Dynamics of the vitreous humour and stress on the retina generated during eye rotations

In the first part of this paper we study the relaxation behaviour of a viscoelastic fluid in a rigid sphere, with the aim of understanding the dynamics of the vitreous humour within the vitreous chamber. The assumption of small displacements and velocities of fluid particles allows us to linearise the equations of motion. Expanding the velocity and pressure fields as a superposition of spherical harmonic functions and demanding the solution to be non-trivial leads to the eigenfunctions and eigenvalues of the system, which depend on the rheological model we use to describe the stress in the fluid. We consider two different models, and for both we find the existence of complex eigenvalues, the imaginary parts of which represent natural frequencies of oscillation of the system. Next, we consider the fluid motion driven by small-amplitude azimuthal torsional oscillations of the domain, which represent saccades of the eyeball. We compute the time-averaged total kinetic energy of the system and show that it assumes large values when the system is forced at resonant frequencies, at which the velocity away from the boundary becomes larger than at the boundary. Finally, we study the effect of a weak departure of the shape of the domain from a sphere, focussing on myopic eyes, which are enlarged in all directions, but mostly along the antero-posterior axis. We find that myopia significantly influences the distribution as well as the magnitude of the stress that is extered on the retina.