Comparative bending behaviors between fully covered and bare biodegradable polydioxanone biliary stents using a numerical approach

Abstract

A comparison of bending flexibility between bare biodegradable polydioxanone biliary stents (BBPBSs) and fully covered biodegradable polydioxanone biliary stents (FCBPBSs) developed for humans is presented in this study. Firstly, a series of BBPBSs and FCBPBSs were prepared by braiding method in order to investigate the relationship between the bending load and structure parameters (monofilament diameter and braid-pin number) through a three-point bending method. In addition, a series of three-point bending models based on actual stent specimens above was established and the bending flexibility of BBPBSs and FCBPBSs in three-point bending models was evaluated by the finite element method (FEM). Results showed that the simulation was in good agreement with the experiment, indicating that the simulation results could be used as the reference to access the mechanical behaviors of BBPBSs and FCBPBSs. Furthermore, the distinction in bending flexibility between BBPBSs and FCBPBSs was compared in this simulation and demonstrated that the existence of a nanomembrane component (NMP) in FCBPBS causes remarkable performance variation including bending load (all FCBPBSs increased by at least 0.65%), stress, plastic strain and energy conversion of the stent (the plastic dissipation energy of all FCBPBSs increased by at least 2.33J) in the bending process.

Keywords

BBPBS FCBPBS FEM three-point bending method bending load stress plastic strain

Postoperative cicatricial and cholangitis stenosis are common clinical diseases of benign biliary stricture (BBS), which presets a high incidence. To date, the main strategies for treating BBS are surgical operation, drainage, endoscopic therapy and drug therapy, but surgical operation is of increasingly limited use for BBS patients because of its disadvantages, which include bigger trauma, high operative difficulty, more complications, and high recurrence and failure rates. With the development of interventional radiological techniques such as endoscopic retrograde cholangio-pancreatography (ERCP)^1,2 and over 90% percutaneous transhepatic cholangiography (PTC),³ the implantation of a biliary stent has been pushed as a suitable treatment method, which considerably relieves the patient’s condition, improves the patency of the bile duct, and leads to little trauma and pain. As a minimally invasive operation, stent placement could reduce hospital stay^4,5, and the success rate was over 90%. A bile duct stent can be one of three types, according to material: plastic, metal and biodegradable.

Plastic biliary stent was first applied to bile duct stricture caused by tumor.⁶ The implantation of the plastic biliary stent was easy to operate and its drainage effect was evident, but stenosis reoccurred in bile duct stented by plastic biliary stent because of its small pore size. By about 6 months after stenting, the stenosis rate was up to 70%⁷ and the obstructed plastic biliary stent needed to be replaced, thus increasing both the risk and cost of treatment.

Due to the disadvantages of the plastic biliary stent described above, a metal biliary stent was applied to treat BBS, with advantages such as larger aperture, good effect of dilatation and drainage and lower restenosis probability.^8.9 However, due to the net structure of bare metal stents, the proliferation of pathological tissue makes removal of the bare metal stents from an obstructed bile duct difficult,^10,11 and could also result in the restenosis of the stent;¹² finally, the bare metal biliary stent become a permanent foreign matter in the human body. In response to these undesirable characteristics of bare metal stents, the covered metal stent appeared on the market. The membrane covering the bare metal stent not only effectively prevented the proliferation of tissue from growing into the interior of the stent through its mesh, but also evenly distributed the radical force of the stent on the inner wall of the bile duct with stricture, so improving the stress relationship between the stent and the obstructed bile duct wall. The dilatation of the covered metal biliary stent was obviously better than that of the bare metal biliary stent.^13.14

However, the covered metal stent has some shortcomings: the membrane of the covered metal stent decreased the friction between the stent and the wall of the bile duct so that stent was easily shifted into the intestinal cavity,^15,16 resulting in an increase of the incidence of inflammation.¹⁷ As a result, the covered metal biliary stent needed to be taken out or adjusted repeatedly under endoscopy, leading to an increase in the operation risk and treatment cost. Plastic and metal (covered or bare) biliary stents could cause an abnormal pathological reaction as the result of foreign matter. The disadvantages of metal and plastic stents described above gave rise to the biodegradable biliary stent as a research hotspot in the field of bile duct stents, due to its outstanding characteristics that include preferable compliance, controllable degradation, better biocompatibility, and having the same mechanical property as a metal stent. The biodegradable biliary stent has been introduced into clinical research and application abroad; for example, biodegradable polylactic acid (PLA) biliary stent¹⁸ and the biodegradable polydioxanone (PDO) biliary stent.¹⁹ In the process of stenting, the biodegradable biliary stent showed good feasibility, safety and long patency time.

