Annals of Biomedical Engineering

, Volume 38, Issue 5, pp 1893–1907

The Influence of Strut-Connectors in Stented Vessels: A Comparison of Pulsatile Flow Through Five Coronary Stents


  • Sanjay Pant
    • School of Engineering SciencesUniversity of Southampton
    • School of Engineering SciencesUniversity of Southampton
  • Alexander I. J. Forrester
    • School of Engineering SciencesUniversity of Southampton
  • Nick Curzen
    • Southampton University Hospitals NHS Trust
    • School of MedicineUniversity of Southampton

DOI: 10.1007/s10439-010-9962-0

Cite this article as:
Pant, S., Bressloff, N.W., Forrester, A.I.J. et al. Ann Biomed Eng (2010) 38: 1893. doi:10.1007/s10439-010-9962-0


The design of coronary stents has evolved significantly over the past two decades. However, they still face the problem of in-stent restenosis, formation of neointima within 12 months of the implant. The biological response after stent implantation depends on various factors including the stent geometry which alters the hemodynamics. This study takes five different coronary stent designs, used in clinical practice, and explores the hemodynamic differences arising due to the difference in their design. Of particular interest is the design of the segments (connectors) that connect two struts. Pulsatile blood flow analysis is performed for each stent, using 3-D computational fluid dynamics (CFD), and various flow features viz. recirculation zones, velocity profiles, wall shear stress (WSS) patterns, and oscillatory shear indices are extracted for comparison. Vessel wall regions with abnormal flow features, particularly low, reverse, and oscillating WSS, are usually more susceptible to restenosis. Unlike previous studies, which have tried to study the effect of design parameters such as strut thickness and strut spacing on hemodynamics, this work investigates the differences in the flow arising purely due to differences in stent-shape, other parameters being similar. Two factors, the length of the connectors in the cross-flow direction and their alignment with the main flow, are found to affect the hemodynamic performance. This study also formulates a design index (varying from 18.81% to 24.91% for stents used in this study) that quantifies the flow features that could affect restenosis rates and which, in future, could be used for optimization studies.


StentsRestenosisComputational fluid dynamicsCoronary arteryPulsatile blood flow



Computational fluid dynamics


Wall shear stress


Coronary artery disease


Bare metal stents


Drug eluting stents


Stent thrombosis


Laser doppler velocimeter


Left anterior descending


Endothelial cell


Finite element analysis


Non-uniform rational B-splines


Modified oscillatory shear index


Hemodynamic low and reverse flow index


Stents are tubular structures (often meshes) which are inserted to the stenotic region on a balloon catheter, usually after angioplasty, and then expanded until they deform plastically to provide a scaffolding feature preventing arterial recoil. Even though stents are widely used today for the treatment of coronary artery disease (CAD), they often induce adverse biological responses. One such response is reduction in lumen size as a result of formation of the neointima within 12 months of the stent-implant. This process, known as restenosis, represents a major clinical limitation of bare metal stents (BMS) but has been successfully attenuated by the advent of drug eluting stents (DES).1 Another process determining stent patency is stent thrombosis (ST)—formation of a blood clot inside the stented vessel. Although all types of coronary stents can be associated with stent thrombosis, there has been recent specific concern in relation to the ongoing risk of ST beyond the first 6 months after implantation.13 As opposed to BMS, DES delay the process of vessel repair including endothelialization,9 and can trigger a thrombogenic response leading to late thrombosis.7 Both these responses, restenosis and ST, are likely to be affected by altered hemodynamics inside the stented vessels.

The process of restenosis is likely to be multifactorial but its causes are not completely understood. However, there are studies that imply a correlation between various flow features and restenosis rates. Kastrati et al.16 analyzed 4510 patients with stent implantations and showed that stent design was the most important factor affecting restenosis, second only to vessel size. Roger and Edelman23 reported that stent material and configuration were critical factors in determining intimal hyperplasia and thrombosis. Specifically, a reduction in strut–strut intersections would help reduce the risk of restenosis significantly. Kastrati et al.15 did an analysis in 651 patients and reported that reduction in strut thickness resulted in significant reduction in angiographic and clinical restenosis. Such data have had an important influence on stent designs. Furthermore, Frank et al.11 showed in an in vitro experimental study that platelet adhesion and endothelial cell (EC) regrowth are affected by the stent design, particularly strut spacing, and the overall flow environment.

