Medical Engineering & Physics 37 (2015) 23–33
`
`Contents lists available at ScienceDirect
`
`Medical Engineering & Physics
`
`j o u r n a l h o m ep a g e : w w w . e l s e v i e r . c o m / l o c a t e / m e d e n g p h y
`
`Morphological and stent design risk factors to prevent migration
`phenomena for a thoracic aneurysm: A numerical analysis
`H.-E. Altnji ∗, B. Bou-Saïd 1, H. Walter-Le Berre 2
`
`Laboratoire de Mécanique des Contacts et des Structures, INSA de Lyon, 18-20 rue des Sciences, 69621 Villeurbanne, France
`
`a r t i c l e
`
`i n f o
`
`a b s t r a c t
`
`Article history:
`Received 20 September 2013
`Received in revised form 21 August 2014
`Accepted 30 September 2014
`
`Keywords:
`Aortic aneurysm
`Migration
`Type I endoleak
`Finite element
`Self-expanding stent
`
`The primary mechanically related problems of endovascular aneurysm repair are migration and type
`Ia endoleaks. They occur when there is no effective seal between the proximal end of the stent-graft
`and the vessel. In this work, we have developed several deployment simulations of parameter-
`ized stents using the finite element method (FEM) to investigate the contact stiffness of a nitinol
`stent in a realistic Thoracic Aortic Aneurysm (TAA). Therefore, we evaluated the following factors
`associated with these complications: (1) Proximal Attachment Site Length (PASL), (2) stent over-
`sizing value (O%), (3) different friction conditions of the stent/aorta contact, and (4) proximal neck
`angulation ˛.
`The simulation results show that PASL > 18 mm is a crucial factor to prevent migration at a neck angle
`of 60◦, and the smoothest contact condition with low friction coefficient ((cid:2) = 0.05). The increase in O%
`ranging from 10% to 20% improved the fixation strength. However, O% ≥ 25% at 60◦ caused eccentric
`deformation and stent collapse. Higher coefficient of friction (cid:2) > 0.01 considerably increased the migra-
`tion risk when PASL = 18 mm. No migration was found in an idealized aorta model with a neck angle of
`0◦, PASL = 18 mm and (cid:2) = 0.05. Our results suggest carefully considering the stent length and oversizing
`value in this neck morphology to strengthen the contact and prevent migration.
`© 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
`
`1. Introduction
`
`Aortic aneurysm disease is characterized by a dilatation of the
`aorta as a result of weakness in the aorta wall. This leads to changes
`in wall tension with reduced tensile strength and finally rupture.
`Therefore, it is essential that aneurysms be repaired prior to fatal
`rupture. Two treatment strategies are possible: traditional surgery
`and endovascular aneurysm repair (EVAR) procedures. EVAR pro-
`poses a less invasive form of treatment and has undergone a
`dramatic technological evolution. An endovascular stent graft is a
`device used to seal off the aneurysm from inside the aorta pro-
`viding a new pathway for the blood flow through the region of an
`aneurysm.
`The main mid- and long-term mechanical related complications
`of EVAR are migration and type Ia endoleaks [1]. An endoleak is
`
`∗ Corresponding author. Tel.: +33 4 72 43 84 52; fax: +33 4 78 89 09 80.
`E-mail addresses: hussameddinaltnji86@gmail.com (H.-E. Altnji),
`benyebka.bou-said@insa-lyon.fr (B. Bou-Saïd), helene.walter-le-berre@insa-lyon.fr
`(H. Walter-Le Berre).
`1 Tel.: +33 4 72 43 84 47; fax: +33 4 78 89 09 80.
`2 Tel.: +33 4 72 43 71 88; fax: +33 4 72 43 89 13.
