Biorheology 44 (2007) 91–102
IOS Press
91
Developed pulsatile flow in a deployed
coronary stent
Rupak K. Banerjee a,b,∗ , Surendra B. Devarakonda a , Divakar Rajamohan a and Lloyd H. Back c
a
Mechanical Engineering Department, University of Cincinnati, Cincinnati, OH 45221, USA
Biomedical Engineering Department, University of Cincinnati, Cincinnati, OH 45221, USA
c
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA
b
Received 19 December 2005
Accepted in revised form 1 February 2007
Abstract. The patho-physiologic process of restenosis and tissue growth may not be completely eliminated and is the primary
concern of clinicians performing angioplasty and stent implantation procedures. Recent evidence suggests that the restenosis process is influenced by several factors: (1) geometry and size of vessel; (2) stent design; and (3) it’s location that alter
hemodynamic parameters, including local wall shear stress (WSS) distributions. The present three-dimensional (3D) analysis
of pulsatile flow in a deployed coronary stent: (1) shows complex 3D variation of hemodynamic parameters; and (2) quantifies
the changes in local WSS distributions for developed flow and compares with recently published WSS data for developing flow.
Higher order of magnitude of WSS of 290 dyn/cm2 is observed on the surface of cross-link intersections at the entrance of
the stent for developed flow, which is about half of that for developing flow. Low WSS of 0.8 dyn/cm2 and negative WSS of
−8 dyn/cm2 are seen at the immediate upstream and downstream regions of strut intersections. Persistent recirculation is observed at the downstream region of each strut cross-link and the regions of low and negative WSS may lead to patho-physiologic
conditions near the stented region. The key finding of this study is that the location of stent in the coronary artery determines
the developing or developed nature of the flow, which in turn, results in varied level of WSS.
Keywords: Coronary artery, stent, pulsatile flow, stenosis, computational fluid dynamics, wall shear stress.
1. Introduction
A major limiting factor to the effectiveness of the stent implantation procedure has been the phenomenon of restenosis, or occurrence of re-narrowing in the treated initially narrowed artery segment.
From the context of hemodynamic perspective, our previous study (Rajamohan et al. [21]) has evaluated
the impact of developing pulsatile flow in a deployed coronary stent on local wall shear stress (WSS)
distributions in addition to other hemodynamic parameters. The present study examines the developed
pulsatile flow in a deployed coronary stent. The authors believe that the literature would remain incomplete without the comparison of results between the developed and the developing [21] flow.
*
Address for correspondence: R.K. Banerjee, Dept. of Mechanical, Industrial and Nuclear Engineering, 688 Rhodes Hall, PO
Box 210072, Cincinnati, OH 45221-0072, USA. Tel.: +1 513 556 2124; Fax: +1 513 556 3390; E-mail: Rupak.Banerjee@UC.
Edu.
0006-355X/07/$17.00  2007 – IOS Press and the authors. All rights reserved
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R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
There are several factors affecting restenosis like geometry and size of vessel, stent design and its
location. These factors impact areas of flow recirculation, flow separation and WSS. Studies have shown
that there are critical interactions between stents and vessel walls [15,16,23,26] and stent design has
played a vital role for tissue damage in neointimal hyperplasia. Researchers [5,12,18] have also shown
the dependence of flow recirculation and flow reattachment on strut spacing. They observed minimum
platelet deposition and continual flow stagnation at low strut spacing, maximum platelet deposition and
partial flow reattachment at intermediate strut spacing, and high platelet deposition and complete flow
reattachment at higher strut spacing. The study by Henry [14] concluded that the occurrence of flow
separation near the strut led to large WSS gradients in the immediate vicinity of the flow separation and
reattachment points, and this might have an impact on the rate of endothelial repair following injury
induced by stent placement. Several other researchers have studied and indicated the effect of wall shear
stress on restenosis [4,10,17,22,24,25,27]. These studies have been discussed in detail in our previous
publication [21]. Due to the space limitation, the authors have refrained from repeating the literature
review in the present manuscript.