From the point of view of altered hemodynamics, a significant body of evidence suggests that sites with low mean shear stress, oscillatory shear stress, high particle residence times, and non-laminar flow are the sites where most intimal-thickening occurs. Ku et al.17,18 reported a strong inverse correlation between low mean wall shear stress (less than 5 dynes/cm2) and atherosclerotic intimal thickening. Wentzel et al.28 studied neointimal thickness in 14 patients, 6 months after Wallstent implantation. They used a 3-D reconstruction of arteries to determine neointimal thickness, and computational flow analysis to calculate shear stress on the surface of the stent. For 9 out of 14 implantations, they observed that neointimal thickening and in-stent shear stress were inversely correlated. Hence, the effect of stent design features that lead to specific wall shear stress (WSS) patterns demands further investigation.

Computational fluid dynamics (CFD) provides an excellent tool for studying micro features of the flow and has been widely used for flow analysis through stented vessels. Berry et al.5 performed an experimental and 2-D computational flow analysis using custom-made models of a braided wire stent, Schneider Wallstent®, to reveal flow separation and formation of stagnation zones between wires. In particular, they studied the effect of wire spacing and diameter on the stagnation zones and reported that stent geometry had a significant effect on arterial hemodynamics. Ladisa et al.19 performed steady state 3-D CFD simulations in a Palmaz-Schatz slotted-tube stent, using data from in vivo measurements of canine left anterior descending (LAD) coronary artery diameter and blood flow velocity. They reported that regions of low wall shear stress are localized around stent struts. They20 also reported that while reducing the number of struts and strut thickness reduced the percentage of arterial wall area exposed to low wall shear stress, the opposite was observed if strut width was decreased. Rajamohan et al.22 studied pulsatile and non-Newtonian blood flow through a stent with a helical strut matrix and identified recirculation zones immediately upstream and downstream of each strut intersection. Similar other studies3,10,12,24 have shown that stents, depending on their design, cause significant alterations in hemodynamics leading to particular zones which could be susceptible to smooth cell proliferation and restenosis. Balossino et al.2 modeled expansion of four different stents against plaque and artery using finite element analysis (FEA) and used the expanded geometries to evaluate the hemodynamics. They compared the WSS distribution for these stent models and also studied the effect of strut thickness on vessel hemodynamics.

Although many studies have tried to understand the effect of stent geometry on altered hemodynamics, most have focused on parameters such as strut spacing and strut thickness. Connectors (mostly flex) are an essential component of a stent design as their presence makes the stent flexible, which in turn improves stent deployment. With the new stent designs now used in clinical practice, especially drug eluting stents, there is a need to study the effect of these connectors on hemodynamics. Consequently, in this study the flow features in and around a variety of different connectors in five contemporary stents are explored. Moreover, based on the results of the hemodynamic analysis, an index is proposed which can be used to compare the hemodynamic performance of various stents and help in conception of new/better designs for coronary stents.



The five stents used in this study resemble the ART stent,26 Bx VELOCITY stent,25 NIR stent,25 the MULTI-LINK Zeta stent,25 and the Biomatrix stent.27 The details of each stent are listed in Table 1.
Table 1

Stents: details



Referred as

ART stent

Arterial Remodelling Technologies

Stent A


Johnson & Johnson

Stent B

NIR stent

Boston Scientific

Stent C


Abbott Vascular

Stent D

Biomatrix stent


Stent E

In order to make a comparison between the stents, representative geometries for each stent are constructed with the same diameter (3 mm), length (8 mm), strut thickness (0.05 mm), and strut height (0.10 mm). It should be noted that the strut spacings used in this study are purely representative and they are likely to differ, to some extent, from the actual spacings for each of the stent designs. Figure 1 shows the flattened out geometries for one quarter of each stent except for Stent E, for which a half section is shown. The straight lines drawn in each model define the line on the artery wall along which wall shear stress (WSS) and modified oscillatory shear index (MOSI) values are calculated and compared in subsequent figures. For all flow simulations the stent is placed at the center of the artery with an axial distance of two times artery diameter on both the proximal and distal ends of the stent. The artery wall is assumed to be straight with a constant diameter. Figure 2 shows the stent–artery assembly for Stent B. Numerical simulations are performed over a quarter of the stented segment for all stents, except for Stent E for which a half segment (owing to the quadrature links which do not allow quarter symmetry) is used, to exploit the periodic symmetry of the stent–artery assembly. All the geometries are constructed in Rhinoceros 4.0, a commercially available NURBS-based modeling software.
Figure 1

