Post-reattachment retinal detachment

A problem presented at the UK MMSG Strathclyde 2004.

Presented by:
Alistair Fitt (School of Mathematics, University of Southampton)
R Dyson, A Fitt, OE Jensen, D Miroshnychenko, N Mottram, S Naire, R Ocone, J Siggers, A Smith

Problem Description

Retinal detachment in the eye happens when the retina comes away from the choroid. This condition is often treated by removing the vitreous humour from the eye (vitrectomy) and spot-welding the retina back on to the choroid. After this, the vitreous body is refilled with saline or silicone oil. The vitreous humour is a viscoelastic material, with a very high effective viscosity, and therefore it remains almost stationary relative to the position of the eyeball. However, after the vitrectomy, linear viscous fluid flows will occur in the vitreous body. One post-operative complication that may arise is re-detachment of the retina, which may occur due to increased wall shear stress in a post-vitrectomy eye, caused by the fluid flows.

Two mechanisms have been postulated for these flows:

  1. The front of the eye is exposed to the cold atmosphere, meaning that the front wall of the posterior chamber will be at a slightly lower temperature than the back wall. The cooler fluid will have a slightly higher density, so it tends to sink, which in turn drives a flow throughout the posterior chamber.
  2. The eyeball will move due to head motion, and also due to rotations of the eyeball within its socket (both voluntary and involuntary). These motions drive a flow in the posterior chamber.

Study Group Report

We investigated the nature of flows driven by each of the two mechanisms by constructing a simple model in each case. Of particular interest is the wall shear stress generated by the flows, which we estimate in both cases. For the buoyancy-driven flow, we consider the limit of very small temperature differences between the front and the back part. For the eyeball-motion-driven flow, we specialise to a model of saccadic motion of the eye, and consider two special limits: the limit of small rotation angle of the eyeball during the saccadic movement; and the limit of very high-frequency oscillations of the eyeball (also with small amplitudes). In the latter case, a Stokes boundary layer forms at the wall, and a steady streaming flow is generated, which persists into the interior of the eye. We also compare these values with an estimate of the wall shear stress in normal eyes, accounting for the viscoelastic properties of the vitreous. Finally, we model the retina as an elastic layer, and investigate its deformation under a prescribed wall shear stress.

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