In 1960, the finite element method (FEM) was developed, and named, by RW Clough²⁰; shortly after this, the first automated FEM computer program analysis was written by Ed Wilson, after which research using FEM began to develop rapidly and it became widely used in various fields.²¹ In 1997, the numerical model of a highly simplified self-expandable nitinol stent was firstly proposed by Whitcher²² and the process of compression-release of a nitinol stent was simulated by Perry using FEM.²³ Their outstanding work could be regarded as the beginning of FEM used for the mechanical simulation of scaffold. Following this, the mechanical simulation on stent expansion by means of FEM gradually became the leading means of modeling in the field of stent development. However, there are few articles focused on modeling the bending flexible performance of stent using FEM. The bending behavior of stent is a more important index in the mechanical field. Fontaine compared implantation results between rigid and flexible stents and found that intimal hyperplasia was generated by rigid stent, differing with flexible stent designs.²⁴ Restenosis was easily apparent in the cavity of stent, which has poor flexibility.²⁵ Etave carried out a three-point bending simulation for two kinds of intravascular stent model.²⁶ A flexible three-dimensional measuring model of a stent was designed by Perini for bending simulation.²⁷ Mori established a two-dimensional stent bending model based on an actual stent specimen,²⁸ but this study largely focused on the vascular stent. To the best of our knowledge, the bending simulation of a biliary stent is much less common, and especially for biodegradable biliary stent, with the exception of the author’s previous work.²⁹ Furthermore, few researchers focus on a comparison of bending behavior simulation between the fully covered biodegradable polydioxanone biliary stent (FCBPBS) and the bare biodegradable polydioxanone biliary stent(BBPBS) and investigate the effect of the membrane covering on FCBPBS on the bending performance of the biliary stent.

In this study, BBPBS was fabricated with polydioxanone (PDO) monofilament, and FCBPBS was prepared through covering the membrane made by polycaprolactone (PCL) on BBPBS.

A three-point bending method with fixed span was applied to evaluate the bending flexibility of a series of FCBPBSs and BBPBSs, the structure of which varied with parameters including braid-pin number and PDO monofilament diameter. Furthermore, a series of bending models of FCBPBS and BBPBS were established by FEM to simulate the experimental results for investigating the stress, plastic strain and energy conversion of the stents described above.

Preparation of FCBPBS and BBPBS

Materials

The FCBPBS was constituted from the BBPBS component which was the primary mechanical bearer of FCBPBS and the nanomembrane which prevented the proliferation of tissue from growing into the cavity of the stent through its mesh. Herein, BBPBS was fabricated by PDO monofilament authenticated by the Food and Drug Administration(FDA) for use in the human body due to good biocompatibility, safety and controllable degradation.^27,28 PCL was chosen as the nanomembrane material, having good biocompatibility and being most widely used and showing higher mechanical strength.³⁰ The properties of PDO monofilament and PCL are shown in Table 1.²⁶
Table 1.
The fundamental properties of PDO monofilament and PCL

Material Number Diameter (mm) Crystallinity (%) Tensile force (N) Linear density (Tex)

PDO A 0.23 70.7 23.56 63.13

B 0.29 70.4 34.81 95.83

C 0.36 70.5 45.92 125.21

Material Density (g/cm³) Relative molecular mass (M_n) T_m (℃) T_e (℃) –

PCL 1.14 80,000 57.3 23.8 –

Braiding mold of BBPBS

BBPBS was fabricated with PDO monofilament which was braided onto the self-made copper pipe mold and heat treatment was applied to the BBPBS with mold at 75℃ for 15 min to improve the structural stability of the stent. The structural schematic of the mold is shown in Figure 1.
Figure 1.
The structural schematic of the mold.

As depicted in Figure 1, the mold used for braiding BBPBS was composed of copper pipe with holes and pins. The mounting holes for the pins are distributed in parallel at both ends of the mold. The region between the two rows of pins of the mold is defined as the braiding area of the stent, which determines the axial length of the scaffold. In the braiding process, the PDO monofilament is braided in the braiding area. When the PDO turns around the pin, the braiding direction changes and the arch structure is formed. A pin corresponds to an arch, and is defined as a braid-pin in this study. The number of mounting holes for pins in the copper pipe defines the number of braid-pins and the braiding density of the stent.

Braiding method of BBPBS

BBPBS with different numbers of braid-pins could be braided by the same method. In this article the braiding process with 6 braid-pins BBPBS is described as an illustrative example. The braiding path of 6 braid-pins BBPBS is shown in Figure 2(a). Firstly, the upper and lower row pins are numbered from right to left. The PDO monofilament was coiled around the pin of 1 and 1′ about a circle, and at pin1′ PDO monofilament was coiled the copper pipe in the braiding area along the downline to arrive at pin 1. PDO monofilament was coiled around the pin 1 to form the arch structure and twined copper pipe along the upline to arrive at pin 2′. At pin 2′, PDO monofilament was coiled to form an arch structure and twined along the downline again. The PDO monofilament was coiled repetitively according to the principle above. Through the interweaving of the PDO monofilament, BBPBS with a reticulate rhombus structure was formed. A 3D arch structure is shown in Figure 2(b).
Figure 2.
The braiding path of 6 braid-pins BBPBS and the structure of a 3D arch and interweaving.