Flat geometries for the five stents. (Left top) Stent A; (left mid) Stent B; (left bottom) Stent C; (right top) Stent D; (right bottom) Stent E
Figure 2

Stent-artery assembly for Stent B

Governing Equations

The following mass conservation (1) and momentum conservation (2) equations are solved over the computational flow domain of the stent–artery assembly:
$$ \nabla\cdot({{\mathbf{v}}}) = 0 $$
$$ {\frac{\partial {{\mathbf{v}}}}{\partial t}} + \rho {{\mathbf{v}}}\cdot\nabla{{\mathbf{v}}} = -\nabla P + \mu \nabla^2 {{\mathbf{v}}} $$
In the above equations v, ρ, μ and P represent blood velocity, density, dynamic viscosity, and pressure, respectively. Blood flow is assumed to be pulsatile, incompressible, laminar, and Newtonian with a density of 1.06 g/cm3 and dynamic viscosity19 of 3.7 cP. Reynolds number (Re) and Womersley parameter (α) are defined as follows:
$$ Re = {\frac{\rho v D}{\mu}}\quad \hbox{and}\quad \alpha = D \sqrt{{\frac{\pi \rho}{2 \mu T}}} $$
where D is the internal diameter of the artery and T denotes the time period of the cardiac pulse.
At every time, t, in the cardiac pulse the following two parameters are defined:
$$ p_l(t) = {\frac{\int\int_{\rm wall} \tau_{\rm w5.0}\,dA}{\int\int_{\rm wall}\,dA}} $$
$$ p_r(t) = {\frac{\int\int_{\rm wall} \tau_{\rm w0.0}\,dA}{\int\int_{\rm wall}\,dA}} $$
$$ \tau_{{\rm{w}}x} = \left\{\begin{array}{ll} 1, & \hbox{if}\;\tau_{\rm w} \le x;\\ 0, & \hbox{otherwise.}\\ \end{array}\right. $$
pl(t) and pr(t) denote the percentages of artery wall area exposed to WSS magnitude less than 5.0 dynes/cm2 and axial WSS less than 0.0 dynes/cm2, respectively. While pl(t) is a measure of low WSS in the artery wall, pr(t) measures the artery wall area exposed to reverse flow.
To compare the oscillatory nature of WSS, the modified oscillatory shear index (MOSI),22 is calculated using the following equation:
$$ \hbox{MOSI} ={\frac{\int_0^T \tau_{\rm w} dt}{\int_0^T |\tau_{\rm w}| dt}} $$
where τw signifies the wall shear stress on the arterial wall and both integrals are calculated over one cardiac pulse.

Boundary Conditions

The outer wall of the stent is assumed to conform to the artery wall with no gaps. Both the stent and the artery wall are assumed to be rigid with a no-slip flow boundary condition imposed on each. A physiologically realistic coronary artery waveform is applied as the velocity inlet condition and the outlet is set to a zero pressure boundary. The inlet velocity profile is based on laser doppler velocimeter (LDV) measurements carried out in a replica of human LAD coronary artery.21 Figure 3 shows the inlet velocity waveform where the eight points of interest are marked. Table 2 summarizes the key features of the inlet waveform.
Figure 3

Inlet velocity profile showing the points of interest in one pulse

Table 2

Inlet velocity: key features



Time period

0.967 s

Mean velocity

16.29 cm/s

Peak velocity

29.0 cm/s

Mean Reynolds number


Peak Reynolds number


Womersley parameter (α)


Eight points of interest

0.026, 0.078, 0.217, 0.340, 0.419, 0.489, 0.677, and 0.897 s

Computational Fluid Dynamics

Star CCM+ 3.06.006, a commercially available flow solver, is used for generating finite volume meshes and for numerically solving the governing equations. Mesh, time-step, and pulse dependence studies are carried out for Stent C. Three different meshes are used: base, mesh-1, and mesh-2 (mesh-1 and mesh-2 have 1.5 and 2.5 times the number of cells relative to the base mesh, respectively). The WSS magnitude results for mesh-1 and mesh-2 vary by less than 1%.

