Numerical Simulation of Vertebral Artery Stenosis Treated With Different Stents AJke Mem. ASME CoHege of Life Science and Bio-engineering, Beijing University of Technology, Beijing 100124, Cfiina e-maii: [email protected]

Zhanzhu Zhang Coilege of Life Science and Bio-engineering, Beijing Universify of Technoiogy, Beijing 100124, China e-maii: [email protected]

We sought to investigate the effects of endovascular stents with different ¡inks for treating stenotic vertebral arteiy and to determine the relationship between the shape of the link and in-stent restenosis (ISR). We also attempted to provide scientific guidelines for stent design and selection for clinical procedures. Models of three types of stent with different links (L-stent, V-stent, and S-stent) and an idealized stenotic vertebral artery were established. The deployment procedure for the stent in the stenotic vertebral artety was simulated for solid mechanics analysis. Next, the deformed models were extracted to construct the blood flow domain, and numerical simulations of the hemodynamics in these models were peiformed using the finite element method. The numerical results demonstrated that: (1) Compared with the L-stent and V-stent, the S-stent has a better fiexibility and induces less stress in the stent strut. Furthermore, less stress is generated in the arterial wall. (2) Vascular straightening is scarcely infiuenced by the shape of the link, but it is closely related to the flexibility of the stent. (3) The S-stent has the smallest foreshortening among the three types of stents. (4) Compared with the V-stent and S-stent, the L-stent causes a smaller area with low wall shear stress, less blood stagnation area, and better blood flow close to the artery wall. From the viewpoitit of the combination of solid mechanics and hemodynamics, the S-stent has better therapeutic effects because of its lower potential for inducing ISR and its better prospects in clinical applications compared with the L-stent and V-stent. [DOI: 10.1115/1.4026229] Keywords: endovascular stent, in-stent restenosis, stent intervention, hemodynamics, numerical simulation

1

Introduction

The extracranial vertebral arteries have been found to be the most common sites of stenosis or occlusion (43.5%), especially the artery ostium [1,2] Stenting technology has emerged as an effective altemative for treating arterial stenosis, which recovers blood fluency through a mechanical scaffold using struts. Although stent implantation is an effective approach to treat stenosis in the vertebral artery, postoperative in-stent restenosis (ISR) remains a major challenge, with the occurrence rate reaching 67% [3,4]. Medical doctors also refiect that the occurrence rate of ISR is larger at the vertebral artery ostium than any other locations according to their clinical follow-up observation and statistics. From the viewpoint of solid mechanics, the artery is subjected to long-term pressure by the stent strut after the intervention, leading to extemal mechanical force acting on the artery. Straightening, mechanical stress, and stress concentration cause extreme in-stent intimai hyperplasia, which, consequently, induce ISR [5-9]. Different types of endovascular stents cause varying degrees of injury to the artery wall, inducing different ratios of ISR [10,11]. Therefore, the design of the stent structure has a significant influence on the therapeutic effect of stent intervention. From the viewpoint of hemodynamics, the hemodynamic environment is changed to a certain extent after stenting; as a result, the local blood flow is changed greatly. Vortex and low Wall Shear Stress (WSS) occur, promoting thrombosis and intimai hyperplasia, which induce ISR more easily [12-15]. The finite element method is widely used in the biomechanical field and is also considered to be a convenient and effective tool 'Corresponding author. Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received July 23, 2013; final manuscript received December 6. 2013; accepted manuscript posted December 12, 2013; published online March 24, 2014. Assoc. Editor: Dalin Tang.

Journal of Biomechanical Engineering

for investigating stent designs. To study the factors that affect ISR and to test and improve stent designs to minimize ISR, solid mechanics simulations of a stent deployed in the artery were studied [8,9,16-20], as well as hemodynamic simulations in the stented artery were investigated using computational fluid dynamics (CFD) methods [12-14,21-25]. However, those studies evaluated stent designs only from the point of view of solid mechanics or hemodynamics, while the assessment of stent designs from the point of view of solid mechanics and hemodynamics combined has rarely been studied. Numerical simulations of solid mechanics and hemodynamics are performed in this study. The solid mechanics simulation provides the boundary condition for the hemodynamics simulation. These simulations combine the boundaries of the stent, the plaque, and the blood in the vertebral artery treated with three types of stents with different links. The effects of stents with different shapes of links on the treatment of stenotic vertebral artery are analyzed comparatively, and the relationship between the shape of the link and ISR is explored in view of the combination of solid mechanics and hemodynamics. This work will provide scientific guidelines for the selection of a stent, the design of the stent structure, and a clinical procedure of stenting. 2

