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A simple hydro-elastic model of the dynamics of a vitreous membrane

Published online by Cambridge University Press:  01 March 2004

R. REPETTO
Affiliation:
Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno, Università dell'Aquila, Monteluco di Roio, 67040, L'Aquila, Italy
I. GHIGO
Affiliation:
Dipartimento di Ingegneria Ambientale, Università di Genova, Via Montallegro 1, 16145, Genova, Italy
G. SEMINARA
Affiliation:
Dipartimento di Ingegneria Ambientale, Università di Genova, Via Montallegro 1, 16145, Genova, Italy
C. CIURLO
Affiliation:
Dipartimento di Neuroscienze, Oftalmologia e Genetica, Università di Genova, Pad. 9, Largo Rosanna Benzi 10, 16132 Genova, Italy

Abstract

We study the motion of a fluid within a rigid spherical container subject to small-amplitude periodic rotations. The sphere is divided into two equal portions by an impermeable stretched elastic membrane whose boundary is attached to the container wall. The model aims to represent in a simplified fashion the dynamics of a vitreous membrane subject to microsaccadic movements of the human eye, assuming the vitreous to be liquefied. The vitreous is modelled as a Newtonian, incompressible fluid in irrotational motion and the problem is linearized, taking advantage of the hypothesis of small-amplitude eye rotations. Results show that, due to the presence of the fluid, the natural frequencies of oscillation of the membrane decrease significantly with respect to the case of a free membrane. Moreover, oscillations of a stretched membrane are found to be resonantly excited by rotations of the sphere with frequencies which are typical of microsaccadic eye movements. This study suggests the possibility that oscillations of vitreous membranes may induce the development of large tensile stresses capable of producing a retinal detachment. Such a conclusion will have to be further substantiated by more refined analyses accounting for further effects, such as nonlinearity and the possible viscoelastic behaviour of the vitreous located on one or both sides of the membrane.

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© 2004 Cambridge University Press

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