Four different times steps viz. 10−2 s, 10−3 s, 5 × 10−4 s, and 10−4 s are used for time-step dependence study on mesh-1. The maximum difference in WSS magnitude between time steps of 10−2 s and 10−3 s is nearly 30%. However, differences in WSS magnitudes for time steps 5 × 10−4 s and 10−4 s when compared to time-step of 10−3 s are less than 1%.

Simulations for five pulses are carried out for mesh-1 and the results show little variation after the second pulse. While the difference in WSS magnitude values for pulse 1 and pulse 2 is quite large, the difference in WSS magnitude for the 2nd pulse onwards is less than 0.02%.

Based on the mesh, time-step and pulse dependence studies, all final simulations are run for two pulses for a time step of 10−3 s and mesh sizes as shown in Table 3. For each time-step 50 inner iterations are carried out.
Table 3

Mesh statistics


Base size (mm)

Cell size in stent

No. of cells



50% of base




50% of base




50% of base




50% of base




30% of base



The flow features in the stented vessels are reported both qualitatively and quantitatively. In particular, differences in wall shear stress patterns, recirculation zones, and oscillatory shear indices are reported, thereby confirming the effect of stent design, especially the connectors, on hemodynamics of stented vessels. Furthermore, the connector design in Stent C is varied to study the effect of connector length, in the cross-flow direction, on flow features.

Wall Shear Stress

Wall shear stress follows a general trend for all the stents except for the regions between the connectors. Figure 4 shows the general axial WSS patterns for all stents at point 5, the point of maximum inlet velocity on the cardiac pulse. For all five stents, axial WSS has a high value proximal to the stent and a relatively lower value in the area occupied by the stent. Artery wall area distal to the stent experiences a higher axial WSS again as the flow disruptions minimize due to absence of stent struts. For Stents D and E, a larger artery area is exposed to relatively low WSS (green area in Fig. 4 after the stent ends), when compared to Stents A, B, and C, at the distal end of the stents. For all stents, and more notably for Stents A, B, and C in Fig. 4, axial WSS at the center of the struts decreases for consecutive struts in the direction of the flow (transition from red to yellow in consecutive struts). The artery wall region around the first strut experiences a relatively high WSS as compared to the area around other struts. The areas of low WSS are found to be localized around the stent struts. This is in agreement with earlier findings of Ladisa et al.19 and Rajamohan et al.22
Figure 4

Axial WSS at point 5: Stents A–E from top to bottom

Recirculation zones are formed at the proximal and distal end of each strut/strut-connector intersection, which cause the WSS to change sign before and after each strut/strut-connector intersection. In Fig. 4, the blue regions show the artery wall area with negative axial WSS implying formation of recirculation zones. The phenomenon of recirculating flow is particularly significant in the decelerating phase of systole (point three, cf. Fig. 3) as the recirculation zones are largest during this phase. Figure 5 shows the axial-WSS variation, along a central line on the arterial wall (as shown in Fig. 1), for the five stents at point 3 of the cardiac pulse. For all stents the WSS values proximal and distal to the ends are the same. In between the struts WSS recovers from zero to a peak value which decreases for consecutive struts in the direction of flow. This peak value is different for all the stents and depends on the overall stent design. Depending on the design of the strut connectors WSS oscillates spatially in the connector region between zero, negative, and a positive value. In contrast to other stents, Stent C connectors allow the WSS to recover to a positive value in between the struts (as apparent in Fig. 5). This can be attributed to the fact that Stent C connectors have more open space between the connectors.
Figure 5

Axial WSS for all stents along the central line at point 3

Previous studies12,17 suggest that areas exposed to WSS magnitude of less than 5 dynes/cm2 correlate to areas that show most intimal thickening. Balossino et al.2 have used this 5 dynes/cm2 limit as a benchmark to compare the performance of stents. Figure 6a shows a histogram of the percentage of vessel wall area, over the axial length occupied by the stent, exposed to WSS less than 5 dynes/cm2, at the eight points listed in Table 2. At points 1 and 3, this area is 100% irrespective of the stent as the flow is decelerating in the systole phase of the cardiac cycle. Point 2, also in the systole phase, shows unexpected behavior of less than 100% area exposed to low WSS. However, the reason for this becomes clear when considering the negative WSS in Fig. 6b. Other points show considerable difference in the area exposed to low WSS which can be used to compare their performance. Stent A outperforms the other stents at all points except point 2. Stents D and E have a significantly higher percentage of low WSS area as compared to the other stents. While the difference between Stents B and C is not very large, Stent C has a slightly higher area exposed to low WSS.
Figure 6

