Computational Modeling of Stents in Arteries

Using the finite element method, it is possible to determine the stresses and displacements induced in a stent when it is expanded by a balloon.  For example, Raamachandran et al. performed numerical simulations using ABAQUS 6.5.1/Explicit on 6 different stent designs  that were all made of  stainless steel 316L.  The elastic properties used were E = 201 GPa, ν = 0.3, σ_y = 170 MPa; isotropic hardening was also assumed.  The balloon was modeled as a cylinder with an internal diameter of 1.24 mm and thickness of 0.02 mm.  To simulate the balloon angioplasty, the internal pressure was increased from 0 to 0.16 MPa from 0 to 30 ms, constant at 0.16 MPa from 30 ms to 40 ms, and then decreased to 0 from 40 ms to 50 ms.  Note that these time intervals did not correspond to real-time; it was used to shorten the time required for the simulation.  Furthermore, the physical contact between the balloon and stent was modeled using the finite sliding surface-to-surface contact algorithm.  Figure 5 shows the axial displacements of the 6 different stent designs after balloon expansion [14].  This kind of quantitative information could be useful for clinicians; it gives a quantitative relationship between applied pressure and the deformation for different stent designs.  Such data could help the clinicians decide which stent to use.  

Kiousis et al. tried to determine the stress distributions as they modeled the physical interactions that occur between the atherosclerotic artery and stent during balloon angioplasty.  They modeled the Express Vascular LD stent and a specific 65-year-old female patient’s atherosclerotic iliac artery.  The computed stresses are shown in Figure 6.  The lumen is the smaller hole and the plaque is situated in the larger hole (not shown).  The principal Cauchy stresses distributions can be seen in the arterial wall under different loading configurations.  These include the arterial wall subject to hydrostatic blood pressure, arterial wall after the balloon angioplasty (with and without stent), and arterial wall during balloon angioplasty with stent.  In all situations, the stresses are highest around the intima.  However, the stresses in the media and adventitia do increase during balloon angioplasty and after balloon angioplasty when the stent is put in place.  In fact, the stresses approach 500 kPa during the expansion of the balloon with the stent.  This is critical since previous research shows that plaque in human iliac arteries can break up at such stresses [8].  These kinds of computer simulations may be useful for clinicians because it gives them quantitative information about what is the increase in the stresses in the arterial wall as a particular type of stent is expanded in the atherosclerotic artery.  It also gives quantitative information about how much the arterial wall will deform due to the balloon angioplasty procedure with a specific type of stent.

Minisini et al. also used the finite element method to analyze the expansion of two different stent designs and its effects on the plaque and coronary arterial wall.  The two stents that they modeled were the Cordis cipher and Medsystem Conor, as shown in Figure 7 [15].

Figure 7.  CAD models for the two different stent designs: Cordis Cypher (left) and Medsystem Conor (right) [15]

The group used the generalized Mooney-Rivlin hyperelastic constitutive equations to model the arterial wall and plaque.  The outer boundary of the arterial wall was subjected to zero axial displacements and the artery was subjected to stresses in the axial direction.  An internal pressure was applied as well.  They were able to solve for the stresses induced in the arterial wall, plaque, and stent.  Figure 8 shows the computed von Mises stress distribution in the arterial wall and plaque.  They were able to determine the locations where the stent struts were in physical contact with the arterial wall and the stresses associated with these locations.  They were also able to determine where the highest compressive radial stresses were [15].  These kinds of simulations can be useful for clinicians because it gives them quantitative information necessary to evaluate the performance of different stent designs.  They can compare the stress distribution induced in atherosclerotic arteries by different stent designs and get information about the effects of the stents on the arterial wall.  

Figure 8.  Von Mises stress distributions in coronary artery (left) and plaque (right) when two different stents (Cordis Cypher and Medsystem Conor) were used [15]