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Swirling Flow Can Suppress Flow Disturbances in Endovascular Stents: A Numerical Study

Chen, Zengsheng*; Fan, Yubo*; Deng, Xiaoyan*; Xu, Zaipin

doi: 10.1097/MAT.0b013e3181b78e46
Biomedical Engineering

To test the hypothesis that by intentionally inducing swirling flow in an endovascular stent, hemodynamic performance of the stent can be improved, we numerically analyzed the flow characteristics in a simplified model of a stent within a straight segment of an artery in which swirling flow was introduced intentionally. The study was designed with two purposes: 1) to investigate whether swirling flow is beneficial to suppress flow disturbance in the stent; and 2) to determine the minimum helical strength of the swirling flow required in the design of a swirling flow stent. The numerical simulation showed that the swirling flow indeed reduced the size of the disturbed flow zones, enhanced the average wall shear stress, and lowered oscillatory shear index in the stent, which have been believed to be adverse factors involved in the development of arterial restenosis after stent deployment. The minimum inlet helicity density (or strength) of the swirling flow required was approximately 6.5 m/s2. Based on the study, it is also believed that a stent with a structure that possesses intrinsic characteristics to automatically induce swirling flow in the stent is better than a stent with a front swirling flow inducer in terms of hemodynamics.

From the *School of Biological Science and Medical Engineering, Beihang University, Beijing; and †College of Animal Science, Guizhou University, Guiyang, Guizhou, China.

Submitted for consideration March 2009; accepted for publication in revised form June 2009.

Reprint Requests: Xiaoyan Deng, School of Biological Science and Medical Engineering, Beihang University, Beijing, China. Email: dengxy1953@buaa.edu.cn.

Endovascular stent is currently one of the main treatments of cardiovascular occlusion diseases. The problem of arterial restenosis after stent deployment is the main problem for the clinical use of stents. According to statistics, the rate of restenosis reaches as high as 20%-30%, 6 months after stent implantation.1,2 Many ways have been tried to resolve the problem; among them, drug-eluting stents have made great success. However, clinical reports gradually came out showing that drug-eluting stents had their own deficiency and could not completely eliminate the problem of restenosis.3,4 Some researchers believe that drug-eluting stents are no better or even worse than the conventional bare-metal stents in long-term clinical use.5

It has been well documented that the initiation and progression of restenosis is often related to altered hemodynamics with flow disturbances resulting from the stent deployed, which always involves low wall shear stress (WSS) with high oscillating shear index (OSI).6–11 It is therefore believed that whether the restenosis occurs or not depends not only on the surface properties of the stent but also on the hemodynamic characteristics of the stent.

Based on the above findings,6–11 we believe that the design of endovascular stents should take a new direction toward improving their hemodynamic performance. The structure of the stent must possess the characteristics of minimizing flow disturbance, enhancing WSS, and eliminating high OSI regions.

We believe that the swirling motion of blood flow in the aortic arch is a typical example of “form follows function” in the vascular system.12,13 This kind of spiral or swirling flow is very different from the disturbed flows observed in arterial sites that are susceptible to atherosclerosis, thrombosis, and intimal hyperplasia, such as arterial branches (bifurcations), bends, and stenoses. These disturbed flow zones are characterized by flow separation and stagnation with low fluid velocities and low WSS/high OSI,14–16 presumably allowing prolonged contact of the vessel wall with platelets, granulocytes, and metabolites that influence atherogenesis. The spiral flow or swirling flow observed in the ascending aorta is a flow form with a corkscrew-like pattern.17,18 We believe that the spiral flow can eliminate stagnation flow regions and prevent the accumulation of atherogenic lipids and the adhesion of platelets and granulocytes, etc. on the wall of the ascending aorta. Therefore, atherosclerotic plaques can hardly form in the ascending aorta. It has been documented that the phenomenon of swirling flow of blood is not only localized in the ascending aorta but also exists in many large arteries.19–21 Based on their careful investigation, Stonebridge et al.19,20 hypothesized that blood flow taking the form of rotation in certain parts of the circulation should be a normal process, which might protect the arterial wall from damage by reducing the laterally directed forces and have beneficial effects on the mechanisms of endothelial damage repair. Moreover, the study by Morbiducci et al.22 suggested that spiral flow might play a very important role in preventing the bypassed arteries from developing intimal hyperplasia.

