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Meccanica

, Volume 41, Issue 1, pp 101–117 | Cite as

An Analytical Model of the Dynamics of the Liquefied Vitreous Induced by Saccadic Eye Movements

  • Rodolfo Repetto
Open Access
Article

Abstract

An analytical model of the dynamics of the vitreous humour induced by saccadic movements within the eye globe is presented. The vitreous is treated as a weakly viscous Newtonian incompressible fluid, an assumption which is appropriate when the vitreous is liquefied or when it is replaced by aqueous humour after surgery. The thin viscous boundary layer generated during a saccadic movement on the side wall is neglected and the flow field is assumed to be irrotational. The vitreous chamber is described as a weakly deformed sphere and this assumption allows a linear treatment of the problem. An analytical solution is found in the form of an expansion of spherical harmonics. Results show that the non-spherical shape of the container generates a flow field characterised by significant velocities and strong three-dimensionality. The model allows the computation of the dynamic pressure on the wall, which may play a role in the generation of retinal detachments. Moreover, results suggest that the irregular shape of the globe may significantly modify tangential stresses on the boundary with respect to the case of motion within a sphere. A simplified analytical solution, for the case of two-dimensional flow within an impulsively rotated container, shows that boundary layer detachment is expected to occur for angles of rotation larger than a threshold value of 15° circa.

Keywords

Eye Vitreous dynamics Biological fluid dynamics Irrotational flow Fluid mechanics 

References

  1. 1.
    Becker, W., ‘Metrics’, in: Wurtz and Goldberg (eds.), The neurobiology of saccadic eye movements. Elsevier Science Publisher BV (Biomedical Division), 1989.Google Scholar
  2. 2.
    Beswick, J.A., McCulloch, C. 1956‘Effect of hyaluronidase on the viscosity of the aqueous humour’Brit. J. Ophthamol40545548Google Scholar
  3. 3.
    David, T., Smye, S., Dabbs, T., James, T. 1998‘A model for the fluid motion of vitreous humour of the human eye during saccadic movement’Phys. Med. Biol4313851399CrossRefGoogle Scholar
  4. 4.
    Lee, B., Litt, M., Buchsbaum, G. 1992‘Rheology of the vitreous body. Part I: viscoelasticity of human vitreous’Biorheology29521533Google Scholar
  5. 5.
    Lindner, K. 1933‘Über die Herstellung von Modellen zu Modellversuchen der Netzhautabhebung’Klin. monatsbl. Augenh90289300Google Scholar
  6. 6.
    Morse, P.M., Feshbach, H. 1953Methods of Theoretical PhysicsMcGraw-HillNew YorkGoogle Scholar
  7. 7.
    Repetto, R., Ghigo, I., Seminara, G., Ciurlo, C. 2004‘A simple hydro-elastic model of the dynamics of a vitreous membrane’J. Fluid Mech503114CrossRefADSGoogle Scholar
  8. 8.
    Rosengren, B., Östrelin, S. 1976‘Hydrodynamic events in vitreous space accompanying eye movements’Ophtalmologica173513524Google Scholar
  9. 9.
    Stuart, J.T. 1963‘Unsteady Boundary Layers’Rosenhead, L. eds. Laminar Boundary LayersClarendon PressOxfordGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria delle Strutture, delle Acque e del TerrenoUniversity of L’AquilaL’AquilaItaly

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