Elastic jump propagation across a blood vessel junction.
| Autor: | Spelman TA; Sainsbury Laboratory, University of Cambridge, 47 Bateman Street, Cambridge CB2 1LR, UK., Onah IS; School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8SQ, UK., MacTaggart D; School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8SQ, UK., Stewart PS; School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8SQ, UK. |
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| Jazyk: | angličtina |
| Zdroj: | Royal Society open science [R Soc Open Sci] 2024 Jul 17; Vol. 11 (7), pp. 232000. Date of Electronic Publication: 2024 Jul 17 (Print Publication: 2024). |
| DOI: | 10.1098/rsos.232000 |
| Abstrakt: | The theory of small-amplitude waves propagating across a blood vessel junction has been well established with linear analysis. In this study, we consider the propagation of large-amplitude, nonlinear waves (i.e. shocks and rarefactions) through a junction from a parent vessel into two (identical) daughter vessels using a combination of three approaches: numerical computations using a Godunov method with patching across the junction, analysis of a nonlinear Riemann problem in the neighbourhood of the junction and an analytical theory which extends the linear analysis to the following order in amplitude. A unified picture emerges: an abrupt (prescribed) increase in pressure at the inlet to the parent vessel generates a propagating shock wave along the parent vessel which interacts with the junction. For modest driving, this shock wave divides into propagating shock waves along the two daughter vessels and reflects a rarefaction wave back towards the inlet. However, for larger driving the reflected rarefaction wave becomes transcritical, generating an additional shock wave. Just beyond criticality this new shock wave has zero speed, pinned to the junction, but for further increases in driving this additional shock divides into two new propagating shock waves in the daughter vessels. Competing Interests: We declare we have no competing interests. (© 2024 The Authors.) |
| Databáze: | MEDLINE |
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