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Application of finite element method to comparing the NIR stent with the multi-link stent for narrowings in coronary arteries
Acta Mechanica Solida Sinica, Vol. 28, No. 5, October, 2015 Published by AMSS Press, Wuhan, China
ISSN 0894-9166
APPLICATION OF FINITE ELEMENT METHOD TO COMPARING THE NIR STENT WITH THE MULTI-LINK STENT FOR NARROWINGS IN CORONARY ARTERIES S. Misagh Imani1⋆ A. M. Goudarzi1 P. Valipour2 M. Barzegar1 J. Mahdinejad1 Seiyed E. Ghasemi3 (1 Department of Mechanical Engineering, Babol University of Technology, Babol, Iran) ( Department of Textile and Apparel, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran) (3 Young Researchers and Elite Club, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran) 2
Received 16 December 2013, revision received 2 July 2014
ABSTRACT ‘Stent versus stent’ studies are a kind of randomized trials which are designed to show the superiority of the new stent designs compared with the previously approved ones. These studies are usually used by regulatory agencies, such as the U.S. Food and Drug Administration (FDA), to give an approval to new stent designs. The problem with these clinical trials is their high cost and difficulty. In this paper, a numerical alternative for ‘stent versus stent’ complicated clinical studies is presented. A finite element model is developed to investigate the influence of stent design on the outcome after coronary stent placement. Two commercially available stents (the NIR and Multi-Link stents) are modeled and their behavior during the deployment is compared in terms of stress distribution, radial gain, outer diameter changes and foreshortening. Moreover, the effect of stent design on the restenosis rate is investigated by comparing the stress distribution within the arteries. An analysis of the arterial wall stresses in the stented arteries indicates that the Multi-Link stent design causes lower stress to an atherosclerotic vessel with a localized stenotic lesion compared to the slotted tube NIR design. The findings correlate with the observed clinical restenosis rates, which have reported higher restenosis rates in the NIR compared with the MultiLink stent design.
KEY WORDS stent vs. stent studies, finite element method, coronary stent, plaque, vessel
I. INTRODUCTION Cardiovascular diseases, also known as atherosclerosis, are the first cause of death in the United States. For two decades, they constituted an important subject of clinical investigations and academic studies. The well-known stenosis pathology (reduction of the vascular lumen of an artery) affects the dynamics of the blood flowing through arteries and may even obturate them[1] . Treatment options include bypass surgery, atherectomy, balloon angioplasty and stenting[2] . Stent placement has become the most frequently used procedure to treat atherosclerosis and is commonly used by practitioners in recent years, because it has not only improved clinical outcomes compared with other possible treatments, but also have vastly enhanced our capability and confidence in tackling increasingly complex patients and lesions traditionally treated with coronary artery bypass graft surgery ⋆
Corresponding author. E-mail: [email protected]
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(CABG)[3, 4] . As reported by Gu et al.[5] , only in the United States, did more than 1.2 million patients undergo stent implantations each year. Since the first implantation of stents in humans in 1986, many improvements, changes and discoveries have been achieved to make them safer and more functional. Nowadays, more than 100 different stent designs are being marketed or are in evaluation for vascular and non-vascular indications, and moreover, every year new stent designs are manufactured and presented in the market[6] . These new stent designs have to be proved to be equivalent to an approved stent (not requiring that a new stent have superior safety or efficacy compared with existing stent(s)) to be confirmed from the regulatory agencies such as the U.S. Food and Drug Administration (FDA)[7] . This sets the stage for a series of ‘stent versus stent’ randomized trials designed to show that each newer stent design was not inferior to (i.e., was equivalent or better than) the prior approved stent[7–9] . These kinds of studies can also be very useful for selecting the appropriate stent type to use. But the problem with these clinical approaches is high cost and difficulty. Moreover, they often refer only to two different stent designs[10] while the results are hardly comparable to those from previous trials, even for the same stent design, because of the different methods adopted (patient recruitment, primary or secondary endpoints, etc.). Recently finite element methods (FEMs) are considered an efficient way of testing and improving stent designs. In comparison with expensive experiments carried out in hospitals and laboratories, numerical simulations accomplished by computers have advantages in both flexibility and cost. A large amount of numerical work is available in recent publications. Chua et al.[11] , Dumoulin and Cochelin[12] and Gu et al.[13] reported their researches, respectively, into the deployment of various stents without contact effect. Furthermore, Chua et al.[14, 15] and Xia et al.[16] considered the contact between the stent and the balloon in the computation of the deformation and stress distribution of the stent. More complicated models considering multi-contacts, i.e. stent/artery/plaque[17], balloon/stent/artery[18] and balloon/stent/artery/plaque[6, 19] were established to investigate both the mechanical behavior of the stents and the biomechanical response of the coronary artery wall. However, published works on the effect of application of different stents geometry by computer simulation are rarely found in the literature and the current knowledge is mostly clinical. In this paper the mechanical behavior of different stent types was compared by means of finite element method. Two commercially available stents, with the same material and different designs, were studied and the behavior of the models was compared in terms of stress distribution, radial gain, outer diameter changes and foreshortening. Moreover, the effect of stent design on the restenosis rate was investigated by comparing the stress distribution in the arteries. The paper tends to present a method which can be used as a simple and economical alternative for ‘stent versus stent’ complicated clinical studies.