IMethod

As an elementary study, idealized models of stenotic vertebral artery and three types of stent are established using Pro/Engineering (Fig. 1). The geometric model of a vertebral artery is constructed based on anatomical and physiological parameters, including the stenotic vertebral artery and the subclavian artery with a physiological geometry of curvature and taper. The intemal diameter of the proximal end of the subclavian artery, the intemal diameter of the distal end of the subclavian artery, and the intemal diameter of the proximal end of the vertebral artery are

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APRIL2014, Vol. 136 / 041007-1

Vertebral arterty

L-sísut

V-stetit

Fig. 2 The blood flow boundary surface reconstructed with the deformed surfaces of the deployed stents and arteries

S-stmt

Fig. 1 Models of the artery (left) and the stents (right) 5.6 X lO""* m, 4.12 x 10"^ m, and 3.6 x 10^^ m, respectively, and the arterial wall thickness is 0.3 x 10"^ m. There is a moderate stenosis in the vertebral artery ostium, and the plaque is simulated using j8-spline. The maximum thickness of the plaque is 1/3 the internal diameter of the vertebral artery, so the minimum intemal diameter of the stenotic vertebral artery is 2.4 x 10^"^ m, and the stenosis ratio is 66.7%. There are two kinds of typical stents: One is a balloon-expanded stent and the other is self-expanded. A balloon-expanded stent is employed in the study while the balloon is ignored in the model. The balloon action is replaced with a uniform radial deformation of stent strut/link for the sake of simplifying the simulation. The three types of stents are L-stent, V-stent, and S-stent, according to the different sliapes of the link. The stents have the same strut dimensions, with the only difference being the shape of link. Before the deployment, the length of the stent is 11.5 x 10"^ m, and the external diameter is 2.24 X 10"' m; the width of the strut is 0.14 x 10"^ m, the thickness of the strut is 0.12 x 10"^ m, and the span tietween the stmts The stent porosity is defined as Eq. (1) [26] pf(w\

'^free

-^total

'

= 1

(1)

where /4fjee is the area of porous region not covered by the stent wire, Ajevice is the area covered by the stent v/ire, and A,o,ai is the total area of the surrounding cylinder. The porosities of the L-stent, V-stent, and S-stent are 74.3%, 72.1%, and 70.4%, respectively. The expansion procedure of stent inside the artery is mimicked using the commercial tool ABAQUS. The material properties of the models chosen in this study are taken from the literature. The specific parameters are presented in Table 1 [27]. The boundary conditions for solid mechanics simulations are defined as follows: The ends of the subclavian artery are fully constrained, and the proximal end of the vertebral artery is free; the end of the stent near the vertebral artery ostium is constrained to allow for only

Table 1 Composition Material Element Model of material Elasticmodulus (GPa) Poisson's ratio Yield strength (GPa)

041007-2 / Vol. 136, APRIL 2014

radial deformation, and the other end of the stent is free; the contact pairs are the intemal surface of the artery and the extemal surface of the stent, and the friction factor is 0.2 based on the Coulomb friction model; the uniform displacement is loaded on the intemal surface of the stent [7-16], which would cause the stent to radially expand to twice its initial diameter. Next, the displacement is unloaded, which leads to the interaction and balance between the stent and the artery [10]. The solid mechanics analysis of stent expansion is performed using ABAQUS/Standard. The deformed meshes of the deployed stents and arteries are extracted and used to obtain the deformed surfaces of the deployed stents and arteries. These deformed meshes are saved in.inp files that can be imported into a package tool Hypermesh. Then the surface models of deformed stent and vessel can be reconstructed by using Hypermesh and saved in.igs files that are imported into a package tool Geomagic. The surface models are repaired by using Geomagic so as to form the complete and close surface models. Boolean operation of the deformed surfaces of the stents and arteries is carried out in the package tool Geomagic so as to obtain the blood fiow boundary surface. The boundary surface is imported into a package tool ICEM and filled to be the flow field (Fig. 2). The flow domain is discretized and the finite element model for hemodynamics simulation is obtained. The boundary conditions for hemodynamics simulations are as follows. The blood is assumed to be incompressible and Newtonian, and the wall is rigid satisfying no-slip conditions. The proximal end of the subclavian artery is the inlet of the blood fiow, and the distal ends of subclavian and vertebral artery are the outlets of the blood flow. Figure 3 shows the axial velocity waveform at the inlet [28]. The outlet boundary condition is the opening where the average pressure is assumed as zero. Actually, the real mean pressure cannot be zero. However, this zero assumption is widely employed in CFD simulations as it should not influence the flow results. The period of iterative computation is arranged to be two cardiac cycles of 1.6 s, which avoids the influence of any initial inaccuracy on the numerical results, and the time step in each iteration is assumed to be 0.01 s. The residual convergence is designated as 10^*. The hemodynamics simulations are performed using ANSYS-CFX.

