**3.2 Framework of design support system**

188 Mechanical Engineering

*Step 4. Selection of stent with the lowest flexural rigidity in adequate range*: If the stent, which is in the adequate range, is selected, it can expand the stenotic part in the blood vessel sufficiently. The stent sometimes has too high flexural rigidity for the lesion because of selection only in terms of the stent stiffness in radial direction. When selecting a stent, its flexural rigidity should be considered. But we have no basis of the flexural rigidity for selecting a stent. Therefore, it is decided to select the stent that has the lower flexural rigidity than any other stent being in the adequate range. For the assumed symptom, SENDAI (SD8,

In this section, we introduced the method to select a stent suitable for the patient's symptom based on mechanical properties of the stent. It is considered that the selection method can help doctors greatly in clinical sites. Commercially available stents are targeted for this selection method. There are limitations to selecting a suitable stent using this method. Therefore, a novel stent has to be designed for providing the stent more suitable for the patient's symptom. The method to design more suitable stent will be described in the

A design support system for a self-expanding stent using CAD and CAE is introduced in this section. This support system can improve the efficiency of the suitable stent design.

Figure 7 shows a two-dimensional diagram of a SENDAI stent. Each wire section is constructed from 12 loosely curved S-shaped wires. The strut section of the stent connects them using three bridge wires. On the two-dimensional shape of the SENDAI stent in Fig. 7, the design variables that might affect the mechanical properties of the stent are set. Here, *lw*

the angle of the wire and the bridge wire to the axial direction, *tw* and *tb* are line element width of the wire and the bridge wire, and *ri* and *ro* are the inner radius and the outer radius of the wire end part. Every wire is structured in an arc shape. When the design variables *lw*,

*<sup>w</sup>*, and others are given, the arc shape is determined and wire section is constructed through laying out these arc shapes continuously. Furthermore, the number of wires *nw*, the number of bridge wires *nb*, and the thickness of the tube material *ts* are also design variables.

Fig. 7. Two-dimensional diagram of SENDAI stent (a) and main design variables for

(a) (b)

*<sup>w</sup>* and *<sup>b</sup>* are

and *lb* are the length of the wire and the bridge wire along the axial direction,

*ds* = 8 mm) and Zilver® (ZIL, *ds* = 10 mm) are most suitable.

**3. Design support system for self-expanding stents** 

**3.1 Design variables of SENDAI stent** 

following sections.

SENDAI stent (b)

Figure 8 shows the design support system for a self-expanding stent. The left-hand side of the figure shows the production process of the SENDAI stent. It has three production stages: a 'manufacture' stage, during which the NC data are created based on the two-dimensional diagram to manufacture the initial stent shape while the initial stent is manufactured by using laser processing; an 'expansion' stage, during which the initial stent is forcibly expanded in the radial direction by inserting a tapered rod into the stent as it is given shapememory treatment; and an 'evaluation' stage, during which the performance of the expanded stent is tested. The right-hand side of Fig. 8 shows the flow of the shape design for self-expanding stents being proposed. A three-dimensional model of the initial stent manufactured by using laser processing is created from the two-dimensional shape by using 3D CAD. Then, by dividing into finite elements, the finite element model representing the initial stent is created based on the 3D CAD model, and the expanded stent shape is predicted by applying an expansion analysis using the finite element method for large deformation. Based on this prediction, a rigidity analysis is conducted using a non-linear finite element method. The mechanical properties of the stent are evaluated from the results. This process corresponds to the actual production process of the 'manufacture,' 'expansion,' and 'evaluation' stages.

Fig. 8. Design support system for self-expanding stent. The left-hand side shows the production process of the SENDAI stent. The right-hand side shows the flow of the proposed design support system.

Design and Evaluation of Self-Expanding Stents

10: Young's modulus of 28 GPa, and Poisson's ratio of 0.3.

Fig. 10. Assumed stress-strain relationship for the stent material

**stent** 

**of stents** 

**5. Estimation of force on vascular wall caused by insertion of self-expanding** 

The forces on a blood vessel are classified into two categories: internal pressure caused by the expansion of the stent and the force resulting from the straightening of the blood vessel, which is a phenomenon whereby a curved blood vessel is straightened by the stent. Straightening of blood vessels often occurs in cases involving the use of a closed-cell stent. As a result, a problem occurs in that the straightening easily encourages kinking of the blood vessel at the flexural area distant from the stented lesion (Tamakawa et al., 2008).

In this section, focusing on a method by which to improve the force distribution on the vascular wall according to the symptoms of the patient, we introduce a method to compute the distribution of the contact force between the stent and the blood vessel under the assumption that the stent is inserted into a straight blood vessel. In the method, the stent and the blood vessel are simplified as axisymmetrical models. Then a method for calculating

**5.1 Computation of contact force distribution on vascular wall caused by expansion** 

The expansion of a stent in a blood vessel induces pressure on the contact surfaces of the stent and the blood vessel. Analysis of pressure or contact force based on the complicated

the distribution of the straightening force on the vascular wall is introduced.

Suitable for Diverse Clinical Manifestation Based on Mechanical Engineering 191

We must know the relationship between the mechanical properties of a stent and the design variables in order to design a stent with specific properties. The mechanical properties of the SENDAI stent, such as radial stiffness, flexural rigidity, and shear rigidity, were evaluated, and their sensitivities to the design variables were also defined, as shown in Fig. 9 (Yoshino & Inoue, 2010). The wire length along the axial direction and the wire width were selected as design variables. Isolines on the maps of mechanical properties are very important for proposing designs. The isoline is plotted onto the maps based on the required mechanical property, and design variables of the proposed design are determined from the isoline. In addition, we assumed the mechanical properties of the stent material as illustrated in Fig.

This support system has design method of a self-expanding stent suitable for the patient's symptom based on mechanical properties of a stent. This method is available to introduce into the existing design support system described above, and has two stages which are the design and modification methods. In the first stage, a stent shape with mechanical properties suitable for the patient's symptom is determined and designed. In the second stage, to modify the stent shape in consideration of the risk of in-stent restenosis realizes designing the stent shape more suitable for the patient's symptom. The risk of in-stent restenosis is evaluated based on a mechanical stimulus to a vascular wall by insertion of a stent. These two stages of the design method will hereinafter be described in more detail (see in Section 6).

After the two-stage design method, the design support system ends with the generation of the NC data of the designed stent necessary for moving onto the actual production process. For change in a stent shape, a subsystem for generating the two-dimensional shape of the initial stent was introduced, and this is available for changing the two-dimensional shape flexibly. It can also be used to generate a two-dimensional diagram of the stent in the first place.
