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Journal of Biomechanics 40 (2007) 3034–3040

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Short communication

Delivery and release of nitinol stent in carotid artery and theirinteractions: A finite element analysis

Wei Wu�, Min Qi, Xiao-Peng Liu, Da-Zhi Yang, Wei-Qiang Wang

Department of Materials Engineering, Dalian University of Technology, No. 2, LingGong Road, Dalian, LiaoNing 116024, China

Accepted 26 February 2007

www.JBiomech.com

Abstract

Carotid angioplasty and stenting (CAS) has emerged as an effective alternative to carotid endarterectomy, and nitinol stents are commonly

used in CAS. To evaluate biomechanical properties of nitinol carotid stents and their interactions with carotid arteries, a finite element method

(FEM) model was built which is composed of a stenotic carotid tissue, a segmented-design nitinol stent and a sheath. Two different stents were

considered to show the influence of stent design on the stent–vessel interactions. Results show that the superelastic stents were delivered into

the stenotic vessel lumen through the sheath and self-expanded in the internal and common carotid artery. The stent with shorter struts may

have better clinical results and the different stent designs can cause different carotid vessel geometry changes. This FEM can provide a

convenient way to test and improve biomechanical properties of existing carotid stents and give clues for new nitinol carotid stent designs.

r 2007 Published by Elsevier Ltd.

Keywords: Carotid artery; Nitinol stent; Finite element methods; Stent–vessel interactions; Biomechanical properties

1. Introduction

Carotid angioplasty and stenting (CAS) has developed asa potential alternative to carotid endarterectomy (CEA) forthe treatment of carotid artery disease (Brott et al., 2004),and nitinol stents are usually used in CEA (Phatouroset al., 2000). However, in-stent restenosis of CAS stillremains (Clark et al., 2006) and a trial to prove noninfer-iority of CAS vs. CEA failed recently (Ringleb et al., 2006).The nitinol stent biomechanical properties and stent–vesselinteractions are considered as two of major factors of short-and long-term stenting outcomes (Hart et al., 2006), whichare studied by experiments (Tanaka et al., 2004; Hanus andZahora, 2005; Grenacher et al., 2006) or finite elementmethods (FEM) (Whitcher, 1997; Migliavacca et al., 2004;Brand and Ryvkin, 2005). However, nitinol stent implanta-tion in carotid arteries has not been studied by FEM yet.This work developed a FEM to model nitinol stent deliveryand release in a stenotic carotid vessel and compared the

e front matter r 2007 Published by Elsevier Ltd.

iomech.2007.02.024

ing author. Tel.: +86411 84708441;

709284.

ess: keyiyizhan@gmail.com (W. Wu).

simulations to some clinical and experimental results, withthe aim to study stent–vessel interactions from a biomecha-nical view. Furthermore, two stent designs were comparedwith the method to show the influence of stent design on theinteractions.

2. Materials and methods

2.1. Geometry models

The geometrical model was generated using Pro/Engineer (Parametric

Technology Corporation) and transformed into finite element analysis

code ANSYS (ANSYS Inc.) for analysis. The model components and

assembly are shown in Fig. 1. The model is composed of a carotid tissue

(vessel and plaque), nitinol stent and sheath. The tissue was built based on

the previous studies (Berkefeld et al., 2002), and the vessel consists of the

common, internal and external carotid artery (CCA, ICA and ECA). The

measure of ICA tortuosity is shown in Fig. 1b. Two kinds of segmented-

design nitinol stents were modeled (the original stent Sori and the modified

stent Smod). The sheath was built to deliver the stent into the tissue.

2.2. Material properties

Nitinol is a well-known engineering material in medical industry for its

superelasticity (Duerig et al., 1999), as shown in Fig. 2a. The nitinol

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Fig. 1. Models of the carotid tissue (vessel and plaque), stent and sheath. (a) Section view of the tissue. The vessel has a thickness of 0.7mm; the inner

diameters of the CCA, ICA and ECA are 8, 6 and 5mm, respectively. The plaque is located between the proximal ICA and carotid bifurcation; it has a

thickness of 1mm and a midaxis length of 10.5mm. With its smallest inner diameter of 4mm, the plaque has the severest stenosis of 56% for the reference