Material properties

S¡tent

Artery

Plaque

304 stainless steel C:iD8R Bilineanty, isotropy 193 0.27 0.207

Calcified plaque C3D4 Linearity, isotropy 0.00175 0.499

Calcified artery C3D4 Linearity, isotropy 0.00219 0.499

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0.6

Î

:

0.5

Table 3 Number of elements and nodes for the solid mechanics simulations

;

t

0.4

Model

0.3

L-stent V-stent S-stent Vertebral artery

- • • •

;

• • • ;



• - •

0.1 -í

-0.1 -

Element number

Node number

9094 9674 10,722 264,325

18,861 20,271 22,185 65,383

• " • • • • • ' — " •

Table 4 Mesh independence analysis for the fluid mechanics simulations 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

t(s) Fig. 3

Element number of L-stent model Computation time Peak velocity of blood flow Relative error of blood flow velocity

Inlet velocity waveform

Meshl

Mesh 2

Mesh 3

2,108,921 10 h 1.104m/s -

3,267,094 17 h 1.223m/s 17.4%

4,681,359 27 h 1.232m/s 0.7%

Table 5 Number of elements and nodes for the fluid mechanics simulations Model

Element number

Node number

L-stent V-stent S-stent

3,267,094 3,259,040 3,299,827

653,572 652,917 663,578

After stent expansion

Before stent expansion

Fig. 4 Meshes for the solid mechanics simulation (left: local view of the stent and stenosis) and the hemodynamics simulation (right: local view of the cross section of stented lumen) Table 2 Mesh independence analysis for the solid mechanics simulations

Element number of L-stent Element number of vessel Computation time Peak stress of stent Relative error of stent stress Peak stress of vessel Relative error of vessel stress

Mesh 1

Mesh 2

Mesh 3

9094 143,673 6h 378 MPa _ 1.285 MPa -

15,107 264,325 15h 381 MPa 0.7% 1.306 MPa 1.6%

28,912 488,721 34 h 383 MPa 0.5% 1.309 MPa 0.2%

For the solid mechanics simulation, the stents are discretized using an eight-node reduced integration hexahedron element C3D8R, and the artery is discretized using a four-node tetrahedron element C3D4 (Fig. 4, left). For the hemodynamics simulation, prism and tetrahedron elements are employed for the mesh generation. To improve the computational accuracy of hemodynamics simulation, three layers of meshes are generated in the boundary layer near all of the walls (Fig. 4, right). The mesh independence analyses are performed using several trials of different element size. Table 2 shows the mesh independence analysis for the solid mechanics simulations. Finally, mesh 1 is selected for the numerical simulation because the relative error between mesh 1 and mesh 2 is very small. Table 3 shows the number of elements and nodes for the solid mechanics simulations. Similarly, Table 4 shows the mesh independence analysis for the hemodynamics simulations. Finally, mesh 2 is selected for the numerical simulation because the relative error between mesh 2 and mesh 3 is very Journal of Biomechanical Engineering

Fig. 5 Straightening of the artery small. Table 5 shows the number of elements and nodes for the hemodynamics simulations. The artery is more flexible than the stent, so a curved artery is straightened because of the stent implantation in the artery. The displacement of the middle point of the distal section of the vertebral artery could indirectly indicate the straightening of the artery, as presented in Fig. 5. The axial length of the stent will foreshorten during radial expansion. This behavior could be described as foreshortening, as determined by Eq. (2) APRIL2014, Vol. 136 / 041007-3

Befare stent expansic« ^Añtt stent expansicai Fig. 6

Foreshortening of the stent

Lo

• X 100%

(2)

where LQ is the initial length, and L is the deployed length (Fig. 6). Both the straightening of the artery and the foreshortening of the stent will be used to exhibit the results of solid mechanics simulations.

