Evaluation of Mechanical Properties of Catheter Shafts under Cyclic Bending

Abstract

Catheter intervention is used for the treatment of various diseases inside the body. This non-surgical technique is widely used because of its clinical and economic benefits. Although the mechanical properties of a catheter shaft are important to conduct operations using catheters safely, there is no standard testing method for the mechanical properties of the catheter shaft. In this study an evaluation method for the mechanical properties of the catheter shaft under cyclic bending was proposed. Cyclic bending tests were conducted to compare mechanical properties (radial strength and resistance of buckling) of three kinds of specimens. One is the outer layer of the catheter shaft, and the other two are a steel-ribbon catheter shaft and a W-ribbon catheter shaft. Load difference defined by the maximum load of each cycle was used to decide the buckling displacement. Additionally, finite element analysis (FEA) was performed to analyze the deformation behavior of the catheter shaft during a three-point bending test. The load-displacement curves obtained from the FEA showed a good agreement with the envelope of the load-displacement curves in the experiment. It was also revealed from FEA that the deformation behavior of the catheter shaft at the loading point was different from the material of the wire mesh in the catheter shaft. These results suggest the radial strength of the wire mesh increases the buckling displacement of the outer tube and enhances the buckling strength of the catheter shaft. These results also showed that the W-ribbon catheter shaft demonstrated the highest load resistance and the highest buckling displacement. Thus, it was shown that the proposed experimental procedure based on the cyclic bending tests was effective to compare the mechanical properties of various catheter shafts.

1. Introduction

A catheter intervention is one of the most effective methods of treatment of various diseases such as stenosis and thrombosis. This method is widely used because it is minimally invasive and the surgery time is shorter than that of a coronary artery bypass grafting (CABG). Compared to many studies related to the coronary stent from the perspective of biological and mechanical engineering using the fatigue test and finite element analysis^1,2), there is few literatures on mechanical properties of catheter shafts. In a percutaneous transluminal coronary angioplasty (PTCA), a catheter shaft is firstly inserted in a femoral artery or a brachial artery and then passes through a main artery and finally reaches a lesioned part in the coronary artery. Before the catheter shaft reaches the lesioned part, it passes through serpentine arteries and subjected to complex loading histories. To prevent the buckling and the perforation of the catheter shaft, the knowledge of the mechanical properties of the catheter shaft is necessary. The mechanical properties required for the catheter shaft are generally tensile strength, buckling resistance, flexibility, and torque transmission characteristics. However, there is no standard testing method for evaluating the mechanical properties of the catheter shaft. In addition, high X-ray contrast is also important to visualize the position of the catheter during insertion and manipulation.

Finite Element Analysis (FEA) is one of the numerical calculation methods for finding solutions to boundary value problems. FEA is also applied in medical field. Ragkousis et al.³⁾ calculated stress distribution of the stent in a coronary artery of the specific patient, and G. A. Holzapfela et al.⁴⁾ investigated the mechanical behavior of blood vessels based on non-linear continuum mechanics. Nevertheless, the application of FEA for the mechanical properties of catheter shaft has not been conducted due to the difficulty in the constitutive model of the materials and contact problems.

The objective of this research is to evaluate the radial strength and the resistance of buckling of the catheter shafts, and to propose an evaluating method of the mechanical properties of the catheter shafts. Cyclic bending tests were carried out to compare these mechanical properties of the catheter shafts with different materials. FEA was also performed to analyze the deformation behavior during a three-point bending test.

2. Materials and Methods

2.1 Materials

A catheter shaft consists of three layers. Outer layer is resin film, which improves stiffness of the shaft and surface slidability. Middle layer is metal mesh, which is inserted to enhance torque transmission of the shaft. Inner layer is thin resin tube, which gives lubricity inside the shaft. In this study, three kinds of specimens were prepared. One is the only outer layer, and the other two are a steel-ribbon catheter shaft and a tungsten-ribbon (W-ribbon) catheter shaft. The outer layer was made of flame resistant polyolefine (G-APEX heat shrinkable tube). The metal meshes of the two catheter shafts were made of stainless steel (SUS304) and doped tungsten (TMIAS 1201), respectively. The tungsten wires were obtained by purifying tungsten-metal powders from ammonium paratungstate, pressing the powder into an ingot, sintering the ingot by self-resistance heating, and then swaging and drawing the tungsten ingot into a fine wire. The W-ribbons were manufactured by hot rolling the tungsten wires. Each metal mesh of the specimens was manufactured with support of Yamaguchi Sangyo Co., Ltd., using a HS80 series horizontal fine wire braiding machine (Steeger USA Inc). Inner layer of the catheter shaft was excluded. As it is far thinner than outer and middle layer, it gives little influence on the mechanical properties of the shaft. Thickness of the outer layer is 270 µm and thickness of the metal mesh is 25 µm. Figure 1 shows X-ray photographs of various types of metal meshes for comparison. There are three types of braiding pitches (35, 50, 70 PPI), two types of sectional shapes (wire and ribbon) and two types of materials (steel and tungsten). The wires have a circular cross section with a diameter of 50 µm and the ribbons have a rectangular cross section with 25 × 150 µm. The observation showed that the W-ribbon meshes provide higher X-ray contrast than commonly used steel wires due to its shape and higher density of the material. Steel ribbon with 50 PPI and W ribbon with 50 PPI were used in the current study. All three specimens were cut to the same length of 30 mm with a diameter of 2.5 mm.