Inspired by the aforementioned findings, we propose to design a new kind of endovascular stent that possesses swirling flow characteristics either with the help of a swirling flow guider placed at the proximal end of the stent or through its build-in structure. We hypothesize that by intentionally inducing swirling or spiral flow in the endovascular stent, the genesis and development of arterial restenosis may be suppressed. Based on this hypothesis, we designed this numerical study with two purposes. The first one is to investigate whether spiral or swirling flow is beneficial to suppress flow disturbance due to the presence of a stent. The second is to determine the minimum swirling flow strength required to suppress flow disturbance when designing the structure of a stent with swirling flow.

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Methods

Model

The three-dimensional stent model in this study is similar to that used by Seo et al.11 To simplify the numerical study, this model consists of six circular rings and therefore is axisymmetric as shown in Figure 1. The thickness d of a single ring is set as 0.5 mm.11,23 The stent model is created with the computer-aided design (CAD) software, SolidWorks 2006 SPO.0. The stent is deployed in a straight vessel with a length of 40 mm and a diameter of 4.0 mm, which are the representative parameters for the human coronary arteries within which stents are usually deployed.11,24 Considering that the swirling flow guider is placed immediately proximal to the stent, the first circular ring of the stent is located at 1 mm from the inlet. The spacing w between two circular rings is 1 mm.

Figure 1.

Figure 1.

Apparently, the rings of the stent will result in flow disturbance in the flow field concerned.25 The disturbed flow distal to each ring of the stent is actually a flow recirculation zone.11 The length of the flow recirculation zone is denoted by L, which is the distance from the flow separation point to the flow reattachment point.

This numerical study was carried out under both steady flow and pulsatile flow conditions. The specific aim of the steady flow simulation is to investigate the impact of swirling flows on the length of the flow recirculation zone, L. It is believed that the pathogenesis of intimal hyperplasia of the arterial wall not only has close correlation with low WSS but also with high OSI.22,26 The WSS vector with high-frequency change in direction has a high value of OSI. Therefore, the specific aim of the pulsatile flow simulation is to look at the influence of swirling flow on OSI of the flow field in the stent. According Ku et al.,27 OSI is defined as:

CV

CV

where WSS(s;t) is the wall shear stress vector, s is the position on the vessel wall, and T is the pulsatile cycle duration.

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Assumptions

The study of blood flow in a bifurcation with an aneurysm by Perktold et al.28 found no essential difference between the Newtonian and non-Newtonian simulations under regular physiological conditions. In this study, blood is simplified as an incompressible, homogeneous, Newtonian viscous fluid, with a density (ρ) of 1060 kg/m3 and a constant viscosity (μ) of 3.5 × 10−3 kg · m−1 · s. According to Cohen et al.29 and Ofili et al.,30 the time averaged Reynolds number for coronary artery is in the range of 150 (rest) to 550 (strenuous exercise). Considering that disturbed flows were favored at high Reynolds numbers,24 the time averaged Reynolds number was set at 360 in this study. The Reynolds number is defined as:

CV

CV

where V is the average velocity, d is the diameter of the vessel, Q is the time-averaged volume flow rate, and

CV

CV

is the kinematic viscosity of blood.

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Governing Equations

The governing equations for flow motion are given as:22,31

CV

CV

CV

CV

where JOURNAL/asaio/04.02/00002480-200911000-00004/ENTITY_OV0550/v/2017-07-29T043214Z/r/image-png and p represent, respectively, the fluid velocity vector and the pressure, and ρ and μ are the density and viscosity of blood.

