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Abstract
Background and purpose Validation of computational fluid dynamics (CFD) in stented intracranial aneurysms (IAs) is still lacking, to reliably predict prone to occlusion hemodynamics, probing, in particular, velocity reduction, and flow pattern changes. This study compares CFD outcome with particle imaging velocimetry (PIV) for three commercial off the shelf (COTS) stents of different material densities.
Material and methods The recently developed uniform and high precision multi-time lag PIV method was applied to a sidewall aneurysm before and after implantation of three COTS stents with high, intermediate, and low material densities. The measured laser sheet flow patterns and velocity reductions were compared with CFD results and correlated with stent material density.
Results Velocity reduction was in good agreement for unstented high and low porosity stented IA, while flow pattern change was fully matched for unstented and high porosity stented IA. Poor CFD–PIV matching in IA was found for intermediate porosity stents.
Conclusions CFD reproduced fully PIV measurements in unstented and high porosity stented IAs. With low porosity stents, CFD reproduced velocity reduction and high velocities close to the neck, while a marked mismatch on sluggish flow was found at the dome. CFD was unable to match PIV with intermediate porosity stents for which hemodynamic transition occurred.
- Aneurysm
- Blood Flow
- Flow Diverter
- Technology
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Introduction
The sought effect of flow diverter stents (FDSs) on intracranial aneurysm (IA) flow is to promote progressive thrombosis leading to irreversible IA healing. Although FDSs have demonstrated outstanding treatment performance, severe complications, such as postoperative rupture, have been reported1 and could be related to patient specific hemodynamic issues. Despite the new digital subtracted angiography peroperative measurements of post-stent hemodynamic indicators correlated with treatment issues,2 ,3 computational fluid dynamics (CFD) remains the main tool that can reproduce impeded IA flow along with a complete set of measurable (ie, velocity fields) and non-measurable (ie, wall shear stress) factors. In this context, CFD results strongly depend on flow, geometry, and stent modeling.
In the past decade, several CFD studies investigated the impact of regular stents (RSs) and FDSs in various configurations and IA geometries.4–7 Most of these studies discussed qualitatively the induced flow change, along with correlations between flow reduction factors and clinical outcomes,8–10 thereby demonstrating the potential of CFD for treatment planning and optimization purposes. Nevertheless, important issues related to (a) computational scheme and resolution11 ,12 and (b) stent modeling13 and deployment14 are still under intense scrutiny. In this context, experimental validation with either particle image velocimetry (PIV)15 or laser Doppler anemometry16 was solicited, particularly to isolate the effect of stent models. While both experimental methods have shown good comparison with CFD in unstented IAs,17–24 few studies have reported quantitative comparison in stented IAs25 ,26 within sidewall and bifurcation IA models.
To assess CFD performance in the presence of realistic stents, we performed high accuracy and uniform precision multi-time lag (MTL) PIV measurements27 ,28 in a sidewall IA model. For the three studied RS and FDS commercial off the shelf (COTS) stents, porosity and design parameters were assessed and correlated with CFD outcome.
Materiel and methods
IA model
The sidewall IA geometry model (figure 1) considered for CFD and for molding of the silicone phantom was previously described by Bouillot et al.27 It is composed of a straight cylindrical tube of radius r=2 mm and a sphere of radius R=5 mm shifted downwards the artery centerline by a distance d3=6 mm. The inlet/outlet lengths are d1=150 mm and d2=110 mm, respectively.
Pictures of the regular stents RS1 (column (1)), RS4 (column (2)), and flow diverter stent FDS3 (column (3)), implanted within the intracranial aneurysm model. Row (a): Experimental configuration for particle imaging velocimetry measurements. The red lines represent the limit of the silicone model. Row (b) and row (c): Virtual configuration for the computational fluid dynamic simulations (side and top view, respectively).
Stent modeling
The three COTS stents (two RSs and one FDS) along with their design properties are summarized in figure 2, assuming a diamond stent unit cell. The computational regular meshes of the virtual stents had cylindrical wires with diameter equal to e. As suggested by Appanaboyina et al4 and Bernardini et al,29 the virtual stents were reduced to a small patch across the IA neck (figure 1). For each stent, two deployments shifted by half a unit cell were considered. In addition, tests of sensitivity were performed for three different RS4 material densities, 1−φ=0.09, 0.15, 0.18. The latter were obtained by varying the unit cell size (l) appropriately.
