**2.1 Target stents**

Four kinds of commercially available stents, which are already in clinical use, are evaluatedin addition to two types of SENDAI stents having different diameters. One of the evaluated stent is Protege® GPS™ (ev3 Endovascular, Inc., Plymouth, Minnesota, U.S.). The Protege® GPS™ has been developed for a bile duct. Zilver® (COOK MEDICAL Inc., Bloomington, Indiana, U.S.) and JOSTENT® SelfX (Abbott Vascular Devices, Redwood City, California, U.S.) are also biliary stents. Bard® Luminexx™(C. R. Bard, Inc., Murray Hill, New Jersey, U.S.) has been developed as a vascular stent. All six kinds of stents are self-


expanding stents made of NiTi shape memory alloy, namely Nitinol. Name, diameter, and length of each target stent are summarized in Table 1.

Table 1. Dimensions of target stents

182 Mechanical Engineering

out for longer use. When using a DES, such serious problem as side effects occurring by drugs must be considered as well. As described above, there have been many reports about the use of a DES to prevent in-stent restenosis. However, there have been few studies to prevent in-stent restenosis by designing and modifying a BMS itself. Most of studies have been undertaken to try improvement or optimization of the BMS. Shape, location, and mechanical properties of a stenotic lesion depend on each patient. Optimization, which derives one specified stent shape, is not always the best for the patient. It is thus necessary to design a stent shape suitable for each patient. Using a suitable stent can reduce the risk of in-stent restenosis. However, there has been no study that has tried to design a stent shape

For providing a bare metal stent with lower risk of in-stent restenosis, two objectives were set up. The first objective of our research is establishment of a method to design a stent for each patient's symptom. The second objective is establishment of a method to select a suitable stent from commercially available stents based on their mechanical properties. In this chapter, we describe the design method and selection method of a stent suitable for

It is important to evaluate mechanical properties of a stent for selecting one suitable for patient's condition. There have been many studies that have evaluated mechanical properties of a stent. (Duda et al., 2000) reported that the important properties of a stent include acceptable weight, stiffness in its radial direction, ease of insertion into the blood vessel, and radiation transmittance capability. They then proposed a method to evaluate stent and its performances. (Mori & Saito, 2005) performed a four-point bending test using a stainless steel stent to assess flexural rigidity for each different stent structure. (Carnelli et al., 2010) performed two mechanical tests on six kinds of carotid stents. They carried out a four-point bending test to assess flexibility of the stent. Their method of bending test was similar to that by (Mori & Saito, 2005). They also conducted a three-point compression test to measure the radial stiffness of the stent. Based on measurement results, they considered the relation between geometrical features of the stent and its mechanical properties. The results of these results provide a medical doctor the important information. If there exists a selection method of stent by using these evaluation results efficiently, the doctor can select a suitable stent easily in a large proportion of cases. However, there has been no study that has tried to propose the method to select a suitable stent by efficiently using evaluated mechanical properties. In this section, we introduce a method to select a stent suitable for

Four kinds of commercially available stents, which are already in clinical use, are evaluatedin addition to two types of SENDAI stents having different diameters. One of the evaluated stent is Protege® GPS™ (ev3 Endovascular, Inc., Plymouth, Minnesota, U.S.). The Protege® GPS™ has been developed for a bile duct. Zilver® (COOK MEDICAL Inc., Bloomington, Indiana, U.S.) and JOSTENT® SelfX (Abbott Vascular Devices, Redwood City, California, U.S.) are also biliary stents. Bard® Luminexx™(C. R. Bard, Inc., Murray Hill, New Jersey, U.S.) has been developed as a vascular stent. All six kinds of stents are self-

**2. Method to select stent suitable for clinical manifestation based on** 

in response to each patient's symptom.

**evaluation of stent rigidities** 

**2.1 Target stents** 

patient's symptom based on mechanical engineering.

patient's symptom based on mechanical properties of the stent.

#### **2.2 Radial compression test and stent stiffness in radial direction**

The stent stiffness in radial direction was measured by using the radial compression test machine designed by reference to the method proposed by (Duda et al., 2000). A stent is mounted on the polytetrafluoroethylene stage with slit and wrapped in a sheet. As illustrated in Fig. 1, one end of the sheet is fixed, and the other end is pulled by the linear actuator (ESMC-A2; ORIENTAL MOTOR Co., LTD., Tokyo, Japan). By applying tensile force to the sheet, the stent is compressed in its radial direction. This tensile force can be measured by using the load cell (LUR-A-200NSA1, load rated capacity: 200 N; KYOWA ELECTRONIC INSTRUMENTS CO., LTD., Tokyo, Japan). In addition, the reduction of the stent diameter is measured by using the LED displacement sensor (Z4WV; OMRON Corporation, Tokyo, Japan). The sheet to wrap the stent consists of a polyethylene film 50 m thick and a polyethylene terephthalate (PET) film 12 m thick. Test temperature is 34 C ± 1 .