Fig. 1

X-ray photographs of the steel mesh and W mesh.

2.2 Bending tests

Two types of bending tests were conducted. One is a cyclic three-point bending test with the three kinds of specimens. Figure 2 shows the schematic diagram of the experiment equipment. The equipment was composed of a small-capacity load cell (LVS-1KA, Kyowa Electronic Instruments) and a motorized stage (ALZ-301-HM, Chuo Precision Industrial) and a controller driver (QT-ADL1-35, Chuo Precision Industrial). The motorized stage moved up and down with a displacement rate of 50 µm･s⁻¹ and the specimens were subjected to displacement-controlled loading. The distance between the support points was 20 mm and the loading point was set at the middle. One cycle was defined as the movement of 0.50 mm up and then 0.45 mm down of the motorized stage. The number of cycles was 150. To make buckling of the catheter shafts clear, the load difference (ΔL) was defined as follows:   

\[\Delta L = L_{\rm max}(n + 1) - L_{\rm max}(n),\](1)

where $L_{\rm max}(n)$ is the maximum load in the cycle n. The buckling displacement of the catheter shaft was defined as the displacement when $\Delta L$ reached the minimum. The cyclic three-point bending tests were conducted three times for each type of specimens to ensure the reproducibility.

Fig. 2

Schematic diagram of the experiment equipment.

In order to calibrate the material parameters in FEA, a monotonic three-point bending test of the outer tube was also conducted. The maximum push-in displacement was 2 mm.

2.3 Finite element analysis

A commercially available FEA solver, ABAQUS/Explicit 6.14-2 (Simulia Corporation) was used. Before conducting an analysis of the catheter shaft, a monotonic three-point bending analysis of the outer tube was conducted to calibrate the material parameters of the outer tube. The deformation behavior of the outer tube was expressed by a hyperelastic model proposed by Yeoh⁵⁾. It is based on the strain energy potential (U) of the reduced polynomial form and defined by:   

\[U = C_{10}(\bar{I}_1 - 3) + C_{20}(\bar{I}_2 - 3)^2 + C_{30}(\bar{I}_1 - 3)^3 + \frac{1}{D_1}(J^{el} - 1)^2,\](2)

where $\bar{I}_1$, $\bar{I}_2$, $\bar{I}_3$ are the invariants of strain deviator, $C_{10}$, $C_{20}$, $C_{30}$ and $D_1$ are the material constants, and $J^{el}$ is the elastic volume strain. Mullins effect is also considered to model the phenomenon of stress softening under cyclic loadings. It is defined by:   

\[U(\bar{\lambda}_i,\eta) = \eta \tilde{U}_{dev}(\bar{\lambda}_i) + \varphi (\eta) + \tilde{U}_{vol}(J^{el}),\](3)

  

\[\eta = 1 - \frac{1}{r} {\rm erf} \left( \frac{U_{dev}^m - \tilde{U}_{dev}}{m + \beta U_{dev}^m} \right)^2,\](4)

where $\tilde{\lambda}_i$ is the deviatoric principal stretches, $\eta$ is the damage variable, $\tilde{U}_{dev}(\bar{\lambda}_i)$ is the deviatoric part of the strain energy density, $\varphi (\eta)$ is a continuous function of the damage variable, $\tilde{U}_{vol}(J^{el})$ is the volumetric part of the strain energy density, and r, m and β are material constants⁶⁾. These equations were used with the hyperelastic model to describe small damage accumulated inside the material.