3 Results 3.1 Results of Solid Mechanics Simulations. Figure 7 shows the contours of the strain in the vessel wall. Th(; contours of the Von Mises stress are quite similar (not shown). T'he peak strain of the artery caused by the L-stent, V-stent, and S-stent are 0.575, 0.566, and 0.541, respectively. The peak stress of the artery caused by the L-stent, V-stent, and S-stent are 1.304 MPa, 1.226 MPa, and 1.059 MPa, respectively. The i)eak strain/stress caused by the three types of stent locates on the plaque at the outer bend of the artery (the left side of the vertebral artery pointed out with arrow in Fig. 7). The extent of the stent embed in the artery increases as the strain increases in the artery, so the potential for injury to the endothelial cells caused by stenting may be increased, which raises the risk of ISR [10]. The plaque is apt to rupture because of the higher stress and highei- strain, possibly causing vascular occlusion and even inducing stroke. The difference of stress between the L-stent and S-stent is ( 1.304 - 1.059)/ 1.304= 18.8%, and the difference of stress between the V-stent and S-stent is (1.226 - 1.059)/1.226= 13.6%. These differences will be enough potential to cause injury with the L-stent and V-stent. Therefore, compared with the L-stent and V-stent, the S-stent has a better therapeutic effect becaustt

(te« n%)

L-Steiit Fig. 7

v-stent

S-steat

Contours of the strain in the vessei waii (the arrow marks the location of the maximum vaiue)

041007-4 / Vol. 136, APRIL 2014

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Fig. 8 Contours of Von iVIises stress (ieft), axiai stress (middie), and circumferentiai stress (right) in tiie L-stent (first row), V-stent (second row), and S-stent (tiiird row) (the arrow marks the iocation of the maximum vaiue) flow fluency in a stenotic vessel by the mechanical support of a stent strut, and it has become an effective procedure for the treatment of stenosis. Table 8 shows the time-averaged mass flow rate in the vertebral artery in different models. The mass flow rates of Tabie 6 Dispiacement of the middle point of the vertebral distai end 1

Vertebral artery

Displacement (mm)

L-stent V-stent S-stent

1.41 1.38 1.36

Table 8 Time-averaged mass flow rate in the vertebral artery ¡n different models

Table 7 Foreshortening of stents Stent L-stent V-stent S-stem

Initial length L,, (mtn)

Deployed length L (mm)

Foreshortening (%)

11.5 11.5 11.5

9.37 9.82 10.04

18.5 14.6 12.7

Journal of Biomechanical Engineering

the L-stent model, V-stent model, and S-stent model are increased 39.75%, 36.26%, and 33.24%, respectively compared with the unstented model. The flow rate in the vertebral artery markedly increases after stent intervention and, hence, improves the blood supply for intracranial arteries; it also decreases the probability of cerebral ischémie stroke. Figure 9 shows the contour of the WSS at the peak velocity, using scales of 0-10 Pa (Fig. 9, upper row) and 0-30 Pa (Fig. 9, lower row) for the sake of illustrating the contour clearly. The lower WSS is located mainly in the region around the struts and links of the stent, while the higher WSS is located in the middle region of the mesh of the stent, where tissue prolapsed into lumen, causing a reduction in the cross-sectional area of the lumen. In

Models Time-averaged mass flow rate Q (ml/s)

Unstented model

L-stent model

V-stent model

S-stent model

0.648

0.906

0.883

0.864

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S-stent

Fig. 9 Contours of the WSS using a scaie of 0-10 Pa (upper) and using a scale of 0-30 Pa (lower)

Table 9 The area ratio of the TAWSS distribution on the artery wall near the stent WSS 0-0.4 Pa

L-stent (%)

V-stent (%)

S-stent (%)

29.86%

33.24%

35.01%

particular, the highest WSS is located in the stenotic region, and this is mainly due to the abrupt decrease in tne cross-sectional area of the lumen. To more easily compare the hemodynamic effect of the different shapes of the link, a parameter is introduced that is designated as the area ratio of time-averaged WSS (TAWSS), which is written as Eq. (3)