Fig. 1. Schematic view of the measuring method

(Duda et al., 2000) defined two kinds of forces for evaluating the scaffolding property of a self-expanding stent. One of the defined forces is chronic outward force, which is necessary to subtract 1 mm from a stent diameter. The other, namely radial resistive force, is needed to subtract 1 mm from a stent diameter. (Yoshino et al., 2008) defined the radial stiffness based on the radial pressure exerted on a stent for evaluating the scaffolding property. Based on these evaluation indicators, the stent stiffness in radial direction is defined as follows.

$$K\_{p.f} = \frac{2\pi F}{\Delta r\_s l\_s} \tag{1}$$

Design and Evaluation of Self-Expanding Stents

Fig. 4. Flexural rigidity of each target stent

**2.4 Method to select stent suitable for clinical manifestation** 

Figure 5 shows flow of the proposed method to select a suitable stent based on mechanical properties. As preparation for selecting a suitable stent, the map of stent rigidity is made.

The selection method is described below according to the flow illustrated in Fig. 5.

follow.

deflection curve at the loading point is presented as follow.

Suitable for Diverse Clinical Manifestation Based on Mechanical Engineering 185

On the four-point bending test, shear force does not act on a stent between pin indenters. This enables us to apply a uniform bending moment to a stent. When considering the stent deformation as the problem of a simply supported beam, the differential equation of the

sup ind sup ind 2 48 *l ll l*

Here, *W* is bending load. The product of Young's modulus *E* of the stent material and the moment of inertia of cross sectional area of the stent *I* exactly denotes the flexural rigidity *Kb* of the stent. Therefore, the flexural rigidity of the stent is derived from equation (2) as

The flexural rigidity was obtained from measurement results by using equation (3). Figure 4 shows the comparison of the flexural rigidity with each stent. For the stent diameter of 10 mm, Protege® GPS™ has the highest flexural rigidity. On the other hand, the flexural

*l ll l <sup>W</sup> <sup>K</sup>*

48 *<sup>b</sup>*

rigidity of Bard® Luminexx™ is the highest in the stents with 8 mm diameter.

sup ind sup ind 2

*EI*

2

2

(3)

*W*

(2)

Here, *F* is the tensile force measured by using load cell, *ls* is the stent length, and *rs* is the radius reduction of the stent.

The stent stiffness in radial direction was obtained from the measurement result by using equation (1). Figure 2 shows the comparison of the stent stiffness with each stent. For stent diameter of 10 mm, Protege® GPS™ has the highest stent stiffness in radial direction. On the other hand, for the stent diameter of 8 mm, the stent stiffness of Bard® Luminexx™ is the highest. Note that there is a difference of the stent stiffness in each stent.

Fig. 2. Stent stiffness in radial direction of each target stent

#### **2.3 Bending test and flexural rigidity**

The flexural rigidity was measured by using the designed four-point bending test machine.

As illustrated in Fig. 3, stent is bent by using two pin indenters and a pair of support pins. The load to bend a stent and deflection of the stent are measured by using the micro load capacity load cell (LTS-1KA, load rated capacity: 10 N; KYOWA ELECTRONIC INSTRUMENTS CO., LTD.) and contact displacement transducers (Head: AT-110, Amplifier: AT-210, measurement range: ±5 mm, measuring force: 0.28 N; Keyence Corporation, Osaka, Japan). Here, the interval between support pins *l*sup and that between pin indenters *l*ind are set for 40 mm and 12 mm, respectively. In addition, the diameter of these pins is 3 mm. Test temperature is 35 C ± 1.

