non-Darcian variable porosity incompressible flow through porous media. – Int. J. Heat and Mass Transf., vol.37, pp.939-954.
  • [2] Amiri A. and Vafai K. (1998): Transient analysis of incompressible flow through a packed bad. – Int. J. Heat and Mass Transf., vol.41, pp.4259-4279.
  • [3] Chotard-Ghodsnia R. and Verdier C. (2007): Rheology of living materials. Chapter in Rheology of Living Materials. – pp.1-31. DOI: 10.1007/978-0-8176-4411-6_1.
  • [4] Fauci L.J. and Gueron S. (2001): Computational Modeling in Biological Fluid Dynamics. – New York: Springer Science+Business Media.
  • [5] Fitt A.D. and Gonzalez G. (2006): Fluid Mechanics of the Human Eye: Aqueous Humour Flow in the Anterior Chamber. – Bulletin of Mathematical Biology, DOI 10.1007/s11538-005-9015-2.
  • [6] Gabelt B.T. and Kaufman P. (1995). Aqueous humor hydrodynamics. – In: Kaufman PL, Alm A, Ed. Alder“s Physiology of the Eye, vol.8. St. Louis, MO: Mosby, pp.237-289.
  • [7] Gedde S.J. (2012): The tube trials: new information to guide clinicians updates on six recent studies. – Ophthalmology Management, vol.12, No.16, pp.52-58.
  • [8] Goldmann H. (1950) Minute volume of the aqueous in the anterior chamber of the human eye in normal state and in primary glaucoma. – Ophthalmologica. vol.120, No.1-2, pp.19-21.
  • [9] Heys J.J., Barocas V.H. and Taravella M.J. (2002): Modeling passive mechanical interaction between aqueous humor and iris. – J. Biomech. Eng.., vol.123, No.6, pp.540-547.
  • [10] Man C.S., Sun Q.X. (1987): On the significance of normal stress effects in the flow of glaciers. – J. Glaciology, vol.33, No.115, 268-273.
  • [11] Millar C.J., Gabelt B. and Kaufman P. (2011): Aqueous Humor Dynamics. – Duane’s Clinical Ophthalmology, Lippincott-Raven Publishers, Chapter 45, pp.1-34.
  • [12] Nakayama A., Kuwahara F. and Hayashi T. (2004): Numerical model ling for three-dimensional heat and fluid flow through a bank of cylinders in yaw. – J. Fluid Mech., vol.498, pp.139-159.
  • [13] Nakayama A., Kuwahara F. and Kodama Y. (2006): A thermal dispersion flux transport equation and its mathematical modeling for heat and fluid flow in a porous medium. – J. Fluid Mech. vol.563, pp.81-96.
  • [14] Niżankowska M.H. (2006): Basic and Clinical Science Course. – Science 10, Glaucoma, Medical Publisher Urban and Partner, Wroclaw.
  • [15] Stokes V.K. (1966): Couple-stresses in fluids. – Phys. Fluids, vol.9, No.9, pp.1709-1715.
  • [16] Tsai C.Y., Novack M. and Roffe G. (1988): Rheological and heat transfer characteristics of flowing coal-water mixtures. – Final Report, DOE/Mc 23255-2763.
  • [17] Verdier C., Etienne J., Duperray A. and Preziosi L. (2009): Review. Rheological properties of biological materials. – C. R. Physique, Special Issue on “Complex and Biofluids”, Ed. C. Misbah, vol.10, pp.790-811.
  • [18] Walicka A. (2012): Porous curvilinear squeeze film bearing with rough surfaces lubricated by a power-law fluid. – Journal of Porous Media, vol.15, No.1, pp.29-49.
  • [19] Walicka A. (2002): Rheodynamics of Non-Newtonian Fluids Flows in Straight and Curved Channels (in Polish). – Zielona Góra: University Press.
  • [20] Walicka A. and Walicki E (2012): Rheodynamics of flows in porous biomaterials. – Mechanics in Medicine, vol.11, pp.181-193.
  • [21] Walicka A. and Walicki E. (1999): Inertia effect in the squeeze film of a couple-stress fluid in biological bearings. – Applied Mechanics and Engineering, vol.4, No.2, pp.363-373.
  • [22] Walicki E. and Walicka A. (1998): Flow of generalized second grade fluids in a circular pipe. – Les Cahiers de Rhéologie, vol.34, No.1, pp.317-324.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c6a068d3-5181-4186-aca5-90d041e3e380
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