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Medical Stents: State of the Art and Future Directions
Hemodynamics in Idealized Stented Coronary Arteries: Important Stent
Design Considerations
SUSANN BEIER,
1
JOHN ORMISTON,
2
MARK WEBSTER,
3
JOHN CATER,
4
STUART NORRIS,
4
PAU MEDRANO-GRACIA,
1
ALISTAIR YOUNG,
1
and BRETT COWAN
1
1
Faculty of Medical and Health Sciences, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand;
2
Mercy
Angiography, 98 Mountain Rd, Mt Eden, Auckland 1023, New Zealand;
3
Green Lane Cardiovascular Service, Auckland City
Hospital, Park Rd, Auckland 1030, New Zealand; and
4
Faculty of Engineering, University of Auckland, Private Bag 92019,
Auckland 1142, New Zealand
(Received 26 February 2015; accepted 8 July 2015)
Associate Editor Peter E. McHugh oversaw the review of this article.
Abstract—Stent induced hemodynamic changes in the coro-
nary arteries are associated with higher risk of adverse
clinical outcome. The purpose of this study was to evaluate
the impact of stent design on wall shear stress (WSS), time
average WSS, and WSS gradient (WSSG), in idealized stent
geometries using computational fluid dynamics. Strut spac-
ing, thickness, luminal protrusion, and malapposition were
systematically investigated and a comparison made between
two commercially available stents (Omega and Biomatrix).
Narrower strut spacing led to larger areas of adverse low
WSS and high WSSG but these effects were mitigated when
strut size was reduced, particularly for WSSG. Local
hemodynamics worsened with luminal protrusion of the
stent and with stent malapposition, adverse high WSS and
WSSG were identified around peak flow and throughout the
cardiac cycle respectively. For the Biomatrix stent, the
adverse effect of thicker struts was mitigated by greater strut
spacing, radial cell offset and flow-aligned struts. In conclu-
sion, adverse hemodynamic effects of specific design features
(such as strut size and narrow spacing) can be mitigated when
combined with other hemodynamically beneficial design
features but increased luminal protrusion can worsen the
stent’s hemodynamic profile significantly.
Keywords—Hemodynamics, Coronary artery disease, Com-
putational fluid dynamics (CFD), Stent design, Wall shear
stress (WSS), Stent.
INTRODUCTION
Percutaneous coronary intervention (PCI) with
stents is a widely used treatment for atheromatous
coronary artery disease, a leading cause of death in the
Western world.
42
Yet, PCI failure is a relatively com-
mon occurrence, with 2% of stent patients dying due
to thrombotic occlusion, and 15% requiring additional
intervention for restenosis.
25
Stent-induced hemody-
namic changes are one of the important determinants
of PCI outcome
18
and stent design drives these
hemodynamic changes.
A link between stent design and adverse clinical
outcome was first established in stented rabbit iliac
arteries,
9
and this was followed by changes in WSS being
associated with neointimal hyperplasia.
24
Further
investigations using simplified numerical
14
and experi-
mental methods,
2,7
revealed that narrow strut spacing
lead to undesirable flow stagnation zones and applica-
tion of these concepts to 2D single stent units
8
subse-
quently guided several computational studies. These
found that strut spacing,
14
stent connectors,
36
strut
peak angle,
12
and strut thickness
15
were all important
hemodynamic considerations in stent design.
Strut thickness was the focus of many clinical
studies with thicker struts causing higher thrombo-
genic risk,
20
restenosis and reintervention rates.
18
Subsequent computational studies however were more
equivocal with some reporting thicker struts causing
unfavorable flow regions,
15,23
and others showing
almost the opposite effect of reduced regions of
adverse flow.
1
Inter-strut spacing was found important
Address correspondence to Susann Beier, Faculty of Medical and
Health Sciences, University of Auckland, Private Bag 92019, Auck-
land 1142, New Zealand. Electronic mails: s.beier@auckland.ac.nz,
Johno@mercyangiography.co.nz, MWebster@adhb.govt.nz, j.cater@
auckland.ac.nz, s.norris@auckland.ac.nz, p.medrano@auckland.ac.nz,
a.young@auckland.ac.nz, and b.cowan@auckland.ac.nz
Annals of Biomedical Engineering (2015)
DOI: 10.1007/s10439-015-1387-3
2015 The Author(s). This article is published with open access at Springerlink.com
and should be large to restore disturbed flow.
14
Struts
which are orientated to the flow direction appeared to
reduce the area of flow recirculation. This includes
connectors which were found only hemodynamically
beneficial when aligned longitudinal to the flow.
14
Computational optimization of the number of crowns
revealed that the optimal number was dependent on
the intra-strut angle
12
(with 40being ideal) and
appeared to be independent of vessel diameter. This
was subsequently refined by the same author, demon-
strating that optimal strut angle may be somewhat
dependent on vessel size.