Fig. 3. Schematic view of the bending test

Here, *F* is the tensile force measured by using load cell, *ls* is the stent length, and *rs* is the

The stent stiffness in radial direction was obtained from the measurement result by using equation (1). Figure 2 shows the comparison of the stent stiffness with each stent. For stent diameter of 10 mm, Protege® GPS™ has the highest stent stiffness in radial direction. On the other hand, for the stent diameter of 8 mm, the stent stiffness of Bard® Luminexx™ is the

The flexural rigidity was measured by using the designed four-point bending test machine. As illustrated in Fig. 3, stent is bent by using two pin indenters and a pair of support pins. The load to bend a stent and deflection of the stent are measured by using the micro load capacity load cell (LTS-1KA, load rated capacity: 10 N; KYOWA ELECTRONIC INSTRUMENTS CO., LTD.) and contact displacement transducers (Head: AT-110, Amplifier: AT-210, measurement range: ±5 mm, measuring force: 0.28 N; Keyence Corporation, Osaka, Japan). Here, the interval between support pins *l*sup and that between pin indenters *l*ind are set for 40 mm and 12 mm, respectively. In addition, the diameter of

highest. Note that there is a difference of the stent stiffness in each stent.

Fig. 2. Stent stiffness in radial direction of each target stent

**2.3 Bending test and flexural rigidity**

these pins is 3 mm. Test temperature is 35 C ± 1.

Fig. 3. Schematic view of the bending test

radius reduction of the stent.

On the four-point bending test, shear force does not act on a stent between pin indenters. This enables us to apply a uniform bending moment to a stent. When considering the stent deformation as the problem of a simply supported beam, the differential equation of the deflection curve at the loading point is presented as follow.

$$\delta = \frac{\left(l\_{\text{sup}} + 2l\_{\text{ind}}\right)\left(l\_{\text{sup}} - l\_{\text{ind}}\right)^2}{48EI} \mathcal{W} \tag{2}$$

Here, *W* is bending load. The product of Young's modulus *E* of the stent material and the moment of inertia of cross sectional area of the stent *I* exactly denotes the flexural rigidity *Kb* of the stent. Therefore, the flexural rigidity of the stent is derived from equation (2) as follow.

$$K\_b = \frac{\left(l\_{\text{sup}} + 2l\_{\text{ind}}\right)\left(l\_{\text{sup}} - l\_{\text{ind}}\right)^2}{48} \frac{W}{\delta} \tag{3}$$

The flexural rigidity was obtained from measurement results by using equation (3). Figure 4 shows the comparison of the flexural rigidity with each stent. For the stent diameter of 10 mm, Protege® GPS™ has the highest flexural rigidity. On the other hand, the flexural rigidity of Bard® Luminexx™ is the highest in the stents with 8 mm diameter.

Fig. 4. Flexural rigidity of each target stent

#### **2.4 Method to select stent suitable for clinical manifestation**

Figure 5 shows flow of the proposed method to select a suitable stent based on mechanical properties. As preparation for selecting a suitable stent, the map of stent rigidity is made. The selection method is described below according to the flow illustrated in Fig. 5.

Design and Evaluation of Self-Expanding Stents

0.48 N/mm/mm (*ds* = 10 mm).

matches the calculated *Kp*,*<sup>f</sup>*

*Kp*,*<sup>f</sup>* 

*Kp*,*<sup>f</sup>* 

stiffness *Kp*,*<sup>f</sup>*

Suitable for Diverse Clinical Manifestation Based on Mechanical Engineering 187

With the symptom information assumed as shown in Table 2, the necessary stent stiffness

can be calculated using equation (5) as *Kp,f* = 0.87 N/mm/mm (*ds* = 8 mm), and *Kp,f*

The least inner diameter of stenotic part, *Dl* (mm) 2.80 Rate of stenosis by ECTS method (%) 50

*Step 2. Cross-checking of stent stiffness in radial direction with map of stent rigidity*: The calculated

*Step 3. Determination of adequate range of stent stiffness in radial direction*: As described above,

stenotic part in the blood vessel. The doctor should normally determine this adequate range of the stent stiffness. In this case, it is determined that the range of *±*10 % for the necessary stent

is adequate. The shaded areas shown in Fig. 6 are the setup adequate ranges.

there exist few stents that have the stent stiffness value equal to the calculated *Kp*,*<sup>f</sup>*

 values are plotted onto the map of stent rigidity, and indicated by broken lines presented in Fig. 6. It is difficult that the stent stiffness of a commercially available stent

Pressure strain elastic modulus of diseased artery *Ep*,*vl* (MPa) 0.145 Target inner diameter after treatment, *Dt* (mm) 5.60

Table 2. Information of symptom assumed for selecting of stent

 value.

Fig. 6. Selection of suitable stent using map of stent rigidity

Therefore, the necessary stent stiffness *Kp*,*<sup>f</sup>*

Artery Carotid artery

is widened to the extent adequate to expand the

Outer diameter, *Do* (mm) 6.82 Inner diameter, *Di* (mm) 5.60 =

value.