The primary focus of the present study is to perform a detailed calculation on WSS distribution,
flow recirculation and flow stagnation for developed flow and compare that with our previous study
[21] for developing flow, where the stent is deployed at the origin of a branched coronary artery. This
study improves upon previously published literatures as a 3D comparative analysis has been conducted
to quantify the stent induced changes on the flow patterns for developed pulsatile flow in relation to
developing flow, having non-Newtonian viscosity of blood.
2. Methodology
2.1. Geometry
A pulsatile flow analysis is performed for a freshly deployed coronary stent with helical strut matrix,
in a human coronary artery having a 3D geometry with an axial length of 10 mm and diameter of 3 mm.
The design and the geometry of the stent strut used in the present study (Fig. 1A) are based on the model
used in the past studies [5,18,21]. The meshing scheme, governing equations, definition of modified
oscillatory shear index (MOSI) and the finite volume method are discussed in our previous study [21].
2.2. Boundary conditions
To simulate the best case scenario of a developed flow in stented artery, a time varying (pulsatile)
parabolic spatial variation of velocity boundary condition is imposed at the inlet [21]. Thus, the present
model represents a best case scenario and evaluates the condition of the stent being deployed at a downstream region of a coronary artery, where a developed flow is expected. For developing flow [21] the
stent was deployed at the origin of a branched coronary artery. To model this worst case flow scenario
at the entrance region of the artery, a time-varying pulse with a uniform spatial variation of velocity
boundary condition was imposed at the inlet with a user-defined subroutine. No-slip boundary condition
is specified on the wall which makes all flow velocity components equal to zero. Considering the diseased condition of the coronary artery, the wall is specified to be rigid [20]. At the outlet, zero gauge
pressure boundary condition is applied.
R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
93
Fig. 1. (A) Geometry and stent struts; (B) validation of wall shear stress.
2.3. Validation
WSS data of the present study (coronary stent: d = 0.3 cm, upeak = 22.8 cm/s, Repeak = 208) of
developed flow as well as developing [21] flow are compared with the past study by LaDisa et al. [17]
(coronary stent: d = 0.274 cm, uavg = 22.5 cm/s, Reavg = 177). Figure 1B shows the comparison of
WSS at the four strut intersections of the stent. For developed flow, WSS near the entrance region of
stented artery i.e. at strut intersection 1 is 53 dyn/cm2 ; this value is within 0.7% of the result reported
by LaDisa et al. [17]. As the flow proceeds from strut 1 to strut 2, WSS decreases to 48.3 dyn/cm2 . This
value further decreases to 46 dyn/cm2 as the flow reaches the strut intersection 4. This trend of reduction
in WSS has also been shown by LaDisa et al. [17]. The parabolic velocity profile at inlet is disturbed
when the flow encounters the struts. The disturbance is higher at the location of strut 1 resulting in
higher WSS compared to downstream strut locations 2, 3 and 4. The flow is relatively more developed
at downstream strut locations. The variation in the WSS values between the present study of developed
flow and LaDisa et al. [17] is around 7% at strut intersections 2 to 4. This variation is primarily due
to some differences in strut spacing and height between the present study and the geometry studied by
LaDisa et al. [17]. WSS value at the entrance for the developed flow is about half of the value that
was obtained for developing flow [21]. As the flow develops, the WSS value decreases rapidly and
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R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
the variation in the WSS values between developed and developing flow decreases from 20.6% at strut
intersection 2 to 9.8% at strut intersection 3, and then to 7.5% at strut intersection 4. It may be noted that
a comparative study of developed and developing pulsatile flows has not been reported in the past. The
additional validation of pressure data of the present study is shown in Fig. 6.
3. Results and discussion
To study the effect of stent implantation on the blood flow, velocity profiles, WSS, recirculation length
and height and pressure drop data are plotted at various locations inside the stent. Figure 1A shows a
pictorial representation of the locations of strut intersections, midpoints and vertices. The results have
been obtained for both basal and hyperemic flow rates, but due to space constraints only the data for
hyperemic flow rates are shown in the figures. Results for basal flow have been discussed wherever
applicable.
