We study the motion of a viscoelastic fluid within a rigid sphere, with the aim of improving our knowledge on the dynamics of the vitreous humour in the eye and the resulting stress on the retina. This is known to be related to the occurrence of retinal detachment. We first analyse the relaxation behaviour of the vitreous. The assumption of small particle displacements allows us to linearise the equations of motion, which we write as an eigenvalue problem. We obtain an expression for the eigenvalues of the system by expanding the velocity and pressure fields as a superposition of spherical harmonic functions. Considering different rheological models for the vitreous behaviour we find complex eigenvalues in most cases. Their imaginary parts represent natural frequencies of oscillation of the system. In the second part of the paper we analyse the motion of the fluid forced by periodic torsional oscillations of the domain and find that the velocity and the stress on the wall significantly increase when the forcing frequency is close to a natural frequency of the system. Finally, we study vitreous motion under more realistic, saccadic eye rotations. We show that a sequence of real eye rotations can possibly resonantly excite vitreous motion, thus leading to large values of the wall shear stress.
A model of the dynamics of the vitreous humour in the eye
REPETTO, RODOLFO;BONFIGLIO, ANDREA;STOCCHINO, ALESSANDRO;
2012-01-01
Abstract
We study the motion of a viscoelastic fluid within a rigid sphere, with the aim of improving our knowledge on the dynamics of the vitreous humour in the eye and the resulting stress on the retina. This is known to be related to the occurrence of retinal detachment. We first analyse the relaxation behaviour of the vitreous. The assumption of small particle displacements allows us to linearise the equations of motion, which we write as an eigenvalue problem. We obtain an expression for the eigenvalues of the system by expanding the velocity and pressure fields as a superposition of spherical harmonic functions. Considering different rheological models for the vitreous behaviour we find complex eigenvalues in most cases. Their imaginary parts represent natural frequencies of oscillation of the system. In the second part of the paper we analyse the motion of the fluid forced by periodic torsional oscillations of the domain and find that the velocity and the stress on the wall significantly increase when the forcing frequency is close to a natural frequency of the system. Finally, we study vitreous motion under more realistic, saccadic eye rotations. We show that a sequence of real eye rotations can possibly resonantly excite vitreous motion, thus leading to large values of the wall shear stress.
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