Vascular stents: Coupling full 3-D with reducedorder structural models

IOP Conference Series: Materials Science and Engineering Vascular stents: Coupling full 3-D with reducedorder structural models To cite this article: I Avdeev and M Shams 2010 IOP Conf. Ser.: Mater. Sci. Eng. 10 012133 View the article online for updates and enhancements. Related content - Computational design analysis for deployment of cardiovascular stents Sriram Tammareddi, Guangyong Sun and Qing Li - A recoil resilient lumen support, design, fabrication and mechanical evaluation Arash Mehdizadeh, Mohamed Sultan Mohamed Ali, Kenichi Takahata et al. - Vascular stents with submicrometer-scale surface patterning realized via titanium deep reactive ion etching Shannon C Gott, Benjamin A Jabola and Masaru P Rao Recent citations - On the Importance of Modeling Stent Procedure for Predicting Arterial Mechanics Shijia Zhao et al This content was downloaded from IP address 148.251.232.83 on 02/05/2018 at 14:06

Vascular Stents: Coupling Full 3-D with Reduced-Order Structural Models I Avdeev 1 and M Shams 1 1 Department of Mechanical Engineering, University of Wisconsin-Milwaukee 3200 North Cramer St., Milwaukee, WI 53211, U.S.A. E-mail: avdeev@uwm.edu Abstract. Self-expanding nitinol stents are used to treat peripheral arterial disease. The peripheral arteries are subjected to a combination of mechanical forces such as compression, torsion, bending, and contraction. Most commercially available peripheral self-expanding stents are composed of a series of sub-millimeter V-shaped struts, which are laser-cut from a nitinol tube and surface-treated for better fatigue performance. The numerical stent models must accurately predict location and distribution of local stresses and strains caused by large arterial deformations. Full 3-D finite element non-linear analysis of an entire stent is computationally expensive to the point of being prohibitive, especially for longer stents. Reduced-order models based on beam or shell elements are fairly accurate in capturing global deformations, but are not very helpful in predicting stent failure. We propose a mixed approach that combines the full 3-D model and reduced-order models. Several global-local, full 3-D/reduced-order finite element models of a peripheral self-expanding stent were validated and compared with experimental data. The kinematic constraint method used to couple various elements together was found to be very efficient and easily applicable to commercial FEA codes. The proposed mixed models can be used to accurately predict stent failure based on realistic (patient-specific), non-linear kinematic behavior of peripheral arteries. 1. Introduction Peripheral Arterial Disease (PAD), or narrowing of the arteries in the leg, is the most common type of peripheral vascular disease, affecting about eight million Americans. According to the American Heart Association, PAD is very common among older Americans (+65 years), affecting from 12 to 20 percent of that group. Timely diagnosis and treatment of PAD is highly important, as people with PAD have a four to five times greater risk of stroke and heart attack. Left untreated, PAD can also lead to gangrene and subsequent amputation of the lower extremities. When drug treatment fails, a few surgical options are available such as peripheral angioplasty (less invasive, but a temporary solution) or peripheral bypass (a surgical procedure required for severely blocked arteries). Treatment of atherosclerotic occlusive disease in peripheral arteries with intraluminal stenting has been studied in several clinical trials [1]. Stenting has proven to be very efficient for endovascular treatment of coronary arteries, mostly because it is less invasive than open surgery. The two most frequently reported problems associated with using stent grafts in the lower extremities are (a) high rates of stent fractures and (b) in-stent scar tissue growth [2] or restenosis. Stent fracture rates observed in clinical trials vary from 1% to 90% and depend on many factors, including stent design. 1 c 2010 Published under licence by Ltd 1