`
`http://dx.doi.org/10.1016/j.medengphy.2014.09.017
`1350-4533/© 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
`
`defined as the presence of blood flow outside the lumen of the
`endoluminal graft, but within the aneurysm sac. Type Ia endoleak
`occurs when there is an ineffective seal of the aneurysm sac at
`the proximal attachment zone of the endograft device [2,3] which
`allows a direct blood flow into the aneurysm sac. The flow will exert
`a pressure force on the aorta wall which can lead to rupture. Migra-
`tion is defined as an endograft movement proximally greater than
`10 mm which leads to type Ia endoleak. These complications have
`undergone clinical investigation and can be related to one or all
`of these Deployment Failure Factors (DFF): endograft undersizing
`[4,5], high drag forces due to severe angulation [6,7], and insuffi-
`cient length of the proximal attachment site [8,9]. Most numerical
`research using Computational Solid Mechanics (CSM) has focused
`on coronary stent deployment mechanisms [10–13] or intracra-
`nial aneurysm [14]. Certain authors [15] have demonstrated the
`efficiency of CSM by experimental validation of the numerical
`results [16] of two commercial stent grafts subject to severe bend-
`ing tests. More recently, investigations [17] have been conducted
`using CSM examining the previous complications, however, this
`work focused mainly on idealized vessel geometry and an unreal-
`istic 3D geometric-connected stent behavior without investigating
`the mechanism of proximal stent migration. Moreover, stent col-
`lapse [18] or eccentric deformation in severe neck angulation has
`
`TMT 2122
`Medtronic v. TMT
`IPR2021-01532
`
`

`

`24
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`H.-E. Altnji et al. / Medical Engineering & Physics 37 (2015) 23–33
`
`Fig. 1. (a) 3D reconstruction of aorta with centerline extraction. (b) Hexahedral mesh discretization. (c) The main definitions regarding the morphological criteria for (TAA).
`
`(cid:3)iso( ¯C) describe the so-called volumetric elas-
`(cid:3)vol(J) and
`where
`tic response, and the isochoric elastic response of the material,
`respectively [26]. The generalized Mooney–Rivlin hyperelastic
`constitutive model was used. The decoupled polynomial represen-
`tation of the strain energy function is given by,
`
`1D
`
`i
`
`N(cid:2)
`
`N(cid:2)
`
`=
`
`(cid:3)
`
`not yet been examined. In another study by Prasad et al. [19] aimed
`endoleak, stented endografts were
`at investigating the type
`subjected to displacement forces to investigate the contact stabil-
`ity at the intermodular junctions of a multi-component thoracic
`endograft in patient-specific TAA. However, the contact stability
`at proximal and distal attachment sites was not evaluated as the
`interaction of the aorta/stent graft at these sites was considered to
`be perfect.
`The present paper is a follow-up to our previous paper [20]
`which was the premise of this project. The main advantages of
`this work are to find, based on a 3D FEM platform, the mechan-
`ical, morphological, and stent design factors which lead to stent
`migration and can cause stent collapse or poor contact between the
`stent and the aorta at the attachment sites. This was accomplished
`by evaluating the contact stiffness in the stent/aorta interaction
`area after stent deployment using a Coulomb frictional model in
`a short-term stent fixation frame. Therefore, seven parameterized
`stent models were used to evaluate the following DFF in a patient-
`specific TAA: (1) the Proximal/Distal Attachment Site Length, (2)
`the stent Oversizing values (O%), (3) different stent/aorta contact
`friction conditions, and (4) the proximal neck angulation (˛).
`
`Ш
`
`2. Materials and methods
`
`2.1. Patient specific TAA and stent models
`
`The FEM patient-specific TAA model was the same as for the
`previous work [20], starting from the planar slices obtained from
`the clinical CT scans in plane resolution. The reconstruction interval
`equals to the slice thickness of 0.73 mm. The pre-stenting vessel
`centerline was calculated to guide stent positioning. The meshing
`of the finite elements was developed using C3D8R element type as
`shown in Fig. 1.
`Although the anisotropy of the wall properties has been well
`recognized [21–23], the blood vessel in our case can be consid-
`ered as isotropic as the degree of anisotropy is small [24,25]. In the
`Abaqus/Explicit software package used, we must provide sufficient
`compressibility for the code to work. It was defined as K0/(cid:2)0 = 20
`(cid:2)0 the initial shear mod-
`where K0 is the initial bulk modulus and
`ulus. The material was considered as isotropic hyperplastic, and
`nearly incompressible. The decoupled representation of the strain-
`=
`(C) is given by the function,
`energy function
`
`(cid:3)
`
`(cid:3)
`
`(1)
`
`(cid:3)iso( ¯C),
`
`
`
`+
`
`(cid:3)vol(J)
`
`=
`
`(cid:3) (C)
`
`(2)
`
`1)2i,
`
`
`
`−
`
`(J
`
`
`
`i
`
`(¯I2 −
` 3)
`
`j +
`
`Cij(¯I1 −
` 3)
`i=1
`i+j=1
`where N, Cij and Di are temperature-dependent material parame-
`ters. The strain invariants are denoted ¯I1 and ¯I2. The symbol J is the
`volume ratio or the elastic volume strain, while Di describes the
`compressibility of the material. The hyperelastic constants were
`determined from the experimental tests [27]. Only radial displace-
`ments of the nodes located on the upper and bottom surfaces were
`allowed. We assumed no internal and external pressure on the
`aneurysm. The effects of residual stresses [1,23] were also neglected
`given the fact that blood vessels can be in a nearly stress-free state
`when they are free from external loads [24]. The nominal uniform
`thickness was considered to be 3 mm [28].
