Riemann problems in the retinal circulation

Onah, Ifeanyi Sunday (2024) Riemann problems in the retinal circulation. PhD thesis, University of Glasgow.

Abstract

Retinal haemorrhage (abnormal bleeding of the blood vessels in the retina) is often observed following traumatic brain injury. The retinal blood vessels, known as the retinal circulation, are supplied by the central retinal artery (CRA) and the central retinal vein (CRV), which pass along the optic nerve after passing through a region of ceresbrospinal fluid (CSF) in the nerve sheath. In this thesis we develop a theoretical model for blood flow in the retinal blood vessels which forms the foundation of a predictive model of retinal haemorrhage.
We first consider a case where sudden change in CSF pressure (i.e. following brain injury) drives a large amplitude pressure perturbation (shock waves), treating the blood vessel as a single compliant tube with uniform material properties. We develop a Riemann problem to consider the response to an instantaneous discontinuity in flow and/or tube cross-sectional area across an interface, and examine the flow propagation. We identify the four classical flow structures that emerge from the discontinuity.
We extend our Riemann problem to consider an abrupt change in material properties coincident with the initial discontinuity, as a model for the central retinal vessels crossing between regions (e.g. between the optic nerve and the retina). Our Riemann problem exhibits the four classical solutions each with an additional stationary wave across the point of discontinuity. However, these classical solutions are not sufficient to cover the entire parameter space, and we demonstrate the existence of transcritical states resulting from a rarefaction wave resonating with the stationary wave, producing additional shock waves. These new resonant solutions were enough to close the gaps in our parameter space left by the classical solutions.
Finally we investigate the propagation of these large-amplitude pressure waves through a symmetric junction (mimicking blood flow through the retinal vessel networks). Our Riemann problem exhibits analogs of the four classical wave structures (again with a discontinuity across the stationary wave at the junction) as well as analogs of the transcritical (resonant) states identified in flow through a single vessel with a discontinuity in material properties. Furthermore, we find that the onset of resonance is delayed when the daughter vessels are chosen to be less stiff than the parent vessel and can be eliminated entirely if the reduction in stiffness is sufficiently large.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by funding from the Petroleum Technology Development Fund (PTDF), Nigeria.
• Subjects: Q Science > QA Mathematics; R Medicine > RE Ophthalmology
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Stewart, Professor Peter
• Date of Award: 2024
• Depositing User: Theses Team
• Unique ID: glathesis:2024-84507
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 27 Aug 2024 15:55
• Last Modified: 28 Aug 2024 08:17
• Thesis DOI: 10.5525/gla.thesis.84507
• URI: https://theses.gla.ac.uk/id/eprint/84507

Related URLs

• Article DOI
• Data DOI