Details of the implanted regular (RS) and flow diverter (FDS) stents together with their geometrical dimensions, assuming a diamond stent unit cell. The two numbers following the model name are the nominal stent diameter and length (in mm). φ=Ahole/Acell is the porosity with the unit cell and hole surface, Acell,hole, respectively. Each stent is named as in Bouillot et al.28 The x axis shows the parent artery orientation.
PIV measurements
The PIV experimental setup and MTL acquisition method were previously described by Bouillot et al.27 Considering optical accessibility, the IA model was oriented downwards. Measurements were performed at the symmetry plane of IA in order to minimize the out of plane velocity components. The inlet flow provided by the pump (MCP-Z Process; Ismatec) is shown in the inset of figure 3. This inflow, measured with an electromagnetic flowmeter (MDL 1401; Skalar), had the typical waveform of an internal carotid artery blood volumetric flow,30 corresponding to a cardiac frequency of 1 beat/s.
Velocity map, v, along with the planar streamlines within the symmetry plane of the idealized model with no stent, and with regular stents RS1, RS4, and flow diverter stent FDS3 (rows (a–d), respectively) at peak systole (time phase t=0.2 s, columns 1–2) and late diastole (time phase t=0.9 s, columns 3–4); columns 1 and 3, and columns 2 and 4 are the representations of particle imaging velocimetry (PIV) and computational fluid dynamic (CFD) results, respectively. The arrows represent flow direction. The small black dots show the beginning of the streamlines.
CFD simulations
Commercial software (ICEM CFD V.12.1; ANSYS Inc, Canonsburg, Pennsylvania, USA) was used to produce high resolution computational unstructured mesh composed of tetrahedrons in the bulk flow and 8 nodes prism elements delineating three boundary layers near the wall outside the parent artery segment encompassing the stents. The number of mesh elements was 5 million, with mesh density larger than 2000 elements/mm3 for the free stent model and 6–9 million elements for the aneurysm model merged with the virtual stents. The OCTREE mesh of merged aneurysm and stent models was completed in a second iteration with Delaunay tetrahedron tessellation matching stent strut size. ANSYS CFX solver was used to simulate circulating fluid. The experimental boundary conditions were imposed for inlet pulsatile flow, along with rigid wall boundary conditions. The circulating fluid (mixture of glycerin (59.1%) and water (40.9%), heated at 37°C for ensuring the correct deployment of thermal shape memory implants) was modeled as a Newtonian fluid with the following parameters: (a) density: ρf=1142 kg/m3; (b) kinematic viscosity: νf=4.67×10−6 m2/s; (c) cycle: 1 s (time steps=100); and (d) number of cycles: 2 (the analysis was performed on the second cycle).
PIV-CFD comparison
Unless otherwise stated, the PIV measurements were compared in the symmetry plane of the IA model with the in-plane components of CFD velocities averaged over the 1 mm laser thickness. The following illustrations and quantitative parameters were used to describe the results.
Qualitative comparison
The qualitative PIV–CFD comparison was provided by the colormap representation of velocity magnitude along with the planar streamlines. The hemodynamics at peak systole and late diastole were considered, respectively.
Quantitative criteria
Differences between CFD and PIV were quantified with various indicators, as summarized in table 1 and described below.
Normalized velocity, magnitude, and angular differences, and averaged velocity difference, between particle imaging velocimetry measurements and computational fluid dynamic simulations for unstented and stented intracranial aneurysms with flow diverter and regular stents
The time–space average of velocity difference in IA,
quantifies the global velocity mismatch between PIV and CFD but is not sensitive to local changes.
The time–space normalized velocity difference (NVD),
quantifies the local PIV–CFD vectorial differences. It was used in the study of Valen-Sendstad and Steinman11 and can be decomposed into both the magnitude term
and the angular term
Normalized magnitude difference (NMD) is sensitive to the local CFD–PIV velocity magnitude difference while normalized angular difference (NAD) quantifies the flow pattern mismatch locally.
In the above formula, θCFD−PIV is the angle between local velocity vectors 
and 
, in CFD and PIV respectively, while 
is the velocity magnitude. 
and 
are the sum and the L2 norm associated to the IA domain during the cardiac cycle, respectively.