Percentage vessel wall area exposed to low WSS and reverse flow: (a) percentage vessel wall area below 5 dynes/cm2 WSS magnitude and (b) percentage vessel wall area exposed to reverse flow

Another factor that could promote restenosis is negative WSS caused by reverse flow. Figure 6b shows a histogram of the percentage vessel area exposed to reverse flow at the eight points for all stents. Point 2, owing to the negative inlet velocity and a hence strong reverse flow, has the highest percentage area exposed to reverse flow. While points 1 and 3 show no difference in terms of the 5 dynes/cm2 WSS benchmark, these points show very significant differences in the area exposed to reverse flow. Stent A, although outperforming other stents at most points, shows a near 100% area exposed to reverse flow at point 2.

Recirculation Zones

The presence of a stent inside the vessel gives rise to the formation of recirculation zones. Figure 7 shows the recirculation zones formed between the struts and the connectors of all the stents at point 3 of the cardiac pulse. Each segment in the connector design gives rise to one recirculation zone. For instance, Stent B has four recirculation zones in the connector region while Stent D has five.
Figure 7

Recirculation zones at point 3: (a) Stent A, (b) Stent B, (c) Stent C, (d) Stent D, and (e) Stent E

Figure 8 shows the velocity profile adjacent to the artery wall for Stents B, C, and D at point 3 of the cardiac pulse. Recirculation zones in the cross-flow direction are observed for these designs close to the artery wall. This can be attributed to the fact that the connectors in these designs, owing to their wavy nature, protrude into the space between the struts and hence cause more alteration in the flow.
Figure 8

Secondary recirculation zones: (top left) Stent B; (top right) Stent C; (botton left) Stent D

Modified Oscillatory Shear Index

For all the five stents, modified oscillatory shear index (MOSI) is calculated using Eq. (6) along the central line in the artery wall as shown in Fig. 1. MOSI is important as this index gives a time average value and hence is a measure of axial WSS over the entire pulse as opposed to single points in time. MOSI values of ‘1’ or ‘−1’ indicate that the axial WSS is positive or negative over the entire cardiac pulse respectively. Figure 9 shows a plot of MOSI values along the central line mentioned above. Each plot shows the MOSI values for the one connector-strut-connector segment from the assembly.
Figure 9

MOSI values for a strut with connectors in each side

Variation in Stent C

In order to further investigate the effect of connector shape on hemodynamics, the design of the connector in Stent C is varied. Keeping the thickness constant, its length in the cross-flow direction is varied. This changes the area between the struts that is covered by the connector. Figure 10 shows the two altered designs—one with a shorter cross-flow length and one with a longer cross-flow length. These will be referred to as Stent C-SC and Stent C-LC, respectively. Simulations are carried out for these designs and the results are compared with Stent C. Figure 11 shows a comparison of percentage vessel area below 5 dynes/cm2, and Fig. 12 shows a comparison of percentage vessel area exposed to reverse flow for Stent C and its variations.
Figure 10

Variations in stent C: (top) normal; (mid) shorter; and (bottom) longer connectors
Figure 11

Area exposed to WSS magnitude below 5 dynes/cm2 for Stent C variations
Figure 12

Area exposed to reverse flow for Stent C variations


WSS, recirculation zones, MOSI, and results for all stent designs are reported above. While the general qualitative features of WSS, such as localization of low WSS regions around struts, match those described in earlier studies,5,10,19,20,22 this study brings forth finer differences at different parts of the cardiac pulse by comparing the factors that could have an effect on restenosis rates. Such differences, when compiled over the entire cardiac pulse, can be used to compare the relative hemodynamic performance of various stents.