3.1. Velocity profiles
To analyze the developed pulsatile flow, axial velocity profiles are plotted along the radius of the
artery at strut intersections and midpoints of the stent. The velocity profiles are plotted for hyperemic
flow rate at different time points: 1.86 s, the early acceleration phase (uin = 0.5uinmax ); 2.00 s, the peak
flow (uin = uinmax ); 2.16 s, the early deceleration phase of the cycle (uin = 0.75uinmax ) and 2.30 s, the
late deceleration phase of the cycle (uin = 0.25uinmax ). Due to space limitation velocity profiles near the
entrance (Intersection 1 & Midpoint 1) and near the exit (Intersection 4 & Midpoint 3) of the stented
artery are reported (Fig. 1A).
Figures 2A and 2B show the axial velocity profiles at strut intersections 1 (near the entrance) and 4
(near the exit) for developed flow. For comparison, these figures are superimposed with a representative
velocity profile for developing flow [21] at t = 2.0 s, the time at which the inlet flow attains its peak.
The velocity profiles are plotted along the radius of the artery i.e. from the center of the artery to the
vessel wall where 0.125 cm represents the point of strut intersection. For developed flow, a near parabolic
velocity profile is observed where the peak velocity during the entire cardiac cycle occurs at the center
of the artery for all flow rates. Peak velocity at t = 2.0 s is 40.2 cm/s (not shown) for basal flow and
160.6 cm/s for hyperemic flow near the entrance (strut intersection 1). Near the exit of the artery (strut
intersection 4), the peak velocity is 42.1 cm/s (not shown) and 166.2 cm/s for basal and hyperemic flows,
respectively. There is no significant variation in the velocity from the entrance to the exit of the artery
for developed flow. For developing flow [21], the peak velocity at the entrance and exit occurs near the
strut intersections 1 and 4, respectively, i.e. near the stented artery wall. There is a decrease of 83% in
the velocity gradient near the entrance and 37% near the exit of the stented artery for developed flow
compared to developing flow.
Figures 2C and 2D show the axial velocity profiles at midpoints 1 and 3 for developed flow. These
figures are also superimposed with a representative velocity profile for developing flow [21] for comparison at t = 2.0 s. Similar to the velocity profiles obtained for developed flow at strut intersections,
near parabolic velocity profiles are observed at midpoints close to the entrance and exit of the artery. For
basal flow rate, the peak velocity remains constant at ∼40 cm/s whereas, for hyperemic flow rate, peak
velocity is 157 cm/s and 161 cm/s near the entrance and exit of the artery, respectively. For developing
flow [21], peak velocity occurs near the stent wall (Figs 2C and 2D) for all flows except at the exit region
for basal flow(not plotted). There is a decrease of 55% in the velocity gradient near midpoint 1 and 34%
R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
95
· · · · · · · · · t = 1.85 s —— t = 2.00 s – – – – – t = 2.20 s
–|–|–|– t = 2.00 s; [21] –·–·–·– t = 2.30 s
Fig. 2. Variation of axial velocity along the radius of the artery at strut intersections 1 (A) and 4 (B) at times of accelerating
(t = 1.85 s), peak (t = 2.00 s) and decelerating flows (t = 2.20 s and 2.30 s); Variation of axial velocity along the radius of
artery at midpoints 1 (C) and 3 (D) at times of accelerating (t = 1.85 s), peak (t = 2.00 s) and decelerating flows (t = 2.20 s
and 2.30 s).
near midpoint 3 for developed flow compared to developing flow. It can be concluded that the developed
flow does not have any significant variation in the velocity profile from the entrance to the exit of the
artery and has lower velocity gradient at the wall, thereby leading to lower WSS value compared to
developing flow.
3.2. Wall shear stress (WSS) distribution
Figures 3A and 3B show the phasic variation of axial WSS for hyperemic flow rates at strut intersections 1 to 4 and midpoints 1 to 3, respectively for developed flow. For comparison, these figures are
superimposed with a representative WSS plot for developing flow [21] at t = 2.0 s. For the pulse cycle,
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R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
Fig. 3. Temporal variation of wall shear stress (WSS) at strut intersections [I] (A) and midpoints [M] (B); (C) Temporal variation
of WSS at vertices. I – upstream of strut intersections: V1, V3, V5, and V7; II – downstream of strut intersection: V2 (values for
V4, V6 and V8 are similar to V2); (D) Axial variation of WSS along arterial wall at times of accelerating, peak and decelerating
flows.
