Mathematical models of a heterogeneous vitreous humour: an investigation into vitreoschisis and the premacular bursa
File(s)
Author(s)
Bevis, Laura
Type
Thesis
Abstract
Retinal detachment affects around 1 in 10,000 people per year, and, since the retina is vital for vision, this quickly leads to sight loss if left untreated [1]. The retina lines the posterior side of the vitreous chamber at the back of the eye, which is filled with the gel-like vitreous humour. The motion of the vitreous, induced by eye movements, imposes mechanical stresses on the retina, which are thought to be the leading cause of rhegmatogenous retinal detachments.
The vitreous is spatially heterogeneous with liquefied regions in the gel. The mechanical effects of this are not clearly understood and are difficult to determine experimentally. We model two cases, the premacular bursa (thought to be an anatomical feature that protects the retina), and a vitreoschisis (occurs due to vitreous degeneration).
We present several mathematical models of a fluid-filled space in the vitreous and investigate the effect of everyday oscillatory eye movements on the shear stresses felt by the retina. We model the spaces both indirectly, using a mathematical slip condition on the eye wall, and directly using boundary integral techniques. We find that the premacular bursa reduces the shear stress significantly over the macula, while the vitreoschisis significantly increases the retinal shear stress towards its edges. Most importantly, we observe a local jump in the shear stress along the retina, at the ends of the vitreoschisis, suggesting that it experiences a constant pushing and pulling there, which could lead to local retinal damage.
As well as providing information of significant clinical interest, the models presented in this thesis are fundamentally interesting mathematical problems in their own right, since we make use of techniques that are more commonly used for other flow regimes.
The vitreous is spatially heterogeneous with liquefied regions in the gel. The mechanical effects of this are not clearly understood and are difficult to determine experimentally. We model two cases, the premacular bursa (thought to be an anatomical feature that protects the retina), and a vitreoschisis (occurs due to vitreous degeneration).
We present several mathematical models of a fluid-filled space in the vitreous and investigate the effect of everyday oscillatory eye movements on the shear stresses felt by the retina. We model the spaces both indirectly, using a mathematical slip condition on the eye wall, and directly using boundary integral techniques. We find that the premacular bursa reduces the shear stress significantly over the macula, while the vitreoschisis significantly increases the retinal shear stress towards its edges. Most importantly, we observe a local jump in the shear stress along the retina, at the ends of the vitreoschisis, suggesting that it experiences a constant pushing and pulling there, which could lead to local retinal damage.
As well as providing information of significant clinical interest, the models presented in this thesis are fundamentally interesting mathematical problems in their own right, since we make use of techniques that are more commonly used for other flow regimes.
Version
Open Access
Date Issued
2022-01
Date Awarded
2022-06
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Mestel, Andrew Jonathan
Tweedy, Jennifer
Overby, Darryl
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Bioengineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)