An approximate theory for the transmission and reflection of simple waves at area changes and junctions in pipes

Woollatt, D.

doi:10.1016/0020-7403(65)90006-8

Cited by 3 publications

(1 citation statement)

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“…For example, recent work has considered flow through a collapsible tube with discontinuous material properties showing the coexistence of multiple steady states when the flow is supercritical [18,19]. Furthermore, similar ideas have been considered in the gas dynamics literature with shock waves propagating through a pipe with a section of expanded cross-sectional area [20,21] with application to exhaust systems.…”

Section: Introductionmentioning

confidence: 99%

Shock wave propagation along the central retinal blood vessels

Spelman

Stewart

2020

Proc. R. Soc. A.

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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.

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