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Boundary Conditions

To investigate the advantage of the swirling flow in a stent, a comparative study on hemodynamic performance of the swirling flow stent with normal flow stent was carried out. The boundary conditions for the numerical simulations under steady-state flow conditions are as follows.

For the normal flow stent under steady flow condition:

  1. Inlet: A uniform inflow velocity profile11 based on the Re of 36029,30 for the axial velocity component V A and zero radial and tangential velocity components were assumed.
  2. Outlet: According to Seo et al.,11 the outlet flow condition has little influence on the flows in the stent. Therefore, at the outlet, the pressure p was set at 1.33 × 104 Pa (100 mm Hg). To verify whether the outlet condition affects the flows in the stent, we also carried out another set of flow simulation with extended outlet so that the flow at the outlet was fully developed. The verification showed that the outlet flow condition indeed had little influence on the flows in the stent as stated by Seo et al. 11 Figure 6A gives the comparison between the two sets of flow simulations in terms of the average WSSSYMBOL
  3. Symbol

    Symbol

Figure 6.

Figure 6.

  1. The stent and the vessel wall were assumed to be rigid and nonslip.

For the swirling flow stent under steady flow condition:

In this study, to simulate the swirling flow created by the swirling flow guider of the stent, swirling flows with different inlet strength were created intentionally in the model artery by assigning different tangential velocities at the inlet.

The helicity density H (the kinetic helicity per unit volume) used to denote the swirl strength of a flow is defined by Equation 5.22 Equation 6 is the area-weighted average of helicity density.22

CV

CV

CV

CV

where A is the area of the cross-section.

  1. Inlet: The axial velocity component V A = 0.3 m/s based on the Re of 360,29,30 the radial velocity component V R = 0 m/s, and the tangential velocity component V T is defined by Equation 7.
CV

CV

where ω is the angular velocity varying from 0 to 20 rad/s and r is the radial location of the model. Therefore, V T varies with r, which is the highest near the wall and zero at the center of the model.

  1. Outlet: At the outlet, the pressure p was set at 1.33 × 104 Pa (100 mm Hg).
  2. The stent and the vessel wall were assumed to be rigid and nonslip.

Changing helicity density for the inlet condition is to serve the second purpose of the study: to determine the minimum effective swirling flow strength for the structure design of a stent with swirling flow.

The boundary conditions for the simulations under pulsatile flow conditions are as follows.

Similar to the studies by Seo et al.11 and Dwyer et al.,32 sinusoidal flow waveforms were used to simulate the flows instead of the in vivo pulsatile flow waveforms.

For the normal flow stent under pulsatile flow condition:

  1. Inlet: The following 1-Hz sinusoidal velocity function was assigned to the inlet
CV

CV

where V in is the axial velocity component at the inlet and V 0 = 0.3 m/s is the time-averaged inlet velocity in one pulse cycle based on a time-averaged Reynolds number of 360.29,30

  1. Outlet: It was set to the outflow condition, i.e., the flow at the outlet was set as a fully developed flow.33
  2. The stent and the vessel wall were assumed to be rigid and nonslip.

For the swirling flow stent under pulsatile flow condition:

  1. Inlet: The axial velocity component V in, the radial velocity component V R = 0 m/s, and the tangential V T.
CV

CV

CV

CV

where again V 0 = 0.3 m/s is the time-averaged inlet velocity in one pulse cycle based on a time-averaged Reynolds number of 36029,30 and V T0 was set to be varied from 0 to 0.04 m/s, the same to the steady flow condition.

  1. Outlet: It was set to the outflow condition, i.e., the flow at the outlet was set as a fully developed flow.31
  2. The stent and the vessel wall were assumed to be rigid and nonslip.

