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The effect of Dean, Reynolds and Womersley numbers on the flow in a spherical cavity on a curved round pipe. Part 2. The haemodynamics of intracranial aneurysms treated with flow-diverting stents

Published online by Cambridge University Press:  31 March 2021

Michael C. Barbour Open the ORCID record for Michael C. Barbour [Opens in a new window] ,
Fanette Chassagne Open the ORCID record for Fanette Chassagne [Opens in a new window] ,
Venkat K. Chivukula Open the ORCID record for Venkat K. Chivukula [Opens in a new window] ,
Nathanael Machicoane Open the ORCID record for Nathanael Machicoane [Opens in a new window] ,
Louis J. Kim Open the ORCID record for Louis J. Kim [Opens in a new window] ,
Michael R. Levitt Open the ORCID record for Michael R. Levitt [Opens in a new window]  and
Alberto Aliseda Open the ORCID record for Alberto Aliseda [Opens in a new window]
Michael C. Barbour*
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98107, USA
Fanette Chassagne
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98107, USA
Venkat K. Chivukula
Affiliation:
Biomedical and Chemical Engineering and Sciences, Florida Institute of Technology, Melbourne, FL32901, USA
Nathanael Machicoane
Affiliation:
University Grenoble Alpes, CNRS, Grenoble-INP, LEGI, F-38000, Grenoble, France
Louis J. Kim
Affiliation:
Department of Neurological Surgery, University of Washington, Seattle, WA98107, USA Department of Radiology, University of Washington, Seattle, WA98107, USA
Michael R. Levitt
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98107, USA Department of Neurological Surgery, University of Washington, Seattle, WA98107, USA Department of Radiology, University of Washington, Seattle, WA98107, USA
Alberto Aliseda
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA98107, USA Department of Neurological Surgery, University of Washington, Seattle, WA98107, USA
*
†Email address for correspondence: [email protected]
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Abstract

The flow in a spherical cavity on a curved round pipe is a canonical flow that describes well the flow inside a sidewall aneurysm on an intracranial artery. Intracranial aneurysms are often treated with a flow-diverting stent (FDS), a low-porosity metal mesh that covers the entrance to the cavity, to reduce blood flow into the aneurysm sac and exclude it from mechanical stresses imposed by the blood flow. Successful treatment is highly dependent on the degree of reduction of flow inside the cavity, and the resulting altered fluid mechanics inside the aneurysm following treatment. Using stereoscopic particle image velocimetry, we characterize the fluid mechanics in a canonical configuration representative of an intracranial aneurysm treated with a FDS: a spherical cavity on the side of a curved round pipe covered with a metal mesh formed by an actual medical FDS. This porous mesh coverage is the focus of Part 2 of the paper, characterizing the effects of parent vessel $Re$, $De$ and pulsatility, $Wo$, on the fluid dynamics, compared with the canonical configuration with no impediments to flow into the cavity that is described in Part 1 (Chassagne et al., J. Fluid Mech., vol. 915, 2021, A123). Coverage with a FDS markedly reduces the flow $Re$ in the aneurysmal cavity, creating a viscous-dominated flow environment despite the parent vessel $Re>100$. Under steady flow conditions, the topology that forms inside the cavity is shown to be a function of the parent vessel $De$. At low values of $De$, flow enters the cavity at the leading edge and remains attached to the wall before exiting at the trailing edge, a novel behaviour that was not found under any conditions of the high-$Re$, unimpeded cavity flow described in Part 1. Under these conditions, flow in the cavity co-rotates with the direction of the free-stream flow, similar to Stokes flow in a cavity. As $De$ increases, the flow along the leading edge begins to separate, and the recirculation zone grows with increasing $De$, until, above $De \approx 180$, the flow inside the cavity is fully recirculating, counter-rotating with respect to the free-stream flow. Under pulsatile flow conditions, the vortex inside the cavity progresses through the same cycle – switching from attached and co-rotating with the free-stream flow at the beginning of the cycle (low velocity and positive acceleration) to separated and counter-rotating as $De$ reaches a critical value. The location of separation within the harmonic cycle is shown to be a function of both $De$ and $Wo$. The values of aneurysmal cavity $Re$ based on both the average velocity and the circulation inside the cavity are shown to increase with increasing values of $De$, while $Wo$ is shown to have little influence on the time-averaged metrics. As $De$ increases, the strength of the secondary flow in the parent vessel grows, due to the inertial instability in the curved pipe, and the flow rate entering the cavity increases. Thus, the effectiveness of FDS treatment to exclude the aneurysmal cavity from the haemodynamic stresses is compromised for aneurysms located on high-curvature arteries, i.e. vessels with high $De$, and this can be a fluid mechanics criterion to guide treatment selection.

JFM classification

Biological Fluid Dynamics: Biomedical flows Biological Fluid Dynamics: Blood flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A124
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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