11
Peak-peak or valley-peak
alignment also appeared to influence the ideal angle.
These studies were often simplified using 2D,
16
geo-
metric simplifications,
8,14
a smaller number of stent
cells,
15
and/or steady-state
23
models.
Commercially realistic stent designs have also been
investigated
1,10,11,32,36
focusing primarily on the com-
parison of hemodynamic parameters
11
and ranges
32
rather than linking design features to hemodynamic
observations. These studies have several limitations:
(1) multiple design features were varied at once, lim-
iting the understanding of each design feature’s con-
tribution to the altered flow,
11
(2) the focus was on a
single design feature only,
36
(3) observations changed
throughout the cycle leading to inconclusive results,
1
and (4) similar stent designs were used when design
parameters were considered in greater detail.
10
Stent apposition is clinically desired during stent
deployment but imposes adverse mechanical stimuli on
the vessel wall.
19
The present study hypothesizes that
stent protrusion rates into the lumen also alter the
hemodynamic profile—an aspect of stent performance
which has not previously been considered. Full stent
malapposition, that is under-deployment with stent
struts fully exposed to the blood flow, has shown to
increase thrombogenicity.
43
Only the hemodynamic
impact of idealized single strut malapposition was
studied before.
37
A variety of in-vivo features impact on the compu-
tational prediction of hemodynamic flow including:
vessel curvature,
22
compressive force of the stent,
3
local deformation, and associated tissue prolapse.
27
These considerations are vessel and lesion specific, and
vary with the degree of disease, presence of tissue
calcification and vessel geometry. Along with a limited
ability to quantify the anisotropic vessel wall proper-
ties, this leads to significant assumptions being made in
simulations. The goal of the present study was to
determine the hemodynamic impact of major stent
design parameters to inform stent development. We
therefore focused on idealized stent geometries to elu-
cidate the underlying aspects of design by eliminating
local deformations occurring as a result of stent
deployment, vessel curvature, and tissue prolapse.
The novelty of the present study therefore resides in
the investigation of the hemodynamic impact of
specific stent design features including strut spacing,
stent size and luminal protrusion rates to full malap-
position, with findings being applied to two commer-
cially available stent designs.
METHODS
Idealized Coronary Artery and Simplified Stent
Geometries
An average geometry of the proximal left main
artery was derived from 101 asymptomatic angiogra-
phy cases (average age 54 ±8 years; 57 females),
29
which yielded an average diameter of approximately
4 mm. Two commonly available commercial stents,
‘‘Omega’’ (Boston Scientific, Marlborough, MA,
USA), and ‘‘Biomatrix Flex’’ (Biosensors Interna-
tional, Singapore), both 10 mm in length, were
deployed ex-vivo in a straight silicone vessel of 4 mm
diameter. These were then scanned using micro-com-
puted tomography with Skyscan-1172 (Bruker Bio-
sciences Corporation, Billerica, MA, USA) with an
isotropic voxel resolution of 0.3 lm to obtain detailed
geometric information, from which an idealized stent
geometry was derived. The computer aided design
software Autodesk Inventor Professional 3D
(Autodesk, San Rafael, CA, USA) was used to correct
local stent deformations and smooth the geometry.
This procedure resulted in an ‘‘as manufactured’’ stent
geometry with a deployed diameter matching the test
vessel, rather than a deployed geometry with local
deformations. Variations in strut cross-sectional shape
causes changes in hemodynamic behavior,
16
so all
cross-sections were simplified to have a circular shape
for the purpose of this study. Vessel walls were circular
with constant diameter and smooth luminal surfaces.
The resulting flow domain was derived and imported
into ANSYS Workbench 14.5 (ANSYS Inc., Canons-
burg, PA, USA).
Computational Fluid Dynamics (CFD)
ANSYS Meshing 14.5 was used to create a patch-
conforming, unstructured tetrahedral mesh with vari-
able mesh spacing to represent the small and rapidly
changing features in the stent region. The mesh size
was chosen to accurately model the shearing at the wall
and was optimized (<4% relative error for 100%
greater element density) to comprise approximately 3
million elements for the strut spacing analysis and
approximately 8 million elements for the more com-
plex analyses of strut size, luminal protrusion, and
BEIER et al.
specific stent designs. ANSYS CFX 14.5 was used to
solve the CFD simulation, using a high performance
parallel computing cluster (New Zealand eScience
Infrastructure, 64-bit 2.7 GHz Intel Xeon, 60CPU,
40 GB RAM) and computation times are provided in
Table 1. Although a quarter or half-section domain
analysis would have been sufficient in some cases, we
performed a full three-dimensional analysis for future
direct comparison with experimental studies.
The shear thinning behavior of blood was
accounted for using the non-Newtonian ‘‘Carreau-
Yasuda’’ model as recommended in the literature.
30
Blood density was assumed to be 1050 kg/m.