Finite volume method is used in the simulation. As shown in Figure 2, the computational meshes of the models created using the CAD software Gambit 2.2 (ANSYS, Inc., Canonsburg, PA) were all unstructured tetrahedron grids. The commercially available computational fluid dynamics (CFD) code, FLUENT 6.2 (ANSYS, Inc., Canonsburg, PA) was used in the numerical simulation. Discretization of the pressure and momentum at each control volume was in a second-order scheme, and temporal discretization was performed using the second-order implicit time integration scheme. The iterative process of computation was terminated when the residual of continuity and velocity were all less than the convergence criterion 1.0 × 10−5.

Figure 2.

Figure 2.

We used the size function in Gambit and the grid adaptation technique in FLUENT to refine the meshes in the computational domain, especially in areas where the velocity gradient was steep, until the computational results reached grid independence. In this study, the average WSS SYMBOL and the length (L) of the six flow recirculation zones induced by the stents were utilized to asses the grid independence. It showed that grid independence was achieved at 1,100,000-1,200,000 cells for the whole model. Figure 3, A and B shows the differences in the two parameters between the coarser mesh and the finer one when grid independence was achieved.

Figure 3.

Figure 3.

Symbol

Symbol

As for time-step independence, we used 250 time steps per pulse cycle based on the work by Dwyer et al.,32 who found that 240 time steps per pulse cycle could give very good results with high resolution. In this study, the average value of SYMBOL (SYMBOL) over the six disturbed flow zones induced by the stents was used to asses the cyclic independence. The computation showed that cyclic independence was achieved at the 4th cycle. Figure 3C shows the differences in SYMBOL among the 3rd, 4th, and 5th cycles.

Symbol

Symbol

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Results

Steady-State Flow

Flow Patterns.

Figure 4 presents the flow patterns at the positions of S (A-A) and S (B-B) for the normal flow and the swirling flows with different inlet helical strength of the swirling flow under steady-state flow conditions. As evident from the figure, an apparent spiral or swirling flow was created in the swirling flow models. The numerical simulation revealed that when compared with the normal flow model, the swirling flows significantly altered the velocity profiles at both S (A-A) and S (B-B). Different from the flow in the normal flow model, the maximums of the axial velocity profiles shifted away from the tube center. The simulation also revealed that the spiral flows were attenuating progressively along the tube, leading to significant reductions in the strengths of the swirl flows at S (B-B). As the strength of the spiral flow decreased, the maximum axial velocity returned to the tube center at S (B-B).

Figure 4.

Figure 4.

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Effect of Inlet Helicity on the Length of Flow Recirculation Zones in the Stent.

Figure 5, A and B shows the effect of inlet helicity density(H) on the length (L) of the six flow recirculation zones indicated in Figure 1 and their average value (

CV

CV

) in the stent. As evident from the figures, L and JOURNAL/asaio/04.02/00002480-200911000-00004/ENTITY_OV0436/v/2017-07-29T043214Z/r/image-png decreases with increasing inlet H, indicating that swirling flow can indeed suppress the flow disturbance in the stent, and the stronger the swirling flow, the shorter the flow recirculation zones in the stent. The flow simulation also revealed that when the inlet H dropped to 3.5 m/s2, the value of JOURNAL/asaio/04.02/00002480-200911000-00004/ENTITY_OV0436/v/2017-07-29T043214Z/r/image-png had almost no difference with the averaged length of the flow recirculation zones in the normal flow stent.

Figure 5.

Figure 5.

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Effect of Inlet Helicity on WSS in the Flow Recirculation Zones.

Figure 6A shows the effect of inlet H on the average WSS (SYMBOL) in each of the flow recirculation zones. As a comparison, the average WSS in the model artery without stent in place was also calculated for the four different inlet H (Figure 6B). As shown in the figures, the average wall shear stresses in the disturbed flow zones induced by the stent are considerably lower than those in the model artery without stent. The results show that the swirling flow can not only reduce the lengths of the flow recirculation zones, hence suppressing the flow disturbance in the stent, but also enhance the average WSS in each of the flow recirculation zones (Figure 6A). SYMBOL in each of the recirculation zones increases with increasing inlet H. Again, the flow simulation revealed that when inlet H dropped to 3.5 m/s2, SYMBOL in the swirling flow stent had no significant difference with that in the normal flow stent.