Averaged IA velocities and flow reduction
As velocity reduction is a key factor in thrombus formation,8 ,10 both the computed and simulated averaged velocity ratio (AVR) (i.e. the ratio of the IA velocities (with/without stenting)) was also investigated. Moreover, the correlations between stent porosity, φ, and both AVR and spatially averaged IA velocity (SAV) were evaluated.
Results
Qualitative comparison
Figure 3 shows that the color patterns of the PIV and CFD velocity maps were in good agreement for both unstented and high porosity stented IAs (figure 3a, b for unstented IA and RS1, respectively). At systole or diastole, the main clockwise ‘vortices’ with strong distal jets were similar, and so was the post-stent reduction in velocity fields (same colors at same positions). For intermediate and low porosity stents, the mismatch was such that the color velocity maps were not fully reproduced in CFD, and so was vortex transport. For low porosity stents, this mismatch was essentially represented, at systole, by the small vortex at the proximal neck in the CFD figures (figure 3d.2), and by the large low velocity eddy at the distal neck (figure 3d.3) at late diastole. Nevertheless, the anticlockwise direction of the main ‘vortex’ with higher velocities at the neck was matching in both CFD and PIV. For intermediate porosity stents, the mismatch was fully, represented by the differences between PIV and CFD in both of the velocity color maps (figure 3c for RS4) and the vortices along with their respective centers. Unlike in CFD, the center of the PIV vortex was mostly shifted towards the proximal neck.
Quantitative criteria
Table 1 summarizes the different CFD–PIV velocity magnitudes (averaged velocity difference (AVD)) and pattern metrics (NVD, NMD, NAD) for the different COTS stents. The levels of those metrics on unstented IAs (column 1) are shown. The velocity magnitude gap between CFD and PIV was quantified by the asymmetry AVD=0.05, corresponding to a relative vectorial error (with regard to CFD velocity) of NVD=0.30. Ninety per cent of NVD2 was due to magnitude difference (NMD=0.28), and 10% was due to angular (pattern) difference (NAD=0.09). The impact of RS1 on CFD outcome was such that the global velocity asymmetry increased to AVD=0.11–0.14 along with local NVD=0.44–0.47. Both the magnitude difference (NMD=0.41–0.42) and angular difference (NAD=0.14–0.20) contributions to CFD flow pattern deviation from PIV were similar to the no stent case (∼86% and ∼14%, respectively). For FDS3, even though the global CFD–PIV velocity asymmetry was null (AVD <0.01), NVD was as high as for RS1 (NVD=0.43), with comparatively less local velocity magnitude deviation (NMD=0.33, 60%) and more local angular deviation (NAD=0.27, 40%). In this case, NAD was high, conformly to low velocity eddy mismatch. For RS4, the global CFD–PIV velocity magnitude difference was very high (AVD=0.35–0.37) along with the local NVD (NVD=0.68–0.71). In this case, the local angular difference accounted for 29% of NVD2 deviation (NAD=0.37–0.38) while local magnitude difference accounted only for 71% (NMD=0.58–0.60).
Averaged IA velocities and flow reduction
The SAVs of PIV and CFD (figure 4A) for unstented IAs, and both high and low porosity stents RS1 and FDS3, had waveforms similar to PIV curves, within constant shift, as assessed by AVD (0.05, 0.11–0.14, and <0.01, respectively). Particularly for FDS3, the good CFD–PIV agreement shows that the SAV parameter was not sensitive to local flow pattern differences. Concerning the intermediate porosity stent RS4, SAV curves were not matching for both PIV waveform and scale.
(A) Time dependence of the spatially averaged intracranial aneurysm velocity (SAV). The continuous lines are the particle imaging velocimetry (PIV) measurements, and the shaded areas represent the range of the computational fluid dynamic (CFD) predictions (considering the two stent configurations and a possible mispositioning of the laser sheet of maximum 0.5 mm around the symmetry plane). (B) Time–space averaged intracranial aneurysm velocity ratio (AVR) versus the metal surface density of the stent (1−φ). The squares (triangles) are assessed with the PIV (CFD) results considering only velocities within the symmetry plane. The error bars represent 95% CIs. The broken lines represent the two main trends suggested by the PIV measurements related to the two shear and differential pressure driven hemodynamic regimens.28 The dashed line shows AVR(φ) computed from CFD simulations with stent porosities surrounding the flow regimen transition (i.e. around RS4). FDS, flow diverter stent; RS, regular stent.