`The stent geometric models were generated by means of a spe-
`cially developed parameterization algorithm, using global variables
`(all in mm) STOD = 17, STH = 0.6, SL = 21, BW = 0.7, SVW = 0.8, G = 4.6,
`GSC = 23.5 mm illustrated in Fig. 2a. Other variables (Ystrut, SW, R1,
`R2, SLS) were linked to previous ones by the equations given in
`Fig. 2a, where R1 and R2 are the inner and outer radius of strut
`vertex, respectively. We denote Ystrut as a circumferential distance
`of a single strut at the given diameter, and Nstruts = 10 is the num-
`ber of struts around the circumference of the stent. The stent was
`modeled starting from the master sketch with six strut columns
`along the stent. The 3D parametric stent model was then created
`with suitable operations in the CATIA V5R20 software. All stent
`models were carefully discretized with the C3D8R element type
`using hourglass control [29]. In order to produce accurate represen-
`tation of the actual stent geometry, the CAD stent model was driven
`by a rigid cylindrical surface, accomplishing the needed oversiz-
`ing value relative to the outer diameter of the aorta, as shown in
`Fig. 2b. In the shape setting simulation, nitinol was considered to be
`an elastoplastic material [30]. Then, the expanded stent model was
`added back into the assembly model in a strain-free manner. After
`mesh convergence analysis (see Appendix), we applied three ele-
`ments through the thickness, and four elements across the width
`with a reasonably refined mesh of the strut (Fig. 2b).
`In the deployment procedure, superelastic behavior of the niti-
`nol was assigned to the stent. The numerical implementation of
`
`

`

`H.-E. Altnji et al. / Medical Engineering & Physics 37 (2015) 23–33
`
`25
`
`Fig. 2. (a) Parametric stent model using variables and equations. (b) Shape setting simulation and mesh refinement.
`
`friction model. The model assumes that no relative motion occurs
`
`(3)
`
`,
`
`(cid:7)
`
`(cid:6)
`
`<
`
`(cid:4)crit =
`
`
`
`(cid:2)p
`
`(cid:5)
`
`(cid:4)
`
`(cid:4)2
`2
`
`+
`
`(cid:4)2
`1
`
`(cid:4)eq =
`
`if,(cid:3)
`
`(cid:4)2 are the two
`(cid:4)1 and
`where ¯(cid:4)eq is the equivalent shear stress; and
`shear stress components that act in the slip directions of the contact
`(cid:4)crit represents the critical shear stress, while
`surfaces. The symbol
`is the friction coefficient, and P is the contact pressure. The slip
`between stent and aorta will not occur when,
`
`(cid:3)
`
`(cid:5)
`
`¯(cid:4)eq
`(cid:2)p <
` 1
`
`(cid:2)
`
`( ¯(cid:4)eq <
`
`
`
`(cid:2)p)
`
`(4)
`
`(5)
`
`(6)
`
`,
`
`⇔
`(cid:3)
`
`,
`
`(cid:5)
`
`but will occur when
`( ¯(cid:4)eq≥(cid:2)p)
`⇔
`
`¯(cid:4)eq
`(cid:2)p≥1
`
`≤ ¯Fcs ≤
` 1,
`
`
`
`The ratio,
`¯Fcs = ¯(cid:4)eq
`(cid:2)p
`
`,
`
`0
`
`this model was developed by writing a user-material subroutine
`following the model proposed by Auricchio et al. [31]. Nitinol
`material characterization was obtained from the literature [32].
`Mesh convergence analysis for both stent and aorta was per-
`formed, as shown in Appendix. The convergence criterion was
`based on the relative difference in von Mises stress and logarithmic
`strain.
