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.

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 ≈ 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.