II. MATERIALS AND METHODS Two models were developed, each constituted by the same balloon and coronary artery with plaque, and a different stent design. Modeling of various parts used in simulating is presented in this section. 2.1. Stent Two different coronary stent designs were taken into consideration. They resemble two commercial intravascular stents. Below they will be referred to as STENT A (NIR, Scimed, Boston Scientific Europe, Verviers, Belgium) and STENT B (Multi-Link, Guidant-Advanced Cardiovascular Systems, Inc., Santa Clara, CA, USA). The primary model of stents was produced using commercially available software. Models were constructed on the basis of images from Ref.[20]. The main geometrical dimensions of the simulated models are assumed to be the same. Both of the stents have an outer diameter of 3 mm, a length of 10 mm, and a thickness of 0.05 mm. Figure 1 shows the two-stent models in their unexpanded configuration. The stents were assumed to be made of stainless steel 304. A bi-linear elasto-plastic material model was used to model the behavior of stents material. The material properties were identically chosen as those assumed in Ref.[15], namely, Young’s modulus = 193 GPa; shear modulus = 75 × 106 MPa; tangent modulus = 692 MPa; density = 7.86 × 10−6 kg/mm3 ; yield strength = 207 MPa; Poisson’s
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Fig. 1. Geometry of two-stent models in their unexpanded configuration.
ratio = 0.27. 2.2. Artery with Plaque The geometrical properties of the vessel and plaque are: vessel’s length = 20 mm; vessel’s inner diameter = 4 mm; vessel’s outer diameter = 5 mm; plaque’s length = 3 mm; plaque’s inner diameter = 3 mm. The data from the work of Prendergast et al.[21] were adopted to describe the mechanical behavior of the coronary artery by means of hyperelastic constitutive law based on a reduced polynomial strain energy density function, of the third order. More details can be found in Ref.[1]. 2.3. Balloon The balloon was modeled to be 12 mm in length. The outer diameter and the thickness of the balloon were 2.9 mm and 0.1 mm, respectively. A polyurethane rubber type material was used to represent the balloon. Polyurethane is an incompressible material and was defined by a nonlinear first-order hyperelastic M-R model. The energy function’s coefficients were obtained from Ref.[15]. 2.4. Meshing and Boundary Conditions Owing to the symmetrical conditions, only one-seventh of STENT A and one-third of STENT B were used to simulate the expansion process. For both of the models, all of the parts were meshed with eight-node linear 3D block elements. Sensitivity analyses were performed to ensure enough meshing refinement. Models A and B include 10060 and 26140 elements, respectively. Figure 2 shows the assembled model for STENT A .
Fig. 2. The assembled model for STENT A.
2.5. Loading and Solutions The loading process of both of the models consisted of two steps. In the first step, without considering the existence of the balloon and the stent, a constant internal pressure equal to 13.3 kPa was applied to
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the vessel and the plaque. This pressure is equal to the blood pressure of 100 mmHgs[17] . The pressure simulates the internal pressure of the blood and causes the vessel to expand, and also, induces an initial stress. In the second step, by maintaining the initial pressure applied to the vessel and plaque, a constant pressure was imposed on the internal surface of the balloon. This pressure was applied with a constant rate in 1.635 seconds and its value was varied from 0 to 0.32 MPa for STENT A and 0 to 0.3 MPa for STENT B .
