Effect of Strut Thickness, Crimping and Expansion Diameters on Radial Strength, Recoil and Foreshortening of a Coronary Stent AMIT DATYE, K H.WU Department of Mechanical and Materials Engineering Florida International University 10555 West Flagler Street, Miami, Florida 33174 USA Abstract A nonlinear finite element simulation was performed to analyze the elasto-plastic behavior a coronary stent undergoing crimping and deploying processes and to understand the effects of crimping diameter, expansion diameter and strut thickness on radial strength, recoil and foreshortening of the coronary stent The commercial package ABAQUS was used for the analysis and PATRAN was used as the pre-processor Only half the stent was considered due to symmetry Both the crimping and the expansion of the stent involve large deformations, therefore the non-linearities of the material are also considered The stent is meshed using solid brick (C3D8 in ABAQUS) and tetrahedral (C3D4) elements for the analysis It was found that the magnitude of the accumulated plastic strain induced by crimping and deployment has a significant effect on the radial strength, recoil and foreshortening of the stent Introduction Coronary heart disease is the most common cause of death in major Western countries The narrowing of the arteries that feed the heart causes Coronary Heart Disease (CHD) The excess cholesterol attaches to the inner smooth artery wall and attracts cellular waste products, calcium and fibrin, which result in plaque This leads to a thickening of the vessel wall, which can narrow or even block an artery Stents are small spring-like, cylindrical mesh tubes placed in arteries to restore the blood flow through the arteries and to keep them from collapsing after angioplasty An ideal stent should be easy to implant, have excellent recrossability, have markers at different locations for accurate positioning, good radial strength to keep the arteries open, be available in different lengths, have good resistance to thrombosis and must have excellent bio and blood compatibility Stents can be classified into two basic types: Self-expanding and Balloonexpanding They can be further classified according to their design, the basic material they are made and the method of deployment It has been known that stent design is an important factor in the restenosis rate of the artery and also the radial strength of the stent; the stent strut thickness has also been linked to the endothelialization of the stent surface after implant To optimize the performance of the new stent design and to further understand the important stent parameters such as radial recoil, foreshortening, stress concentrations and deploying pressure, a cardiovascular stent was systematically analyzed using non-linear Finite Element Analysis with varying strut thickness and deployment diameters Finite element model In this analysis, a 3D geometrical model of the new heart-shaped-joint stent is shown in the Figure 1.1 The stent is fabricated from a 316L stainless-steel cylindrical tube by laser cutting and then polished using suitable methods The sharp edges at the joints are rounded to reduce the stress concentrations at the joints and also reduce the chances of the stent cutting into the artery walls The stent was modeled with a strut thickness of 0.127, 0.15, 0.20, and 0.25mm to determine the optimum thickness models were made using ProEngineer Modeling Software The nodes and the elements are generated in ABAQUS using size controls Results were compared to find the effects of mesh refinement and also the effect of using different type of elements The effect of the mesh size i.e the mesh sensitivity on the solution of the model of the stent is also analyzed using various mesh refinements The stent mesh is as shown in Figure 3.1 Figure 1-1: Geometric Models of the new Stent The dimensions of the stent used in this analysis are as listed below: As fabricated outer diameter: Crimped diameter: Length: Number of coils: The metal artery contact ratio: Width of the strut: Thickness of the strut: 3.048 mm variable 12.445mm 0.17 0.127mm variable Solid elements are used in this analysis of the stent, including brick elements (C3D8, C3D8R), wedge elements (C3D6) and tetrahedral elements (C3D4) Since there is significant plastic strain involved in the crimping and deploying