Areas of low WSS (<5 dynes/cm2) and reverse flow are found for all the stents during the entire cardiac cycle. For points 1 and 3, 100% of wall area is exposed to low WSS. This can be attributed to the decelerating nature of flow at these points and that the inlet velocity is low. The peculiar behavior of point 2, which too is in the decelerating phase and yet has a less than 100% area exposed to low WSS, can be explained by the fact that in this phase the inlet velocity gradients are high which cause a strong reverse flow thereby causing the axial WSS to be negative but higher than 5 dynes/cm2 in magnitude. This is confirmed in Fig. 13 for the following index, AWI, as defined below for one cardiac pulse:
$$ \text{AWI}(t) = {\frac{\int\int_{\rm wall} \tau_{\rm w}(t)dA}{\int\int_{\rm wall}dA}} $$
where τw is the axial WSS. The horizontal dashed lines bound the region with axial WSS magnitude less than 5 dynes/cm2. Since other components of WSS are very small when compared to axial WSS, the major factor determining the WSS magnitude is its axial component. Zones 1 and 2 mark the time zones in the cardiac pulse where the axial WSS magnitude exceeds 5 dynes/cm2 during the systole. Since point 2 lies in zone 2, the WSS magnitude at some regions in the artery wall is greater than 5 dynes/cm2.
Figure 13

AWI for all stents for one cardiac pulse

Returning to Fig. 6a, points 4, 5, 6, 7, and 8 also show considerable differences in the percentages of areas exposed to low WSS. Stents D and E stand out, both for low and reverse WSS, because of the relatively lower strut spacing. However, even though Stents A, B, and C have the same strut spacing, percentage areas exposed to low WSS differ significantly. Similarly, for all points there are significant differences in the percentages of area exposed to reverse flow between stents A, B, and C. This can be attributed to the difference in the design of the connector.

The connectors in Stents B, C, and D have a finite length in the cross-flow direction—this cross-flow area coverage being largest for Stent C. Consequently, the struts tend to project into the central part of the space between struts. This causes a further disruption of the flow in that area—illustrated by Fig. 8 which shows the velocity profile adjacent to the artery wall at point 3 in the cardiac pulse. Recirculation in the top ends of the connectors is clear in these designs. Such a phenomenon is absent in Stents A and E as the connectors are a straight segment joining the struts. The difference of such a protruding connector design is further confirmed when Stent C is altered to make the connector shorter and longer in the cross-flow direction (Stent C-SC and Stent C-LC). It can be seen in Figs. 11 and 12 that areas exposed to low WSS and reverse flow are proportional to the connector length in the cross-flow direction.

Traditionally,22 MOSI has been used to quantify the oscillatory nature of WSS. In Fig. 9 we see that MOSI takes a value close to ‘−1’ at each strut-connector intersection and between the connectors. This implies incessant reverse flow or formation of recirculation zones over a large part of the cardiac cycle at such points. In Stents B and D, due to the presence of multiple gaps in the connector design, multiple areas of persistent reverse flow are formed. This is consistent with the results of dye injection flow visualization studies5 where more dye accumulation was observed at each strut–strut intersection. The number of recirculation zones formed is directly related to the design, specifically the number of gaps either between struts or between the connector; see Fig. 7 which illustrates this point. However, the recirculation lengths depend on the overall strut-connector-strut configuration. Another factor which affects the extent of recirculation zones is the cross section of the struts. This was shown in a study14 where stents with cross sections of a circular arc shape were compared with those having a rectangular shape. Streamlining of the strut cross section would reduce the size of the recirculation zones and consequently reduce the areas exposed to low and reverse WSS.

An in vitro experimental study8 showed that vascular endothelium responds to shear stress gradients. It was reported that endothelial cells migrate from areas where shear stress is low but the shear stress gradient is large, and that cells remaining in such regions divide at a faster rate compared to the cells exposed to uniform shear. Hence, the endothelial response to different WSS patterns created by different stents could be important in the process of re-endothelialization. Furthermore, if the tangential components on a plane perpendicular to the flow direction are considered, additional recirculation of flow is observed; see Fig. 14 which shows the in-plane velocity components, at the center of the stent, at point 3. This additional recirculation of flow, although with velocity magnitudes of roughly 1/100th of the inlet velocity, induces transverse WSS and WSS gradients which could have an effect on endothelial cell response. Qualitatively, Stents A and E have minimum recirculation (when the tangential components are considered) on planes perpendicular to the flow direction.
Figure 14