III. RESULTS AND DISCUSSION In this section, the results of the finite element analysis of the expansion of stents inside an atherosclerotic coronary artery are presented. The quantities of interest include stress distribution, radial gain, outer diameter changes, foreshortening and restenosis rate. 3.1. Stress Distribution The distribution of von Mises stress in the two-stent models is shown in Fig.3 at maximum expansion instant. As can be seen in this figure, the value of maximum stress in the stent is 297.7 MPa and 254.7 MPa, for STENT A and B, respectively. The distribution of von Mises stress in the expanded vessels is pictured in Fig.4 for the two geometries investigated. The highest arterial stresses are in the areas where maximum changes occurred in stents diameter. The value of maximum von Mises stress in the vessel is 0.262 MPa and 0.244 MPa, for STENT A and B, respectively. A possible damage to the artery might occur at these critical points.
Fig. 3. Distribution of von Mises stress.
Fig. 4. Distribution of von Mises stress in the expanded vessel at maximum expansion.
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3.2. Radial Gain and Outer Diameter Changes Radial gain (RG) is one of the most important parameters for evaluating the performance of the stent, which is defined as follows: RG = Rexpansion − R0 (1) where Rexpansion and R are the outer radius of the stent, after and before the expansion, respectively. RG is measured at the middle of the stent. Note that the value of RG represents the final radial deformation, and a greater value of RG is more appropriate in actual applications. The value of RG is 0.361 mm and 0.363 mm, for STENT A and B, respectively. This means that their final diameters are approximately equal. For a better understanding of the expansion behavior of the two-stent models, Fig.5 plots the outer diameter of stents against the expanding pressure. As can be seen in Fig.3, because of the existence of the plaque and the pressure applied by it, different positions of stents have different diameters. Here, in order to verify the behavior of the models, the outer diameter changes of points A1 , B1 in STENT A and points A2 , B2 in STENT B (as shown in Fig.3) were derived and shown.
Fig. 5. The relation between the outer diameter of the stent and expanding pressure.
Figure 5(a) shows that the rate of increment of stent diameter at points A1 and B1 is almost identical as pressure changes from 0 MPa to 0.14 MPa. From the pressure 0.14 to 0.25 MPa, because of the contact between point A1 and the plaque, stent diameter increases with a low rate at point A1 , while at point B1 , the rate of increment of the diameter grows significantly. Finally, for pressures larger than 0.25 MPa, because of the contact between the stent and the vessel, the variation of diameter at point B1 becomes small. The same behavior was observed for STENT B (Fig.5(b)), although the critical points are different (The critical points are 0.11 MPa and 0.28 MPa, respectively). 3.3. Foreshortening When the stent expands, because of different distributions of circumferential stress between the free ends and the central part, it bends on edges that causes the diameter at the end sides to become larger than that in the middle of the stent. This results in a reduction in the stent length which is called ‘foreshortening’. In fact, foreshortening defines the effective length of the stent and according to the findings of the clinical studies, a stent is expected to have a low value of foreshortening[22]. The foreshortening is defined as L0 − L foreshortening = × 100% (2) L0 where L0 and L are the initial and final length of the stent, respectively. Figure 6 depicts the relation between the foreshortening and the expanding pressure. As can be seen in this figure, expansion of the stents causes the reduction of 5.5 % and 0.0351 % in the length of STENT A and B, respectively. STENT B has a lower value of foreshortening in comparison to STENT A because of its special structure. Moreover, for this kind of stent, in some pressures the value of foreshortening becomes negative which means this design has increased in length.
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Fig. 6. The relation between the forshortening and expanding pressure.
3.4. Restenosis Rate One of the most important issues that usually have been considered during the comparison process is in-stent restenosis (ISR). In-stent restenosis is a re-narrowing or blockage of an artery at the same site where stenting has already taken place. In the early days of stent implantation, approximately one-third of patients suffered from restenosis within 6 months of stent deployment[23] . It has recently been shown that stress concentration in the stented artery wall correlates with the restenosis rate and the possibility of ISR increases by increasing the stress in the vessel wall[5] . Changes of stent cell geometry may affect the stress field within the artery wall and consequently influence the restenosis rate. Numerous clinical trials have looked into the influence of stent design on the outcome after coronary stent placement[7–9, 24] . These works can confirm the results obtained in this study. The findings of the current paper indicate that the possibility of restenosis in STENT A is greater than STENT B owing to the higher value of maximum arterial stresses in STENT A. This agrees with the results obtained in the study by Kastrati et al.[8] where 1147 patients received randomly five types of stainless steel stents. Two of these stents resemble model A and B and the restenosis rate is higher for the former. Moreover, the same conclusion can be drawn from analyzing the study by Kastrati et al.[9] . 3.5. Verification To validate the present method, the models identical to those presented in Ref.[15,25] were constructed with the results obtained compared in Table 1. The comparison indicates that the results are in good agreement in terms of maximum von Mises stress in the stent, which confirm the validity of the present method. Table 1. Comparison between the results obtained in this study and other researches
Present study Chua et al.[15] Ju et al.[25]
Maximum stress in the stent (MPa) 261.5 250 288. 2
Difference (%) — 4.6 10.2
IV. CONCLUSION The paper presents a method which can be used as a simple and economical alternative for ‘stent versus stent’ complicated clinical studies to compare the behavior of different stent designs. In order to achieve a more realistic description of the stent implantation procedure, the model includes internal pressure of blood, balloon, stent, vessel and plaque. Two commercially available stent models were analyzed and compared in this study. According to the analysis, even when both of the stents expanded to the same final diameters, the maximum stress induced in the artery by the NIR stent was found to be 7.4 % greater than the Multi-Link stent. Consequently, it is predictable that using the NIR stent results in more injury in vessel than the other one, which increases the possibility of restenosis. These
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results agree with the clinical studies which confirm that the restenosis rate of the NIR stent is higher than that of the Multi-Link stent[8, 9] . Finally, it should be mentioned that from analyses like those carried out in this study, it is difficult to find a strict correlation between the in-stent restenosis and the geometrical design, such as the length of the links. The testing methodology outlined here is proposed as a pre-clinical testing tool presumably useful when joined with a clinical trial aimed at comparing the influence of the stent design on the degree of restenosis.