Electrospinning method

FCBPBS was fabricated by covering the nanomembrane on the BBPBS using an electrospinning method. Electrospinning is a technology for preparing micro and nano fibers from a polymer solution which is ejected from a spinning nozzle under the action of an electrostatic field. Micro and nanofibers have the advantages of having small diameter, larger specific surface area and high porosity,³⁰ so are convenient for cell adhesion and the growth and exchange of nutrients though the gaps in the nanomembrane. In this experiment, PCL was used as membrane material, as shown in Table 1, and the organic solvent of the PCL was the mixed solution of dimethylformamide (DMF) and dichloromethane (DCM). The experiment parameters for electrospinning were obtained from existing literature³¹ and the electrospinning method itself and the schematic for the electrospinning process were obtained from reference data.²⁹

In conclusion, using the braiding mold method for BBPBS and an electrospinning method, a series of BBPBSs and FCBPBSs with different parameters for PDO diameter (0.23 mm, 029 mm, 0.36 mm) and braid-pin number (8, 10, 12) were prepared. The configuration of BBPBS and FCBPBS is shown in Figure 3, and the structure parameters of BBPBSs and FCBPBSs are shown in Tables 2 and 3.
Figure 3.
The configuration of BBPBS and FCBPBS.

Table 2.
The structure parameters of BBPBSs

Material Number of specimens Braiding number (pins) External diameter (mm) Internal diameter (mm)

PDO A2-B 8 8.83 8

A3-B 10 8.90 8

A4-B 12 8.92 8

B2-B 8 9.15 8

B3-B 10 9.17 8

B4-B 12 9.21 8

C2-B 8 9.52 8

C3-B 10 9.56 8

C4-B 12 9.67 8

Table 3.
The structure parameters of FCBPBSs

Material Number of specimens Braiding number (pins) External diameter (mm) Thickness of film (mm) Internal diameter (mm)

PDO A2-C 8 8.83 0.07 8

A3-C 10 8.90 0.069 8

A4-C 12 8.92 0.068 8

B2-C 8 9.15 0.072 8

B3-C 10 9.17 0.07 8

B4-C 12 9.21 0.073 8

C2-C 8 9.52 0.068 8

C3-C 10 9.56 0.069 8

C4-C 12 9.67 0.071 8

The test method of stent bending flexibility

The bending flexibility of a stent is a very important index of its mechanical properties, If the flexibility of a stent does not match that of the obstructed bile duct, complications including restenosis and hyperblastosis could be arise. For this reason, the bending behavior of a stent needs to be assessed. In this study, the three-point bending method was applied in order to investigate the bending behavior of the stent described above, made by us according to the standard F2606-08. The fixture of the three-point bending method is shown in Figure 4, the whole device was composed of upper load applicator and lower support system. In the process of bending, the stent, mounted to the lower static supports, was bent by the upper load applicator to reach a set deflection of about 4 mm; meanwhile, the values of load and deflection of the stent were recorded to draw a force vs. deflection curve. The lower support system consisted of two parallel walls with a span of 35 mm in which was cut a semi-circular hole of 8 mm diameter in which to place the stent. The speed of the upper load applicator bending the stent was set as 20 mm/min.
Figure 4.
Schematic of three-point bending apparatus with stent.

Specifications of bending model of FCBPBS and BBPBS

FEM is a classical numerical approach to optimizing product design which possess advantages such as high precision, high efficiency and lower cost. Before fixing the structure of a product, its likely performance with different materials and structural design can be obtained by FEM, providing theoretical guidance for product research and development. In this research, FEM was used for simulating a bending experiment in order to understand the variations of bending performance which could not be measured in the bending process, such as internal stress and strain, energy, and so on. Based on the actual specimens of FCBPBS and BBPBS and the three-point bending fixture, structural models of FCBPBS and BBPBS were established by Solidworks software (Version 2012) as shown in Figure 5(a). The three-point bending model of FCBPBS and BBPBS were constructed with ABAQUS (Version 2012) software as shown in Figure 5(b). The structure parameters of models of a series of FCBPBSs and BBPBSs involved in this simulation used different braid-pin numbers (8, 10, 12) and PDO monofilament diameters (0.23 mm, 0.29 mm, 0.36 mm). The detailed structure parameters of FCBPBS and BBPBSs involved to this simulation are illustrated in Tables 2 and 3.
Figure 5.
The structural model (a) and the structure of a three-point bending model (b) of FCBPBS and BBPBS.

Mesh generation and step choice

The same mesh and step were applied for the three-point bending models for FCBPBS and BBPBS. Firstly, the three-point bending model was seeded for controlling the amount of mesh element in the mesh part, and the appropriate mesh element type was assigned; finally, the three-point bending models were meshed, based on the size and type of mesh element. Before the size and type of a mesh element is fixed, different types and sizes of mesh element should be simulated to check the convergence efficacy of the simulation. In this bending simulation, the approximate global size of rollers (the upper load applicator and the two lower static supports were replaced by three rollers), and each monofilament of the biliary stent and nanomembrane were set as 4, 0.2 and 1 mm respectively, due to the convergence result described above. Meanwhile, the same element type (an 8-node linear brick, incompatible element, C3D8I in ABAQUS software) was assigned for the three rollers, nanomembrane and PDO monofilaments to ensure the accuracy of the computed analysis and meet the requirements of elastic-plastic and contact simulation.³² In this three-point bending simulation, the type of analysis step was set as ‘Dynamic, Explicit’ to simulate quickly and exactly. The meshing schematic of the three-point bending model for FCBPBS and BBPBS are shown in Figure 6.
Figure 6.
The meshing schematic of the three-point bending model for FCBPBS (a) and BBPBS (b).