3
An
inlet boundary condition of flow rate vs. time (rang-
ing from 0–102 mL/min) was adapted from Nichols
et al.
33
, assuming a heart rate of 75 beats/min
(Fig. 1). The bulk Reynolds number (Re) was
approximately 80. Due to the simplification of using
straight vessel geometries, a parabolic, laminar flow
profile was used at the inlet boundary and the en-
trance length extended by 36 mm (0.06Re 9
4 mm vessel diameter) to ensure fully developed flow.
A constant static pressure condition was prescribed at
the outlet.
Transient simulations consisted of four consecutive
cardiac cycles. Results were derived only from the
fourth cycle to minimize transient start-up effects. A
time step of 0.001 s was used to ensure a Courant
number (Cr) below 5, with every 5th time step saved
for subsequent analysis. A laminar numerical fluid
model governed the simulation solution with residual
targets of 10
24
(a stricter residual target of 10
26
resulted in a 0.02% change in RMS flow and increased
computation time from 10 to 26 h computation time)
and a maximum of 5 coefficient loops as convergence
control. No-slip boundary conditions were applied on
all internal surfaces. The geometries were rigid as stent
deployment and calcification of the arterial wall stiffen
the vessel
28
and a recent study showed little difference
between rigid-wall and compliant fluid-structure sim-
ulations.
4
Simulations
The following simulation studies were conducted:
I. Strut spacing: Eight straight vessels with sim-
plified stent geometries (regularly spaced cir-
cumferential rings with spacings of 0.83, 1.25,
1.67, and 2 mm) were created with strut sizes of
81 and 120 lm. The stent length was 10 mm,
with a 4 mm diameter and no connectors were
modeled (Fig. 2a).
II. Strut size: The Omega stent geometry was
modeled with a manufactured strut size of
81 lm and a hypothetical thicker strut size of
120 lm for comparison.
III. Stent protrusion: Luminal protrusion of the
Biomatrix stent was studied (Fig. 2b) with the
stent apposed with 25, 50, and 75% of the
stent cross-section in the flow domain, and
the remainder embedded in the vessel wall
(Fig. 2b). In a second phase, a completely
malapposed Biomatrix stent was simulated
with a gap of 0.29 mm between the stent edge
and vessel surface was simulated.
IV. Stent comparison: The Biomatrix and Omega
stent geometries were modeled with a 50%
luminal protrusion which resulted in the
Omega stent’s connectors being fully embed-
ded in the vessel wall. The Omega geometry
TABLE 1. Computation time for each simulation.
Case study Type Computation time (h)
Strut spacing All <3
Strut size 81 lm27
120 lm16
Protrusion 25% 35
50% 25
75% 14
Malapposed 5
Stent comparison Omega 27
Biomatrix 25
As accurate stent geometry modeling is computationally extensive,
the high performance computing facility ‘NeSI’ was utilized. This is
a shared facility of a number of supercomputing clusters, and thus
overheads and competing demand can vary significantly. For this
reason no overheads are reported. Computation times are reported
for a four node cluster with 40 CPU and 20 GB memory each.
Thus, the total number of core hours can be estimated by multi-
plying the reported times by 160.
FIGURE 1. Left main coronary blood flow over time pre-
scribed as the inlet boundary condition (adapted from Nichols
et al.
33
). Red circles indicate timepoints selected for transient
analysis throughout the manuscript taken from the fourth
simulated cardiac cycle.
Hemodynamics in Idealized Stented Coronary Arteries
has 81 lm struts, 1.4 mm mean cell spacing,
diagonally aligned straight connectors
embedded in the vessel wall, and 8 strut peaks
per cell which were aligned from cell to cell.
The Biomatrix geometry has 120 lm struts,
1.6 mm mean cell spacing, 9 strut peaks per
cell with a radial peak offset from cell to cell,
and three approximately circular connectors
per cell set. Both stents were 10 mm long and
4 mm in diameter (Fig. 2c).
Hemodynamic Metrics
In order to understand the effects of hemodynamic
changes, the three most established hemodynamic
metrics were studied: wall shear stress (WSS), time
averaged WSS (TAWSS), and WSS gradient (WSSG).
Low WSS and TAWSS were studied due to their
strong relevance to atherogenesis, and high WSS and
WSSG due to their recent emergence as key regulators
of vascular pathophysiology.
6
FIGURE 2. (a) Struts with 0.83, 1.25, 1.67, and 2 mm spacing (upper to lower) modeled with 81 and 120 lm strut sizes.
(b) Biomatrix geometry with 25, 50, and 75% luminal protrusion and malapposition of the stent protruding into the vessel lumen.
(c) Biomatrix (left) and Omega (right) geometries with stent design labels.
BEIER et al.
Wall Shear Stress (WSS)
Common atheromatous disease locations charac-
teristically have low WSS. Intimal hyperplasia is pro-
moted by the release of tissue growth factors at
WSS <1.5 Pa.