The stent deployed into a peripheral artery is subjected to several loading conditions. Normal (radial) pressure on the walls is generated by stent expansion (either a self-expansion for nitinol stents or balloon-assisted expansion for stainless steel stents). The patient s movement causes the stented artery to stretch, bend or twist, depending on the stent location and the type of motion. Both the artery and the stent undergo complex three-dimensional deformations, which over time lead to device fatigue and stent fracturing, and to the artery wall tissue stimulation and in-stent restenosis. For example, using planar radiography on human cadaver models, Nikanorov and his colleagues determined axial strains (from 3% to 23% for various locations) for stented and unstented SFA at 70 /20 and 90 /90 knee/hip flexion [3]. Using static in vivo MRI of the SFA, Cheng and his colleagues measured significant shortening (13% ± 11%) and twisting (60% ± 34%) of unstented SFA between supine and fetal positions [4]. The goal of this study is to investigate various approaches to modeling long peripheral stents to combine into one model the accurate, non-linear kinematics of the entire stent with the accurate description of the localized strains and stresses leading to fatigue failures. The junction of various types of finite elements requires the use of nodal or element constraints. Three methods commonly used to introduce constraints into the governing equations are: (1) penalty function; (2) Lagrange multipliers; and (3) direct elimination of dependant variables [5]. The penalty method is simple and proven to be very effective in various applications, including studying edge effects in sandwich structures [5]. The primary disadvantage of the penalty function method is that the constraints are satisfied approximately. The accuracy of the overall solution also strongly depends on the choice of the penalty factor. For the Lagrange multipliers method, the primary disadvantage is the introduction of additional unknowns that might lead to indefinite algebraic forms of the FEA system and cause numerical instabilities. The direct elimination method is computationally efficient and easily understandable [6], which is especially true for Derichlet conditions or single-point constraints. One of the main advantages of the direct elimination method is that the stiffness matrix remains positive definite and a variety of commercial FEA solvers can be used. The direct method will be used in this study for coupling 3-D solid elements with 3-D beam or 3-D solid shell elements. 2. Methods 2.1. Stent design and materials Typically, stent dimensions vary from 5 to 14 mm in diameter and from 20 to 200 mm in length. The key features that a stent should possess are (1) adequate scaffolding, (2) acceptable levels of flexibility and radial strength to track to the lesion, and (3) control recoil [7]. For this study, we used a 7-mm (diameter)/150-mm (length) Protege EverFlex self-expanding biliary stent system (ev3 Endovascular, Inc., Plymouth, MN). The stent is designed for the palliative treatment of malignant neoplasms in the biliary tree. The stent is made of a nickel titanium alloy (nitinol) and comes premounted on an over-the-wire delivery system (catheter). The stent is laser-cut from a nitinol tube into an open lattice design. When deployed, the stent achieves its predetermined diameter and exerts a constant outward force to establish patency in the biliary ducts. To achieve desired flexibility, strength, and scaffolding, each ring consists of 16 V-shaped struts (100 x 100 microns), which are connected to the next ring via four connectors at 90 degrees apart from each other. The connectors are offset from each other along the circumference by one cell forming a spiral structure for additional flexibility (figure 1). 2 2

r2 r1 x3 r3 a2 a1 r3 (A) Stent design (fragment) x1 x2 (B) V-shaped cell design Figure 1. Protege EverFlex Self-Expanding Biliary Stent System. Nitinol self-expanding stents have drawn much attention because of certain advantages over balloonexpandable stents. In addition to ease of deployment, self-expanding nitinol stents can maintain high resistance to inward pressure while providing a lower outward pressure on the artery wall. Nitinol's extraordinary ability to accommodate large strains, coupled with its physiological and chemical compatibility with the human body, has made it one of the most commonly used materials in medical device engineering and design. Another advantage of nitinol stents is superelasticity, which is the ability to return to an original shape after severe deformation, and is it is unique property of shape memory alloys; for example, if nitinol is stretched over 10%, it will return to its original length. Permanent strains accumulated in deformed nitinol wires at a low temperature (martensitic phase) are caused by changes of its crystal lattice structure. These strains can be recovered by heating the material to a higher temperature (austenitic phase), which reverses the crystal lattice structure to its pre-deformed shape. For nitinol stents, the stress, strain, temperature, and martensite volume fraction provide a complete set of state variables to describe them. The thermomechanical constitutive equation, which takes into account geometrical nonlinearities of the nitinol, is given by [8]: σ σ = C ε ε 0 ) + θ( T T ) + Ω( ξ ) (1) 0 ( 0 ξ0 where σ is the Piola-Kirchhoff stress tensor, C is the stiffness tensor, ε is the Green-St. Venant strain tensor, θ is the thermoelastic tensor, T is the temperature, Ω is the metallurgical transformation tensor, ξ is the martensite volume fraction, and variables with the subscript 0 refer to the initial conditions where the material properties are constant. 3 3