Interaction and boundary conditions

The interaction and boundary conditions of FCBPBS and BBPBS are shown in Figures 7 and 8 respectively. For interaction, for the contact analysis of the three-point bending model for FCBPBS and BBPBS, Interaction Property’ with 0.2 friction parameter was used in simulating for both models.³² In order to avoid friction analysis between the surface of the nanomembrane and the stent PDO monofilaments increasing the simulation efficiency of the three-point bending model for FCBPBS, the interaction between the internal surface of the film and the monofilaments’ surface with the stent was set as a ‘Tie’ constraint, the internal surface of the film was set as ‘Master surface’ and the monofilaments’ surface was set as the ‘Slave surface’, as depicted in Figure 7(a). For the three-point bending model of BBPBS, there was no need to set the ‘Tie’ constraint because of the absence of nanomembrane, as shown in Figure 7(b). In relation to boundary conditions, as shown in Figure 8, three reference points (RP3, RP4 and RP5) were established for the three-point bending model of both FCBPBS and BBPBS in order to simplify extraction of the bending force and exert deflection conditions. At the same time, the upper load applicator and two lower static supports were replaced by three rollers, restricted by a ‘rigid body’ constraint to avoid the complex calculation of their deformation, and associated with three reference points, respectively. The boundary condition was applied here, the deflection value on the RP3 determined by actual bending deflection and set as 4 mm in the ‘Y’ coordinate direction. The boundary condition on RP4 and RP5 were fixed in all the dimensions for the entire simulation. The actual values of deflection throughout the entire simulation are shown in Table 4.
Figure 7.
The interaction schematic of three-point bending model of FCBPBS (a) and BBPBS (b).

Figure 8.
The boundary condition schematic of three-point bending model for FCBPBS (a) and BBPBS (b).

Table 4.
The actual value of deflection of three references

Name X coordinate (mm) Y coordinate (mm) Z coordinates (mm)

RP3 0 4 0

RP4 0 0 0

RP5 0 0 0

Property

Because the plastic simulation of a three-point bending model for FCBPBS and BBPBS were simulated in this work, the plastic mechanical parameter of the PDO monofilament and the PCL nanomembrane, which includes the true stress ( $σ_{true}$ ) and true strain ( $ɛ_{true}$ ) in the loading process, needed to be obtain through a tensile test. Firstly, the nominal stress ( $σ_{nom}$ ) and strain ( $ɛ_{nom}$ ) of PDO monofilaments and PCL nanomembrane could be obtained through the tensile test by the following formulae³³
$ɛ_{nom} = \frac{Δ l}{l_{0}}$
(1)

$σ_{nom} = \frac{F}{A_{0}}$
(2)
where $σ_{nom}$ and $ɛ_{nom}$ is the nominal stress and nominal strain respectively, $Δ l$ is whole variation of the length, l₀ is original length, F is the load, and A₀ is the original cross area.

Secondly, $σ_{true}$ and $ɛ_{true}$ could be calculated by the following formulae³⁴
$\begin{matrix} ɛ_{true} = \int_{l_{0}}^{l} \frac{d l}{l} = \ln (\frac{l}{l_{0}}) = \ln (1 + ɛ_{nom}) \end{matrix}$
(3)

$σ_{true} = \frac{F}{A} = \frac{F}{A_{0} \frac{l_{0}}{l}} = σ_{nom} (1 + ɛ_{nom})$
(4)

$ɛ_{pl} = | ɛ_{true} | - | ɛ_{el} | = | ɛ_{true} | - \frac{| σ_{true} |}{E}$
(5)
where A is cross area at one moment in the tensile process, l is length at one moment in the tensile process, $ɛ_{pl}$ is the plastic strain, $ɛ_{el}$ is the elastic strain, and E is elastic modulus. We had calculated the plastic mechanical parameters including the true stress ( $σ_{true}$ ) and true strain ( $ɛ_{true}$ ) previously.³⁴

Results and discussion

The stress response of FCBPBS and BBPBS during load

The stress nephograms of FCBPBS and BBPBS were extracted from the three-point bending model, it could be clearly observed that the internal stress distribution of FCBPBS and BBPBS changed at different locations in the FCBPBS and BBPBS bending process, as shown in Figures 9 and 10, where lower stress is indicated by cool colors (blues) and higher stress by warmer colors (reds), because the FCBPBS was composed of a bare stent part (BSP) and nanomembrane part (NMP). Duo to the bending deformation, the squeezing and friction action of PDO monofilaments and the effect between FCBPBS and the three rollers replacing external effect, the higher stress area for the BSP of the FCBPBS was generated at the central location: (1) in Figure 9(a), along the z-axis direction, and the higher stress for the NMP of the FCBPBS also distributed at central position: (2) in Figure 9(b). Comparing the color variation between NMP and BSP of the FCBPBS, it is obviously apparent that the stress variation for BSP was more drastic than that of NMP and lesser stress occurred in NMP than in BSP.
Figure 9.
The stress distribution during bending for the FCBPBS: (a) the stress distribution of bare stent part (BSP); (b) the stress distribution of the nanomembrane part (NMP).