26
Atherosclerotic intimal thickening
increases with lower WSS and regions with WSS <
0.5 Pa are prone to atherosclerosis, although this is
typically a stiffer and more stable plaque phenotype.
26
Areas of coronary arteries with WSS greater than
1.2 Pa have been found to have less atheromatous
narrowing
40
and more positive remodeling.
39
In con-
trast, an intravascular ultrasound study found an
increase in the necrotic core area for WSS >2.5 Pa,
38
suggesting that the development of a more vulnerable
disease phenotype with plaques more prone to rupture,
and consequent thrombus and occlusion. It is possible
that sites of low WSS are prone to atheromatous lesion
formation, whereas sites of high WSS may be at
increased risk of plaque rupture and thrombosis.
6
Ku
21
established that adverse vascular shear envi-
ronments represent a continuum and demonstrated
unfavorable behavior from <1 Pa (whereas 0.5 Pa
had commonly been accepted as the cut-off). The same
continuum is likely to exist for adverse high WSS
behavior. There may be an intermediate ‘‘ideal’’ WSS
range of approximately 1–2 Pa.
Time Averaged Wall Shear Stress (TAWSS)
TAWSS is WSS averaged over the cardiac cycle.
Low TAWSS is associated with endothelialization
of stent struts, with levels <0.5 Pa associated with
cellular proliferation, intimal thickening, and inflam-
mation.
21,24,41
Wall Shear Stress Gradient (WSSG)
Rapid changes of WSS over short distances are
quantified by the WSSG. Regions of high WSSG
(>200 Pa/m) have been linked to intimal hyperplasia,
formation of atherosclerotic lesions, and increased
vessel wall permeability; and accelerate platelet acti-
vation and thrombus formation.
5
The following thresholds were therefore considered
to be unfavorable for the purposes of this study:
(i) WSS <0.5 Pa, (ii) WSS >2.5 Pa, (iii) TAWSS <
0.5 Pa, and (iv) WSSG >200 Pa/m. The present study
uses CFD to determine WSS, TAWSS, and WSSG
changes caused by variations in stent design parame-
ters such as strut spacing, strut size, stent luminal
protrusion, and specific stent geometry.
RESULTS
Table 2summarizes the area-averaged statistical
quantities of the TAWSS distribution and the per-
centage area of TAWSS <0.5 Pa. Figures 3a, 4e, 5a,
and 6a show the percentage area meeting the adverse
hemodynamic criteria of low WSS (<0.5 Pa), and high
WSSG (>200 Pa/m) at different times points in the
cardiac cycle. Endothelial cells respond to shear
stress
26
and ideally cover the stent surface area within a
few days after PCI.
16
For this reason, the area con-
sidered is vessel and stent surface plus 5 mm of vessel
TABLE 2. TAWSS distribution and area-averaged statistical quantities.
Strut
spacing
(mm)
Stent
type
Strut
size
(lm)
Luminal
protrusion
(%)
TAWSS (Pa)
Mean SD Skewness Kurtosis Area <0.5 Pa (%)
Strut spacing—81 lm strut size 0.83 R 81 50 0.30 0.11 0.46 8.07 95.0
1.25 R 81 50 0.42 0.12 0.29 11.76 96.7
1.67 R 81 50 0.42 0.11 0.16 14.69 97.4
2 R 81 50 0.43 0.10 0.05 16.78 97.8
Strut spacing—120 lm strut size 0.83 R 120 50 0.38 0.16 0.46 5.66 93.3
1.25 R 120 50 0.40 0.13 0.28 8.28 95.6
1.67 R 120 50 0.41 0.13 0.79 12.49 96.6
2 R 120 50 0.42 0.12 0.74 14.24 97.0
Strut size 1.44 O 81 50 0.39 0.17 0.75 7.15 93.5
1.44 O 120 50 0.39 0.17 0.74 6.00 91.4
Luminal protrusion 1.60 B 120 25 0.41 0.15 0.56 6.57 92.0
1.60 B 120 50 0.39 0.16 0.29 5.49 92.0
1.60 B 120 75 0.38 0.18 0.68 11.36 91.6
1.60 B 120 100 0.64 0.51 1.79 5.57 65.5
Stent comparison 1.44 O 81 50 0.39 0.17 0.75 7.15 93.5
1.60 B 120 50 0.39 0.16 0.29 5.49 92.5
R, ring shaped; B, biomatrix; O, Omega.
Hemodynamics in Idealized Stented Coronary Arteries
on each side of the stent to capture any proximal or
distal flow disturbances.
Strut Spacing
Figure 3a shows the percentage area of adverse
stress vs. strut spacing for 81 and 120 lm thick struts.
