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Elastic jump propagation across a blood vessel junction
Tamsin A Spelman1, Ifeanyi S Onah2, David MacTaggart2
1Sainsbury Laboratory, University of Cambridge, 47 Bateman Street, Cambridge CB2 1LR, UK.
Royal Society Open Science
|July 18, 2024
Summary
Nonlinear waves, like shocks, behave uniquely at blood vessel junctions. Increased pressure can split waves or create new ones, altering blood flow dynamics.
Area of Science:
- Fluid dynamics
- Biomedical engineering
- Cardiovascular research
Background:
- Linear analysis of small-amplitude waves in blood vessel junctions is established.
- Nonlinear wave propagation, including shocks and rarefactions, requires further investigation.
Purpose of the Study:
- To investigate the propagation of large-amplitude, nonlinear waves through a parent-to-daughter blood vessel junction.
- To analyze the behavior of shock and rarefaction waves at vessel bifurcations.
Main Methods:
- Numerical computations using a Godunov method with patching.
- Analysis of a nonlinear Riemann problem near the junction.
- Analytical theory extending linear analysis to higher amplitudes.
Main Results:
- An abrupt pressure increase generates a shock wave in the parent vessel.
- For modest driving, the shock divides into daughter vessels, reflecting a rarefaction wave.
- Larger driving causes the rarefaction wave to become transcritical, generating new shock waves.
Conclusions:
- Nonlinear wave dynamics at vessel junctions are complex and depend on driving pressure.
- Transcritical rarefaction waves can lead to the formation of new, speed-varying shock waves.
- Understanding these phenomena is crucial for cardiovascular modeling and treatment.
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