CHARACTERIZATION OF BLOOD FLOW AROUND A STENTED CORONARY
ARTERY
Cíntia Soares 1
, Adrieli T. O. Dal´Toé
1
, Sérgio R. Janesch
1
, Luismar M. Porto
1
1
Chemical and Food Engineering Department, Federal University of Santa Catarina,
Florinópolis (SC), Integrated Tecnologies Laboratory (Intelab), Brazil
E-mail: {cintia, adrieli, sergio, luismar}@intelab.ufsc.br
Abstract . In the cardiovascular system, altered flow conditions, such as regions of separation and reverse flow have a strong influence on the development of cardiovascular disease. One of the most common diseases is atherosclerosis, which reduces the size of the lumen through a plaque formation and arterial wall thickening.
Traditional treatments were limited to “open heart” surgery until the advent of therapies based on the use of catheters and stents. The stent is defined as an expandable mesh tube (usually of metals, especially nitinol), which is inserted into the artery to treat narrow or weak arteries and to prevent the obstruction of the flow.
Based on these statements, local changes in the flow caused by the presence of a metallic stent were simulated using computational fluid dynamics techniques. The values of shear stresses at the implant site were evaluated since there is a direct relationship between restenosis (reoccurrence of the initial injury) and this characteristic parameter of the flow. Different geometries have been defined in order to verity the effects of the stent strut spacing on the flow patterns adjacent to the artery. The results showed that the stents generate a complex flow pattern at the implant site. The presence of the stent also has a strong implication in the value of shear stress near the strut. These low values are associated with a thickening in the arterial wall and are the main cause of restenosis, which is common in about 30% of cases of stent implantation.
Key-words: Stent, Coronary artery, Shear stress, Restenosis.
1. INTRODUCTION
Coronary artery disease occurs due to the build up of plaque in the coronary arteries which supply fresh blood to the constantly active heart muscle [Murphy and Boyle, 2006], especially in regions of separation and reverse flow. The plaque is known as atherosclerosis, a common disorder of the arteries, characterized by accumulation of cells, lipids, connective tissue, calcium, and other substances inside the inner lining of the arterial wall, resulting in the arterial wall thickening [Kious, 2008].
Atherosclerosis has the propensity to occur in arteries bifurcations involving the outer edges of the vessel [Malek, Alper and Izumo, 1999] and is directly affected by hemodynamics factors. In these areas, the blood flow presents low levels of wall shear stress with high levels of oscillating amplitude, hypothesis proposed by Caro et al . [1971 apud Chaniotis et al ., 2010, p. 2], and validated by subsequent studies [Zarins et al ., 1983; Asakura and Karino, 1990;
Bharadvaj, Mabon and Giddens, 1982; Motomiya and Karino, 1984].
Traditional treatments were limited to “open heart” surgery, the most invasive procedure, until the advent of therapies based on the use of catheters and stents, considered minimally invasive techniques. The stent is defined as an expandable mesh tube with the priorities functions to holds the artery open, preserving the lumen cylindrical [Frank, Walsh and Moore, 2002], and restore the blood flow, in order to suit perfusion to the cardiac tissue.
However, the interaction between stent-strut and artery cause injuries in the vessel wall,

contributing to neointimal growth, phenomenon known as restenosis [Garasic et al ., 2000], which is straight related with stent design [LaDisa et al ., 2005]. Restenosis has a considerable recurrence in patients of about 10% to 30%, requiring new revascularization procedures
[Centemero et al ., 2004].
The aim of this study was to assess local changes in the flow caused by the presence of a metallic stent making use of computational fluid dynamics (CFD) models. The values of shear stress at the implant site were evaluated since there is a direct relationship between restenosis and this characteristic parameter of the flow. Different geometries have been defined in order to verity the effects of the stent strut spacing on the flow patterns adjacent to the artery. All the studies were carried out on COMSOL Multiphysics
®
4.3.
2. METHODOLOGY
A free model stent provided by the project available in Open Stent Design
[Bonsignore, 2012] was taken as model for the simulations. As an open design, with copyleft license, modifications in drawings could be done in order to study the influence of altered designs in the flow profile. The differences in each stent design are presented in Table 1 and
Fig. 1.
Table 1 – Differences between the stent geometries.
Variables
Columns
Struts
Bridges
Stent A
6
12
2
Stent B
6
18
3
Stent C
6
24
4
Figure 1 - Models of stents used in the numerical evaluation.
The simulations were implemented on a stented coronary artery using a 2D - axisymmetric domain for the geometries presented in Fig. 1. The aim was to investigate the effects of the stent struts on the flow pattern, considering velocity and pressure fields and shear stress profile. To better visualize the results, a standard domain representing the artery without the stent was add to the simulations.