References [1] Imani,M., Goudarzi,A.M., Ganji,D.D. and Latif Aghili,A., The comprehensive finite element model for stenting: The influence of stent design on the outcome after coronary stent placement. J. Theor. Appl. Mech., 2013, 51: 639-648. [2] Pericevic,I., Lally,C., Toner,D. and Kelly,D.J., The influence of plaque composition on underlying arterial wall stress during stent expansion: The case of lesion-specific stents. Med. Eng. Phys., 2009, 31: 428-433. [3] Katritsis,D.G., Karvouni,E. and Ioannidis,J.P., Meta-analysis comparing drug-eluting stents with bare metal stents. Am. J. Cardiol., 2005, 95: 640-643. [4] Stettler,C., Wandel,S., Allemann,S., Kastrati,A., Morice,M.C., Schomiq,A., et al., Outcomes associated with drug-eluting and bare-metal stents: a collaborative network meta-analysis. Lancet., 2007, 370: 937948. [5] Gu,L., Zhao,S., Muttyam,A.K. and Hammel,J.M., The relation between the arterial stress and restenosis rate after coronary stenting. J. Med. Devices, 2010, 4: 031005. [6] Eshghi,N., Hojjati,M.H., Imani,M. and Goudarzi,A.M., Finite element analysis of mechanical behaviors of coronary stent. Procedia Eng., 2011, 10: 3056-3061. [7] Baim,D.S., Cutlip,D.E., Midei,M., Linnemeier,T.J., Schreiber,T., Cox,D., et al., Final results of a randomized trial comparing the MULTI-LINK stent with the Palmaz-Schatz stent for narrowings in native coronary arteries. Am. J. Cardiol., 2001, 87: 157-162. [8] Kastrati,A., Dirschinger,J., Boekstegers,P., Elezi,S., Schuhlen,H., Pache,J., et al., Influence of stent design on 1-year outcome after coronary stent placement: A randomized comparison of five stent types in 1147 unselected patients. Catheter. Cardiovasc. Interv., 2000, 50: 290-297. [9] Kastrati,A., Mehilli,J., Dirschinger,J., Pache,J., Ulm,K., Schuhlen,H., et al., Restenosis after coronary placement of various stent types. Am. J. Cardiol., 2001, 87: 34-39. [10] Pache,J., Kastrati,A., Mehilli,J., Schuhlen,H., Dotzer,F., Hausleiter,J., et al., Intracoronary stenting and angiographic results: strut thickness effect on restenosis outcome (ISAR-STEREO-2) trial. J. Am. Coll. Cardiol., 2003, 41: 1283-1288. [11] Chua,S.N.D., MacDonald,B.J. and Hashmi,M.S.J., Finite-element simulation of stent expansion. J. Mater. Process. Technol., 2002, 120: 335-340. [12] Dumoulin,C. and Cochelin,B., Mechanical behaviour modelling of balloon-expandable stents. J. Biomech., 2000, 33: 1461-1470. [13] Gu,L., Santra,S., Mericle,R.A. and Kumar,A.V., Finite element analysis of covered microstents. J. Biomech., 2005, 38: 1221-1227. [14] Chua,S.N.D., MacDonald,B.J. and Hashmi,M.S.J., Effects of varying slotted tube (stent) geometry on its expansion behaviour using finite element method. J. Mater. Process. Technol., 2004, 155-156: 1764-1771. [15] Chua,S.N.D., MacDonald,B.J. and Hashmi,M.S.J., Finite element simulation of stent and balloon interaction. J. Mater. Process. Technol., 2003, 143-144: 591-597. [16] Xia,Z., Ju,F. and Sasaki,K., A general finite element analysis method for balloon expandable stents based on repeated unit cell (RUC) model. Finite Elem. Anal. Des., 2007, 43: 649-658. [17] Lally,C., Dolan,F. and Prendergast,P.J., Cardiovascular stent design and vessel stresses: a finite element analysis. J. Biomech., 2005, 38: 1574-1581. [18] Walke,W., Paszenda,Z. and Filipiak,J., Experimental and numerical biomechanical