the WSS attains its maxima at peak diastole (t = 2.0 s). WSS values at strut intersections are generally
higher than that at midpoints due to high velocity gradient at the strut intersections. Maximum peak
WSS values of 252 dyn/cm2 and 76 dyn/cm2 are observed for hyperemic flow rates near the entrance at
strut intersection 1 and midpoint 1, respectively. For basal flow, peak WSS values are between 20 to 25%
of that of hyperemic flow. There is an average decrease of 30% in peak WSS values at strut intersections
and 20% at midpoints near the entrance for developed flow compared to developing flow. As the flow
develops along the stent from strut intersection 1 to strut intersection 4, the reduction in peak WSS value
is 20% and 41% for developed and developing flows, respectively. Thus, the developed flow has less
impact on changes in local WSS distributions than the developing flow.
Figure 3C shows the phasic variation of axial WSS at the vertices 1 to 8. Vertices 1, 3, 5 and 7
represent the upstream and vertices 2, 4, 6 and 8 represent the downstream of strut intersections 1, 2,
3 and 4, respectively. These figures are also superimposed with a representative pulsatile WSS profile
for developing flow [21] for comparison at t = 2.0 s. Overall positive WSS occurs at the upstream and
R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
97
negative WSS occurs at the downstream of strut intersections during the entire cardiac cycle for all flow
rates, except for the basal flow (not shown) rate where negative shear stress occurs even at the upstream
location of strut intersection 1 for both developed and developing flows. For developed flow, peak values
of WSS of ∼11 dyn/cm2 and −5.5 dyn/cm2 , occur near the entrance at vertices 1 and 2, respectively for
hyperemic flow. These results show that the peak positive WSS at the immediate upstream and the peak
negative WSS at the immediate downstream of each strut intersection for developed flow are about 20%
and 75% of that for developing flow, respectively.
Figure 3D shows the axial variation of WSS along the artery wall for hyperemic flow rates at times
of accelerating, peak and decelerating flows. For developed flow, there is an increase of 5 to 6 times in
WSS at strut intersections for hyperemic flow (Fig. 3D) as compared to the basal flow (not shown) for
which 52 dyn/cm2 is calculated near the entrance at strut intersection 1 and 47 dyn/cm2 is seen near
the exit at strut intersection 4. For hyperemic flow, WSS of 290 dyn/cm2 occurs just upstream of strut
cross-link intersection 1 (x = 0.062 cm). As the flow proceeds in the axial direction, there is a sharp
decrease of WSS to a negative value of −8 dyn/cm2 at the immediate downstream of strut intersection 1
(x = 0.071 cm) showing recirculation. Due to the flow reattachment between strut intersections 1 and 2,
the WSS increases from negative value gradually to 80 dyn/cm2 and then decreases to a low value of 0.8
dyn/cm2 at the immediate upstream of strut intersection 2 (x = 0.3 cm), where there is flow stagnation.
Axially downstream the WSS again increases to 250 dyn/cm2 at the strut intersection 2. The percentage
reduction in WSS from strut intersection 1 to 4 is higher for hyperemic flow (24%) than for basal flow
(9%) because at hyperemic flow the flow disturbance is higher at the upstream location of strut 1. The
comparison of axial variation of WSS for the developed flow at peak inlet velocity (at t = 2.0 s) with
developing flow data [21] is also presented in Fig. 3D for hyperemic flows. From Fig. 3D, it can be seen
that for developed flow WSS values are half of that for developing flow near the entrance and nearly
coincide at the exit.
3.3. Modified oscillatory shear index (MOSI)
Figure 4 shows the variation of MOSI with flow rate. To analyze the flow, MOSI is plotted at upstream
and downstream of each strut intersection (vertices 1 to 8) from basal to hyperemic flow rates. For
developed flow, MOSI value of nearly +1 and −1 are observed at the upstream and downstream of
each strut intersection, respectively for all flow rates. This shows that there is negative WSS at the
Fig. 4. Variation of modified oscillatory shear index (MOSI) with mean flow rate at vertices (V) near stent intersections.