Narrow strut spacing was the main cause of adverse
WSSG over the whole cycle and its area approximately
doubled when the strut spacing was reduced from 2 to
0.83 mm. Similar effects were found for adverse low
WSS around peak flow (2.68 and 2.72 s). Strut thick-
ness had a smaller impact on both adverse WSSG and
WSS regions. Adverse low WSS coverage was between
94 and 100% during the rest of the cardiac cycle. It is
hence not surprising that TAWSS area below <0.5 Pa
(Table 2) was similar for all spacings, demonstrating
that momentary WSS effects are usually small when
averaged over the cardiac cycle. Larger differences
were found for the detailed TAWSS distributions with
lower TAWSS for narrower spacings, especially for
thicker struts (Fig. 3b).
Strut Size
Thinner struts (Fig. 4a) represent smaller obstacles
to the flow and allow for more rapid flow recovery.
16
Higher near-wall velocities are therefore generated
between cells (with slower central lumen velocities that
are consistent with conservation of flow), with a con-
sequent increase in WSS. Figure 4b shows the differ-
ence in WSS between both strut sizes at peak flow
(2.72 s), demonstrating that the strut size affects the
WSS distribution between strut cells with thinner struts
leading to higher WSS between cells. The effect is even
more apparent for TAWSS (Fig. 4c). Figure 4d shows
that the thicker struts shifted the distribution to lower
TAWSS values. The threshold of TAWSS <0.5 Pa is
close to the statistical mode of the distribution (kur-
tosis 7.1 for 120 lm vs. 5.9 for 81 lm) so the area
results are sensitive to small changes in geometry (and
to the cut-off chosen). The threshold analysis therefore
did not reflect the unfavorable distribution effect
(91.4% for thicker vs. 93.5% for thinner struts,
Table 2).
Stent Protrusion
Greater luminal protrusion generally caused larger
areas of adverse WSSG throughout the cardiac cycle
for all apposed cases (30–60% area for 25, 50, and
75% protrusion respectively) and this increased
significantly when the stent was fully malapposed
(undersized) with nearly 100% area (with area nor-
malized to account for stent and vessel surfaces) for all
time points analyzed (Fig. 5a). Apposed protrusion
(25, 50, and 75%) also generated areas of adverse
WSS <0.5 Pa immediately adjacent to the struts at
peak flow (red areas in Fig. 5b at 2.72 s). There were
no areas of adversely high WSS (>2.5 Pa) for apposed
stents. However, once the struts were fully protruded,
the entire stent surface exhibited shear stresses
>2.5 Pa (shown in green in Fig. 5b) around peak flow
at 2.68, 2.72 and 2.88 s (Fig. 5c). In this case, the ad-
verse low WSS regions (<0.5 Pa) encompassed the
entire vessel after the stent for approximately one
longitudinal cell length (Fig. 5b, right, shown in red).
Conversely, the adverse low WSS at the vessel wall was
reduced to small circular regions (red) located perpen-
dicular to the regions between strut peaks, beginning at
the second cell and growing in area in the flow direction
(Fig. 5b). The malapposed stent had higher TAWSS
(Fig. 5d, right) as expected from the WSS data.
For apposed stents, minor changes were found for
adverse TAWSS areas (Table 2) but the TAWSS dis-
tribution shifted to lower TAWSS values with
increased luminal protrusion. Again the statistical
modes were close to the threshold of <0.5 Pa
(Fig. 5d).
Stent Design Comparison
Flow induced stress differed between the two simpli-
fied clinical stent geometries and showed less favorable
values for the Omega geometry compared to the
Biomatrix (Figs. 6a and 7). Omega showed consistently
greater areas of adverse WSSG >200 Pa/m over the
cardiac cycle with up to a 16% increase in area when flow
accelerated (2.68 s) to peak flow. High WSSG values
were located immediately adjacent to the stent struts
(Fig. 6d). Areas of low WSS <0.5 Pa were slightly
larger for Omega during most of the cycle (but not when
flow velocity rapidly reduced at 2.45 and 2.62 s).
Figure 7shows WSS, TAWSS, and WSSG along
the longitudinal axes of the Biomatrix and Omega
geometry with strut positions indicated by arrows on
the x-axis. Peaks in WSS and TAWSS were slightly
higher for Omega and occurred at the struts, while
WSSG peaks were significantly higher for Omega
(17,000 for Biomatrix vs. 39,000 Pa/m for Omega) and
were located immediately proximal and distal to the
struts. The Omega’s higher WSSG peaks indicate that
the WSS changed more rapidly over short distances.
Struts represent obstacles to blood flow, which stag-
nates upstream of the strut causing reduced WSS
and TAWSS. Recirculation zones are created with
BEIER et al.
changing flow direction proximal and distal to the strut
resulting in high WSSG values. The flow at the
exposed crest of the strut is higher than at the base,
creating peak WSS and TAWSS stress. Between struts,
the flow and shear quantities nearly recovered for both
stents.