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Pressure Drop (Δp) Across the Stent.

Figure 7 shows pressure drops of the stent with swirling flow with different inlet helicity densities. The flow simulation showed that Δp of the stent with swirling flow was 164, 167, and 173 Pa for inlet H = 3.5, 6.5, and 14.5 m/s2, respectively, whereas for the stent with normal flow, Δp was 163 Pa. The flow simulation therefore indicated that though a stent with swirling flow had beneficial effects on hemodynamics of the stent, it could lead to a higher pressure drop across the stent when compared with a stent with normal flow.

Figure 7.

Figure 7.

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Pulsatile Flow

Effect of Inlet Helicity on the Average Value of OSI in the Stent.

Figure 8A shows the local value of oscillating shear index (SYMBOL) in each disturbed flow zone of the stent. SYMBOL was calculated using the method described by Morbiducci et al. 22 and with respect to an area of 0.1 cm2 immediately distal to each ring of the stent. Figure 8B shows the average value of SYMBOL (SYMBOL) over the six disturbed flow zones denoted by P1, P2, P3, P4, P5, and P6,

CV

CV

The pulsatile flow simulation showed that when compared with the flow in the stent under the normal flow condition (H = 0 m/s2), the swirling flow reduced SYMBOL and SYMBOL in all the disturbed flow zones. The higher the H, the higher the reduction in SYMBOL and SYMBOL.

Figure 8.

Figure 8.

Symbol

Symbol

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Determination of Minimum Inlet Helicity

Based on all the results obtained from the flow simulations, it can be concluded that too small H would have almost no beneficial impact on the hemodynamic performance of endovascular stents. For instance, an H of 3.5 m/s2 can only produce approximately 3% reduction in JOURNAL/asaio/04.02/00002480-200911000-00004/ENTITY_OV0436/v/2017-07-29T043214Z/r/image-png with no significant change in SYMBOL when compared with the normal flow stent. Therefore, it has been decided that the minimum swirling flow strength required should be approximately 6.5 m/s2, which can reduce 16% of JOURNAL/asaio/04.02/00002480-200911000-00004/ENTITY_OV0436/v/2017-07-29T043214Z/r/image-png 44% of SYMBOL and enhance 46% of SYMBOL when compared with the normal flow stent. The computation showed that the reduction in helicity from the inlet to the first ring stent was negligibly small because the distance between the inlet and the first ring stent was only 1 mm. For instance, when the inlet helicity was 6.5 m/s2, the helicity at first ring stent was 6.3 m/s2, only 3% reduction in helicity.

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Discussion

Studies have shown that because of the structure of the endovascular stent, blood flow will be inevitably disturbed in the stent.2,25 These disturbed flow zones are always characterized by vortices with low WSS/high OSI and therefore play an important role in the development of in-stent restenosis.6,24 Therefore, eliminating or suppressing disturbed flow zones in a stent might be a solution to the restenosis problem of endovascular stents. But the question now is how to achieve this target with the inherent functional structure of the stent.

In this study, we propose to apply the swirling flow mechanism of the human ascending aorta to the design of the stent to eliminate/suppress the flow disturbance. We believe that in this way, the genesis and development of arterial restenosis might be suppressed. To test this hypothesis, we used a simplified ideal circular ring stent model similar to the one used by Seo et al. 11 and numerically analyzed the flow patterns in the stent.

The numerical study demonstrated that by intentionally creating swirling flow in the stent, the flow disturbance was indeed suppressed and the average WSS in the stent was enhanced with a significantly reduced OSI, depending on the strength of the swirling flow created. The numerical simulation showed that though swirling flows had a beneficial effect on the hemodynamic performance of endovascular stents, the strength of the swirling flow required to suppress the flow disturbance must be larger than a minimal value. The minimal strength of swirling flow required for the present stent model was determined to be 6.5 m/s2.