ICA lumen area (28.3mm2). (b) ICA offset and ICA–CCA angle of the vessel, which show the tortuosity of ICA. Definition of ICA offset is the maximum

deviation of ICA outer curvature perpendicular to the CCA midaxis; definition of CCA–ICA angle is the angulation between the CCA midaxis and the

proximal ICA midaxis. The original ICA offset and CCA–ICA angel are 14.2mm and 381, respectively. (c) The segmented nitinol stent models Sori and

Smod. Both models have an original outer diameter of 8mm, a length of 22mm, a thickness of 0.23mm and a strut width of 0.15mm; the stent strut units

have 12 rings in the circular direction, and every two strut units are connected by four straight links in the longitudinal direction. The Sori has six strut

units; the strut length of the Smod (2.10mm) is 2/3 of the Sori strut length (3.15mm), and the Smod has nine strut units. (d) The sheath was composed of

continuous cylinder and torus areas following the midaxes of CCA and ICA, and theses areas were tangent connected and meshed as rigid bodies. The

sheath has a uniform original lumen diameter of 8mm. (d) The assembly of the tissue, stent (the Sori is used for this illustration) and sheath in the global

coordinate system. The midaxes of the stent, CCA and the proximal part of the sheath coincide with each other, and the midaxes are parallel to the Z

direction. The distances between the proximal edges of the stent and CCA, and proximal edges of the sheath and CCA, are 5.5 and 6.5mm, respectively.

The displacement loading on the two proximal stent links is indicated by arrows. The constraints to fix the vessel extremes are indicated by circles.

W. Wu et al. / Journal of Biomechanics 40 (2007) 3034–3040 3035

properties required for the ANSYS (2004) material model (Auricchio and

Taylor, 1997) were obtained from Favier et al.’s (2006) work, and the

FEM material model was tested and compared with the experimental data

(Fig. 2b). The vessel and plaque were regarded as hyperelastic materials

and modeled using four-parameter and six-parameter Mooney–Rivlin

hyperelastic constitutive equations, respectively, which were derived from

test data reported previously (Lee, 2000). Table 1 lists all material

parameters.

2.3. Meshing and boundary conditions

The tissue was meshed with eight-node hyperelastic Hyper58 elements

and the stent eight-node Solid185 elements. Flexible–rigid and flexible–

flexible contact pairs were created between the sheath and stent outer

surface, and stent outer surface and tissue inner surface, respectively.

A friction coefficient (0.05) was set to all contact pairs for simulation

stability (Petrini et al., 2005). A sensitivity test was performed to ensure

enough meshing refinement. Both components and contact element

numbers are listed in Table 2.

The tissue was fixed just at extreme surfaces and rotation of the stent

around its axis was inhibited. The sheath was constrained in all directions

at first.

2.4. Loadings and solutions

First, a displacement of �19mm parallel to the global Z direction was

applied on two proximal stent links and the stent was pushed forward in

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Table 1

Material parameters of the stent and tissue

Material

models

Material

parameters

Nitinol E (GPa) n sAMs

(MPa)

sAMf

(MPa)

sMAs

(MPa)

sMAf

(MPa)

eL a

60 0.3 346 365 83 57 0.063 0.09

Mooney–

Rivlin

(MPa)

C1 C2 C3 C4 C5 C6

Vessel 0.020 0.003 0.175 0.090 – –

Plaque �0.452 0.510 0.101 1.256 0 0.301

W. Wu et al. / Journal of Biomechanics 40 (2007) 3034–30403036

the sheath. To keep the modeling conform to reality, ‘‘element birth

and death’’ was introduced into the simulation (Lally et al., 2005). In this

step, the contact elements between the stent and tissue were inactivated.

Second, the diameter of the sheath reduced to 3mm, and the stent

was totally compressed in the stenotic ICA lumen. At last, the

contact pairs between the stent and tissue were activated and the

sheath expanded to an enough diameter, ensuring a thorough separation

of the stent from the sheath and interactions just between the stent and

tissue.

After simulations, the following aspects were collected: (1) the stent

delivery and release procedures; (2) the malapposition areas between the

stent and tissue; (3) the severest stenosis (the minimum ICA lumen area)

after stent implantation; (4) the changes of ICA tortuosity and (5) the first

principle stresses in the vessel.