— x 100% So

(3)

where S is the area of low TAWSS, with a range between 0-0.4 Pa, and So is the area of the TAWSS in the whole range. Table 9 shows the area ratio of the TAWSS distribution on the artery wall near the stent. The area ratio of low TAWSS caused by the S-stent is 35.01%, and that caused by the L-stent was 29.86%. The area ratio caused by the S-stent is the highest, and the area ratio caused by the L-stent is the lowest, with a difference between these two area ratios of 5.15%. The difference between the S-stent and the L-stent is significant from the viewpoint of the area ratio difference. The low TAWSS, specifically the range between 0-0.4 Pa, could induce ISR. The greater the area of low TAWSS, the greater the possibility for increasing the potential of inducing ISR. From this point of view, compared with the V-stent and the S-stent, the L-stent has a better hemodynamic effect, and it has a better clinical application. Figure 10 shows the distribution of the oscillatory shear index (OSI) on the vessel wall. OSI ranges from 0 to 0.5 and denotes the oscillatory change of flow direction. High OSI means violent oscillation of flow direction, which is closely related with the

1.4S M 0.02. 0.015. 0.01.

9.»

'•••••-ï^Wc•••••-I

g - . -

O.OOS.

0. J005. .0.01-

*015

L-stent

V-stent Fig. 10

041007-6 / Vol. 136, APRIL 2014

^^^....^^ .002 .0.02

.0.01

S-stent

Contours of OSI distributed on the vessel wall Transactions of thie ASiUIE

Table 10 The area ratio of OSI in five different ranges OSI

L-stent

V-stent

S-stent

0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5

80.97% 9.68% 4.84% 3.80% 0.71%

80.20% 9.96% 5.16% 3.83% 0.85%

80.27% 9.79% 5.29% 3.87% 0.79%

genesis of intima] hyperplasia and thrombus in the vessel lumen. This may induce the injury of endothelium cells and the cyclic stress change acting on cell structure [29], which correlates with the initiation and development of ISR [14]. Figure 10 demonstrates that high OSI locates at the vicinity of the stent wire where the blood flow direction oscillates more violently. The vicinity of stent wire is the region with not only high OSI but also low WSS. Studies have shown that low WSS and high OSI are prone to induce intimai hyperplasia and ISR [14]. In addition, more vortices appear in the vicinity of stent wire and, hence, result in flow separation and reversion, slow down the blood flow in this area, prolong the residence time of blood cells and low density lipid, enhance the development of plaque, and promote the initiation and development of ISR. Table 10 illustrates the area ratio of OSI in five different ranges. More attention should be paid to the high OSI values of 0.4-0.5 since high OSI is closely related with intimai hyperplasia and thrombus. Compared with the V-stent and S-stent, the L-stent features less area ratio of high OSI. Thus, the L-stent can reduce the probability of intimai hyperplasia and thrombus and, hence, reduce the probability of ISR. Flow pattems in the proximity of the stent show that, compared with the L-stent, the links for the V-stent and the S-stent have a transverse structure, which results in a blocking effect on blood flow. Blood flow hardly exists in the region close to the artery wall between the strut and the litik or between the links. Therefore, the blood stagnation zone, as well as low WSS, occurred in that region, increasing the stagnation time for toxic substances in the blood. Moreover, a vortex appears in the L-stent between two struts, while two vortices appear in the V-stent and the S-stent. A vortex could cause flow separation, low WSS, and a blood stagnation zone, which would induce stagnation of toxic substances, such as hemocytes, lipids, etc. Compared with the V-stent and S-stent, the L-stent has better blood flow pattems close to the artery wall. It, therefore, could decrease the potential possibility of inducing ISR from a hemodynamic viewpoint.

because of the interactions mentioned above. When the direction of the curvature was changed to just the reverse as that of the numerical simulation of Wu et al., the peak stress appeared in the inner curvature of the artery. It follows that the effect of the branch on the artery is more prominent and visible than the effect of the curvature of the artery. Therefore, compared with deployment in a simple curved artery, the deployment of the stent in a curved artery with a branch is more complex and is of more significance. An artery will be straightened during the implantation of a stent, and a compliance mismatch is induced between the stenotic artery where the stent is implanted and the normal arteries at the two ends of the stenotic artery. Compared with a stenotic artery with plaque, an artery at the end of a stent is moreflexible,and the most serious compliance mismatch between the artery and the stent appears at the ends of stents, where significant stress concentration occurs and the curvature of the artery changes abruptly. Therefore, the artery experiences a higher degree of stimulation due to contact with the foreign body than in other regions [21]. Thus, the stent is prone to induce ISR. Apparently, both the straightening and compliance mismatch are closely related to the flexibility of a stent. The flexibility should be fully taken into account when designing a stent, especially considering the ends of the stent. For this purpose, the shape of the link can be gradually changed from the middle to the ends of stent and the opened and closed loop of the stent mesh can be combined in the stent structure. The above-mentioned considerations for stent design may lead to a gradual transition in the flexibility from the middle to the ends of the stent, which could be more effective for preventing ISR.