Figure 10.
The stress distribution of BBPBS during bending.

As depicted in Figure 10, the higher stress area of BBPBS was mainly distributed at location (1) along the z-axis direction, because of the bending deformation, the squeezing and friction action of PDO monofilaments and the effect between BBPBS and three rollers replacing external effect. Through comparing the stress of BSP of the FCBPBS and BBPBS, we found that the area of stress distribution of BBPBS was smaller than that of BSP of the FCBPBS and the stress value of BBPBS (24.3 MPa) was also smaller than that of BSP (77.41 MPa). Because of covering added to the BBPBS to make the FCBPBS, the maximum stress of the FCBPBS increased almost 3 times more than the BBPBS with the same structure parameters.

Comparison of bending flexibility between FCBPBS and BBPBS with different structures

The bending flexibility of FCBPBSs and BBPBSs was evaluated in this work using the three-point bending method with fixed span. The higher the bending load of the stent specimen at the given deflection, the worse its bending flexibility. The bending load of FCBPBSs and BBPBSs with different structures is shown in Figure 11. For nine types of FCBPBSs, 12 braid-pins FCBPBS with 0.36 mm diameter has the biggest bending load, indicating that it has the worst bending flexibility, and 8 braid-pins FCBPBS with 0.23 mm diameter has the lowest bending load at the given 4 mm deflection, showing that it has the greatest bending flexibility. Nine types of BBPBSs have the same tendency as FCBPBSs, 12 braid-pins BBPBS with 0.36 mm diameter has the worst bending flexibility and 8 braid-pins BBPBS with 0.23 mm diameter has the greatest bending flexibility. When the diameter of FCBPBSs and BBPBSs were the same, the bending flexibility of FCBPBSs and BBPBSs decreased with increasing braid-pin numbers. By contrast, for the bending flexibility of FCBPBSs and BBPBSs with the same braid-pin number throughout, bending flexibility decreased with increasing PDO monofilament diameter. Comparing the bending load between FCBPBSs and BBPBSs with same structure, including braid-pin number and PDO monofilament diameter, the bending loads of FCBPBSs were all higher than that of BBPBSs, indicating that bending flexibility for nine BBPBSs were better than that of FCBPBSs with a corresponding structure. The increase in the bending load of FCBPBSs was at least 0.65% more than that of BBPBSs. The bending flexibility of the FCBPBS which we design could match the requirements of clinical use, comparing the bending load of FCBPBS with that of the full covered MTN-DA biliary stent which has been in clinical use for some time,²⁹ so the bending flexibility of BBPBSs could also meet clinical requirements.
Figure 11.
The bending flexibility of nine FCBPBSs and BBPBSs.

The comparison of bending load between simulation and experiment of FCBPBS

The simulation and experimental results of FCBPBS could be obtained using the three-point method. In the bending process, the concrete deflection in experiment and simulation with the stent specimen was the same, at 4 mm; experiment (EXP) and simulation (FEM) results for the bending load versus deflection of FCBPBSs are compared in Figure 12. The comparison shows the simulation was in agreement with the experiment, indicating that the simulation result could be referred for mechanical analysis of the stent. Because of the simplifying of the stent model in the simulation process, the bending load of each experiment curve was higher than that of each corresponding simulation curve. From Figure 12, the relationship between the bending load and structure parameters, including braid-pin number and PDO monofilament diameter, could be obtained. As depicted in Figure 12(a), when the braid-pin number of FCBPBS was the same, the bending load increased with the growth of PDO monofilament diameter. For FCBPBS which has the same PDO monofilament diameter, the bending load rises with an increase in braid-pins, as shown in Figure 12(b).
Figure 12.
The bending load-deflection curve of FCBPBSs.

The comparison of plastic dissipation energy between BBPBS and FCBPBS

When the stent specimen was bent, the internal energy, including plastic dissipation energy, could be converted from the work done by external bending load. The relationship between different energy types could be converted by the following equations:²⁹
$E_{TOTAL} = E_{W} = E_{I} + E_{K}$
(6)

$E_{I} = E_{S} + E_{PD} + E_{DMD}$
(7)
where $E_{TOTAL}$ is the total energy of the system, E_W is the work done by the external loading and E_I, E_K, E_S, $E_{PD}$ and $E_{DMD}$ are the internal energy, kinetic energy, elastic strain energy, plastic dissipation energy and damage energy, respectively.

