**6.1.3 Range of selectable flexural rigidity and the dilemma of selecting the design**

After inserting an originally straight stent into a curved blood vessel and leaving it there, the stent generally conforms to the blood vessel shape. Nevertheless, because the flexural

Design and Evaluation of Self-Expanding Stents

the geometrical symmetry.

addition to both ends of the stent.

Suitable for Diverse Clinical Manifestation Based on Mechanical Engineering 201

(a)

Fig. 18. Computational results of forces which are exerted on the coronary artery wall by insertion of the SDCO. (a) The distribution of the contact force between the SDCO and the coronary artery (upside), and the radius of the coronary artery after stenting (downside). The dot-dashed line indicates the initial shape of the artery wall with the assumed symptom. (b) The distribution of the straightening force on the coronary artery wall by insertion of the SDCO. The right side of the distribution is displayed from a consideration of

(b)

First, let us focus attention on the force on the vascular wall. Although the contact force is large at the stenotic part, the generation of this large force is unavoidable for expansion of the stenotic part. The contact force is also concentrated at both ends of the stent. The straightening force on the vascular wall is concentrated at the end of the stenotic part in

It has been reported that the hyperplasia of smooth muscle cells and the neointimal proliferation occur at the stented part of an artery (Grewe et al., 2000; Clark et al., 2006). It is assumed that the hyperplasia and proliferation are caused by the mechanical stimulus acting on the vascular wall due to insertion of the stent. (Schweiger et al., 2006) reported that

rigidity of the stent is greater than that of the blood vessel, the blood vessel tends to become straighter. This phenomenon of straightening of the blood vessel was previously described in detail, and a method to calculate the force resulting in the straightening of the blood vessel was described in previous section. It is apparent that this force depends on the flexural rigidity of the stent, and that greater flexural rigidity results in a larger force. A force too large can damage the vascular wall. Consequently, it is important to choose the most appropriate flexural rigidity of the stent.

By plotting the proposed designs obtained from the required radial stiffness *Kp* on a flexural rigidity map, the broken line shown in Fig. 17(a) is obtained. For one radial stiffness value, multiple flexural rigidity values can be selected as long as they are within the range given in the figure. None of the limiting values for the flexural rigidity, which might prevent damage on the vascular wall or neointimal thickening, are yet quantitatively available. Therefore, the flexural rigidity should be made smaller to decrease the force acting on the vascular wall. In other words, the designer should select the smallest flexural rigidity from the range of selectable values shown in Fig. 17(a).

Figure 17(b) shows the stent shape designed in consideration of the rules described above. The designed stent is referred to as SDCO and has a wire length *lw* of 2.01 mm, and a wire width *tw* of 0.16 mm. In addition, the length of the designed stent is determined so that it occupies the blood vessel from the stenotic part to the normal part at each end in consideration of actual clinical use. The length of the SDCO is 22.0 mm (the stent consists of 8 wire sections and 7 strut sections). The flexural rigidity of the SDCO is *Kb* = 25.1×10*-*6 Nm2. Similarly, the shear rigidity of the SDCO, based on the map of the rigidity, is *Ks* = 1.33 N.

Fig. 17. Selection of the proposed design from the viewpoint of flexural rigidity. (a) The selectable range of flexural rigidities is indicated by the broken line. The corresponding part of the map is magnified and displayed as in Fig. 16. (b) A stent 6 mm in diameter is designed to suit the assumed symptom of the coronary artery.

#### **6.2 Evaluation of the risk of in-stent restenosis based on the mechanical stimulus**

Figure 18 shows the distributions of the contact force and the straightening force when the SDCO is inserted into the coronary artery. These distributions were calculated by the previously described method, which was proposed by (Yoshino et al., 2011).

rigidity of the stent is greater than that of the blood vessel, the blood vessel tends to become straighter. This phenomenon of straightening of the blood vessel was previously described in detail, and a method to calculate the force resulting in the straightening of the blood vessel was described in previous section. It is apparent that this force depends on the flexural rigidity of the stent, and that greater flexural rigidity results in a larger force. A force too large can damage the vascular wall. Consequently, it is important to choose the

By plotting the proposed designs obtained from the required radial stiffness *Kp*

flexural rigidity map, the broken line shown in Fig. 17(a) is obtained. For one radial stiffness value, multiple flexural rigidity values can be selected as long as they are within the range given in the figure. None of the limiting values for the flexural rigidity, which might prevent damage on the vascular wall or neointimal thickening, are yet quantitatively available. Therefore, the flexural rigidity should be made smaller to decrease the force acting on the vascular wall. In other words, the designer should select the smallest flexural rigidity from

Figure 17(b) shows the stent shape designed in consideration of the rules described above.

occupies the blood vessel from the stenotic part to the normal part at each end in consideration of actual clinical use. The length of the SDCO is 22.0 mm (the stent consists of

(a) (b)

Fig. 17. Selection of the proposed design from the viewpoint of flexural rigidity. (a) The selectable range of flexural rigidities is indicated by the broken line. The corresponding part

**6.2 Evaluation of the risk of in-stent restenosis based on the mechanical stimulus** 

Figure 18 shows the distributions of the contact force and the straightening force when the SDCO is inserted into the coronary artery. These distributions were calculated by the

of the map is magnified and displayed as in Fig. 16. (b) A stent 6 mm in diameter is

previously described method, which was proposed by (Yoshino et al., 2011).

designed to suit the assumed symptom of the coronary artery.

of 0.16 mm. In addition, the length of the designed stent is determined so that it

on a

of 2.01 mm, and a wire

= 25.1×10*-*6 Nm2.