Recirculation zones on a cross section perpendicular to the flow direction: (top left) Stent A; (top mid) Stent B; (top right) Stent C; (bottom left) Stent D; (bottom right) Stent E

From Figs. 6a and 6b it can be concluded that differences in stent designs are apparent for areas of both low WSS and reversed flow. Keeping both the factors in mind and assuming that both the phenomena are equally unwanted, an index can be proposed which takes a weighted average of these percentages at the relevant points. Thus, the hemodynamic low and reverse flow index (HLRFI) is defined as:
$$ \hbox{HLRFI} ={\frac{\sum\nolimits_{i=1}^n (w_ip_{il} + w_ip_{ir})}{2 \sum\nolimits_{i=1}^n w_i}} $$
where wi are the weights for each of the n points in the cycle, and pil and pir denote percentages of areas exposed to low and reverse flow, respectively.

It is expected that the higher the value of n, the better will be the efficacy of the index in determining the hemodynamic alteration due to stents. The reason for taking a weighted average is that some specific points, such as the point of negative inlet velocity (point 2), could be clinically more relevant than others and may require (a higher) differential weighting. The peculiar nature of such points on the cardiac pulse can be seen for Stent A, for which percentage area, exposed to both low WSS and reverse flow, at point 2, is abnormally high in reference to its relative performance at other points.

In order to capture the entire pulse, HLRFI can be modified as follows:
$$ \text{HLRFI} = {\frac{\int_0^T (w(t)p_l(t) + w(t)p_r(t)))dt} {2 \int_0^Tw(t) dt}} $$
where w(t) is the weight function for the cardiac pulse and pl(t) and pr(t) is the percentages of area, A, exposed to low and reverse WSS at time t. pl(t) and pr(t) can be defined as in Eqs. (3) and (4), respectively.
It should be noted that the wall area over which the surface integrals for pl(t) and pr(t) are calculated includes only the area exposed to flow, i.e. it excludes the wall area covered by the stent. Assuming the weight function to be unity, HLRFI for all the stents and Stent C variations, as calculated using Eq. (9), are shown in Figs. 15 and 16, respectively. HLRFI, being one single number evaluated over the entire pulse, can be used to rank stents based on their hemodynamic performance. Lower HLRFI values indicate lesser alteration of hemodynamics and hence better resistance of a stent toward restenosis.
Figure 15

HLRFI for all the stents
Figure 16

HLRFI for all the Stent C variations

As the length of Stent C connector is lowered in the cross-flow direction, the hemodynamic alteration decreases. This is reflected in decreasing HLRFI values for Stent C variations from 25.95% to 22.61% to 19.91%. This decreasing trend tends toward a value of 18.81% for Stent A, which can be seen as a Stent C variation with minimal connector length in cross-flow direction. It is also interesting to note that Stent C-LC has the largest HLRFI value, even higher than Stents D and E which have a shorter strut spacing. This further emphasizes the effect design of strut connectors can have on stented vessel hemodynamics.

It is clear from the above findings that stent design dictates hemodynamic alteration. Although strut thickness and spacing are the most important factors, blood flow depends strongly on the shape of the struts and the connectors. Strut thickness is governed mostly by material properties of the stent to minimize post-expansion recoil and manufacturing processes. Strut spacing is governed by the constraints of structural strength and flexibility. Thus, the shape of the struts and connectors can be varied to improve the hemodynamic performance. It is important to be conscious of the fact that changing the stent design impacts other properties too, especially drug distribution. For instance, hemodynamic results for Stent C, C-SC, and C-LC show that Stent C-LC has poor hemodynamic performance; however, it is likely to have better drug distribution potential as the links cover a larger wall area in the cross-flow direction.

Significant differences exist between the stents with regards to the number and extent of recirculation zones in the directions of both axial and cross-flow. Although it is not currently very clear how endothelial cells respond to complex flow phenomenon, it is possible that restenosis rates could be affected by them. It is notable that Stent A produces minimal alteration of flow both in the axial direction and the direction perpendicular to the main flow. This is reflected in its lowest HLRFI value (Fig. 15) and minimal recirculation in the direction perpendicular to the main flow (Fig. 14). This behavior can be attributed to the fact that Stent A has straight segments as connectors between the struts. These straight segments, being aligned in the direction of the flow, disturb the flow to a lesser extent when compared to other connectors which, owing to their wavy nature, do not align completely with the direction of the flow.