As the bending deflection reaches a displacement of about 4 mm, the whole bending process takes 0.02 s. The plastic dissipation energy of FCBPBSs and BBPBSs (C2-B, C3-B, C4-B) increases with growth of deflection, as shown in Figure 13. From Figure 13(a), it can be seen that the plastic dissipation energy of BBPBSs (C2-B, C3-B, C4-B) was more than that of the other models. However, the plastic dissipation energy of BBPBSs (A2-B, A3-B, A4-B, B2-B, B3-B, B4-B) was zero, indicating that the plastic dissipation energy was not generated in those models above. As depicted in Figure 13(b), the plastic dissipation energy is produced in all nine FCBPBSs. The plastic dissipation energy of C3-C is higher than the other stent model, indicating that the plastic deformation of C3-C is more difficult to generate by comparison with other models, while model B2-C is easiest in all stent models. Because of the nanomembrane of FCBPBS, the plastic dissipation energy of all nine FCBPBSs is much more than that of nine BBPBSs, through comparing the plastic dissipation energy between FCBPBSs and BBPBSs. The growth of the plastic dissipation energy of all FCBPBSs was bigger than 2.33 J compared with BBPBSs.
Figure 13.
Plastic dissipation energy of nine BBPBSs and FCBPBSs: (a) BBPBSs, (b) FCBPBSs.

The comparison of maximum stress and plastic strain between BBPBS and FCBPBS

Structural stability was closely connected with mechanical parameters, including stress and plastic strain. The bigger the maximum stress and plastic strain, the worse the structure stability of the stent. For this reason, we investigated the maximum stress and plastic strain of BBPBS and FCBPBS using FEM, as shown in Figures 14 and 15. The FCBPBS was composed of BSP and NMP. Because the BSP was the main mechanical carrier of FCBPBS, stress and plastic strain of BSP was studied, as described below. The comparison of the maximum stress between BSP of FCBPBSs and BBPBSs in the bending simulation is shown in Figure 14. From the Figure 14, The maximum stress of three groups of BSP of FCBPBSs (A-group, B-group, C-group) has the same trend. The maximum stress of BSP of FCBPBSs with same PDO diameter increases with the growth of its braid-pin number. The maximum stress of BSP of FCBPBSs with same braid-pin number (10, 12) also increases with an increase in its PDO diameter, except for BSP of FCBPBSs with 8 braid-pins. However, the maximum stress of BBPBSs with same braid-pin number (8, 10, 12) grows with increasing PDO diameter. When the PDO diameter (0.23 mm, 0.29 mm) is the same, the maximum stress of BBPBSs increases with its braid-pin number. By comparing the maximum stress between BSP of FCBPBSs and BBPBSs in the bending simulation, it is obvious that the maximum stress of nearly all BSP of FCBPBSs was more than that of BBPBSs with corresponding structure parameters due to the existence of NMP in FCBPBS, except for 0.36 mm PDO diameter FCBPBS with 8 and 10 braid-pins, indicating that the structure of NMP of FCBPBS leads to an increasing of maximum stress of NMP of FCBPBS. The maximum stress of seven of all nine FCBPBSs above increased at least 45.62% compared with the BBPBS, except for 0.36 mm PDO diameter FCBPBS with 8 and 10 braid-pins. According to our previous work,²⁹ the maximum stress of FCBPBS was the same with its BSP so that the regularity of the maximum stress of FCBPBS was same with BSP of FCBPBSs.
Figure 14.
The maximum stress of nine BBPBSs and FCBPBSs.

Figure 15.
The comparison of maximum value of equivalent plastic strain: (a) between BBPBSs and BSP of FCBPBSs; (b) between BBPBSs and FCBPBSs.

The regularity of the maximum value of equivalent plastic strain of BBPBSs and FCBPBSs can be observed in Figure 15. As depicted in Figure 15(a), the maximum values of equivalent plastic strain of BSP of FCBPBSs (C-group) and BBPBSs (C-group) are more than zero, indicating that the plastic deformation has been generated in these stents as the same as 0.23 mm PDO diameter BSP of FCBPBS with 10 braid-pins and 0.23 mm PDO diameter BBPBS with 10 braid-pins. The maximum value of equivalent plastic strain of BBPBSs (B-group, 0.23 mm PDO diameter BBPBSs with 8 and 12 braid-pins), BSP of FCBPBSs (B-group), are all equal to zero, showing that the plastic deformation has not been produced in those stents. The plastic deformation occurred in all nine FCBPBSs in the bending process, as shown in Figure 15(b). By comparing the maximum value of equivalent plastic strain between BSP of FCBPBSs and BBPBSs in Figure 15(a), we can find that the maximum value of equivalent plastic strain of BSP of FCBPBSs (C-group) are more than that of BBPBSs with corresponding structure parameters, but the maximum value of equivalent plastic strain of 0.23 PDO diameter BSP of FCBPBS with 10 braid-pins is less than that of BBPBSs with corresponding structure parameters. As depicted in Figure 15(b), it is clear that the maximum value of equivalent plastic strain of nearly all nine FCBPBSs more than that of BBPBSs with corresponding structure parameter different with 0.23 PDO diameter FCBPBS with 10 braid-pins, the maximum value of equivalent plastic strain of which is less than that of BBPBSs with corresponding structure parameter. So, we could conclude that the maximum value of equivalent plastic strain of FCBPBSs tends to be increased because of existence of NMP of FCBPBS, the maximum value of equivalent plastic strain of nine FCBPBSs increase at least 0.0637 except 0.23 mm PDO diameter FCBPBS with 10 braid-pins.