`
`2.2. FEM stent deployment procedure
`
`The stent deployment was performed using a virtual deformable
`catheter surface meshed with a SFM3D4R element type, as shown
`in Ref. [20]. Starting from a straight configuration of the catheter,
`we calculated the needed displacements of the nodes comprising
`the aorta centerline (i.e., compression, displacement and bend-
`ing). The displacements were obtained in the insertion phase,
`and re-enlarging in the deployment phase (Fig. 3a). When the
`stent was deployed, the distance between two adjacent columns
`of struts Y was calculated along and around the circumference
`of the stent to evaluate the strut deformation, see Fig. 3 and
`Table 1.
`Concerning the high nonlinearity of the model, Abaqus/explicit
`6.11 was used as the finite element solver in a quasi-static analy-
`sis. We used a mass scaling technique [29,33,34] to decrease the
`time period without generating significant inertia forces (again,
`see Appendix). Since the solution converged with the applied
`mesh for contact and pressure forces, the results were con-
`sidered to be acceptable. The analysis was performed in the
`framework of classical continuum mechanics under large strain
`conditions.
`
`3. Stability of the stent/vessel contact
`
`Defines the friction contact stability ¯Fcs and stick/slip behav-
`ior between stent and aorta. High values of ¯Fcs mean high shear
`wall stress which can lead to an unstable contact until high slip
`is expected when ¯Fcs≥1. In this case, small values of the so called
`“pullout” or static downward forces needed to dislodge the stent
`from its attachment site may lead to significant migration. A total
`of eleven simulations were performed as illustrated in Table 2.
`
`4. Results
`
`4.1. Post processing
`
`Fig. 3a illustrates the reference deployment simulation process
`for stent 1 with PASL = 18 mm and O% = 15%. An idealized opposition
`⇔ ¯Fcs =
` 0, so that no slip is expected
`is assumed meaning
`once stent–aorta contact occurs. In the deployment phase, the stent
`expands with the superelastic effects until it contacted with the
`
`∞
`=
`(cid:2)
`
`The interaction between the contacting surfaces is controlled by
`two components, one being normal and the other tangential to the
`surfaces. The tangential behavior defines the relative motion (slid-
`ing) between the contacting surfaces. Hard contact model behavior
`[35] was used as the behavior in the normal direction. The tan-
`gential behavior was described by the classical isotropic Coulomb
`
`

`

`26
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`H.-E. Altnji et al. / Medical Engineering & Physics 37 (2015) 23–33
`
`Fig. 3. Reference deployment simulation. (a) Deployment procedure. (b) Principal stresses distribution (MPa) in the aorta.
`
`Table 1
`Distance between two adjacent columns of struts.
`
`Group (G)
`
`Initial state (X = Y)
`G1SC = 23.549
`G2SC = 23.549
`G3SC = 23.549
`G4SC = 23.549
`G5SC = 23.549
`
`(G1) with bar
`
`Deployed state (Y)
`Y1 = 23.541
`Y2 = 23.544
`Y3 = 23.566
`Y4 = 23.559
`Y5 = 23.548
`
`(G2)
`
`Y1 = 22.5
`Y2 = 29.97
`Y3 = 30.22
`Y4 = 24.7
`Y5 = 23.8
`
`(G3)
`
`Y1 = 22.86
`Y2 = 24.74
`Y3 = 23.34
`Y4 = 23.28
`Y5 = 27.33
`
`(G4)
`
`Y1 = 23.93
`Y2 = 15.41
`Y3 = 14.75
`Y4 = 22.4
`Y5 = 34.33
`
`(G5)
`
`Y1 = 24.33
`Y2 = 18.15
`Y3 = 16.35
`Y4 = 23
`Y5 = 31
`
`aorta applying Radial Force RF. At the proximal and distal attach-
`ment sites, a radial decrease was observed in the deployed stent
`due to the Radial Compressive Forces (RCF) applied by the aorta.
`When the stent was fully deployed, RF and RCF forces were in equi-
`librium [36]. The previous history of deployment behavior can be
`described only when no migration or folding takes place. Fig. 3b
`shows the stress distribution in the aorta when the stent is fully
`deployed.
`The maximum values of the principal stresses were always
`observed near the proximal and distal attachment sites, where the
`cross-section of the vessel is undergoes large change.