In order to rank stents, an objective function (figure of merit) is needed which quantifies the flow features and hence determines the patency of stents. In the past, relatively few metrics have been defined to quantify the distribution of WSS in arterial flow. One such metric is defined by Bressloff6 to quantify relevant WSS information in a human carotid bifurcation. Along similar lines, the proposed HLRFI index captures and quantifies the two phenomena of low and negative WSS which are detrimental to the resistance of a stent against restenosis. HLRFI, defined as in Eq. (9), can be used as an objective function to compare a family of related stent designs solely on their hemodynamic performance. For instance, Stent E, with an HLRFI value of 24.91%, has almost 33% worse hemodynamic performance when compared to Stent A (with an HLRFI value of 18.81%). Similarly, Stent C-LC has 30% and 38% worse performance when compared with Stent C-SC and Stent A, respectively. HLRFI should be coupled with other objective functions derived from other features viz. metal to artery ratio, drug distribution, flexibility, and structural properties, in order to pass an engineering judgement to the overall efficacy of a stent.


Different points in the cardiac pulse produce different responses to the stent when measured by artery wall areas exposed to low WSS and reverse flow. Substantial differences in the flow features exist when both these factors are considered simultaneously. Even for similar strut spacings, the design of the connector, especially its length in the cross-flow direction, significantly influences blood flow. Particularly for Stent C, it can be concluded that the hemodynamic alteration, measured by percentages of areas exposed to low and reverse WSS, is proportional to the length of the connector in the cross-flow direction. The relatively better performance of Stent A can be attributed to its connector’s minimal cross-flow length and better alignment with the flow. Furthermore, the number of recirculation zones formed, and hence the oscillations in the MOSI values along any axial line on the arterial wall, is equal to the gaps between the stent struts and connectors. The differences in HLRFI values, which may be indicative of a stent’s resistance to restenosis, reinforce the effect of stent design on alteration of hemodynamics. In essence, overall stent efficacy can be improved by improving the connector designs (in particular, their cross-flow length and alignment with flow) in the stent for minimal alteration of blood flow or as a tradeoff to improve other features such as drug distribution or flexibility.

Limitations and Future Work

One of the limitations that most studies in stent hemodynamics have faced is that they assume arteries to be non-moving straight segments, which is rarely the case in reality. This study too assumes arteries to be stationary segments with constant diameter which could lead to non-realistic results. It has been proven in earlier studies4 that the flow in curved pipes is significantly different to that in straight segments. Flow in curved pipes leads to differential WSS on the inner and outer curvatures along with the formation of secondary recirculation zones. Consequently, addition of curvature to the stented artery segments would be more realistic. Moreover, stent geometries are constructed in their expanded state and are symmetric. This might not be true in reality. As the symmetric crimped stent expands against generally asymmetric plaque, the expanded geometries can be significantly different in reality to the idealized ones used in this study. Though a number of studies exist on the modeling of stent expansion, relatively few studies have studied the hemodynamics using the geometries obtained by modeling the process of balloon expansion. A study by Balossino et al.2 uses an approach to study hemodynamics post-stent expansion and assuming a symmetric plaque distribution. Another study by Zunino et al.29 presents a complete framework for numerical simulation of stent expansion, flow evaluation, and drug distribution. This study, however, does not include plaque in the simulations. In future, efforts should be made to introduce asymmetries in artery and plaque models, and extract design metrics (like HLRFI), in order to be able to rank stents based on each of their hemodynamic performances.

Another important aspect of a stent design is the drug coating and its distribution as the drug is released from the stent. Essentially, both the WSS and drug distribution patterns are dictated by stent design. An overlay of these two patterns along with the structural properties of strength and flexibility form an interesting multi-objective design problem. The authors are working in the direction to optimize stent design using multiple objectives.

Conflict of Interest

Pant, Bressloff, and Forrester have no financial relationships with any organizations that could influence this work. Curzen is involved in unrestricted research grants with Medtronic and Medicell. He also advises Medtronic, Boston Scientific, Cordis, Abbott, and Lilly.

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© Biomedical Engineering Society 2010