analysis of vascular stent. J. Mater. Process. Technol., 2005, 164-165: 1263-1268. [19] Imani,M., Simulation of mechanical behaviors of NIR stent in a stenotic artery using finite element method. World Appl. Sci. J., 2013, 22: 892-897. [20] Serruys,P.W. and Kutryk,M.J.B., Handbook of Coronary Stents. third ed., Martin Dunitz Ltd., London, 2000. [21] Prendergast,P.J., Lally,C., Daly,S., Reid,A.J., Lee,T.C., Quinn,D., et al., Analysis of prolapse in cardiovascular stents: a constitutive equation for vascular tissue and finite element modelling. ASME J Biomech Eng, 2003, 125: 692-699.
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[22] Mario,C.D. and Karvouni,E., The bigger, the better: true also for in-stent restenosis? Eur. Heart J., 2000, 21: 710-711. [23] Versaci,F., Gaspardone,A., Tomai,F., Crea,F., Chiariello,L. and Gioffre,P.A., A comparison of coronaryartery stenting with angioplasty for isolated stenosis of the proximal left anterior descending coronary artery. N. Engl J. Med., 1997, 336: 817-822. [24] Kobayashi,Y., De Gregorio,J., Kobayashi,N., Reimers,B., Albiero,R., Vaghetti,M., et al., Comparison of immediate and follow-up results of the short and long NIR stent with the Palmaz-Schatz stent. Am. J. Cardiol., 1999, 84: 499-504. [25] Ju,F., Xia,Z. and Sasaki,K., On the finite element modelling of balloon-expandable stents. J. Mech. Behav. Biomed. Mater., 2008, 1: 86-95.
ISSN 0894-9166
APPLICATION OF FINITE ELEMENT METHOD TO COMPARING THE NIR STENT WITH THE MULTI-LINK STENT FOR NARROWINGS IN CORONARY ARTERIES S. Misagh Imani1⋆ A. M. Goudarzi1 P. Valipour2 M. Barzegar1 J. Mahdinejad1 Seiyed E. Ghasemi3 (1 Department of Mechanical Engineering, Babol University of Technology, Babol, Iran) ( Department of Textile and Apparel, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran) (3 Young Researchers and Elite Club, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran) 2
Received 16 December 2013, revision received 2 July 2014
ABSTRACT ‘Stent versus stent’ studies are a kind of randomized trials which are designed to show the superiority of the new stent designs compared with the previously approved ones. These studies are usually used by regulatory agencies, such as the U.S. Food and Drug Administration (FDA), to give an approval to new stent designs. The problem with these clinical trials is their high cost and difficulty. In this paper, a numerical alternative for ‘stent versus stent’ complicated clinical studies is presented. A finite element model is developed to investigate the influence of stent design on the outcome after coronary stent placement. Two commercially available stents (the NIR and Multi-Link stents) are modeled and their behavior during the deployment is compared in terms of stress distribution, radial gain, outer diameter changes and foreshortening. Moreover, the effect of stent design on the restenosis rate is investigated by comparing the stress distribution within the arteries. An analysis of the arterial wall stresses in the stented arteries indicates that the Multi-Link stent design causes lower stress to an atherosclerotic vessel with a localized stenotic lesion compared to the slotted tube NIR design. The findings correlate with the observed clinical restenosis rates, which have reported higher restenosis rates in the NIR compared with the MultiLink stent design.