`
`When deployed, some peaks of stent (group 2) move further
`apart and others move closer, see Fig. 3 and Table 1. The abso-
`lute distances between the peaks of struts in group 2 (Y2, Y3, and
`Y4) showed the longest deformation distance between the stent
`struts. These rings were slightly opened further during deployment
`(Fig. 3a).
`Based on the contact output variables, i.e., the normal, shear and
`pressure contact forces; we evaluated the ‘average contact stability’
`¯Fcs in both the proximal and distal landing zones from Eq. (6) for
`every deployment procedure, where only positive contact pressure
`stresses were generated.
`
`VI(Stent 2)
`
`D2P = 21
`D2D = 18
`15%
`= 0.05
`
`(cid:2)
`
`20%
`= 0.05
`
`(cid:2)
`
`V(
`
`Stent 1)
`
`D1P = 18
`D1D = 15
`15%
`∞
`=
`(cid:2) = 0.05
`(cid:2) = 0.1
`(cid:2) = 0.5
`
`(cid:2)
`
`Table 2
`Parameterized-deployment simulations to evaluate the impact of several factors on migration.
`
`IV
`(Stent 3)
`
`D3P = 23
`D3D = 23
`25%
`= 0.05
`
`(cid:2)
`
`III
`(Stent 3)
`
`D3P = 23
`D3D = 23
`20%
`= 0.05
`
`(cid:2)
`
`II
`(Stent 3)
`
`D3P = 23
`D3D = 23
`15%
`= 0.05
`
`(cid:2)
`
`I(
`
`Stent 3)
`
`D3P = 23
`D3D = 23
`10%
`= 0.05
`
`(cid:2)
`
`Deployment simulation (Angulated proximal neck)
`
`Proximal attachment site (mm) (PASL)
`Distal attachment site length (mm) (DASL)
`Oversizing value (O%)
`Tangential contact behavior (coefficient of friction)
`
`(non-Angulated proximal neck)
`
`Proximal attachment site length (mm)
`Distal attachment site length (mm)
`Oversizing value (O%)
`Tangential contact behavior (coefficient of friction)
`
`(Stent 1)
`
`D1P = 18
`D1D = 15
`15%
`
`((cid:2) = 0.05)
`
`

`

`H.-E. Altnji et al. / Medical Engineering & Physics 37 (2015) 23–33
`
`27
`
`Fig. 4. Proximal and distal attachment site lengths (D) (mm) just after the first interaction moment (stent–aorta), (O%) = 15%. We consider (D = P/DASL); D represent the
`complete contact distance (stent–aorta).
`
`were proximally controlled by accurate positioning at the insertion
`phase.
`In simulation V15% (Fig. 5), stent 1 was deployed with
`is
`longer than the critical clinic safety
`PASL = 18 mm, which
`distance of 15 mm [1,2,37]. However, in the critical contact con-
`
` = 60◦) with
`dition ((cid:2) = 0.05) and high proximal neck angulation (˛
`O% = 15%, stent 1 migrated at the proximal site by more than 15 mm,
`resulting in a higher stress concentration against the aorta [20] with
`a highly instable contact ( ¯Fcs = 1) proximally, and ( ¯Fcs = 0.99) dis-
`
`
`tally, as shown in Fig. 10a. No significant migration was observed at
`the distal attachment site. On the other hand, stent 2 and stent 3 in
`
`4.2. The effect of proximal-distal attachment site length
`(PASL-DASL)
`
`Three simulations of deployments have been performed (V15%,
`џ). The stent sizes are as follows: stent 1 = 144 mm, stent
`VI, and
`2 = 160 mm, and stent 3 = 185 mm, respectively; with the attach-
`ment zone lengths indicated in Table 2 and an oversizing value
`of O% = 15%. The smoothest contact condition between stent and
`aorta was considered to be
`= 0.05. Fig. 4 shows the length of the
`attachment sites when the stent-aorta interaction starts and the
`total superelastic recovery has not yet taken place. These lengths
`
`(cid:2)
`
`Fig. 5. Impact of proximal-distal attachment site length on migration and stability of deployment, (O%) = 15%.
`
`

`

`28
`
`H.-E. Altnji et al. / Medical Engineering & Physics 37 (2015) 23–33
`
`Additionally, the 20% oversized stent 3 showed more connected
`strut points with the vessel in the attachment sites, see Fig. 6b.