Using the calibrated parameters, three-point bending simulations of the steel-ribbon catheter shaft and W-ribbon catheter shaft were conducted. Due to the computational cost, one cycle of the three-point bending test of the catheter shaft was simulated. The dimension of the outer layer and metal meshes of the catheter shaft was similar to the specimens used in the experiment. To reconstruct the metal mesh with 16 intersections per loop and the braid angle of 30˚, a development model of the mesh was created based on the following equations:   

\[y = \left\{ \begin{array}{@{}ll@{}} \displaystyle A\tanh \left( \frac{8\sqrt{3} x}{\pi R} \right) & \displaystyle \left( \frac{{\rm n}\pi R}{8\sqrt{3}} \le x \le \frac{({\rm n} + 1)\pi R}{8\sqrt{3}} \right) \\ \displaystyle -A\tanh \left( \frac{8\sqrt{3} x}{\pi R} \right) & \displaystyle \left( \frac{({\rm n} + 1)\pi R}{8\sqrt{3}} < x \le \frac{({\rm n} + 2)\pi R}{8\sqrt{3}} \right) \end{array} \right.,\](5)

  

\[A = 0.015\,{\rm mm},\ R = 2.015\,{\rm mm},\ {\rm n} = 0, 1, 2, 3\]

where y is center line of a ribbon, A is the amplitude of the line and R is the radius of the metal mesh. The ribbon has the rectangular cross section with 25 × 150 µm. The height of this ribbon changes due to the overlapping of the ribbons. The geometry of the development view of the mesh is shown in Fig. 3. After rolling this development model into a cylindrical shape with a diameter of approximately 2 mm, both ends were merged. Figure 4 shows the created model of the metal-ribbon catheter shaft and the cross-section view. The materials of the metal mesh are assumed to be elastic because the stress value is assumed to be under the yield stress during the experiments. Table 1 shows material parameters of the ribbon meshes. The dynamic friction coefficients between the outer tube and the loading pins, and the outer tube and the metal meshes were assigned to 0.2, and that between the metal ribbons was assigned to 0.1. The maximum push-in displacement was 4 mm.

Fig. 3

Development view of the metal mesh: (a) global view, (b) local view.

Fig. 4

(a) Model of three-point bending test and (b) cross-sectional view of catheter shaft.

Table 1 Material constants of metal mesh.

Material	Density (g/cm3)	Young's modulus (GPa)	Poisson ratio
Stainless steel	7.93	197.0	0.30
Tungsten	19.3	402.7	0.284

3. Results and Discussion

3.1 Cyclic bending test

Figure 5 shows the load-displacement curves of the outer layer tube, the steel-ribbon catheter shaft and the W-ribbon catheter shaft. In the outer layer tube, the load increased until the displacement reaches around 3 mm and in the steel-ribbon catheter shaft and the W-ribbon catheter shaft the load increased until the displacement reaches around 5 mm. W-ribbon catheter shaft showed the highest value of the maximum load among the three types of samples in the cyclic bending test. Although the difference of the displacement at the maximum load between the outer layer tube and metal ribbon catheter shafts was observed clearly, it is difficult to see the difference between steel-ribbon and W-ribbon. To make the buckling displacement of the catheter shafts clear, the load difference ($\Delta L$) was also plotted in the figure. The buckling displacement of the catheter shaft was defined as the displacement when the ΔL reached the minimum. The results of the maximum load and the buckling displacement for all three tests are summarized in Figs. 6 and 7, respectively. The results showed that the W-ribbon catheter shaft demonstrated the highest load resistance and the highest buckling displacement.

Fig. 5

Load-displacement curves of (a) outer layer tube, (b) steel-ribbon catheter shaft and (c) W-ribbon catheter shaft.

Fig. 6

Maximum load of the three kinds of specimens.

Fig. 7

Buckling displacement of the three kinds of specimens.

To observe the details of the load response, the load-displacement curves of the steel-ribbon catheter shaft and W-ribbon catheter shaft in the displacement from 0 mm to 4 mm are plotted in Fig. 8 and the envelope curves are also displayed in the figure. Comparing both envelope curves, it was found that there is little difference in the displacement from 0 mm to 2 mm. It is considered that in the early stage the metal mesh has little influence on the load response of the catheter shaft and the mechanical properties of the outer layer is dominant for the load response. In the displacement from 2 mm to 4 mm, the load value of the W-ribbon catheter shaft is higher than that of the steel-ribbon catheter shaft. These results indicated that the elastic constants of the materials of the ribbon mesh affect the load response in the displacement from 2 mm to 4 mm.

Fig. 8

Load-displacement curves in the displacement from 0 mm to 4 mm.

3.2 Finite element analysis

Hyperelastic material parameters of the outer tube were calibrated to match the experimental load response of the outer tube under the monotonic bending test. The calibrated parameters of Yeoh model with Mullins effect are given in Table 2. Figure 9 shows the tensile stress-strain curve of the hyperelastic material with the calibrated parameters. It was shown that the nominal stress under unloading becomes slightly lower than that in tensile loading. The stress-strain curve was described by eq. (2) in the loading and described by eqs. (3) and (4) in the unloading. Figure 10 shows the load-displacement curve of the outer tube under three-point bending from both experiment and FEA. The load-displacement curves from FEM showed a good agreement with the experimental results except for the permanent strain. It is one of the drawbacks of Yeoh's hyperelastic model with Mullins effect that the permanent strain is not described. The modification of the constitutive model will be required for more accurate simulation of the deformation behavior of the outer tube of the catheter shaft.

