Figure 1.
Idealized sidewall IA model geometry in (a).
Gravity direction g points down to the dome. Time dependence of the inflow rate in (b).
Figure 2.
Raw PIV picture of the seeding particles in the idealized IA model without (a) and with (b) FDS1 implanted.
The yellow line in (a) defines the IA domain, VIA. The red line in (b) shows the contour of the free-seeding-particle domain in the IA dome.
Table 1.
List of implanted regular stents (RSs) and flow diverter stents (FDSs).
Figure 3.
Picture of the assumed parallelogram stent unit cell and table of the stent geometrical dimensions in descending order of porosity, φ = Ahole/Acell. Acell,hole are the unit cell and hole surface, respectively.
The index 1, 2 identifies the strut orientation. x-axis shows parent artery orientation. is the wire number (assuming a woven stent made of two different wire orientations). The number in parentheses represents the 95% confidence interval on the last digit.
Figure 4.
Time averaged velocity map, TAV, in the unstented and stented idealized IA.
The black arrows represent the flow direction.
Figure 5.
Oscillation velocity index map, OVI, in the unstented and stented idealized IA.
The black arrows represent the flow direction.
Figure 6.
Time dependence of the spatially averaged IA velocity, SAV, in (a).
Cumulative distribution of the time averaged IA velocity, TAV, in (b). Cumulative distribution of the oscillation velocity index, OVI, in (c). The dashed lines represent the 95% confidence interval.
Figure 7.
Time-space averaged IA velocity ratio, AVR versus (a) the metal surface density, 1−φ, and (b) the scaling factor of the permeability, min(hi)2φ, proposed in Ref. [34].
The squares, triangles and circles show AVR computed in the full IA domain and in the volumes spanning the highest and lowest 25% of velocities. The black solid and dashed lines represent the linear trends (AVR(φ) = 7.2 φ −6.2 and AVR(φ) = 0.13 φ in (a), respectively). The error bars and dotted line (in (b)) represent 95% confidence intervals.
Figure 8.
Velocity map, v, and planar streamlines measured at time phase t = 0, 0.1, 0.2, 0.4 and 0.6 s (in column (1)-(5)) in the symmetry plane of the idealized sidewall IA without stent (row (a)) and with RS1, RS4 and FDS3 (in row (b), (c) and (d)).
The time phase is represented by a star in the inflow rate time curve inserted at the top of each column. The black arrows represent the flow direction, and the little black dots indicate the beginning of the streamlines.
Figure 9.
Schematic representation of the two main flow regimes and their physical interpretation.
(a) In the shear driven regime, the shear stress at the IA neck, , induced by the strong velocity gradient in the parent artery, drives a clockwise intra-aneurysmal flow. (b) In the pressure driven regime, the pressures
and
at the proximal and distal side of the neck in the parent artery are such as
due to the increase of pressure gradient along the parent artery after stent implantation (
being the IA pressure). Consequently, the pressure differentials between the parent artery and the IA,
and
, push the circulating fluid inward and outward the IA at the proximal and distal side of the neck, respectively, leading to a counterclockwise flow at the IA neck.