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R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
downstream of each strut intersection and positive WSS at the upstream of each strut intersection during
the entire cardiac cycle for all flow rates except near the entrance (vertex 1), where there is a negative
WSS (negative MOSI value) for 50, 100 and 150 ml/min flow rates. Similar observation is seen for
developing flow [21] at vertex 1 at basal flow; however, as the flow rate increases, positive WSS is seen
at vertex 1. This happens due to the suppressed recirculation region at the upstream of vertex 1 because
of high momentum of the fluid at hyperemic flow rate. In general, there is a persistent recirculation at
the downstream of each strut intersection. It is evident from the Figs 3C, 3D and 4 that zones of flow
stagnation and recirculation zones are formed at the immediate upstream and downstream of each strut
intersection, respectively. In line with these results, previous studies have show that large amounts of
dye accumulated between adjacent struts [5].
3.4. Recirculation length and height
Figure 5 shows the variation of recirculation length and height for basal to hyperemic flow rates at
times of accelerating, peak and decelerating flows. Recirculation length and height [21] are calculated as
the maximum length of recirculation zone formed at the immediate downstream of each strut intersection
in axial and radial directions, respectively. For developed flow, there is no significant variation in size
Fig. 5. Variation of recirculation length along the struts for basal & hyperemic flow rates at times of accelerating (A), peak (B)
and decelerating (C, D) flows.
R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
99
of the recirculation zone formed at the downstream of each strut intersection except for hyperemic flow.
For hyperemic flow, at time of peak diastole (t = 2.0 s) and during deceleration (t = 2.20 s), the
length and height of recirculation zone formed near the entrance i.e. strut intersection 1 is smaller than
those formed near strut intersections 2, 3 and 4. Maximum recirculation length of 0.22 mm (Fig. 5B)
and height of 0.04 mm (not shown) are observed near strut intersection 2 at peak diastole for developed
hyperemic flow. It can be seen that the developed flow recirculation length and height are either less
than or equal to the developing flow values for the basal flow rate. Near strut intersection 2, at peak
diastole, the maximum recirculation length and recirculation height for developing hyperemic flow are
100% and 50% higher, respectively, than that for developed flow. Thus, the nature of the flow is critical
in determining the size of recirculation zones [2,3] formed inside the stented artery.
3.5. Pressure drop
Figure 6A shows the pressure drop (∆p = pout − pin ) between outlet and inlet of the artery for a
pulse cycle for developed and developing [21] flows at basal and hyperemic conditions. As expected,
the ∆p profile follows the inlet velocity profile. The existence of the stent causes the minimum ∆p to be
Fig. 6. Pressure drop along the stent for a pulse cycle (A) and a comparison between developing and developed time-averaged
mean pressure drops for a deployed stent (B).
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R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
−0.35 mmHg for basal flow rate and −1.78 mmHg for hyperemic flow rate at peak diastole (t = 2.0 s)
for developed flow. When compared with the developed flow, the minimum ∆p for developing flow
is more than 50% higher for basal flow (−0.55 mmHg) and more than twice for hyperemic flow (−4
mmHg). There is a positive ∆p occurring at the end (t = 2.4 s) of the pulse cycle because of the
flow reversal occurring near the arterial and stent wall regions. Integration of ∆p(t) over the pulse cycle
provides the time averaged (mean) pressure drop, ∆p̃. The ∆p̃ − Q̃ (mean flow rate) relation is shown
in Fig. 6B. As the flow rate increases from basal to hyperemic, the ∆p̃ increases by a factor of 4.5 for
developed flow and 6.4 for developing flow. Also, as the Q̃ increases, there is a sharp increase in mean
∆p̃ for developing flow reaching a maximum of 1.8 mmHg at hyperemic condition, which is more than
twice that of developed flow (0.8 mmHg).
4. Conclusions
The present study quantifies and compares the effect of developed and developing [21] pulsatile flows
on hemodynamic parameters in a stented artery. Past studies report that the WSS reaching a value of
20 dyn/cm2 over a short span depict a rapid increase in the activation of platelets [6,26,27]. The present
results show peak WSS value of 290 dyn/cm2 at the entrance of the stent for developed flow, which
is half of that for developing flow. This implies that the developing flow might have a larger impact
on the arterial wall such as higher level of platelet activation compared to developed flow. Negative
WSS, signifying recirculation region, is observed at the immediate downstream region of each strut
cross-link for developed flow. When compared to developed flow, maximum recirculation length and
height for developing flow are 100% higher and 50% higher, respectively. Caro et al. [7] and Nerem and
Levesque [19] have shown that recirculation zones of low shear stresses are susceptible to the deposition
of macromolecules and other lipid derivatives. The present results show that the location of stent in
the coronary artery determines the developing or developed nature of the flow, which in turn, results in
varied level of WSS. Developing flow may be subjected to increased patho-physiologic conditions.