2.2. Experimental setup for FEA model validation To validate the developed FEA models, we designed and built easily configurable stent bench testing apparatus capable of axial, bending, and twisting steady and transient deformation modes (figure 2). The deformations are prescribed in a transient-mode testing, while the loads are controlled in the static mode. The stent deformations were recorded optically using a Point Grey DragonFly2 CCD camera (Point Grey Research, Richmond, BC, Canada) and measured using image analysis algorithms. (1) Experimental Setup (2) Mixed FEA model Figure 2. (1) Stent testing apparatus: (A) stent, (B) high-resolution camera, (C) and (D) axial load/deformation fixtures, and (D) vertical clamp fixture. (2) Mixed FEA model diagram. 2.3. Finite element models Full 3-D finite element, non-linear analysis of an entire stent is computationally expensive, especially for long superficial femoral artery stents; therefore, reduced order and mixed models have to be studied. All FEA models were developed using ANSYS r.12.0 commercial FEA package [9] and can be categorized into three groups: (1) 3-D models with 20-node structural solid elements. (2) 3-D models with Timoshenko beam elements. (3) 3-D solid shell models. (4) 3-D mixed models: beam/solid (figure 2). (5) 3-D mixed models: shell/solid (figure 2). Model specifications are summarized in table 1. The beam element formulation is based on Timoshenko beam theory, and the elements are well suited for accurately modeling shear deformations in a relatively thick beam. Since standard ANSYS beam elements do not support shape-memory alloy material formulation and require user-defined material models [9], we limited our pure beam and beam/solid mixed models to linear modal analysis assuming the elastic material properties of nitinol. The solid shell formulation is generally used for modeling shell structures with a wide range of thicknesses; it supports SMA non-linear material models, making it suitable for large deformation non-linear analysis. The direct elimination method was used for coupling elements of different types in the mixed models (figures 3 and 4). 4 4

Model Type Table 1. Specifications of the finite element models. Element Type [9] Number of Elements Number of Nodes Number of equations Beam BEAM188 27,216 27,976 167,856 Solid Shell SOLSH190 74,340 223,808 671,424 3-D Solid (coarse mesh) 3-D Solid + Solid Shell 3-D Solid + Beam SOLID186 59,220 602,856 1,808,568 SOLID186 SOLSH190 SOLID186 BEAM188 63,768 71,880 2,820 25,952 405,788 213,280 13,872 26,680 1,217,364 639,840 83,232 160,080 (A) (B) Figure 3. Mixed beam/solid model: (A) mesh interface at the ring connectors and (B) mixed mesh interface (mesh fragment). (A) (B) Figure 4. Mixed shell/solid model: (A) mesh interface at the ring connectors and (B) mixed mesh interface (mesh fragment). 5 5

3. Results 3.1. 3-D solid model validation A uniaxial tension test of the stent was used to validate the 3-D solid FEA model. A stent was clamped at both ends (figure 2); the bottom-end of the stent was subjected to a series of loads (weights) and the maximum stent deformation was optically captured and measured. The force/displacement curve is depicted in figure 5. Finite element results for a 3-D solid model are also presented in figure 5. The curve is slightly non-linear and FEA results agree well with the experimental data. The 3-D solid model will be used as a reference model for the reduced-order and mixed models discussed below. Figure 5. Maximum axial stent deformation: experimental results vs. 3-D structural element solid model. 3.2. Static analysis with the solid/shell model We used a mixed, shell/solid model (figure 2) for a static non-linear (large deformations and shapememory alloy material) analysis for a fixed value of tension load (F = 0.2N). The distribution of equivalent stress is depicted in figure 6. It should be noted that, due to interface mesh mismatch, stress discontinuity was observed, which is local in nature and does not affect stress distribution as far away as the next ring (figure 6). 3.3. Modal analysis Using fixed support boundary conditions at both ends and assuming a linear elastic material model of the stent, we computed 15 undamped natural frequencies (table 2) and free vibration mode shapes (figure 7). Five FEA models were compared with each other. Using solid 3-D model as a reference, we observed that the beam model was off by 25% - 30%; the beam/solid model was off by up to 35%; the shell model was off by 7% - 9%, and shell/solid model was only off by 7.5% - 8%. The mode shapes were qualitatively similar for all five models. 6 6