Table 2 Calibrated material parameters of Yeoh model with Mullins effect for the outer tube.

C10 (mJ/mm3)	C20 (mJ/mm3)	C30 (mJ/mm3)	D1 (mm3/mJ)
21.3	−568	9250	0.00238
r	m (mJ/mm3)	β
1.001	0.050	2.76

Fig. 9

Tensile stress-strain curves of material used in the outer tube.

Fig. 10

Load-displacement curve of the outer tube under the monotonic three-point bending test obtained from both the experiment and FEA.

Cross-sectional views of Mises stress distributions of the catheter shafts of the steel-ribbon catheter shaft and the W-ribbon catheter shaft at the push-in displacement of 4 mm are shown in Fig. 11. To see the inside easier, the outer tube is not displayed in this figure. It is obvious that stress value of the ribbon mesh of W-ribbon catheter is totally higher than that of steel-ribbon catheter and high stress value generated around the loading point. Figure 12 shows the load-displacement curves of steel-ribbon catheter shaft and W-ribbon catheter shaft obtained from FEA. Similarly to the comparison of Mises stress distributions of both models, the load value of the W-ribbon catheter shaft is totally higher than that of the steel-ribbon catheter shaft. The shapes of these curves are in a good agreement with the envelope curves of the experiments (Fig. 8). As mentioned in the discussion of Fig. 8, there is little difference in the envelope curves in the displacement from 0 mm to 2 mm and the load value of the W-ribbon catheter shaft is higher than that of the steel-ribbon catheter shaft in the displacement from 2 mm to 4 mm. To examine the deformation behavior inside the catheter shafts, the cross-sectional views of Mises stress distributions of the catheter shafts at the push-in displacement of 2 mm and 4 mm are shown in Figs. 13 and 14, respectively. The maximum values of Mises stress displayed in these contour plots are set very low to see Mises stress value generated in the outer tube. Comparing the shapes and stress values of the outer tube in Fig. 13, there is no significant difference between the steel-ribbon catheter shaft and the W-ribbon catheter shaft. It is corresponding to the difference of the load-displacement curves from the experiment from 0 mm to 2 mm. On the other hand, there is a clear difference in the deformation shapes of the outer tubes at the displacement of 4 mm (Fig. 14). The outer tubes of the W-ribbon catheter shaft showed a smaller deformation at the loading point than that of the steel-ribbon catheter shaft. The penetration depth of the outer layer at the loading point in the steel-ribbon catheter shaft and the W-ribbon catheter shaft are 0.122 mm and 0.193 mm, respectively. It is considered that the deformation at the loading point was suppressed by support of W ribbon with a higher elastic modulus. Thus, the different load response from 2 mm to 4 mm (Fig. 8) can be explained by the difference of materials of the metal ribbon. These results suggested that the W-ribbon mesh increased the radial strength of the outer tube and resulted in an improvement of the buckling resistance of the catheter shaft.

Fig. 11

Cross-sectional view of Mises stress distributions of the catheter shafts: (a) steel-ribbon catheter shaft and (b) W-ribbon catheter shaft.

Fig. 12

Load-displacement curves of steel-ribbon catheter shaft and W-ribbon catheter shaft obtained from FEA.

Fig. 13

Cross-sectional view of Mises stress distributions of the catheter shafts at the push-in displacement 2 mm: (a) steel-ribbon catheter shaft and (b) W-ribbon catheter shaft.

Fig. 14

Cross-sectional view of Mises stress distributions of the catheter shafts in the push-in displacement 4 mm: (a) steel-ribbon catheter shaft and (b) W-ribbon catheter shaft.

4. Conclusion

In this study, three kinds of specimens were prepared. One is the outer layer of the catheter shaft, and the other two are a steel-ribbon catheter shaft and a W-ribbon catheter shaft. The mechanical properties of the three specimens under cyclic bending were examined by the experiments and the numerical simulation. The following conclusions were drawn.

• (1)   The experimental results of the cyclic three-point bending tests showed that the W-ribbon catheter shaft exhibited the highest maximum load and the highest buckling displacement comparing with the stainless-steel catheter shaft. The buckling displacement was successfully evaluated by the load difference of the cyclic three-point bending tests.
• (2)   The load-displacement curves from FEA have a good correlation with the envelope curves of the load-displacement curves in the experiment. These FEA results suggested that the deformation at the loading point was suppressed by support of W ribbon with a higher elastic modulus.
• (3)   It was demonstrated that the proposed experimental procedure based on the cyclic bending tests was effective to compare the mechanical properties of various catheter shafts.

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