Nearly 3% of people in the UK are living with some degree of sight loss, and fluid mechanics plays an important role in many of the underlying conditions.

The eye is a pressurised container, and this leads to several fascinating mechanical phenomena. The intraocular pressure (IOP) is maintained by the flow dynamics of the aqueous humour, and constrained outflow of this fluid leads to glaucoma, a common cause of sight loss affecting about 2% of those aged over 40 years. This fluid is produced in the posterior chamber (the region between the lens and the iris) and from there it flows anteriorly through the pupil (a hole in the iris) into the anterior chamber (at the front of the eye between the iris and the cornea). It then leaves the eye by two main routes: the so-called conventional and unconventional outflows.

I will start by describing my research on the unconventional outflow, which is a seeping flow through the tissues of the eye. The tissues are modelled as porous media, while osmotic pressure differences between the plasma in the blood capillaries in a layer of tissue (choroid) supplying the retina and the interstitial fluid in the tissue surrounding these vessels in the choroid are captured by accounting for albumin concentration, and modelling the albumin transport. There is also a narrow gap (suprachoroidal space, SCS) between the choroid and sclera (the white of the eye), and its thickness is hypothesised to depend on pressure differences; we show that the fluid flow in this gap plays an important role. The tissues involved are thin, and we exploit this to simplify the equations considerably, resulting in four ordinary differential equations to describe the flow dynamics and albumin transport, which can be solved numerically.

Drugs to treat primary open-angle glaucoma act by increasing the unconventional flow, and we use the model to investigate their action. We also extended the model to include the presence of an implanted device to treat glaucoma, connecting the anterior chamber to the SCS, which relieves the IOP by bypassing some of the tissues in the unconventional outflow.

I will more briefly describe three pieces of research on the flow dynamics of the aqueous humour in the anterior and posterior chambers. Drivers of this flow include pressure differences, thermal effects and eye rotations. The analysis is greatly simplified by making use of lubrication theory, and we use the results to investigate both the flow in health and the flow in the presence of treatments for various eye conditions.

If time permits, I will describe work to understand the flow of the vitreous humour. This is a gel that lies in an approximately spherical chamber behind the lens and in front of the retina, constituting about 80% of the volume of the eye. Its flow is driven primarily by eye rotations. We idealise the geometry, fluid rheology and rotations, and these approximations permit a semi-analytical solution for the flow, driven by small-amplitude rotations; the steady streaming component of this flow plays a key role in mass transport. In further work, the simplifying assumptions are relaxed.