Figure 6. Equivalent stresses in shell and solid elements (mixed model), MPa. Table 2. Stent s natural frequencies (undamped, Hz). Mode # Beam Beam/Solid Shell Shell/Solid Solid 1 0.564 0.503 0.880 0.869 0.810 2 0.564 0.503 0.880 0.869 0.810 3 1.514 1.344 2.342 2.322 2.161 4 1.514 1.344 2.342 2.322 2.161 5 2.870 2.590 4.283 4.253 4.034 6 2.870 2.590 4.393 4.331 4.064 7 3.237 3.030 4.393 4.331 4.064 8 4.562 4.087 6.529 6.478 6.171 9 4.562 4.087 6.904 6.841 6.404 10 5.026 4.705 6.904 6.841 6.404 11 6.471 5.925 8.564 8.436 8.066 12 6.529 5.925 9.772 9.646 9.086 13 6.529 6.217 9.772 9.646 9.086 14 8.715 7.877 12.84 12.74 12.03 15 8.715 7.877 12.91 12.79 12.03 7 7

#1 (0.503 Hz) #2 (0.503 Hz) #3 (1.344 Hz) #4 (1.344 Hz) #5 (2.590 Hz) #6 (2.590 Hz) #7 (3.030 Hz) #8 (4.087 Hz) #9 (4.087 Hz) #10 (4.705 Hz) #11 (5.925 Hz) #12 (5.925 Hz) #13 (6.217Hz) #14 (7.877 Hz) #15 (7.877 Hz) Figure 7. Mode shapes: mixed beam/solid model (undamped, free vibration). 8 8

4. Conclusions Global-local, full 3-D/reduced-order finite element models of a peripheral self-expanding stent were developed and calibrated. Model accuracy and sensitivity to various coupling methods were investigated. The direct elimination method was found to be very efficient and easily applicable to the most commercial FEA codes. The shell/solid mixed model approach was the most accurate method compared with the full 3-D solid model. The proposed approach of coupling full 3-D with reducedorder finite element models can be used to accurately predict stent failure based on realistic (patientspecific), non-linear kinematic behavior of a peripheral artery. In the future, the developed models can be adapted for fluid-structural and stent-artery interaction analyses. Acknowledgements The authors thank the Department of Mechanical Engineering, University of Wisconsin-Milwaukee for financial support; ANSYS, Inc. for academic research license support; and A. Hastert for his help with the experimental work. References [1] Higashiura W, Kubota Y, Sakaguchi S, Kurumatani N, Nakamae M, Nishimine K and Kichikawa K 2009 Prevalence, factors, and clinical impact of self-expanding stent fractures following iliac artery stenting J. of Vasc. Surg. 49 645-52 [2] Schlager O, Dick P, Sabeti S, Amighi J, Mlekusch W, Minar E and Schillinger M 2005 Longsegment SFA stenting the dark sides: in-stent restenosis, clinical deterioration, and stent fractures J. of Endovasc. Therapy 12 676-84 [3] Nikanorov A, Smouse H, Osman K, Bialas M, Shrivastava S and Schwartz L 2008 Fracture of selfexpanding nitinol stents stressed in vitro under simulated intravascular conditions J. of Vasc. Surg. 48 435-40 [4] Cheng C, Wilson N, Hallett R, Herfkens R and Taylor C 2006 In vivo MR angiographic quantification of axial and twisting deformations of the superficial femoral artery resulting from maximum hip and knee flexion J. of Vasc. Intervent. Radiol. 17 979-87 [5] Avdeev I, Borovkov A, Kiylo O, Lovell M and Onipede D 2002 Mixed 2D and beam formulation for modelling sandwich structures Int. J. Comp.-Aid. Eng. and Soft. 19 451-66 [6] Zienkiewicz O and Taylor R The Finite Element Method. Vol. 1: Basic Formulation and Linear Problems 4 th Edition (McGraw-Hill, London) [7] Bonsignore C 2003 Proceedings of the International Conference on Shape Memory and Superelastic Technologies SMST-2003 519-28 [8] Onipede D, Avdeev I and Sterlacci G 2000 Proc. of SPIE vol. 4348 328-37 [9] ANSYS 12.0 documentation 2009 ANSYS, Inc., Canonsburg, PA, USA 9 9