The Influence of Strut-Connectors in Stented Vessels: A Comparison of Pulsatile Flow Through Five Coronary Stents
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- Pant, S., Bressloff, N.W., Forrester, A.I.J. et al. Ann Biomed Eng (2010) 38: 1893. doi:10.1007/s10439-010-9962-0
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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.
KeywordsStentsRestenosisComputational fluid dynamicsCoronary arteryPulsatile blood flow
Computational fluid dynamics
Wall shear stress
Coronary artery disease
Bare metal stents
Drug eluting stents
Laser doppler velocimeter
Left anterior descending
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.
Arterial Remodelling Technologies
Johnson & Johnson
Inlet velocity: key features
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%.
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
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.
Modified Oscillatory Shear Index
Variation in Stent C
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.
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.
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.
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.