If the foreshortening of the stent is greater, the axial deformation will also be greater. With greater axial deformation, the relative displacement between the stent and the artery is greater, increasing the potential possibility of injury to artery wall. In addition, plaques with irregular shape and size may be randomly scattered on the artery wall [30], and some plaques may prolapse into the mesh of stent. In the deployment of a stent, when relative movement between the stent and the artery occurs, plaques that have prolapsed into the mesh may be denudated by the stent. The greater the relative displacement between stent and artery, the greater the potential possibility of denudation of the plaque by the stent and, therefore, the greater the risk of stroke. With an increase in the number of plaques denudated, the injury to the artery is greater, and ISR will be more likely to occur. Therefore, compared with the L-stent and the V-stent, the S-stent is a better interventional treatment option for the prevention of ISR. In addition to straightening, blood flow changes greatly because of the implantation of the stent in the view of hemodynamics. A stent with a certain thickness protrudes into the arterial lumen, 4 Discussion forming a step shape on the artery wall. Thus, step flow occurs, The results in the present study show that the peak stress on an significantly influencing the blood flow near the artery wall [31], artery caused by a stent appears in the outer curvature of the ar- inducing low WSS, vortex and flow separation and damaged nortery, which is opposite the results reported by Wu et al. [9], where mal laminar blood flow close to the artery wall. The blood flow the peak stress appeared in the inner curvature of the artery. Com- velocity is extremely low near the artery wall, leading to increased pared with the numerical simulation by Wu et al. [9], the present stagnation time of toxic substances in blood, where ISR initiates study is similar in certain respects, such as the boundary condi- frequently [15]. Friction and collision between the blood cotpustions of the model and the simulation process of stent deployment. cle and endothelial layer occur because of the damage to the norHowever, the present work differed with regard to thefiniteele- mal laminar flow near the artery wall, increasing the platelet ment analysis software used and the artery model. Wu et al. activity and platelet adhesion and aggregation, which promote used ANSYS as the finite element analysis software [9], while thromtDosis. Furthermore, the endothelium is more likely to prolifABAQUS was used in the present study. Theoretically, the result of erate in a low WSS region, leading to intimai hyperplasia. Extennumerical simulation may be slightly influenced by thefiniteele- sive or local intimai hyperplasia causes arterial remodeling, which ment analysis software. The opposite results may be closely promotes the occurrence and development of ISR [15-32]. related to different artery models. The artery model established by The result of hemodynamics simulation indicates that the Wu et al. was a simple curved artery, while the artery model in hemodynamic effect of the L-stent is better. Compared with the the present study was a complex curved artery with a branch. In L-shaped link, links with a V-shape and an S-shape have a transthe process of stent deployment, the interaction between the stent verse structure, which has a blocking effect on blood flow and and artery occurs not only in a curved artery but also in the generates large regions of low WSS. It has been well accepted branched artery. The greatest extent of the interaction between the that low and oscillating WSS correlate positively with intimai stent and artery appeared in the outer curvature of the artery thickening and atherosclerosis progression [33]. Thus, the area of Journal of Biomechanical Engineering