= 1.33 N.

most appropriate flexural rigidity of the stent.

the range of selectable values shown in Fig. 17(a).

width *tw*

The designed stent is referred to as SDCO and has a wire length *lw*

8 wire sections and 7 strut sections). The flexural rigidity of the SDCO is *Kb*

Similarly, the shear rigidity of the SDCO, based on the map of the rigidity, is *Ks*

Fig. 18. Computational results of forces which are exerted on the coronary artery wall by insertion of the SDCO. (a) The distribution of the contact force between the SDCO and the coronary artery (upside), and the radius of the coronary artery after stenting (downside). The dot-dashed line indicates the initial shape of the artery wall with the assumed symptom. (b) The distribution of the straightening force on the coronary artery wall by insertion of the SDCO. The right side of the distribution is displayed from a consideration of the geometrical symmetry.

First, let us focus attention on the force on the vascular wall. Although the contact force is large at the stenotic part, the generation of this large force is unavoidable for expansion of the stenotic part. The contact force is also concentrated at both ends of the stent. The straightening force on the vascular wall is concentrated at the end of the stenotic part in addition to both ends of the stent.

It has been reported that the hyperplasia of smooth muscle cells and the neointimal proliferation occur at the stented part of an artery (Grewe et al., 2000; Clark et al., 2006). It is assumed that the hyperplasia and proliferation are caused by the mechanical stimulus acting on the vascular wall due to insertion of the stent. (Schweiger et al., 2006) reported that

Design and Evaluation of Self-Expanding Stents

to *Kp*

adopt the radial stiffness *Kp*

distributed contact force *Pi*

vascular radius of the target, *lw*

distributed contact force on the stenotic part.

, as follows:

*Kp*

part from *Kp*

stiffness *Kp*

stiffness *Kp*

wall.

Suitable for Diverse Clinical Manifestation Based on Mechanical Engineering 203

objective for blood flow must be attained. Therefore, the stent should have a radial stiffness

The methods using the influence matrix described in Section 5 are used for the shape modification. Figure 19 shows the concept for modification of the stent shape. The

\*

*i*

*P*

\* \*

. Also, *n*CP represents the number of calculation points on the wire section.

CP *t p t w*

*n*

where *Dt* is the inner diameter of the blood vessel after treatment, *rt* is the increase in the

For simplicity, it was assumed that a uniform contact force was exerted on the vascular

Fig. 19. Concept for modification of the stent shape. The distributed contact force is obtained from the radial stiffness of the stent on the stenotic part by using the design method. The force that should be applied on the normal artery is calculated by using the obtained

As described in Section 5, the radial displacement of the vascular wall {*r*(*<sup>v</sup>*)} = (*r*1(*<sup>v</sup>*), *r*2(*<sup>v</sup>*), ...,

where [*C*(*<sup>v</sup>*)] is the influence matrix of the blood vessel, defined by the radial displacement of

*rn*(*<sup>v</sup>*))T due to the unknown contact force {*P*} = (*P*1, *P*2, ..., *Pn*)T is given as follows:

the vascular wall due to the unit radial force. The calculated contact force *Pi*

*DK rl*

 to expand the vascular wall at normal part only for the stent thickness *t*. This can achieve the flat expansion of the artery. By changing the stent radial stiffness at the normal

, the contact force can also decrease. In this study, it was decided to

on the stenotic part can be calculated based on the radial

is the wire length of the stent designed based on the radial

*v v C Pr* (23)

is substituted

(22)

as a compromise between the two design objectives.

in-stent restenosis occurred primarily at both ends of the stent during the period one to three months after stenting. In the study of (Lal et al., 2007), the majority of patients in the target patient population showed in-stent restenosis at the stent ends. (Yazdani and Berry, 2009) cultured a stented native porcine carotid artery under physiologic pulsatile flow and pressure conditions for a week. They confirmed that the proliferation of smooth muscle cells occurred significantly at both ends of the stent. By summarizing these reports and evaluation results of the forces on the vascular wall, it is concluded that the force concentration provokes neointimal thickening due to the hyperplasia of smooth muscle cells, i.e., in-stent restenosis.

Next, the expansion of the vascular wall is examined. The normal part of the artery is expanded to become much larger than the target diameter. This excessive expansion causes expansion of the entire stented part. As a result, stagnation and vortices of blood flow are induced, further increasing the potential for stent thrombosis.

The designed stent has mechanical properties sufficient to expand the stenotic part of theartery, but is not suitable for the normal part of the artery. Thus, it requires modification.