KEY WORDS stent vs. stent studies, finite element method, coronary stent, plaque, vessel
I. INTRODUCTION Cardiovascular diseases, also known as atherosclerosis, are the first cause of death in the United States. For two decades, they constituted an important subject of clinical investigations and academic studies. The well-known stenosis pathology (reduction of the vascular lumen of an artery) affects the dynamics of the blood flowing through arteries and may even obturate them[1] . Treatment options include bypass surgery, atherectomy, balloon angioplasty and stenting[2] . Stent placement has become the most frequently used procedure to treat atherosclerosis and is commonly used by practitioners in recent years, because it has not only improved clinical outcomes compared with other possible treatments, but also have vastly enhanced our capability and confidence in tackling increasingly complex patients and lesions traditionally treated with coronary artery bypass graft surgery ⋆
Corresponding author. E-mail: [email protected]
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(CABG)[3, 4] . As reported by Gu et al.[5] , only in the United States, did more than 1.2 million patients undergo stent implantations each year. Since the first implantation of stents in humans in 1986, many improvements, changes and discoveries have been achieved to make them safer and more functional. Nowadays, more than 100 different stent designs are being marketed or are in evaluation for vascular and non-vascular indications, and moreover, every year new stent designs are manufactured and presented in the market[6] . These new stent designs have to be proved to be equivalent to an approved stent (not requiring that a new stent have superior safety or efficacy compared with existing stent(s)) to be confirmed from the regulatory agencies such as the U.S. Food and Drug Administration (FDA)[7] . This sets the stage for a series of ‘stent versus stent’ randomized trials designed to show that each newer stent design was not inferior to (i.e., was equivalent or better than) the prior approved stent[7–9] . These kinds of studies can also be very useful for selecting the appropriate stent type to use. But the problem with these clinical approaches is high cost and difficulty. Moreover, they often refer only to two different stent designs[10] while the results are hardly comparable to those from previous trials, even for the same stent design, because of the different methods adopted (patient recruitment, primary or secondary endpoints, etc.). Recently finite element methods (FEMs) are considered an efficient way of testing and improving stent designs. In comparison with expensive experiments carried out in hospitals and laboratories, numerical simulations accomplished by computers have advantages in both flexibility and cost. A large amount of numerical work is available in recent publications. Chua et al.[11] , Dumoulin and Cochelin[12] and Gu et al.[13] reported their researches, respectively, into the deployment of various stents without contact effect. Furthermore, Chua et al.[14, 15] and Xia et al.[16] considered the contact between the stent and the balloon in the computation of the deformation and stress distribution of the stent. More complicated models considering multi-contacts, i.e. stent/artery/plaque[17], balloon/stent/artery[18] and balloon/stent/artery/plaque[6, 19] were established to investigate both the mechanical behavior of the stents and the biomechanical response of the coronary artery wall. However, published works on the effect of application of different stents geometry by computer simulation are rarely found in the literature and the current knowledge is mostly clinical. In this paper the mechanical behavior of different stent types was compared by means of finite element method. Two commercially available stents, with the same material and different designs, were studied and the behavior of the models was compared in terms of stress distribution, radial gain, outer diameter changes and foreshortening. Moreover, the effect of stent design on the restenosis rate was investigated by comparing the stress distribution in the arteries. The paper tends to present a method which can be used as a simple and economical alternative for ‘stent versus stent’ complicated clinical studies.
II. MATERIALS AND METHODS Two models were developed, each constituted by the same balloon and coronary artery with plaque, and a different stent design. Modeling of various parts used in simulating is presented in this section. 2.1. Stent Two different coronary stent designs were taken into consideration. They resemble two commercial intravascular stents. Below they will be referred to as STENT A (NIR, Scimed, Boston Scientific Europe, Verviers, Belgium) and STENT B (Multi-Link, Guidant-Advanced Cardiovascular Systems, Inc., Santa Clara, CA, USA). The primary model of stents was produced using commercially available software. Models were constructed on the basis of images from Ref.[20]. The main geometrical dimensions of the simulated models are assumed to be the same. Both of the stents have an outer diameter of 3 mm, a length of 10 mm, and a thickness of 0.05 mm. Figure 1 shows the two-stent models in their unexpanded configuration. The stents were assumed to be made of stainless steel 304. A bi-linear elasto-plastic material model was used to model the behavior of stents material. The material properties were identically chosen as those assumed in Ref.[15], namely, Young’s modulus = 193 GPa; shear modulus = 75 × 106 MPa; tangent modulus = 692 MPa; density = 7.86 × 10−6 kg/mm3 ; yield strength = 207 MPa; Poisson’s
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Fig. 1. Geometry of two-stent models in their unexpanded configuration.