stages, an elastoplastic large deformation analysis was carried out on the stent An isotropic hardening rule is assumed in this study Loading and Solution The stent is assumed to have a uniform internal pressure due to the balloon inflation Furthermore, since the stent is symmetric about the XY plane the nodes on the plane are constrained by using symmetric boundary conditions The meshing of the stent was done using the FEA commercial code ABAQUS Version 6.2.7 (Hibbitt, Karlsson & Sorenson, Inc., Pawtucket, RI, USA) The 3D stent Figure 3-1: Mesh of the stent The stent was crimped to an external diameter of about 2.4 mm, which is the average diameter of the stent when it is mounted on the delivery system, i.e., the balloon catheter for deployment Figure 3-2: Loads during crimping and expansion of the stent Elastic Recoil after Crimping: All boundary conditions are released to allow the elastic recoil after crimping Expansion of the stent: The stent is expanded to a maximum outer diameter of 4, 4.25, 4.50 and mm Elastic Recoil after Expansion Again, all boundary conditions are released during this step Only the nodes in the symmetric plane were constrained and one other node was constrained to remove the fixed body rotations Results and Discussion Mesh Sensitivity Simulations were carried out with varying degrees of mesh refinement to characterize the mesh sensitivity of the analysis The stent was compressed radially to the crimped outer diameter of 2.4mm and the results obtained are shown in Table 4-1.It can be seen from Table 4-1 that this analysis is not particularly sensitive to mesh refinement after the third mesh refinement i.e after the mesh has been increased to about 15,000 nodes expected, the radial force increases linearly with an increasing strut thickness The stent radial force data obtained from this analysis were verified with the actual inflated force in practice For instance, in this analysis a stent with 0.2 and 0.15mm strut thickness require a radial force of 13.18 N (2.9617 lbs) and 9.54 N (2.14 lbs), respectively Theses forces are compatible with real force in the implantation stage of a stent The Figures 4-2 and 4-3 show the Mises stress distribution in the stent with a 0.1mm radial compression it can be seen that the Mises stress levels are not above the yield stress of stainless steel RADIAL STRENGTH (N) 20 Table 4-1: Mesh sensitivity ELEMENT TYPE # NODES # ELEMENTS TOTAL RADIAL FORCE (N) C3D8 5134 10214 15394 31359 43568 52246 60124 1764 3854 6144 16082 24320 34468 41124 12.87 13.03 13.10 13.24 13.31 13.43 13.76 26196 20888 13.17 C3D6 The maximum change between the total radial force for 15,000 nodes and for 60,124 nodes is about 5% Therefore all the other analysis for effect of thickness and effect of deployment diameter are run with a mesh of approximately 15,000 nodes to decrease the analysis time 18 RADIAL FORCE (N) CRIMP TO OUTER DIAMTER =2.4 mm 16 14 COMPRESSION - 2.2 mm DIA EXPANSION - DIA: 3.25mm 12 10 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 STRUT THICKNESS (mm) Figure 4-1: Radial force with varying thickness during crimp and expansion Effect of Thickness Various stent models were prepared with different strut thickness The thickness of the strut of the stent was varied from 0.125mm to 0.25mm with an increment of 0.025mm To illustrate the effect of the strut thickness on the radial strength of a stent, the stress/strain and the reaction force data were collected from the crimping and the expansion steps to optimize the stent thickness to provide the best balance between the radial force and the flexibility of the stent The results are tabulated in Table 4-2 for a crimped diameter of 2.4mm and an expansion diameter of 3.25mm Figure 4-1 shows the relationship between the radial force during the crimping and deployment stages As Figure 4-2: Mises stress distribution over the stent at 0.1 mm radial compression Figure 4-3: Mises stress distribution front view at 0.1mm radial compression Table 4-2: Radial strength and max Mises stress with varying thickness TOTAL RADIAL FORCE vs DEPLOYMENT DIAMETER 20 TOTAL RADIAL FORCE (N) 19 18 17 16 15 14 13 12 11 10 DEPLOYMENT DIAMETER (mm) Figure 4-5: Total radial force with varying deployment diameters using FEA FORSHORTENING vs DEPLOYMENT DIAMETER % FORESHORTENING 3 3.5 4.5 5.5 DEPLOYMENT DIAMETER (mm) To understand the effect of deployment diameter on the overall mechanical behavior of a stent, an FE analysis was performed on a stent with varying deployed diameters of 3.25, and mm The crimped diameter of the stent was fixed at 2.4 mm It can be seen from Figures 4-5 to 4-7 that the radial force required to expand the stent increases as the deployment diameter increases The percentage foreshortening increases while the percentage radial recoil decreases as expected with an increase in deployment diameter RADIAL RECOIL vs DEPLOYMENT DIAMETER 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 DEPLOYMENT DIAMETER (mm) Figure 4-7: Percentage Radial Recoil with varying deployment diameters using FEA MAX MISES STRESS DURING EXPANSION AND RECOIL vs EXPANSION DIAMETER 500 MISES STRESS (N/mm ^2) Figure 4-6: Percentage foreshortening with varying deployment diameters using FEA % RADIAL RECOIL Effect of Deployed Diameter Effects of Accumulated Plastic Strain on Radial Strength, Recoil and Foreshortening 480 460 440 AFTER FINAL RECOIL AFTER EXPANSION 420 400 3.5 4.5 5.5 EXPANSION DIAMETER (mm) Figure 4-4: Mises stresses during/after recoil In order to clearly understand the effect of accumulated plastic strain on the radial strength, recoil and foreshortening, the following analysis was conducted by varying the crimped diameter while maintaining the initial outside diameter constant Table 4-3 shows the accumulated plastic strain after the crimping process Table 4-3: Analysis of plastic strains with varying crimp diameters CRIMP RADIUS mm PEEQ S-MISES 1.100 1.125 1.150 1.175 1.189 9.59E-02 8.97E-02 8.35E-02 7.73E-02 7.39E-02 N/mm^2 422.89 422.74 422.59 422.44 422.35 Figure 4-8: Mises stress and plastic strain with varying crimping diameter Analysis of the plastic strain during crimping shows that the equivalent plastic strain increases with a decrease in the crimp radius, radial force required for crimping also increases though not by a significant amount with a decrease in the crimping radius The elastic recoil after crimping stays nearly the same with the maximum recoil being at the largest crimping diameter The Mises stress and the equivalent plastic strain during crimping to various radii is shown in Figure 4-8 After crimping, the stent was deployed to various diameters Once this step was completed, the radial strength, recoil, and foreshortening of the stent were determined Table 4-4 demonstrates the effect of totally accumulated plastic strain on these important indicators of a coronary stent Figures 4-9 through to 4-12 show the analysis of the stent during expansion to varying diameters the effects of the accumulated plastic strain can be seen from these figures Table 4-4: Analysis of stent with varying crimp and expansion diameters CRIMP RADIUS mm EXPANSION DIAMETER mm S-MISES RADIAL % CHANGE % CHANGE STRENGTH IN RADIAL IN MISES N/mm^2 (N) STRENGTH STRESS 1.100 1.125 1.150 3.25 4.00 5.00 3.25 4.00 5.00 3.25 4.00 5.00 428.4 462.1 495.6 426.5 458.4 490.4 422.1 449.3 487.2 11.83 15.94 19.14 11.54 15.33 18.7 11.23 14.91 18.62 5.34% 6.91% 2.79% 2.76% 2.82% 0.43% 0 CRIMP EXPANSION % RADIAL % FORE RADIUS DIAMETER RECOIL SHORTENING mm mm 1.100 1.125 1.150 3.25 4.00 5.00 3.25 4.00 5.00 3.25 4.00 5.00 0.388 0.164 0.138 0.42 0.173 0.142 0.498 0.285 0.193 0.27 5.58 8.42 0.25 5.62 8.46 0.22 5.78 8.51 1.49% 2.85% 1.72% 1.04% 2.03% 0.66% 0 It can be seen that the maximum Mises stress in the stent after expansion increase with an increase in the accumulated plastic strain This is not a concern because the maximum stress levels are below the yield stress for 316L stainless steel Figure 4-10 shows that the radial strength of the stent increases with an increase in the accumulated plastic strain This means that the stent can hold more pressure from the arterial walls i.e the stent is stronger It can also be seen from Figures 411 and 4-12 that the radial recoil and the foreshortening is reduced due to accumulated plastic strains Figure 4-11: Radial recoil with changes in expansion diameter for different crimp diameters MISES STRESS 500 490 1.100E+ 00 480 1.125E+ 00 470 1.150E+ 00 460 450 440 430 420 410 2.5 3.0 3.5 4.0 4.5 5.0 5.5 E XPANSI ON DI AME T E R (mm) Figure 4-9: Mises stress with changes in expansion diameter for different crimp diameters R A DIAL STR ENGTH 20 19 1.100E+ 00 18 1.125E+ 00 