3. Results

As Fig. 3 shows, both Sori and Smod were delivered to thetarget location of the plaque through the sheath, andcompressed into the stenotic vessel lumen with thesheath diameter reduced, then released from the sheathand interacted with the vessel. After stent implantation,the Sori had more malapposition areas than that ofthe Smod (Figs. 3a3 and b3); and the Smod had theleast severe stenosis of 37% (the minimum ICA lumenarea of 17.7mm2), as compared to 46% (15.5mm2) ofthe Sori.For the ICA tortuosity changes, the vessel implanted

with the Sori had more ICA offset and larger CCA–ICA

Fig. 2. Material properties of the stent and tissue. (a) Sketch map of

uniaxial behavior of nitinol superelasticity. Nitinol can undergo very large

deformation while keeping the ability to restore to its original shape when

unloading. The material presents itself in an austenite phase (A) without

loading. When the load is beyond a certain stress, the austenite phase

transforms into a martensite phase (M). This transformation produces a

substantial amount of strain, which is reversible on unloading. The

description of material parameters in the case of a uniaxial tensile state: E,

the Young’s modulus, assumed equal for the austenite (A) and martensite

(M); ssAM, the starting stress value for the forward phase transformation

(from A to M); sfAM, the final stress value for the forward phase

transformation (form A to M); ssMA, the starting stress value for the

reverse phase transformation (fromM to A); sfMA, the final stress value for

the reverse phase transformation (from M to A); eL, the maximum

transformation strain reached at the end of the austenite to martensite

transformation; a (not shown in the sketch), the parameter measuring the

difference between material responses in tension and compression

(a ¼ ððss�AM � ssþAMÞ=ðss�AM þ ssþAMÞÞ, where ssþAM and ss�AM are the initial

stress value of the austenite into martensite conversion in tensile and

compress state, respectively. (b) Experimental data of nitinol uniaxial

tensile behavior and the simulation of the stent material property. With

consideration of the mechanical and thermal treatments applied to the

material to produce the stent, the superelastic behavior of constrained-

aged Ti-50.8 at%Ni thin wall tubes (Favier et al., 2006, with permission)

was used for the experimental data. For the lack of the compress

experiment, a was set as 0.09. The corresponding parameters are listed in

Table 1. (c) The stress–strain curves of Mooney–Rivlin material properties

for the vessel and plaque. Because there is no experimental data of the

carotid vessels, the data from coronary arteries were used (Lee, 2000). The

corresponding parameters are listed in Table 1.

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Table 2

Sum of model component and contact element number

Stent Vessel Plaque Stent–sheath

contact

Stent–tissue

contact

Sori 7968 1656 576 4824 4920

Smod 9120 1656 576 5496 5544

Fig. 3. The stent delivery and release procedures of the Sori and Smod (both ful

shown in local view). (a1) and (b1) The Sori and Smod were pushed forward in th

of the two proximal links reached�19mm in the global Z direction. (a2) and (b

diameter of the sheath reduced to 3mm. (a3) and (b3) When the sheath was e

released from the sheath and fully contacted with the tissue. The stent mal

respectively.

W. Wu et al. / Journal of Biomechanics 40 (2007) 3034–3040 3037

angle than the Smod (12.8 vs. 12.4mm and 27.51 vs. 26.31,respectively), indicating the Smod caused more ICAtortuosity changes (Figs. 4a1 and b1). Furthermore, theSmod caused higher maximum vessel stress than the Sori

(0.099 vs. 0.074MPa), and the stresses concentrated at thelocation of the plaque (Figs. 4a2 and b2). The results aresummed in Table 3.

l view and local view are shown for every procedure, and the sheath is not

e sheath and delivered to the location of the plaque when the displacement

2) The Sori and Smod were compressed into the stenotic ICA lumen after the

xpanded and separated completely with the stent, the Sori and Smod were

apposition areas of the Sori and Smod are highlighted in (a3) and (b3),

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Fig. 4. (a1) and (b1) Displacement in the global X direction of the tissue deformed by the Sori and Smod, respectively. The original shape edge is also shown

for comparison. (a2) and (b2) The first principle stresses of the vessel caused by the interaction with the Sori and Smod, respectively. (a3) and (b3) VonMises

stress distribution of the Sori and Smod after stent release, respectively.