`However, oversizing the stent 3 by 25% in the tortuous geome-
`try produced a considerable amount of eccentric stent deformation
`[18] during the insertion phase. As a result, the eccentric stent
`expanded with unequal radial forces which caused the struts to be
`oriented away from the aorta when the stent was fully deployed.
`This produced inconstant frictional forces, and consequently a very
`poor interaction with the aortic wall (Fig. 6c).
`
`4.4. The effect of tangential contact behavior
`
`(cid:2)
`
`≤
`(cid:2)
`≤
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`for vessel/stent contact is
`The value of friction coefficient
`ranged between 0.05
`0.5 [41]. The pathological state of the
`aorta (atherosclerotic plaques, calcifications, etc.) can significantly
`change the
`value. Thus, it seems necessary to investigate the
`effect of
`on the contact stability for the migrated stent 1 only.
`Three extracted experimental friction coefficients [41] were used
`= 0.05, 0.1, and 0.5.
`for the simulation V15%, namely,
`As seen previously, stent 1 migrated under the smoother con-
`= 0.05. On the other hand, when
`= 0.1, the
`tact condition
`results showed that stent 1 has also slipped, but by a negli-
`gible proximal migration distance. The distance involved was
`MIG = 3.5 mm < 10 mm, i.e., no migration failure, see Fig. 7. More-
`over, no distal migration was reported.
`Additionally, when
`= 0.5, the stent was deployed with almost
`no slip or migration. A higher friction coefficient
`= 0.5 proximally
`improved the contact stability by an average 17.5% decrease, rel-
`ative to the moderate contact condition at
`= 0.1, (0.80 vs. 0.97);
`and a 20% decrease from the smoothest contact condition
`= 0.05
`(0.80 vs. 1). It also improved the distal contact stiffness, see Fig. 10c.
`Fig. 7b also displays the stress distribution of stent 1 for three dif-
`ferent coefficients of friction.
`The average contact pressure history introduced in the ves-
`sel during deployment was almost constant for every element
`in the proximal and distal sites when
`= 0.1 and
`= 0.5. Dur-
`ing stent deployment, the contact pressure stresses decreased
`slightly because of radial compressive stresses applied by the aorta
`until equilibrium was reached, see Curves 1, 2 and 3 in Fig. 8.
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`(cid:2)
`
`џ
`
`were deployed without any migration failure
`simulations VI and
`(Fig. 5). Stent 2 and stent 3 resulted in a better contact stability,
`with 10% improvement in the proximal zone compared to stent 1
`(0.90 vs. 1). Only stent 3 improved the contact stability at the distal
`site, see Fig. 10a. These results are in good agreement with clinical
`findings that associate short PASL with unstable deployment and
`migration [2,8,9,37,38]. However, PASL is not the only component
`that leads to migration, as clinical results show [2,4].
`
`4.3. The effect of the oversizing value O%
`
`Stent oversizing is defined as,
`
`Oversizing (%)
`
`= Dstent
`Daorta
`
`,
`
`where Dstent is the outer diameter of stent and Daorta is the outer
`џ,
`diameter of aorta. Five simulations were performed (V20%, I,
`Ш, and IV). Initially, the migrated stent 1 was oversized by 20%
`and deployed with
`= 0.05. The result showed that stent 1 with
`O% = 20% has also undergone migration failure with high insta-
`ble contact ¯Fcs = 1 proximally, and ¯Fcs = 0.99 distally, see Fig. 10b.
`
`
`However, the proximal slip distance was MIG = 13.5 mm > 10 mm
`(Fig. 6a). The migration distance was not particularly important
`compared to the 15% oversized stent 1 MIG = 18 mm
`10 mm, i.e.,
`25% improvement of migration behavior. These results agree with
`experimental findings [4] which associate the insignificant impact
`of oversizing with the contact strength at high neck angulation
`[9,39].
`Moreover, four simulations of stent 3 were performed with
`10–25% oversizing values to investigate the risk of neck enlarge-
`ment [40] or stent collapse [18]. The results showed that oversizing
`stent 3 from 10% to 20% resulted in an almost constant normal and
`frictional force distribution, without aortic neck enlargement [40]
`or migration failure. For larger oversizing value, the radial forces
`were larger. Therefore, the 20% oversized stent 3 resulted in a more
`stable contact with ¯Fcs = 0.6 proximally, i.e., a 24.4% improvement
`
`compared with the 15% oversized stent 3 (0.68 vs. 0.9). A 28.6%
`improvement was found in the distal site (0.60 vs. 0.84), see Fig. 10b.