APRIL2014, Vol. 136 / 041007-7

low WSS distribution caused by the L-stent is smaller, reducing the region of thrombosis and intimai hyperplasia, decreasing the potential for ISR. Moreover, there is less blood fiow stagnation and vortex caused by the L-stent, indicating that blood flow near the artery wall is related to the span between the strut and the link to a certain extent. As a result of the reduced stagnation zone and vortex, it is possible to reduce platelet adhesion and aggregation, which could effectively restrain thrombosis and decrease the potential possibility of ISR. Therefore, compared with the V-stent and S-stent, the L-stent is a better option for interventional treatment and prevention of ISR. However, the step effect of a stent only contributes to the preliminary stage of stenting because the stent will be covered by endothelial cells after two or three weeks. A long-term mechanical effect of stent scaffolding would exist because of the existence of the stent. Thus, from the viewpoint of the combination of solid mechanics and hemodynamics, the S-stent has better therapeutic effects because of its lower potential for inducing ISR and its better prospects in clinical applications compared with the L-stent and V-stent. The interaction between the motion of the arterial wall and the blood flow promotes the pulse wave propagation. Fluid-structure interaction (FSI) between the blood flow and the arterial-wall deformation in various arteries has been widely investigated. Malvé et al. compared the computational results between rigid and compliant arterial walls and showed that WSS distributions are similar for both CFD and FSI simulations, while qualitative discrepancies in the WSS distribution and relevant differences in the WSS temporal profiles are also available, especially in the areas characterized by high displacement [34]. The temporal variation of WSS shows lower WSS values computed with FSI simulation than the CFD analysis. Torii et al. studied the FSI in a patient-specific model of the cerebral artery and found that the WSS distributions are affected by the arterial-wall deformations [35]. Lantz et al. investigated the WSS in a Magnetic Resonance Imaging (MRI)based subject-specific human aorta, using both FSI and rigid wall models, and found that the influence of wall motion is low on time-averaged WSS and OSI, but when regarding instantaneous WSS values the effect from the wall motion is clearly visible [36]. Kelly et al. performed fluid, solid, and FSI simulations on three patient-based abdominal aortic aneurysm geometries [37]. They concluded that solid stress simulations are adequate to predict the maximum stress in an aneurysm wall, while FSI simulations should be performed if accurate prediction of the WSS is necessary. However, studies about FSI simulations of a stented stenotic artery are relatively rare because of the complexity of model geometry and the material mechanical property and also the difficulty of defining the 0-stress state of arterial wall. FSI simulation based on a deformed model of stenotic artery treated with endovascular stent needs the initial condition of residual stress/strain induced by the stent expansion. The assignment of this initial condition is still a challenging problem. The achievement of the present study provides an elementary and feasible approach for the hemodynamic simulation based on deformed models of a stenotic vertebral artery treated with a stent. The main limitations of this study are the following: (1) The artery model is an idealized vertebral artery and (2) the artery wall is assumed to be a rigid wall in the hemodynamics simulation. A more accurate personalized artery model can be established using the image reconstruction technique so that the numerical simulation will be closer to the real situation. The WSS and velocity distribution of the elastic wall are essentially the same as a rigid wall. The numerical values decrease slightly when the elastic wall is used, but the time cost of numerical computation increases greatly. The aim of the present study was to investigate the influence of different shapes of link on blood flow, as well as to examine the relationship between the different shapes of link and ISR. Thus, a rigid wall with a low time cost was used in the hemodynamics simulation in this study. Studies evaluating the fluidstructure interaction will be performed in future work. Anisotropic viscoelastic or hyperelastic materials can be applied to the artery 041007-8 / Vol. 136, APRIL 2014

wall, whose properties change spatially. In addition, a model of nonlaminar and non-Newtonian blood flow also could be used for the hemodynamic simulation. To investigate the impact of the different factors and conditions on ISR in the vertebral artery, in-depth studies conceming the fluid-structure interaction of the stent, the artery wall, and the blood flow will be of particular importance in the future.

5

Conclusions

In this paper, numerical simulations were performed to investigate the effects of endovascular stents with different links for treating stenotic vertebral artery and to determine the relationship between the shape of the link and in-stent restenosis. The following conclusions could be remarked: (1) Compared with the L-stent and V-stent, the S-stent has a better flexibility and induces less stress in the stent strut. Furthermore, less stress is generated in the arterial wall. (2) Vascular straightening is scarcely influenced by the shape of the link, but it is closely related to the flexibility of the stent. (3) The S-stent has the smallest foreshortening among the three types of stents. (4) Compared with the V-stent and S-stent, the L-stent causes a smaller area with low WSS, less blood stagnation area, and better blood flow close to the artery wall. From the viewpoint of the combination of solid mechanics and hemodynamics, the S-stent has better therapeutic effects because of its lower potential for inducing ISR and its better prospects in clinical applications compared with the L-stent and V-stent.

Acknowledgment This work was supported by National Natural Science Foundation of China (81171107, 11172016, 10972016), Higher School Specialized Research Fund for the doctoral program funding issue (20111103110012), and the Natural Science Foundation of Beijing (3092004, KZ201210005006).

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APRIL2014, Vol. 136 / 041007-9

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Numerical simulation of vertebral artery stenosis treated with different stents.

We sought to investigate the effects of endovascular stents with different links for treating stenotic vertebral artery and to determine the relations...
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