Stent A Stent B Stent C
Figure 2 – Physical domains considered in the simulations.
Standard
The blood properties and flow parameters needed to the problem implementation in
COMSOL Multiphysics

4.3 are presented in Table 2. The artery diameter was obtained based on studies carried out by Funabashi et al . (2003) and Dodge et al.
(1992), whereas the blood properties were taken from Frank, Walsh and Moore (2002). The maximum velocity in the coronary artery at peak of systole was available in Chuchard et al . (2011).
Table 2 - Physical parameters used in the simulation.
Parameter Value
Artery diameter (mm)
Blood density (kg
 m
-3
)
Viscosity (Pa
 s)
Maximum velocity (m
 s -1 )
3.5
1,055
0.0035
0.29179
The mathematical model used was a single-phase model, presenting a laminar flow and steady-state condition. Blood was treated as an incompressible, homogenous and
Newtonian fluid. The transport equation involved in the model to predict the flow in the stented coronary artery can be written as follows:

Mass conservation equation: 𝜌∇ ∙ 𝐮 = 0

Momentum conservation equation: 𝜌(𝐮 ∙ ∇)𝐮 = ∇ ∙ [−𝜌𝐈 + 𝜇(∇𝐮 + (∇𝐮) 𝑇 )] + 𝐅
(1)
(2)

where ρ is the density (Kg.m
-3 ), u is the velocity field (m.s
-1 ), I is a 3x3 identity matrix, µ is the dynamic viscosity (Pa.s) and F are the body forces field (N).
In this study, the vessel was considered being rigid, hence the wall and stent are not moving due to the heart contraction. Thus, the no-slip boundary condition was specified at the vessel wall and at the struts. The effect of the fluid-structure interaction was not taken under consideration as the aim was to analyze the behavior of flow near the struts. The remaining boundaries conditions were constant pressure as outlet, and a parabolic blood velocity profile
(Fig. 3) as inlet condition. As the condition of symmetry is being used, only a half of the velocity curve is used in the inlet. The software uses a finite element analysis to solve equations, satisfying conservation of mass and momentum.
0,3
0,25
0,2
0,15
0,1
0,05
0
0 0,5 1 1,5
Radius (mm)
2 2,5 3 3,5
Figure 3 - Velocity profile of blood flow in a coronary artery.
3. RESULTS AND DISCUSSION
3.1 Velocity Profile
The velocity profile, represented by Fig. 4, shows the behavior of the blood flow in the presence of a stent. When contrasting the stented cases and the standard, a deviation of the laminar velocity layers was noticed as the flow reaches the stent struts. It is possible to observe that for Stent A, this disturbance was greater, being lower in Stent B and even more in C. Another analysis that can be made in Fig. 4 is that the enlargement of the spacing between the struts effectively reduces the disturbance experienced by the flow.
The flow patterns can be deeper investigated visualizing the flow streamlines, presented in Fig. 5 for all cases analyzed. The flow field in the vicinity of the struts demonstrated the presence of stagnation zones localized in the regions upstream and downstream of the struts, where the velocity is a small fraction of the velocities found in a distance above the struts, where their influence is not significant. This stagnation zones are higher forward the strut and smaller afterward for all the stent cases. In other words, the stagnation zones magnitude depends on the flow direction, which is upwards. This flow behavior was also obtained by Berry et al . (2000).

Stent A Stent B Stent C
Figure 4. Velocity profile for each stent.
Stantard
Stent A Stent B
Figure 5. Flow streamlines for each stent.
Stent C
As can be seen, the disturbance suffered by the flow is directly related with the stent geometry. Depending on the width and height of the strut, stagnation zones appear bigger or smaller.