FIGURE 3. Strut spacing: (a) Percentage area of adverse stress over the cardiac cycle; WSS <0.5 Pa (top) and WSSG >200 Pa/m
(bottom), for 81 (left) and 120 lm (right) strut sizes for all strut spacings. (b) TAWSS histogram for 0.83 mm (blue), 1.25 mm (cyan),
1.67 mm (yellow), and 2 mm (red) strut spacing with 81 lm (left) and 120 lm (right) strut sizes.
Hemodynamics in Idealized Stented Coronary Arteries
FIGURE 4. Strut size: (a) Omega geometry with 81 lm (left) and 120 lm (right) strut size, (b) WSS, (c) TAWSS contour for 81 lm
(left) and 120 lm (right) strut size, (d) histogram of TAWSS distribution and (e) percentage areas of low WSS (<0.5 Pa, left) and high
WSSG (>200 Pa/m, right) over the cardiac cycle for the 81 lm (blue) and 120 lm (green) Omega geometry.
BEIER et al.
FIGURE 5. Stent protrusion comparison between 25, 50, 75% luminal protrusion and malapposition: (a) Percentage area of
adverse haemodynamic parameters (WSS <0.5 Pa and WSSG >200 Pa/m) over cardiac cycle. (b) Areas of WSS <0.5 Pa (red) and
>2.5 Pa (green) for 25–75% luminal protrusion and malapposition (left to right) at peak flow (2.72 s). (c) High WSS >2.5 Pa for
malapposition over the cardiac cycle. (d) TAWSS distribution for 25, 50, and 75% luminal protrusion (left) and malapposition (right).
Hemodynamics in Idealized Stented Coronary Arteries
FIGURE 6. Biomatrix vs. Omega: (a) Area of adverse low WSS (<0.5 Pa, left) and high WSSG (>200 Pa/m, right) for Biomatrix (red)
and Omega (blue) over the cardiac cycle. (b–d) Comparison between the Biomatrix (left panel) and Omega (center panel)
geometries with histograms (right panel, where the Biomatrix is shown in red, and Omega in blue) of (b) WSS at peak flow (2.72 s);
(c) TAWSS; and (d) WSSG at peak flow (2.72 s).
BEIER et al.
DISCUSSION
Design Parameters
Strut Spacing
Narrower strut spacing has previously been found
to be hemodynamically adverse.
14
Similarly, the pre-
sent study showed narrower strut spacing created areas
of unfavorable low WSS and high WSSG. It was also
demonstrated however, that thicker struts have an
additional secondary effect but this can be mitigated
by widening the strut spacing. Both thicker struts and
narrower spacing led to low near-wall velocities (and
higher velocities in the central flow), with a consequent
reduction in WSS. Previous studies are contradictory
about the importance of strut size,
1,15,17,20,23
and the
present findings may explain some of these differences.
Our results suggest that a critical strut-size to strut-
spacing relationship exists and previous studies show
this may be linked to vessel size.
14,18,25
Here, in the case
of a 4 mm diameter stented vessel, similar stress values
were found for a strut spacing of 1.67 mm with 120 lm
strut, and 1.25 mm with 81 lm strut (Fig. 3a).
Adverse TAWSS area <0.5 Pa was universally
high. However, the TAWSS distributions indicated
that narrow stent spacing shifts the TAWSS distribu-
tion toward lower values (<0.4 Pa), especially for
thicker struts. This may indicate another link between
strut spacing and strut size where, for greater strut
spacing (here ‡1.25 mm), strut size becomes less
important for TAWSS.
Strut Size
Clinical observations on the significance of strut
thickness are equivocal,
17,20
as are computational
studies on hemodynamic significance: A reduction in
adverse WSS areas (87%) was found for 56 vs.
96 lm,
23
while an increase in adverse WSS areas was
reported for 50 vs. 150 lm stents.
1
In our study, low
WSS area for the manufactured Omega 81 lm and a
hypothetical thicker strut of 120 lm were similar (15.4
vs. 16.3% area). These differences may be due to the
use of only Newtonian fluid properties and steady state
solutions,
23
single cell research with deployment
deformation
1
or strut sizes differences. Even though
FIGURE 7. WSS at peak flow (2.72 s, left), TAWSS (middle), and WSSG at peak flow (2.72 s, right) along the longitudinal axis of
the vessel, crossing the strut peaks for the Biomatrix (red) and Omega (blue) geometries for the first struts to 2 mm within the
stented region. Strut positions are indicated by arrows.
Hemodynamics in Idealized Stented Coronary Arteries
the differences for all hemodynamic stress thresholds
were found to be small, a tendency was demonstrated
for thicker struts to reduce TAWSS between stent cells
and shift the TAWSS distribution (Figs. 4c and 4d).
This is not reflected in the TAWSS threshold com-
parison (Table 2), suggesting that the simple threshold
of <0.5 Pa is dependent on the specific conditions of
the study and may not always deliver an accurate
indication if flow is favorable or unfavorable. Similar
observations have been made in the literature.