Now that swirling flow created in an endovascular stent can improve its hemodynamic performance, the question is whether it is feasible to design such a stent with the structure that can not only fulfill the task of a conventional stent but also automatically induce blood flow to rotate in the stent. The work by Seo et al.11 demonstrated that a stent consisting of three successive 360-degree spirals with no rings at its downstream end exhibited the flow characteristics of a helical flow. Their flow simulation showed that with this kind of structure, no flow recirculation occurred in the stent. Therefore, designing endovascular stents with the feature of helical flows is not impossible.

Here, it should be mentioned that the minimal strength of swirling flow required to suppress the flow disturbance in a stent is not a fixed value. It should depend on the structure of the stent concerned. Therefore, the minimum swirling flow strength is a very important parameter that has to be taken into consideration in the design of a swirling flow stent. In addition, the present flow simulation study showed that because of the attenuation in the strength of swirling flow along the stent, its beneficial effect on the hemodynamic performance of the stent was compromised significantly in the distal part of the stent. Therefore, this study indicates that a stent with a build-in structure that possesses intrinsic characteristics to automatically induce swirling flow in the stent is better than a stent with a front swirling flow inducer in terms of hemodynamics.

It should be mentioned that the axisymmetric model used in the study was unrealistic because no commercial stent is purely axisymmetric. Nevertheless, as a preliminary study, the numerical simulation theoretically substantiated our hypothesis and provided us with useful information for the design of swirling flow endovascular stents.

In this article, although it is premature to make a conclusion based solely on a CFD study and animal experiments have to be carried out to validate the swirling flow hypothesis, we have proposed a new direction to improve the performance of the endovascular stent.

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Acknowledgment

Supported by Grants-in-Aid from the National Natural Science Foundation of China (No. 10632010, 30670517, 10772054).