The limitation of the present study is that it is carried out for a straight rigid artery. However, the coronary arteries are curved and, hence, there would be alterations in WSS distributions due to centrifugal
acceleration. As reported in several previous studies, diseased coronary arteries behave as rigid tubes
and, thus, the impact of either compliant arterial wall or compliance mismatch has been ignored. To delineate the effects of compliance and compliance mismatch, further investigations are needed. Flow field
downstream of stent needs to be studied to obtain a better understanding of the flow disturbances induced
by stent. Also, stent implantation resulting in residual stenosis requires investigation. Currently, clinicians use: (1) stents of improved designs with complex structures than that used in the present study; and
(2) drug coated stents. Flow through the stents of improved design needs to be evaluated in conjunction
with pharmacokinetics associated with drug coated stents.
Nomenclature
d
p
∆p
Q̃
R̃e
t
vessel diameter, cm
static pressure, mmHg
pressure drop (pout − pin ), mmHg
mean flow rate, ml/min
mean-flow Reynolds number (4Q̃/πνd)
time, s
R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
u
x
α
γ̇
γ̇ij
η
ν
ρ
τ
T
ω
101
axial velocity, cm/s
axial distance, cm
frequency parameter (d/2)(ω/ν)0.5
shear rate, s−1
rate of strain tensor, s−1
blood viscosity, poise
kinematic viscosity (η/ρ), cm2 /s
density, g/cm3
wall shear stress [WSS], dyn/cm2
period of cardiac cycle, s
circular frequency (2π/T ), s−1
Subscript
avg spatial average
in
inlet of artery
out
outlet of artery
peak peak of cardiac cycle
w
wall condition
Superscript
∼
time-average (mean over cardiac cycle)
References
[1] R.K. Banerjee, L.H. Back and Y.I. Cho, Computational fluid dynamics modeling techniques, using finite element methods
to predict arterial blood flow in: Biomechanical Systems Techniques and Applications: Biofluid Methods in Vascular and
Pulmonary Systems, Vol. 4, CRC Press, 2001, Chapter 8.
[2] A.I. Barakat and E.T. Cheng, Numerical simulation of fluid mechanical disturbance induced by intravascular stents, Proceedings of the 11th International Conference on Mechanics in Medicine and Biology, Maui, Hawaii, April 2–5, 2000.
[3] A.I. Barakat and L.G. Schachter, Computational study of arterial flow disturbance induced by intravascular stents, in:
Proceedings of the Summer Bioengineering Conference, BED 50 (2001), 877–878.
[4] J.L. Berry, J.E. Moore, E. Manoach and P.H. Rolland, Hemodynamics and wall mechanics of a compliance matching
stent: in vitro and in vivo analysis, J. Vasc. Int. Rad. 13 (2002), 97–105.
[5] J.L. Berry, A. Santamarina, J.E. Moore, S. Roychowdhury and W.D. Routh, Experimental and computational flow evaluation of coronary stents, Ann. Biomed. Eng. 28 (2000), 386–398.
[6] D.Y. Bluestein, Y.M. Li and I.B. Krukenkamp, Free emboli formation in the wake of bi-leaflet mechanical heart valves
and the effects of implantation techniques, J. Biomech. 35 (2002),1553–1540.
[7] C.G. Caro, J.M. Fitzgerald and R.C. Schroter, Arterial wall shear and distribution of early atheroma in man, Nature 223
(1969), 1159–1161.
[8] Y.I. Cho, L.H. Back, D.W. Crawford and R.F. Cuffel, Experimental study of pulsatile and steady flow through a smooth
tube and an atherosclerotic coronary artery casting of man, J. Biomech. 16 (1983), 933–946.
[9] Y.I. Cho and K.R. Kensey, Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel: part I,
steady flows, Biorheology 28 (1991), 241–262.