17 1.150E+ 00 16 15 14 13 12 11 10 2.5 3.0 3.5 4.0 4.5 5.0 5.5 EX PA NSION DIA M ETER (mm) Figure 4-10: Radial force with changes in expansion diameter for different crimp diameters Figure 4-12: Foreshortening with changes in expansion diameter for different crimp diameters CONCLUSION In this paper the effect of the strut thickness, the deploying diameter and the effect of residual plastic strain is presented Also other important parameters like radial recoil and foreshortening after deployment are studied in this paper A finite element model of a coronary stent is created and analyzed to characterize the effects of the various parameters mentioned above on the mechanical properties of the stent It is found that the thickness of the strut has a major effect on the radial strength of the stent The radial strength increases with an increase in the strut thickness of the stent, this corresponds to a decrease in the flexibility of the stent Since the stent is used in very complex areas it is important to have a balance between the radial strength and flexibility of the stent The stent strut thickness has an important effect on the radial strength of the stent The radial strength increases with an increase in the strut thickness while the max stress in the stent also increases The deploying diameter also has an effect on the radial strength, the foreshortening and the radial recoil The radial strength increases, as there is an increase in the deployment diameter, which means that there is an increase in the stress levels with an increase in the deployment diameter The foreshortening increases with an increase in the deploying diameter while the percentage radial recoil reduces with an increase in the deployment diameter The analysis of the effects of accumulated plastic strain shows that the radial strength of the stent increases when there is an increase in the accumulated plastic strain also there is less radial recoil and foreshortening of the stent This demonstrates that if the stent can be fabricated at a greater diameter and then crimped to its minimum diameter then the radial strength of the stent can be further increased REFERENCES L B Tan, D C Webb, K Kormi and S T S Al-Hassani A method for investigating the mechanical properties of intracoronary stents using finite element numerical simulation, International Journal of Cardiology, Volume 78, Issue 1, March 2001, Pages 51-67 Etave, F., Finet, G., Boivin, M., Boyer, J.C., Rioufol, G., Thollet, G., 2001 Mechanical properties of coronary stents determined by using finite element analysis Journal of Biomechanics 34, 1065–1075 F Auriccio, M Di Loreto and E Sacco Finite-element Analysis of a Stenotic Artery Revascularization through a Stent Insertion.Computer Methods in Biomechanics and Biomedical Engineering, Vol 00, pp 1-15 Hui Zhu, John J Warner, Thomas R Gehrig and Morton H Friedman Comparison of coronary artery dynamics pre- and post-stenting, Journal of Biomechanics, Volume 36, Issue 5, May 2003, Pages 689-697 S N David Chua, B J Mac Donald and M S J Hashmi Finite element simulation of stent and balloon interaction, Journal of Materials Processing Technology, In Press, Corrected Proof, Available online 21 April 2003 Francesco Migliavacca, Lorenza Petrini, Maurizio Colombo, Ferdinando Auricchio and Riccardo Pietrabissa Mechanical behavior of coronary stents investigated through the finite element method, Journal of Biomechanics, Volume 35, Issue 6, June 2002, Pages 803-811 S N David Chua, B J Mac Donald and M S J Hashmi Finite-element simulation of stent expansion, Journal of Materials Processing Technology, Volume 120, Issues 1-3, 15 January 2002, Pages 335340 ABAQUS, 6.2 ed., Hibbitt, Karlsson, and Sorenson (HKS) Inc., Pawtucket, RI 02860, 2001 ... using FEA % RADIAL RECOIL Effect of Deployed Diameter Effects of Accumulated Plastic Strain on Radial Strength, Recoil and Foreshortening 480 460 440 AFTER FINAL RECOIL AFTER EXPANSION 420 400... allow the elastic recoil after crimping Expansion of the stent: The stent is expanded to a maximum outer diameter of 4, 4.25, 4.50 and mm Elastic Recoil after Expansion Again, all boundary conditions... max stress in the stent also increases The deploying diameter also has an effect on the radial strength, the foreshortening and the radial recoil The radial strength increases, as there is an