Conclusion

In this work, the bending flexibility of BBPBSs and FCBPBSs was investigated using FEM. The simulation was in good agreement with the actual experimental result, indicating that the simulation could be used as the reference for mechanical analysis for the stents described. Through comparing the bending flexibility between BBPBSs and FCBPBSs, NMP in FCBPBS initiates changes in the mechanical performance of the stent as shown in the following conclusions:
The internal stress distribution of FCBPBS and BBPBS changes, with different locations in the FCBPBS and BBPBS during the bending process. By comparing the color variation between NMP and BSP of the FCBPBS, it was obvious that stress variation for BSP was more drastic than that of NMP and lesser stress was occurred in NMP than BSP. Through comparing the stress of BSP of the FCBPBS with BBPBS, we found that the area of stress distribution of BBPBS was smaller than that of BSP of the FCBPBS and the stress value of BBPBS was also smaller than that of BSP. We could conclude that the area of stress concentration of BSP of the FCBPBS was enlarged by the existence of NMP, but the lower and undramatic variation of stress in NMP of FCBPBS could be used as a retarder, preventing a higher and dramatic variation of stress of BSP of the FCBPBS from being transferred to the outside.

The higher the bending load of the stent specimen at the given deflection, the worse its bending flexibility. In comparing the bending load between FCBPBSs and BBPBSs with the same structure, including braid-pin number and PDO monofilament diameter, the bending loads of FCBPBSs were all higher than that of BBPBSs, indicating that bending flexibility of nine BBPBSs was better than that of FCBPBSs with a corresponding structure. The growth of the bending load of FCBPBSs was at least 0.65% by comparison with BBPBSs.

Comparing the plastic dissipation energy between FCBPBSs and BBPBSs, the plastic dissipation energy of all nine FCBPBSs was seen to be much more than that of nine BBPBSs because of the NMP of the FCBPBS. The plastic dissipation energy of all FCBPBSs increased more than 2.33 J compared with BBPBSs.

Comparing the maximum stress between BSP of FCBPBSs and BBPBSs in the bending simulation, it was obvious that the maximum stress of nearly all BSP of FCBPBSs are more than that of BBPBSs with corresponding structure parameter, due to the existence of NMP in the FCBPBS, indicating that the structure of NMP of FCBPBS leads to increasing of maximum stress of NMP of FCBPBS with the same regularity as the maximum stress of FCBPBS. The maximum stress of nearly all FCBPBSs above increase at least 45.62% through comparing the BBPBS, except for 0.36 mm PDO diameter FCBPBS with 8 and 10 braid-pins.

Comparing the maximum value of equivalent plastic strain between FCBPBSs and BBPBSs, it is clear that the maximum value of equivalent plastic strain of BSP of FCBPBSs (C-group) is more than that of BBPBSs with a corresponding structure, but the maximum value of equivalent plastic strain of 0.23 PDO diameter BSP of FCBPBS with 10 braid-pins is less than that of BBPBSs with corresponding structure. And it is clear that the maximum value of equivalent plastic strain of nearly all nine FCBPBSs are more than that of BBPBSs with corresponding structure parameter, but different with 0.23 PDO diameter FCBPBS with 10 braid-pins, where the maximum value of equivalent plastic strain is less than that of BBPBSs with corresponding structure parameters. So, we could conclude that the maximum value of the equivalent plastic strain of BSP of FCBPBSs and FCBPBSs tends to be increased because of the existence of NMP of FCBPBS, the maximum value of equivalent plastic strain of nine FCBPBSs increases at least 0.0637 except for 0.23 mm PDO diameter FCBPBS with 10 braid-pins.