32
Stent Protrusion
Even when struts are apposed, adverse WSS and
WSSG increased with luminal protrusion. This may
indicate that greater luminal protrusion creates
unfavorable flow, whereas a well-embedded stent
(25% luminal protrusion) has less adverse hemody-
namic effect. This is also demonstrated in the
TAWSS distribution, which shifted to lower, unfa-
vorable values for increased protrusion rates
(Fig. 5d). In conjunction with the previous presented
findings it can be hypothesized that strut thickness
and spacing may have a stronger effect for increased
luminal stent protrusion, which represents an area of
future study.
Stent Design Comparison
The simplified Biomatrix geometry generally
showed a more favorable hemodynamic stress profile
than the Omega design.
Considering the results of the strut size experiment,
the greater strut size of the Biomatrix stent would be
expected to generate larger regions of adverse WSSG
and lower TAWSS values. However, the WSSG
observed was actually higher for the Omega stent and
TAWSS distributions were similar. This suggests that
either other design features outweigh the hemody-
namic impact of strut size, and/or the strut spacing was
large enough to mitigate the effect of the thick struts
(see ‘‘Strut Spacing’’ section). The difference in mean
cell spacing is small (1.4 mm for Omega and 1.6 mm
for Biomatrix). These values can be misleading how-
ever, as the Biomatrix cells are offset which creates
larger gaps (diamond shaped) between cell peaks
rather than a consistent distance for the aligned Omega
cells. Figure 6d demonstrates this by showing WSSG
at peak flow (2.72 s), where the large inter-cell
Biomatrix gaps lead to reduced spatial gradient of
WSS and allow the generation of favorable WSSG <
200 Pa/m between cells. For Omega however, the
inter-cell distance is uniform and not great enough for
recovery to WSSG <200 Pa/m. Similarly, Fig. 6b
shows larger areas of higher WSS between cells for
Biomatrix compared to Omega at peak flow (2.72 s).
Thus, the Biomatrix stent’s larger strut thickness may
be mitigated by the larger strut distance created by the
cell offset.
Other design features also contribute to the hemo-
dynamic profiles, such as the number of peaks and
connectors in the stent. Biomatrix has nine strut peaks
per cell which leads to geometrically narrower peaks
(smaller angles) that are relatively more ‘‘flow-aligned’’
compared to Omega which has eight strut peaks. Pre-
vious research has demonstrated that for aligned cell
designs like Omega’s, fewer peaks can adversely affect
TAWSS due to greater flow misalignment (struts are
more cross-flow directed) and this was found to out-
weigh the competing factor of minimizing stent-vessel
area.
11
For Biomatrix with the offset (peak-to-valley)
design, more cell peaks increase the stent-to-vessel
area, but also result in a better flow alignment of the
struts.
11
Thus, it is hypothesized that the greater
hemodynamic stresses at the Omega struts (Fig. 7)
were also caused by its less flow-aligned design of eight
peaks with wider strut angles (56) compared with the
Biomatrix stent’s nine peaks with narrower strut angles
(32).
12,14
This could explain why TAWSS is similar
rather than less favorable as would be expected from
the effects of its thicker struts.
The hemodynamic profiles did not change
throughout the stented vessel region. This suggests that
higher restenosis risk in the proximal stented vessel
segments
19
might be stent design independent, but this
needs to be investigated further.
Theoretical stent design testing
13
showed a similar
TAWSS difference (16% greater area of TAWSS <
0.4 Pa compared with 11% in this study) for a stent
with peak-peak alignment (as in the Omega design)
relative to the valley-peak alignment (like Biomatrix’s
design). It is important to note however that the stents
studied differed in many other attributes (primarily
open vs. closed, while here both Omega and Biomatrix
are open designs).
The Omega stent’s connectors were considered to be
embedded in the vessel wall, meaning its strut-vessel
ratio was not fully represented and this may have led to
a minor overestimation of its performance.
14,36
It is
also likely that Omega’s strut alignment with reduced
inter-strut spacing outweighed the advantages of
thinner struts and a lower strut-vessel ratio. This could
explain Biomatrix’s preferable distributions for all
stresses analyzed in this study and agrees with similar
research
10
(Fig. 6).
The regions of highest WSS were located at the strut
tips, which align to the flow, with low WSS recorded
adjacent to the struts, which is also consistent with
previous findings.
1
Sites immediately downstream of
strut intersections have also been identified as sites of
abnormal flow.
14
BEIER et al.
Clinical Implications
Strut Spacing
Strut spacing should be considered in conjunction
with strut size when assessing hemodynamic perfor-
mance. Larger spacing has a beneficial effect on flow
and the adverse effect of larger strut size appears to be
reduced in combination with larger strut spacing’s.