3.2 Pressure
The pressure drop along the stented artery is showed in Fig. 6. The pressure drop for the standard was obtained using the same conditions as for the stented cases. Comparing the results, it can be seen that exists a pressure drop in stented cases.
Stent A Stent B Stent C Standard
Figure 6. Pressure drop along the stented section.
Normal coronary arteries provide no resistance to blood flow. Therefore, optimum coronary stenting should at least result a minimal pressure drop within the respective coronary segment. Also, the presence of a persistent pressure gradient across the stented segment indicates an abnormal blood flow pattern with heterogeneous and abnormal low shear stress [Pijls et al ., 2002].
3.3 Shear Stress
From the velocity fields, the shear stress distribution was computed. The results, presented in Fig. 7, showed that wall shear stress (WSS) distribution was sensitive to stent strut spacing, as obtained by Dehlaghi, Shadpoor and Najarian (2008). In all the simulations, excepted for the standard, lower WSS values were localized between the wires, very close to vessel wall, independent of the strut width, thickness, number, or stent-to-vessel diameter ratio. In contrast, the highest WSS values were noticed over the surface of stent struts, as observed by Murphy and Boyle (2006) and Sanmartín et al . (2006). The standard case presented a higher WSS along the vessel, and thereby, it can be seen the magnitude of the stent influence on the hemodynamic conditions in the artery.

Stent B Stent A Stent C Standard
Figure 7. Shear stress distribution.
Figure 8 shows an enlargement of shear stress distribution presented on Fig. 7 in order to enable an accurate view of this parameter near the struts. A comparison between the cases shows that the increase in strut-strut spacing tends to smooth the variation in shear stress next the vessel wall. In summary, the change in face structures creates changes in the shear stress field indicating that the number, width, and thickness of stent struts cause distinctive patterns of WSS, as obtained by Ladisa Jr et al . (2003). Hence, the difference of shear stress field is particularly obvious between the input area of stent and the stagnation zones related to the stent geometry [Bénard, Coisne and Perrault, 2001].
Stent A Stent B
Figure 8. Shear stress distribution enlargement.
Stent C

As mentioned, stagnation zones appearance is directly related to the strut geometry. In this case is not different, as the shear stress is very small near the wall. So it can be concluded that small shear stress and stagnation zones are related, and both contribute to thrombus accumulation by inhibiting the removal of platelets and others substances from the wall
[Berry et al., 2000]. This fact backs to the issue of restenosis that limits the efficiency of the artery stenting in long term.
An evidence of the WSS influence in the cellular proliferation is the in vivo human model study developed by Sanmartín et al . (2006) that found there is a negative correlation between wall shear stress and neointimal growth. In other words, regions with lowest values of WSS presented higher degree of cell proliferation.
The study presented demonstrated the importance of understanding the factors involved in hemodynamic alterations occurred due to the stent presence in the artery. The determination of the flow patterns disturbances related to a given stent is crucial to the optimization of stent design and stent-placement protocols, as well as to limit vascular injury and perhaps reduce restenosis [Rogers et al ., 1999].
As can be seen, arteries are living organs that can adapt to and change with the varying hemodynamic conditions. According to Glagov et al . [1988 apud Ku, 1997, p. 417] decreased flow rates, presented in stagnation zones, as well as, lower WSS, will cause the intimal layer to thicken to reestablish a normal wall shear stress.
4. CONCLUSION
Computational tools are useful to predict, when there is not enough data available, or verify, when an experimental data exists, the behavior of a physical issue. In this case, the local hemodynamic and flow pattern, changed due to the presence of stent, were qualitatively provided by computational fluid dynamics, and the results were consistent with the studies available in the literature.
A disturbance of normal blood flow in an artery occurs in the presence of the stent.
What determinates the magnitude and significance of this disturbance is the geometry of the stent, since the blood properties do not change. The existence of lower shear stress near the arterial wall was verified, which contributes to restenosis, a problem that still achieves a high proportion of treated patients.
Thus, it is understood that such investigations are important because it is possible to optimize the stent design in order to minimize effects on the flow, avoiding health problems such as restenosis.
5. ACKNOWLEDGEMENTS
The authors acknowledge financial support from FAPESC (Fundação de Amparo à
Pesquisa e Inovação do Estado de Santa Catarina) and CAPES (Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior).
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