Computational Modeling of Stents in Arteries

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3D Geometrical Models

 

An important step in modeling the arterial wall, plaque, and stent is to determine how to mathematically describe the geometries.  In some numerical simulations, some have used a simple cylindrical model for arterial wall.  However, a more accurate physical model can lead to more realistic computed stresses and displacements of the arterial wall.  For instance, Kiousis et al. constructed a specific 3-D geometry of the iliac artery based on high resolution MRI data of a patient.  Then they used the non-uniform rational B-spline (NURBS) to mathematically describe the surface.  A schematic of their model is shown in Figure 4.  Note that the artery is atherosclerotic as the lumen has been substantially narrowed.  The different layers of the artery is represented by “I” for the intima, “M” for media, “A” for adventitia.  The lipid pool is represented by “I-lp” [8].  

Figure 4. 3-D model of a patient’s femoral artery constructed using high resolution MRI data [8]

A three-dimensional model must also be generated for the stent.  Using data of the structure and dimensions of the stent acquired by a digital camera, a 3-D computer model can be constructed by using a method called the parametrization algorithm.  Essentially, this method is able to specify the dimensions and relevant parameters of the stent geometry.  This method can also help in the generation of the mesh of the stent [8] (which will be required when using the finite element method).  Oftentimes, there is repetition in the overall stent structure.  As a consequence, only part of the stents needs to be generated.  The entire stent can then be assembled from these parts.  For instance, Figure 5 (left) shows a meshed geometrical model of a stent cell constructed by Pro/Engineer and imported into the commercial FEM software ANSYS [9].  Meshing is discussed in Computational Methods.  

               

Figure 5. Meshed model of a stent cell from Wu et al (left);  meshed model of stent inside a curved atherosclerotic blood vessel (right)  [9]

Figure 5 (right) shows the entire stent geometry constructed from the stent cell.  The stent is situated inside a curved blood vessel containing plaque.  The blood vessel was modeled with an inner radius of 1.5 mm, a thickness of 0.5 mm, and a length of 12 mm.  The plaque has a length of 8 mm and a specific shape that they modeled using uniform rational B-splines [9]. 

   

  

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