Mathematical model of flow in the vitreous humor induced by saccadic eye rotations: effect of geometry

Abstract

Saccadic eye rotations induce a flow in the vitreous humor of the eye. Any such flow is likely to have a significant influence on the dispersion of drugs injected into the vitreous chamber. The shape of this chamber deviates from a perfect sphere by up to 10-20% of the radius, which is predominantly due to an indentation caused by the lens. In this paper we investigate theoretically the effect of the domain shape upon the flow field generated by saccades by considering an idealized model. The posterior chamber geometry is assumed to be a sphere with a small indentation, undergoing prescribed small-amplitude sinusoidal torsional oscillations, and, as an initial step towards understanding the problem, we treat the vitreous humor as a Newtonian fluid filling the chamber. The latter assumption applies best in the case of a liquefied vitreous or a tamponade fluid introduced in the vitreous chamber after vitrectomy. We find the flow field in terms of vector spherical harmonics, focusing on the deviation from the flow that would be obtained in a perfect sphere. The flow induced by the departure of the domain geometry from the spherical shape has an oscillating component at leading order and a smaller-amplitude steady streaming flow. The oscillating component includes a circulation cell formed every half-period, which migrates from the indentation towards the center of the domain where it disappears. The steady component has two counter-rotating circulations in the anterior part of the domain. These findings are in good qualitative agreement with the experimental results of Stocchino et al. (Phys Med Biol 52:2021-2034, 2007). Our results predict a significant reduction in the expected time for drug dispersal across the eye compared with the situation in which there is no fluid flow present.