ratio = 0.27. 2.2. Artery with Plaque The geometrical properties of the vessel and plaque are: vessel’s length = 20 mm; vessel’s inner diameter = 4 mm; vessel’s outer diameter = 5 mm; plaque’s length = 3 mm; plaque’s inner diameter = 3 mm. The data from the work of Prendergast et al.[21] were adopted to describe the mechanical behavior of the coronary artery by means of hyperelastic constitutive law based on a reduced polynomial strain energy density function, of the third order. More details can be found in Ref.[1]. 2.3. Balloon The balloon was modeled to be 12 mm in length. The outer diameter and the thickness of the balloon were 2.9 mm and 0.1 mm, respectively. A polyurethane rubber type material was used to represent the balloon. Polyurethane is an incompressible material and was defined by a nonlinear first-order hyperelastic M-R model. The energy function’s coefficients were obtained from Ref.[15]. 2.4. Meshing and Boundary Conditions Owing to the symmetrical conditions, only one-seventh of STENT A and one-third of STENT B were used to simulate the expansion process. For both of the models, all of the parts were meshed with eight-node linear 3D block elements. Sensitivity analyses were performed to ensure enough meshing refinement. Models A and B include 10060 and 26140 elements, respectively. Figure 2 shows the assembled model for STENT A .
Fig. 2. The assembled model for STENT A.
2.5. Loading and Solutions The loading process of both of the models consisted of two steps. In the first step, without considering the existence of the balloon and the stent, a constant internal pressure equal to 13.3 kPa was applied to
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the vessel and the plaque. This pressure is equal to the blood pressure of 100 mmHgs[17] . The pressure simulates the internal pressure of the blood and causes the vessel to expand, and also, induces an initial stress. In the second step, by maintaining the initial pressure applied to the vessel and plaque, a constant pressure was imposed on the internal surface of the balloon. This pressure was applied with a constant rate in 1.635 seconds and its value was varied from 0 to 0.32 MPa for STENT A and 0 to 0.3 MPa for STENT B .
III. RESULTS AND DISCUSSION In this section, the results of the finite element analysis of the expansion of stents inside an atherosclerotic coronary artery are presented. The quantities of interest include stress distribution, radial gain, outer diameter changes, foreshortening and restenosis rate. 3.1. Stress Distribution The distribution of von Mises stress in the two-stent models is shown in Fig.3 at maximum expansion instant. As can be seen in this figure, the value of maximum stress in the stent is 297.7 MPa and 254.7 MPa, for STENT A and B, respectively. The distribution of von Mises stress in the expanded vessels is pictured in Fig.4 for the two geometries investigated. The highest arterial stresses are in the areas where maximum changes occurred in stents diameter. The value of maximum von Mises stress in the vessel is 0.262 MPa and 0.244 MPa, for STENT A and B, respectively. A possible damage to the artery might occur at these critical points.
Fig. 3. Distribution of von Mises stress.
Fig. 4. Distribution of von Mises stress in the expanded vessel at maximum expansion.
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3.2. Radial Gain and Outer Diameter Changes Radial gain (RG) is one of the most important parameters for evaluating the performance of the stent, which is defined as follows: RG = Rexpansion − R0 (1) where Rexpansion and R are the outer radius of the stent, after and before the expansion, respectively. RG is measured at the middle of the stent. Note that the value of RG represents the final radial deformation, and a greater value of RG is more appropriate in actual applications. The value of RG is 0.361 mm and 0.363 mm, for STENT A and B, respectively. This means that their final diameters are approximately equal. For a better understanding of the expansion behavior of the two-stent models, Fig.5 plots the outer diameter of stents against the expanding pressure. As can be seen in Fig.3, because of the existence of the plaque and the pressure applied by it, different positions of stents have different diameters. Here, in order to verify the behavior of the models, the outer diameter changes of points A1 , B1 in STENT A and points A2 , B2 in STENT B (as shown in Fig.3) were derived and shown.
Fig. 5. The relation between the outer diameter of the stent and expanding pressure.