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References

1. Elezi S, Kastrati A, Neumann FJ, et al: Vessel size and long-term outcome after coronary stent placement. Circulation 98: 1875–1880, 1998.
2. Wentzel JJ, Krams R, Schuurbiers JC, et al: Relationship between neointimal thickness and shear stress after Wallstent implantation in human coronary arteries. Circulation 103: 1740–1745, 2001.
3. Morice MC, Serruys PW, Sousa JE, et al: A randomized comparison of a sirolimus-eluting stent with a standard stent for coronary revascularization. N Engl J Med 346: 1773–1780, 2002.
4. Moses JW, Leon MB, Popma JJ, et al: Sirolimus-eluting stents versus standard stents in patients with stenosis in a native coronary artery. N Engl J Med 349: 1315–1323, 2003.
5. Barlis P, Di Mario C: Still a future for the bare metal stent. Int J Cardiol 121: 1–3, 2007.
6. Thury A, Wentzel JJ, Vinke RV, et al: Focal in-stent restenosis near step-up: roles of low and oscillating shear stress. Circulation 105: e185–e187, 2002.
7. Benard N, Coisne D, Donal E, Perrault R: Experimental study of laminar blood flow through an artery treated by a stent implantation: characterisation of intra–stent wall shear stress. J Biomech 36: 991–998, 2003.
8. He Y, Duraiswamy N, Frank AO, Moore JE Jr: Blood flow in stented arteries: a parametric comparison of strut design patterns in three dimensions. J Biomech Eng 127: 637–647, 2005.
9. LaDisa JF Jr, Guler I, Olson LE, et al: Three-dimensional computational fluid dynamics modeling of alterations in coronary wall shear stress produced by stent implantation. Ann Biomed Eng 31: 972–980, 2003.
10. LaDisa JF Jr, Olson LE, Guler I, et al: Circumferential vascular deformation after stent implantation alters wall shear stress evaluated with time-dependent 3D computational fluid dynamics models. J Appl Physiol 98: 947–57, 2005.
11. Seo T, Schachter LG, Barakat AI: Computational study of fluid mechanical disturbance induced by endovascular stents. Ann Biomed Eng 33: 444–456, 2005.
12. Kilner PJ, Yang GZ, Mohiaddin RH, et al: Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping. Circulation 88: 2235–2247, 1993.
13. Houston JG, Gandy SJ, Sheppard DG, et al: Two-dimensional flow quantitative MRI of aortic arch blood flow patterns: Effect of age, sex, and presence of carotid atheromatous disease on prevalence of spiral blood flow. J Magn Reson Imaging 18: 169–174, 2003.
14. Buchanan JR, Kleinstreuer C, Hyun S, Truskey GA: Hemodynamics simulation and identification of susceptible sites of atherosclerotic lesion formation in a model abdominal aorta. J Biomech 36: 1185–1196, 2003.
15. Glagov S, Zarins C, Giddens DP, Ku DN: Hemodynamics and atherosclerosis. insights and perspective gained from studies of human arteries. Arch Pathol Lab Med 112: 1018–1031, 1988.
16. Karino T: Microscopic structure of disturbed flows in the arterial and venous systems and its implication in the localization of vascular diseases. Int Angiol 5: 297–313, 1986.
17. Segadal L, Matre K: Blood velocity distribution in the human ascending aorta. Circulation 76: 90–100, 1987.
18. Frazin L, Lanza G, Mehlman D, et al: Rotational blood flow in the thoracic aorta. Clin Res 38: 331A, 1990.
19. Stonebridge PA, Brophy CM: Spiral laminar flow in arteries? Lancet 338: 1360–1361, 1991.
20. Stonebridge PA, Hoskins PR, Allan PL, Belch JJF: Spiral laminar flow in vivo. Clin Sci (Lond) 91: 17–21, 1996.
21. Uchida Y, Tomaru T, Nakamura F, et al: Percutaneous coronary angioscopy in patients with ischemic heart disease. Am Heart J 114: 1216–1222, 1987.
22. Morbiducci U, Ponzini R, Grigioni M, Redaelli A: Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study. J Biomech 40: 519–534, 2007.
23. Capelli C, Gervaso F, Petrini L, et al: Assessment of tissue prolapse after balloon-expandable stenting: Influence of stent cell geometry. Med Eng Phys 31: 441–447, 2009.
24. Asakura T, Karino T: Flow patterns and spatial distribution of atherosclerotic lesions in human coronary arteries. Circ Res 66: 1045–1066, 1990.
25. Berry JL, Santamarina A, Moore JE Jr, et al: Experimental and computational flow evaluation of coronary stents. Ann Biomed Eng 28: 386–398, 2000.
26. Rhee K, Tarbell JM: A study of the wall shear rate distribution near the end-to-end anastomosis of a rigid graft and a compliant artery. J Biomech 27: 329–338, 1994.
27. Ku DN, Giddens DP, Zarins CK, Glagov S: Pulsatile flow and atherosclerosis in the human carotid bifurcation. Arteriosclerosis 5: 293–302, 1985.
28. Perktold K, Peter R, Resch M: Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm. Biorheology 26: 1011–1030, 1989.
29. Cohen A, Gallagher JP, Leubs ED, et al: The quantitative determination of coronary flow with a positron emitter (rubidium-84). Circulation 32: 636–649, 1965.
30. Ofili EO, Kern MJ, St. Vrain JA, et al: Differential characterization of blood flow, velocity, and vascular resistance between proximal and distal normal epicardial human coronary arteries: Analysis by intracoronary Doppler spectral flow velocity. Am Heart J 130: 37–46, 1995.
31. Utter B, Rossmann JS: Numerical simulation of saccular aneurysm hemodynamics: Influence of morphology on rupture risk. J Biomech 40: 2716–2722, 2007.
32. Dwyer HA, Cheer AY, Rutaganira T, Shacheraghi N: Calculation of unsteady flows in curved pipes. J Fluids Eng 123: 869–877, 2001.
33. Hong J, Wei L, Fu C, Tan W: Blood flow and macromolecular transport in complex blood vessels. Clin Biomech 23: S125–S129, 2008.
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