Fig. 5. Flow of selecting stent suitable for clinical manifestation

*Step 1. Determination of stent stiffness in radial direction necessary to expand stenotic part*: First, the stent stiffness in radial direction necessary to expand stenotic part is determined based on information of the patient's symptom. Requirements are the stent diameter *ds*, the outer diameter *Do*, the inner diameter *Di*, and the least inner diameter *Dl* of the stenotic part. The pressure strain elastic modulus *Ep*,*vl* of the diseased blood vessel is also needed. Other important information is the percentage by which to improve the blood flow level, namely the target diameter *Dt* after treatment. Given all the values listed above, the necessary radial stiffness can be obtained by the following equation (see in Section 6 for details).

$$K\_p^\* = \mathcal{Z}E\_{p,vl} \frac{D\_t - D\_l}{D\_o \left(d\_s - D\_t\right)}\tag{4}$$

Equation (4) is derived from the radial pressure necessary to expand the stenotic part in the blood vessel. In this chapter, the radial force necessary to expand the stenotic part is considered as a standard. Therefore, *Kp* of equation (4) is converted into the necessary stent stiffness *Kp,f* using the circumferential length of the vascular inside wall after treatment as follow.

$$K\_{p,f}^{\*} = 2\pi E\_{p,vl} \frac{D\_t \left(D\_t - D\_l\right)}{D\_o \left(d\_s - D\_t\right)}\tag{5}$$

Fig. 5. Flow of selecting stent suitable for clinical manifestation

considered as a standard. Therefore, *Kp*

follow.

*Step 1. Determination of stent stiffness in radial direction necessary to expand stenotic part*: First, the stent stiffness in radial direction necessary to expand stenotic part is determined based on information of the patient's symptom. Requirements are the stent diameter *ds*, the outer diameter *Do*, the inner diameter *Di*, and the least inner diameter *Dl* of the stenotic part. The pressure strain elastic modulus *Ep*,*vl* of the diseased blood vessel is also needed. Other important information is the percentage by which to improve the blood flow level, namely the target diameter *Dt* after treatment. Given all the values listed above, the necessary radial

> \* , 2 *t l*

Equation (4) is derived from the radial pressure necessary to expand the stenotic part in the blood vessel. In this chapter, the radial force necessary to expand the stenotic part is

stiffness *Kp,f* using the circumferential length of the vascular inside wall after treatment as

 \* , , <sup>2</sup> *tt l*

*D D K E*

*os t*

*os t DD D*

*Dd D*

(4)

of equation (4) is converted into the necessary stent

(5)

*Dd D*

stiffness can be obtained by the following equation (see in Section 6 for details).

*p p vl*

*p f p vl*

*K E*

With the symptom information assumed as shown in Table 2, the necessary stent stiffness *Kp*,*<sup>f</sup>* can be calculated using equation (5) as *Kp,f* = 0.87 N/mm/mm (*ds* = 8 mm), and *Kp,f* = 0.48 N/mm/mm (*ds* = 10 mm).


Table 2. Information of symptom assumed for selecting of stent

*Step 2. Cross-checking of stent stiffness in radial direction with map of stent rigidity*: The calculated *Kp*,*<sup>f</sup>* values are plotted onto the map of stent rigidity, and indicated by broken lines presented in Fig. 6. It is difficult that the stent stiffness of a commercially available stent matches the calculated *Kp*,*<sup>f</sup>* value.

*Step 3. Determination of adequate range of stent stiffness in radial direction*: As described above, there exist few stents that have the stent stiffness value equal to the calculated *Kp*,*<sup>f</sup>* value. Therefore, the necessary stent stiffness *Kp*,*<sup>f</sup>* is widened to the extent adequate to expand the stenotic part in the blood vessel. The doctor should normally determine this adequate range of the stent stiffness. In this case, it is determined that the range of *±*10 % for the necessary stent stiffness *Kp*,*<sup>f</sup>* is adequate. The shaded areas shown in Fig. 6 are the setup adequate ranges.

Fig. 6. Selection of suitable stent using map of stent rigidity

Design and Evaluation of Self-Expanding Stents

**3.2 Framework of design support system** 

and 'evaluation' stages.

proposed design support system.

Suitable for Diverse Clinical Manifestation Based on Mechanical Engineering 189

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,'

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

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

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 following sections.