Figure 5(a) shows that the rate of increment of stent diameter at points A1 and B1 is almost identical as pressure changes from 0 MPa to 0.14 MPa. From the pressure 0.14 to 0.25 MPa, because of the contact between point A1 and the plaque, stent diameter increases with a low rate at point A1 , while at point B1 , the rate of increment of the diameter grows significantly. Finally, for pressures larger than 0.25 MPa, because of the contact between the stent and the vessel, the variation of diameter at point B1 becomes small. The same behavior was observed for STENT B (Fig.5(b)), although the critical points are different (The critical points are 0.11 MPa and 0.28 MPa, respectively). 3.3. Foreshortening When the stent expands, because of different distributions of circumferential stress between the free ends and the central part, it bends on edges that causes the diameter at the end sides to become larger than that in the middle of the stent. This results in a reduction in the stent length which is called ‘foreshortening’. In fact, foreshortening defines the effective length of the stent and according to the findings of the clinical studies, a stent is expected to have a low value of foreshortening[22]. The foreshortening is defined as L0 − L foreshortening = × 100% (2) L0 where L0 and L are the initial and final length of the stent, respectively. Figure 6 depicts the relation between the foreshortening and the expanding pressure. As can be seen in this figure, expansion of the stents causes the reduction of 5.5 % and 0.0351 % in the length of STENT A and B, respectively. STENT B has a lower value of foreshortening in comparison to STENT A because of its special structure. Moreover, for this kind of stent, in some pressures the value of foreshortening becomes negative which means this design has increased in length.
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Fig. 6. The relation between the forshortening and expanding pressure.
3.4. Restenosis Rate One of the most important issues that usually have been considered during the comparison process is in-stent restenosis (ISR). In-stent restenosis is a re-narrowing or blockage of an artery at the same site where stenting has already taken place. In the early days of stent implantation, approximately one-third of patients suffered from restenosis within 6 months of stent deployment[23] . It has recently been shown that stress concentration in the stented artery wall correlates with the restenosis rate and the possibility of ISR increases by increasing the stress in the vessel wall[5] . Changes of stent cell geometry may affect the stress field within the artery wall and consequently influence the restenosis rate. Numerous clinical trials have looked into the influence of stent design on the outcome after coronary stent placement[7–9, 24] . These works can confirm the results obtained in this study. The findings of the current paper indicate that the possibility of restenosis in STENT A is greater than STENT B owing to the higher value of maximum arterial stresses in STENT A. This agrees with the results obtained in the study by Kastrati et al.[8] where 1147 patients received randomly five types of stainless steel stents. Two of these stents resemble model A and B and the restenosis rate is higher for the former. Moreover, the same conclusion can be drawn from analyzing the study by Kastrati et al.[9] . 3.5. Verification To validate the present method, the models identical to those presented in Ref.[15,25] were constructed with the results obtained compared in Table 1. The comparison indicates that the results are in good agreement in terms of maximum von Mises stress in the stent, which confirm the validity of the present method. Table 1. Comparison between the results obtained in this study and other researches
Present study Chua et al.[15] Ju et al.[25]
Maximum stress in the stent (MPa) 261.5 250 288. 2
Difference (%) — 4.6 10.2
IV. CONCLUSION The paper presents a method which can be used as a simple and economical alternative for ‘stent versus stent’ complicated clinical studies to compare the behavior of different stent designs. In order to achieve a more realistic description of the stent implantation procedure, the model includes internal pressure of blood, balloon, stent, vessel and plaque. Two commercially available stent models were analyzed and compared in this study. According to the analysis, even when both of the stents expanded to the same final diameters, the maximum stress induced in the artery by the NIR stent was found to be 7.4 % greater than the Multi-Link stent. Consequently, it is predictable that using the NIR stent results in more injury in vessel than the other one, which increases the possibility of restenosis. These
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results agree with the clinical studies which confirm that the restenosis rate of the NIR stent is higher than that of the Multi-Link stent[8, 9] . Finally, it should be mentioned that from analyses like those carried out in this study, it is difficult to find a strict correlation between the in-stent restenosis and the geometrical design, such as the length of the links. The testing methodology outlined here is proposed as a pre-clinical testing tool presumably useful when joined with a clinical trial aimed at comparing the influence of the stent design on the degree of restenosis.
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[22] Mario,C.D. and Karvouni,E., The bigger, the better: true also for in-stent restenosis? Eur. Heart J., 2000, 21: 710-711. [23] Versaci,F., Gaspardone,A., Tomai,F., Crea,F., Chiariello,L. and Gioffre,P.A., A comparison of coronaryartery stenting with angioplasty for isolated stenosis of the proximal left anterior descending coronary artery. N. Engl J. Med., 1997, 336: 817-822. [24] Kobayashi,Y., De Gregorio,J., Kobayashi,N., Reimers,B., Albiero,R., Vaghetti,M., et al., Comparison of immediate and follow-up results of the short and long NIR stent with the Palmaz-Schatz stent. Am. J. Cardiol., 1999, 84: 499-504. [25] Ju,F., Xia,Z. and Sasaki,K., On the finite element modelling of balloon-expandable stents. J. Mech. Behav. Biomed. Mater., 2008, 1: 86-95.