`
`(cid:8)
`
`(cid:2)
`
`Fig. 6. (a) Impact of 20% oversizing value on stent 1 migration. (b) Contact pressure stresses (MPa) in the aorta for different values of oversizing. (c) Stent 3 collapse when
`excessive oversizing.
`
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`
`29
`
`Fig. 7. (a), (c) Stent 1 migration risk and principal stresses (MPa) contour with respect to different tangential behaviors, simulation (V). (b) Vector plot of the dominant shear
`forces (N) in the migrated stent.
`
`results showed that stent 1 did not migrate in the straight proxi-
`
`mal neck even for the smoothest contact condition ((cid:2) = 0.05), see
`Fig. 9b.
`The average contact stability decreased significantly with 20%
`of contact improvement in the proximal site (0.80 vs. 1), and 23% of
`contact improvement in the distal site (0.99 vs. 0.76), see Fig. 10d.
`= 0◦, more stent/aorta surface interaction was reported, and
`When
`higher contact pressure was obtained.
`
`˛
`
`5. Discussion
`
`We found that proximal length was a crucial factor in contact
`strength to prevent migration in the smoothest contact condi-
`tion with severe angulation. In such conditions, the length of the
`safety-clinical proximal landing zone (15 mm) was not sufficient
`
`However, this behavior was different for many aorta elements
`that lost contact with stent 1 when
`= 0.05 after migration failure
`(Curve 4).
`
`(cid:2)
`
`4.5. Effect of proximal neck angulation
`
`The previous patient-specific morphology shows high proximal
`= 60◦, see Fig. 1. According to Sternbergh [43],
`angulation with
`neck angulation severity can be classified into the cases of mild
`(<40◦), moderate (40–60◦), or severe (>60◦).
`investigate the effect of challenging neck anatomy on
`To
`the incidence of migration, we used an idealized aneurysmal
`
`aorta model with zero proximal angulation (˛ = 0◦) assuming the
`
`smoothest contact behavior ((cid:2) = 0.05) and oversizing O% = 15% for
`= 60◦, the
`stent 1 (Fig. 9a). Contrary to the migrated stent 1 when
`
`˛
`
`˛
`
`Fig. 8. The maximal contact pressure stresses (p) contour (MPa) induced in the aorta for three different ((cid:2)) values after stent 1 deployment. Curves 1, 2, and 3 represent
`the average (p) evolution with time simulation in both proximal and distal attachment sites. Curve 4 shows the behavior of one vessel element that lost the contact after
`migration failure.
`
`

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`30
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`H.-E. Altnji et al. / Medical Engineering & Physics 37 (2015) 23–33
`
`to prevent migration failure. One important issue is that ¯Fcs was
`calculated just after the first instant of interaction for the stents
`undergoing migration (>10 mm), and when full stent deployment
`was reached for non-migrated stents (<10 mm).
`= 60◦, with O% = 15% and 20%, (Simulation
`When
`= 0.05 and
`V), stent 1 began to interact with the vessel, and the radial contact
`forces at the proximal site began to increase. Subsequently, when
`superelastic recovery took place, the shear forces which dislodge
`the stent increased due to the angulation that decreased the surface
`of interaction. These forces became higher than the radial stiffness
`strength of stent 1, while the normal contact forces decreased sig-
`nificantly and migration failure took place. Fig. 7b shows a metric,
`namely, a vector plot of the dominant shear force direction, just
`before the instant of stent 1 migration.
`These results are in good agreement with the clinical findings
`that associate short PASL with unstable deployment and migration
`[2,8,9,37,38]. However, it is clear that PAS is not the only component
`that leads to migration as clinical results show [2,4].
`showed that the length of stent 3 (185 mm)
`The simulations VI,
`was more than enough to avoid migration. Moreover, oversizing
`stent 1 by 20% was beneficial, but insufficient, to avoid migration
`failure. This is particularly true when the proximal attachment zone
`is critical, as in stent 1. The distal attachment length does not seem
`to have a significant effect on the risk of rupture, as notable migra-
`tion was not in evidence. This result agrees with the clinical finding
`
`˛
`
`(cid:2)
`
`џ
`
`Fig. 9. (a) Idealized aneurysmal aorta. (b) Principal stress contour (MPa) induced
`when stent 1 deployment without migration.