This could have important implications for future stent
design as strut sizes introduces important mechanical
considerations such as flexibility, vessel conformabil-
ity, deployment recoil.
34
Strut Size
In a similar manner, reducing strut size appears to
have beneficial hemodynamic effects. Here, the
TAWSS threshold analysis with a cut-off near the
mode of the stress distribution was potentially mis-
leading, and this may have contributed to the vari-
ability previously reported in the literature.
25
Consideration of the stress distribution may provide
better insight when considering physiological and
pathophysiological responses.
21
Stent Protrusion
Thrombogenetic risk associated with stent under-
sizing is well recognized
43
and adverse high WSS
regions, which are associated with atherosclerotic
plaque destabilization,
6
were identified for the fully
malapposed stent. Over-sizing stents may increase
adverse compressive forces on the vessel
19
but it has
been demonstrated for the first time that the degree of
protrusion may have adverse hemodynamic effects.
Further, hemodynamic profiles introduced by stent
design are then secondarily influenced by clinical
deployment. Ideally, stents should be fully embedded
in the vessel wall to avoid adverse hemodynamic effects
on one hand, but this must be well balanced against
high vessel wall tension on the other.
19
Precise
deployment is technically difficult with current clinical
techniques, but imaging tools such as optical coherence
tomography are able to detect stent apposition and
may have an important future role in deployment.
35
Stent Design Comparison
Mechanically desirable design features often have
undesirable hemodynamic effects, requiring a balanced
optimization. For example, increasing the number of
peaks provides more scaffolding but also lowers
TAWSS adversely. Similarly, thicker struts create a
stronger stent, yet adversely affect WSS and WSSG.
From the Omega and Biomatrix comparison, it was
demonstrated how mechanically beneficial design
attributes can be implemented with their undesirable
hemodynamic effects being mitigated using other
hemodynamically desirable design features.
Study Limitations
Our study had several limitations. First, the ideal-
ized geometries were rigid, straight and atherosclerotic
plaque was not included. However, idealized models
have been found to be adequate for the investigation of
straight geometries without plaque
31
and lesion specific
curvature or plaque deposition may prohibit observa-
tions exclusively of stent design. Further, a rigid- wall
assumption has been demonstrated to be a reasonable
simplification.
4
Secondly, neglecting the local vessel
deformation results in overestimation of the hemody-
namic parameters, depending on the stent design.
27
This variation may be amplified in-vivo where lesion
type, stent design and deployment parameters result in
a unique patient specific scenario. The present results
provide an indication of the hemodynamic perfor-
mance of stent design features only. Thirdly, cross-
sectional shape was set to circular for all experiments,
and comparison with other cross-sections is an area for
future study. Beneficial effects of circular cross-sec-
tions have been demonstrated.
16
Finally, it should be
noted that stenting is a complex biological process
depending on the vessel characteristics and disease
stage, stent type, deployment technique, and patho-
physiological tissue responses which are still not fully
understood—a complex interdependent system which
cannot be fully captured by entirely by CFD.
CONCLUSION
This study describes the effect of major stent design
considerations including strut spacing, stent size and
luminal protrusion (with full malapposition) on
hemodynamic stress and extends this analysis to
compare two commercially available stent designs. As
stents must be deployed in a wide range of vessels,
these simplified geometries provide data with generic
applicability in a range of clinical situations. Within
the stated assumptions, we have shown how the
adverse hemodynamic effect of specific design features
(for example strut size) can be mitigated when com-
bined with other hemodynamically favorable design
features. We also demonstrated that stent protrusion
rates worsened the stent’s hemodynamic profile, espe-
cially when fully malapposed. Thus, this study delivers
useful data and guidelines on interacting hemodynamic
effects of stent design and demonstrates the importance
of stent apposition when considering stent introduced
coronary hemodynamics. This may contribute in part
Hemodynamics in Idealized Stented Coronary Arteries
to understanding stent thrombosis and restenosis fol-
lowing PCI with stent implant.
ACKNOWLEDGMENTS
The authors wish to acknowledge NeSI high per-
formance computing facilities (https://www.nesi.org.nz)
for their support of this research. New Zealand’s
national facilities are provided by the New Zealand
eScience Infrastructure and funded jointly by NeSI’s
collaborator institutions through the Ministry of Busi-
ness, Innovation & Employment Research Infrastruc-
ture. Funding was provided by Auckland Heart Group
Charitable Trust.
DISCLOSURE
JO and MW provide consulting advice to the
advisory boards of Abbott Vascular and Boston Sci-
entific.
OPEN ACCESS
This article is distributed under the terms of the
Creative Commons Attribution 4.0 International Li-
cense (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted use, distribution, and re-
production in any medium, provided you give appro-
priate credit to the original author(s) and the source,
provide a link to the Creative Commons license, and
indicate if changes were made.
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Hemodynamics in Idealized Stented Coronary Arteries