[10] E.R. Edelman and C. Rogers, Pathobiologic responses to stenting, Am. J. Cardiol. 81 (1998), 4E–6E.
[11] Fluent User Manual, ver. 6.1.18, Fluent Inc., Lebanon, NH, 2003.
[12] A.O. Frank, P.W. Walsh and J.E. Moore, Computational fluid dynamics and stent design, Artif. Organs 26 (2002), 614–
621.
[13] Heart and Stroke Statistical Update, American Heart Association, 2001, pp. 1–33.
[14] F.S. Henry, Simulation of flow through model stented arteries, Proceedings of the Summer Bioengineering Conference,
BED 50 (2001), 329–330.
[15] A. Kastrati, J. Mehilli, J. Dirschinger, F. Dotzer, H. Schuhlen, F.J. Neumann, M. Fleckenstein, C. Pfafferott, M. Seyfarth
102
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
R.K. Banerjee et al. / Developed pulsatile flow in a deployed coronary stent
and A. Schomig, Intracoronary stenting and angiographic results – Strut thickness effect on restenosis outcome (ISARSTEREO) trial, Circulation 103 (2001), 2816–2821.
A. Kastrati, J. Mehilli, J. Dirschinger, J. Pache, K. Ulm, H. Schuhlen, M. Seyfarth, C. Schmitt, R. Blasini, F.J. Neumann
and A. Schomig, Restenosis after coronary placement of various stent types, Am. J. Cardiol. 87 (2001), 34–39.
J.F. LaDisa, I. Guler, L.E. Olson, D.A. Hettrick, J.R. Kersten, D.C. Warltier and P.S. Pagel, Three-dimensional computational fluid dynamics modeling of alterations in coronary wall shear stress produced by stent implantation, Ann. Biomed.
Eng. 31 (2003), 972–980.
J.E. Moore and J.L. Berry, Fluid and solid mechanical implications of vascular stenting, Ann. Biomed. Eng. 30 (2002),
498–508.
R.M. Nerem and M.J. Levesque, Fluid mechanics in atherosclerosis, in: Handbook of Bioengineering, R. Skalak and S.
Chien, eds, 1987, Chapter 21, 21.1–21.22.
W.W. Nicholas and M.F. O’Rourke, McDonald’s Blood Flow in Arteries Theoretical, Experimental and Clinical Principles, Oxford University Press, New York, 1998, pp. 396–401.
D. Rajamohan, R.K. Banerjee, A.L. Ibrahim, M.A. Jog and L.H. Back, Developing pulsatile flow in a deployed coronary
stent, ASME J. Biomech. Eng. 128 (2006), 347–359.
C. Rogers and E.R. Edelman, Endovascular stent design dictates experimental restenosis and thrombosis, Circulation 91
(1995), 2995–3001.
T. Seo, L.G. Schachter and A.I. Barakat, Computational study of fluid mechanical disturbance induced by endovascular
stents, Ann. Biomed. Eng. 33(4) (2005), 444–456.
J.J. Wentzel, R. Krams, C.H. Schuurbiers, J.A. Oomen, J. Kloet, W.J. van der Giesen, P.W. Serruys and C.J. Slager,
Relationship between neointimal thickness and shear stress after Wallstent implantation in human coronary arteries, Circulation 103 (2001), 1740–1745.
J.J. Wentzel, D.M. Whelan,W.J. van derGiessen, H.M.M. van Beusekom, I. Andhyiswara, P.W. Serruys, C.J. Slager and
R. Krams, Coronary stent implantation changes 3-D vessel geometry and 3-D shear stress distribution, J. Biomech. 33
(2000), 1287–1295.
N. Li, A.H. Goodall and P. Hjemdahl, Efficient flow cytometric assay for platelet–leukocyte aggregates in whole blood
using fluorescence signal triggering, Cytometry 35 (1999), 154–161.
K.T. Nguyen, S.-H. Su, A. Sheng, D. Wawro, N.D. Schwade, C.F. Brouse, P.E. Greilich, L. Tang and R.C. Eberhart, In
vitro hemocompatibility studies of drug-loaded poly-(L-lactic acid) fibers, Biomaterials 24 (2003), 5191–5201.