`
`Fig. 10. Contact stability vs. factors affecting stent 1 migration. (a) Proximal stent length. (b) Oversizing value. (c) Coefficient of friction. (d) Proximal neck angulation.
`
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`
`31
`
`Fig. 11. ALLKE/ALLIE ratio for stent 1 and aorta during insertion and deployment procedures in the reference model simulation.
`
`that suggests giving more control for precise proximal placement,
`with minimal control over the distal attachment site [1,2]. The 20%
`oversized stent 3 resulted in the best contact stiffness outcomes
`compared to 10% and 15% oversized stent 3. The 10% and 15% over-
`sized conditions of stent 3 did not show considerable differences
`in their respective results. More importantly, despite the fact that
`many devices have been deployed in angulated necks (>60◦) with-
`out stent enfolding, stent collapse becomes more critical when both
`oversizing and neck angulation increase; particularly, when the
`stent is placed higher in both the proximal and distal attachment
`sites, i.e., stent 3. This placement can lead to single-side progressive
`strut dilation and subsequent rupture.
`These results are consistent with the medical findings which
`associate eccentric stent deformation with migration and type
`Ia endoleaks [18,38,43]; and excessive oversizing (>25%) with an
`increased potential of stent enfolding [4,42,44,45], and neck dilata-
`tion with subsequent migration [6]. Therefore, a suitable level of
`oversizing should be chosen for a specific level of neck angulation
`and the stent should be placed higher only in the proximal case
`(stent 2) as supported by clinical studies [1].
`The results also show the importance of the pathological state
`of the aorta represented by different coefficients of friction. The
`roughest contact condition produced the best contact stiffness
`and high normal contact forces compared with tangential contact
`forces. These results can explain the different clinical deployment
`results for different pathological aorta states [46].
`Finally, severe proximal neck angulation was the most impor-
`tant cause of poor deployment where
`the fixation
`length,
`interaction surface quality, and stent opposition are reduced, and
`the struts are not circumferentially uniform. In the non-angulated
`aorta, stent 1 applied a higher radial force distribution on the larger
`surface of the vessel. Thus, the contact normal forces increased and
`became higher than the shear forces. Therefore, a good opposi-
`tion was obtained. This finding is consistent with reported clinical
`results [1,2,6–8,44,47]. Although severe angulation has been identi-
`fied as potential risk factor associated with migration failure, other
`factors, such as the short proximal landing zone and smooth contact
`condition, should be considered; they may also increase the shear
`downward forces. High angulation can be a major factor in stent
`folding and poor deployment, increasing the risks of migration and
`type Ia endoleaks.
`
`Moreover, our results show that in our real morphology, not
`every point on the strut surface is in contact with the aortic wall
`when it exhibits irregular contour at the attachment sites. This
`fact becomes more apparent in cases of high angulation and blood
`vessel pathology.
`
`6. Limitations
`
`The present study considers that deployment success is deter-
`mined only by the mechanical fixation applied by the stent [48].
`Similar to previous research [19], we did not investigate the influ-
`ence of the graft on the results. Other authors [19] assumed that
`the graft has little contribution to the proximal radial stiffness com-
`pared to the nitinol stent when final device deployment is achieved.
`The study in Ref. [49] states that the graft material can contribute
`to different mechanical behavior as the rings can be constrained by
`the graft material exerting upward component forces. Our study
`focused only on short-term stent fixation. In this case, we suspect
`that the wall shear stresses induced by the blood flow are negligi-
`ble compared to normal forces applied by the spring action when
`the stent had just been deployed. Future work will include the graft
`and the residual stresses [23,50] to evaluate long-term fixation of
`the stent graft under hemodynamic factors [51,52] throughout the
`cardiac cycle.
`Moreover, the lumen of the vessel was reconstructed in the
`model regardless of the calcifications and the varied thickness [53].
`We believe that this approximation will not significantly affect the
`contact behavior at attachment sites. Finally, for the objectives of
`our study, we believe the isotropic hyperelastic model of the aorta
`is appropriate. However, many other models [21,22,54] can be used
`to describe an anisotropic mechanical response of thoracic aorta.
`
`7. Conclusion
`
`In this work, we evaluated the contact s