Table 3

Sum of the results

The severest stenosis rate (min.

stenotic lumen area)

ICA offset (mm) CCA–ICA angle Max. vessel stress

(MPa)

Sori 45% (15.5mm2) 12.8 27.51 0.074

Smod 37% (17.7mm2) 12.4 26.31 0.099

W. Wu et al. / Journal of Biomechanics 40 (2007) 3034–30403038

4. Discussion and conclusions

Nitinol stents are widely used in peripheral vesselinterventions for nitinol’s superelasticity, good corrosionresistance and biocompatibility (Stoeckel et al., 2004).Although some FEM works have studied nitinol stent

properties, the interactions between nitinol stent andtortuous bifurcate carotid vessels are seldom modeled,because the stent has to enter the curved vessel lumen in acompressed configuration, and then bridge the arteries withabrupt changes of the vessel diameter. In our model, wedelivered and released the nitinol stent using a sheath,

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which was meshed as continuous rigid bodies and couldchange its diameter uniformly. The simulated delivery andrelease steps (Fig. 3) can basically correlate with nitinolstent deployments in carotid vessels (Phatouros et al.,2000). Furthermore, this method could model nitinol stentimplantation in other kinds of vessels, if the appropriatesheath was modeled. To the authors’ best knowledge, it’sthe first work to simulate the nitinol stent implantation incarotid arteries.

Although the Smod resulted in a less final stenosis rate(37%) than the Sori (45%), both rates are not acceptableand a post-deployment angioplasty must be performed,which is a routine clinical procedure for carotid stenting(Clark et al., 2006). The insufficient stent scaffolding alsoaccords with the experimental results of nitinol stents,which had considerably lower radial expansion force thanstainless-steel stents (Grenacher et al., 2006). This phenom-enon can be partially explained by much lower Young’smodulus of nitinol (60GPa here) than that of stainless steel(about 200GPa). Despite of high stenosis rates, the resultsstill show the effects of stent design on stent–vesselinteractions. For the larger ICA lumen area, the Smod withshorter struts had more strut units to scaffold the samestenotic vessel than the Sori (Fig. 3); on the other hand, theshorter struts were deformed more when the Smod wascompressed to the same diameter as the Sori, so whenreleased from the sheath, the struts of the Smod had higherradial expansion force than that of the Sori (Figs. 4a3 andb3). Furthermore, the more segmented structure of theSmod can conform to the tortuous vessel better with lessmalapposition areas (Figs. 3c1 and c2). These areas mayinduce irregular blood flow patterns to favor the throm-bosis creation, or adversely influence the drug effects offuture drug-eluting carotid stents (Tepe et al., 2006).

The stenting also changed the geometry of the carotidbifurcation and the course of ICA (Figs. 4a1 and b1),which was observed in clinical results (Berkefeld et al.,2002) and in vitro experiments (Tanaka et al., 2004).Although the long-term clinical impacts of these changesare not clear now (Vos et al., 2005), the results indicate thatthe different stent designs can cause different vesseltortuosity changes.

The main limitation of this study is that the possiblecontact between the struts was not considered forsimplicity (Figs. 3a2 and b2). However, the stent issuperelastic and the real strut contact can only temporarilyinfluence the relative locations between some struts duringstent delivery. After release, the stent will try to restore itsoriginal diameter without strut contact. Another limitationis that only one kind of nitinol property was modeled. Infact, the nitinol property can be changed significantly withdifferent thermomechanical treatments (Favier et al., 2006)and therefore influences the stent mechanical propertiesgreatly (Stoeckel et al., 2004). More nitinol propertiesshould be modeled in the future.

In conclusion, through modeling nitinol stent implanta-tion in carotid vessels, we tried to study the biomechanisms

of stent–vessel interactions in CAS. Furthermore, two stentdesigns were compared using the method, with the resultssuggesting the stent with shorter struts may have betterclinical outcome. This three-dimensional FEM model canprovide a tool to test and improve existing carotid stentproperties and help designers to device novel carotid stentsfor better CAS results.

Acknowledgments

This work was financially supported the NationalNatural Science Foundation of China (No. 30470521 and50471066).

Appendix A. Supplementary material

Supplementary data associated with this article can befound in the online version at doi:10.1016/j.jbiomech.2007.02.024.

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