The scatterplot of velocity ratios AVR versus material density (1−φ) showed similar CFD–PIV trends (Figure 4B) for high and low porosity stents (RS1 and FDS3). AVR ranged between 50% and 60% for RS1, and decreased to less than 10% for FDS3. For RS4, characterized by poor qualitative and quantitive CFD–PIV agreement, AVR was two times smaller for PIV than for CFD (16% and 31%, respectively). The PIV extrapolated transition between the fast and slow decreasing AVR trends occurred at material density 1−φ=0.12–0.15. The CFD decreasing trend of AVR, which corresponded to the additional RS4 stent porosities (1−φ=0.09, 0.15, 0.18, figure 4B), was significantly softer than for PIV.
Discussion
Summary and physical interpretation
In the present study, we aimed to evaluate the accuracy of CFD in assessing IA flow across three COTS stents with high, intermediate, and low porosities. To this end, we compared global and local CFD and PIV velocity field differences in a sidewall IA model extended by a straight tube. The choice of such a simple IA geometry allows operating at nominal stent porosities, experimentally (for PIV) and virtually (for CFD). The recently developed MTL method, which uniformly reduces the experimental velocimetry precision below the 1% level,27 was very sensitive to CFD and PIV flow pattern differences, particularly for low velocity fields. The downward orientation of IA was essential for optical accessibility.
The four porosity cases (no stent, RS1, RS4, and FDS3) allowed us to explore IA flow reduction patterns initiated by the different flow conditions at the neck, which ranged between full shear driven (no-stent, porosity φ=100%) and full differential pressure (FDS3, porosity φ=70%). In the former, the differential pressure at the neck was negligible, and in the latter, shear was negligibly transported at the neck as if flow was restored in the tube without an IA bulge, hence reducing the exchanged flow to an almost stagnant volume at the IA dome.28 The interplay between these two forces (pressure differential and shear stress) at the sidewall IA neck governs the hemodynamic transition through the stents with intermediate porosities. Globally, CFD simulations were consistent with the PIV measurement despite an overestimation of the measured velocities by up to 5% (AVD asymmetry) for unstented IAs, 14% for high (RS1), and <1% for low porosity (FDS3) stents. An abnormally high AVD (37%) was also observed for RS4.
Even though the velocity color maps were consistent with global AVD values, the flow pattern differences were larger locally for intermediate and low porosity, and sensitive to details of low motion eddies at the IA dome. In this almost stagnant volume, the velocities are low enough (of the order of 1 mm/s) that small convective differences induced by unknown temperature change during PIV acquisitions can lead to important hemodynamic deviations of both density and viscosity that would not be taken into account in the CFD model. For instance, it has been shown by Torrance et al,31 Iwatsu and Hyun,32 and Iwatsu et al33 that a temperature gradient in the driven cavity could promote bottom flow stagnation. In particular, Torrance et al31 reported a shift of the low motion eddy due to a buoyancy effect. For the no stent and RS1 cases, the normalized local velocity field differences between CFD and PIV ranged between NVD=0.30–0.47, where the local magnitude differences accounted for 82–90% of the whole differences, and only 10–18% accounted for the orientation differences. For FDS3, NVD was similar to RS1, but the local orientation velocity difference between CFD and PIV was higher (up to 40%). On the other hand, the asymmetry was much larger for RS4 (AVD=35–37%) and consistent with the velocity colormap differences represented in figure 3C. The local NVD index was also larger (0.68–0.71), 71% of the whole difference being due to local velocity magnitude difference and 29% from complementary direction differences.
For RS4, the intermediate interplay between shear and pressure driven flow exchange conditions at the neck could be more sensitive to experimental parameters such as temperature in IA flow. Although these differences are related to experimental issues, similar phenomena in real IAs may occur due to red cell aggregation or non-Newtonian blood rheology, playing important roles, especially in low and transitional hemodynamic regimens.34 Additional investigations are therefore required to evaluate the relevance of these various physical ingredients in CFD. It is remarkable that despite sensible deviations in flow patterns for RS1 and FDS3 with respect of PIV measurements, the velocity ratio AVR was accurately assessed by CFD, which was not the case for the intermediate RS4 stent. Figure 4B shows compatible AVR change trends for high and low porosities, but not for the intermediate stent.
