Shock wave propagation along the central retinal blood vessels

Spelman, T.A. and Stewart, P.S. (2020) Shock wave propagation along the central retinal blood vessels. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 476, 20190269. (doi: 10.1098/rspa.2019.0269)

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Abstract

Retinal haemorrhage is often observed following brain injury. The retinal circulation is supplied (drained) by the central retinal artery (vein) which enters (leaves) the eye through the optic nerve at the optic disc; these vessels penetrate the nerve immediately after passing through a region of cerebrospinal fluid (CSF). We consider a theoretical model for the blood flow in the central retinal vessels, treating each as multi-region collapsible tubes, where we examine how a sudden change in CSF pressure (mimicking an injury) drives a large amplitude pressure perturbation towards the eye. In some cases, this wave can steepen to form a shock. We show that the region immediately proximal to the eye (within the optic nerve where the vessels are strongly confined by the nerve fibres) can significantly reduce the amplitude of the pressure wave transmitted into the eye. When the length of this region is consistent with clinical measurements, the CSF pressure perturbation generates a wave of significantly lower amplitude than the input, protecting the eye from damage. We construct an analytical framework to explain this observation, showing that repeated rapid propagation and reflection of waves along the confined section of the vessel distributes the perturbation over a longer lengthscale.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Stewart, Dr Peter and Spelman, Dr Tamsin Anne
Authors: Spelman, T.A., and Stewart, P.S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
Publisher:The Royal Society
ISSN:1364-5021
ISSN (Online):1471-2946
Published Online:12 February 2020
Data DOI:10.5525/gla.researchdata.795

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300264Elastic jumps on networks: Quantifying patterns of retinal haemorrhagePeter StewartEngineering and Physical Sciences Research Council (EPSRC)EP/P024270/1M&S - Mathematics
172141EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - Mathematics