Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation

Stewart, P. S. and Foss, A. J.E. (2019) Self-excited oscillations in a collapsible channel with applications to retinal venous pulsation. ANZIAM Journal, 61(3), pp. 320-348. (doi: 10.1017/S1446181119000117)

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Abstract

We consider a theoretical model for the flow of Newtonian fluid through a long flexible-walled channel which is formed from four compliant and rigid compartments arranged alternately in series. We drive the flow using a fixed upstream flux and derive a spatially one-dimensional model using a flow profile assumption. The compliant compartments of the channel are assumed subject to a large external pressure, so the system admits a highly collapsed steady state. Using both a global (linear) stability eigensolver and fully nonlinear simulations, we show that these highly collapsed steady states admit a primary global oscillatory instability similar to observations in a single channel. We also show that in some regions of the parameter space the system admits a secondary mode of instability which can interact with the primary mode and lead to significant changes in the structure of the neutral stability curves. Finally, we apply the predictions of this model to the flow of blood through the central retinal vein and examine the conditions required for the onset of self-excited oscillation. We show that the neutral stability curve of the primary mode of instability discussed above agrees well with canine experimental measurements of the onset of retinal venous pulsation, although there is a large discrepancy in the oscillation frequency.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Stewart, Dr Peter
Authors: Stewart, P. S., and Foss, A. J.E.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:ANZIAM Journal
Publisher:Cambridge University Press
ISSN:1446-1811
ISSN (Online):1446-8735
Published Online:15 August 2019
Copyright Holders:Copyright © 2019 Australian Mathematical Society
First Published:First published in ANZIAM Journal 61(3):320-348
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
Data DOI:10.5525/gla.researchdata.845

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
694461EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - MATHEMATICS
3002640Elastic jumps on networks: Quantifying patterns of retinal haemorrhagePeter StewartEngineering and Physical Sciences Research Council (EPSRC)EP/P024270/1M&S - Mathematics