Clinical issues
Despite the simplification of the experimental conditions (geometry and blood modeling), it appears that CFD cannot straightforwardly reproduce the hemodynamic behavior of stented IAs, let alone complex patient specific geometry models where even physiological flow is not always measured. However, the following issues should be taken into account when using CFD:
for pure shear (no stent) or pressure driven (FDS3) flow transport at the sidewall IA neck, CFD can be considered as reliable in predicting the stent/no stent velocity ratio. This indication can be important in finding the velocity or derived wall shear stress reduction thresholds that would help in modeling thrombosis engineering in stented IAs.8 It would also help in optimizing treatments by anticipating the number of implanted devices and the association with coils, ensuring fast IA healing at the least risk of complications. Therefore, extra layer implantation could be avoided whenever per-procedural complications and overcosts are reliably evaluated. On the other hand, blood flow simulation with intermediate hemodynamics (e.g. RS4) requires additional effort to reduce the mismatch with experimental and in vivo velocimetry. In more realistic geometry, a similar transitional regime could occur depending on the combination of the effective stent porosity at the neck and the orientation of the IA with respect to the parent vessel curvature.
FDSs are efficient tools to efficiently treat internal carotid artery sidewall aneurysms characterized by low reported complications rates. However, their use is still lacking standard guidelines and per-operative flow reduction interpretations. For instance, eclipse sign, representing partial contrast agent stagnation in IAs, was intuitively and wrongly associated with a marker of device efficacy. Nevertheless, the experiments with FDS3 showed that the partial stagnant eddy at the aneurysm dome was very sensitive to local variations in circulating fluid properties and contrast agent injection operation. Consequently, the grading scale of contrast agent stagnation proposed to classify IA flow reduction35 should be considered carefully.
Experimental limitations
The experimental limitations in this study are as follows:
the geometry mismatch between actual IA geometry and silicone models was estimated with µCT to 102 µm.27 The influence of this mismatch accounted for up to 50% of CFD–PIV local velocity differences evaluated by NVD. This mismatch had no influence on global AVD metrics.
both the stent design uniformity and exact positioning were subject to unavoidable uncertainties. Stent design irregularities such as wire cross section and unit cell were not taken into account in the computational mesh. Indeed, the genuine wire cross section is generally different from the assumed circle (e.g. in laser cut stents as in RS1), and the exact radial wire location in braided stents was not easily modeled in RS4 and FDS3. Sensitivity tests of each stent with two positions shifted by half a unit cell were therefore performed, showing a decrease in the sensitivity of IA hemodynamics with a decrease in porosity. The homogeneity of the covered surface at the IA neck increased while increasing strut density, hence justifying the use of a porous media approach (e.g. FDS).9 ,13
Conclusion
CFD reproduced PIV velocity reduction in a sidewall IA model for high (RS1) and low (FDS3) porosity stents, but not for an intermediate porosity stent (RS4). On the other hand, CFD velocity fields, characterized by local velocity normalized metric NVD, either moderately (RS1, FDS3) or largely (RS4) deviated from PIV outcomes, respectively, although they were not always visible on colormap velocity maps (unstented and RS1).
Special care must be taken when stagnant volume or a transitional hemodynamic regimen is investigated. In these special cases, slight modifications of the circulating fluid properties, such as density or viscosity due to small inhomogeneities or temperature variations, can lead to strong hemodynamic deviations. These physical phenomena have been broadly neglected in most of the recent published studies.
References
Footnotes
Contributors Design and planning: PB, VMP, OB, RO, and MF. Particle image velocimetry set-up and experiments: PB, VMP, OB, and MF. Segmentation and post processing: PB, RO, OB, and HY. Computational fluid dynamics: RO, OB, and PB. Writing and revision: all authors.
Funding This research received a grant from the Swiss National Science Foundation (SNF 32003B_141192).
Competing interests None.
Provenance and peer review Not commissioned; externally peer reviewed.