Material	Number	Diameter (mm)	Crystallinity (%)	Tensile force (N)	Linear density (Tex)
PDO	A	0.23	70.7	23.56	63.13
B	0.29	70.4	34.81	95.83
C	0.36	70.5	45.92	125.21
Material	Density (g/cm³)	Relative molecular mass (M_n)	T_m (℃)	T_e (℃)	–
PCL	1.14	80,000	57.3	23.8	–

Material	Number of specimens	Braiding number (pins)	External diameter (mm)	Internal diameter (mm)
PDO	A2-B	8	8.83	8
A3-B	10	8.90	8
A4-B	12	8.92	8
B2-B	8	9.15	8
B3-B	10	9.17	8
B4-B	12	9.21	8
C2-B	8	9.52	8
C3-B	10	9.56	8
C4-B	12	9.67	8

Material	Number of specimens	Braiding number (pins)	External diameter (mm)	Thickness of film (mm)	Internal diameter (mm)
PDO	A2-C	8	8.83	0.07	8
A3-C	10	8.90	0.069	8
A4-C	12	8.92	0.068	8
B2-C	8	9.15	0.072	8
B3-C	10	9.17	0.07	8
B4-C	12	9.21	0.073	8
C2-C	8	9.52	0.068	8
C3-C	10	9.56	0.069	8
C4-C	12	9.67	0.071	8

Name	X coordinate (mm)	Y coordinate (mm)	Z coordinates (mm)
RP3	0	4	0
RP4	0	0	0
RP5	0	0	0

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article. This work was sponsored by Shandong Provincial Natural Science Foundation, China (Grant Number ZR2018BA023).

References

Kawai

Akasaka

Murakami

et al.

Endoscopic sphincterotomy of the ampulla of Vater. Gastrointest Endosc 1974; 20: 148–151.

Sivak

Sullivan

. Endoscopic retrograde pancreatography. Am J Dig Dis 1976; 21: 263–269.

Cameron

Gayler

Zuidema

et al.

Long term transhepatic intubation for hilar hepatic duct strictures. Ann Surg 1976; 183: 488–495.

Huang

et al.

Endoscopic retrograde biliary drainage for 122 patients with malignant biliary obstruction. World Worl Chin J Disges 2008; 28: 3234–3237.

Huang

et al.

Internal biliary drainage treatment of malignant obstructive jaundice. J Hepatob Surg 2001; 6: 455–456.

Soehendra

Reynders-Frederix

. Palliative bile duct drainage – a new endoscopic method of introducing a transpapillary drain. Endoscopy 1980; 12: 8–11.

Carrasco

Wallace

Charnsangavej

et al.

Expandable biliary endoprosthesis: an experimental study. Am J Roentgenol 1985; 145: 1279–1281.

Tringali

Mutignani

Perri

et al.

A prospective randomized multicenter trial comparing DoubleLayer and polyethylene stents for malignant distal common bile duct strictures. Endoscopy 2003; 35: 992–997.

Cipolletta

Rotondano

Marmo

et al.

Endoscopic palliation of malignant obstructive jaundice: an evidence based review. Dig Liver Dis 2007; 39: 375–388.

10.

Cheng

Bruno

Bergman

et al.

Endoscopic palliation of patients with biliary obstruction caused by nonresectable hilar cholangiocarcinoma: Efficacy of self-expandable metallic Wallstents. Gastrointest Endosc 2002; 56: 33–39.

11.

Libby

Leung

. Prevention of biliary stent clogging: A clinical review. Am J Gastroenterol 1996; 91: 1301–1308.

12.

Norbert

Andrea

Ulrich

et al.

Human tissue responses to metal stents implanted in vivo for palliation of malignant stenosis. Gastrointest Endosc 1996; 436: 596–596.

13.

Carrasco

Wallace

Chamsangavej

et al.

Expandable biliary endoprosthesis: An experimental study. AJR Am J Roentgenol 1985; 145: 1279–1281.

14.

Dua

Reddy

Rao

et al.

Impact of reducing duodenobiliary reflux on biliary stent patency: An in vitro evaluation and a prospective randomized clinical trial that used a biliary stent with an antireflux valve. Gastrointest Endosc 2007; 65: 819–828.

15.

Kullman

Frozanpor

Soderlund

et al.

Covered vs uncovered self-expandable nitinol stents in the palliative treatment of malignant distal biliary obstruction: Results from a randomized, multicenter study. Gastrointest Endosc 2010; 72: 915–923.

16.

Telford

Carr-Locke

Baron

et al.

A randomized controlled trial comparing uncovered and partially covered self-expandable metal stents in the palliation of distal malignant biliary obstruction. Gastrointest Endosc 2010; 72: 907–914.

17.

Fumex

Coumaros

Napolean

et al.

Similar performance but higher cholecystitis rate with covered biliary stents: Results from a prospective multicenter evaluation. Endoscopy 2006; 38: 787–792.

18.

Gregory

Cope

Shah

et al.

In vivo evaluation of a new bioabsorbable self-expanding biliary stent. Gastrointest Endosc 2003; 58(5): 777–784.

19.

Mauri

Michelozzi

Melchiorre

et al.

Biodegradable biliary stent implantation in the treatment of benign bilioplastic-refractory biliary strictures: preliminary experience. Eur Radiol 2013; 23: 3304–3310.

20.

Zeng

. Analysis and application of finite element method (in Chinese), Beijing, China: Tsinghua University Press, 2004.

21.

Zhuang

You

Liao

. Finite element analysis and application based on ABAQUS (in Chinese), Beijing, China: Tsinghua University Press, 2004.

22.

Whitcher

. Simulation of in vivo loading conditions of nitinol vascular stent structures. Comput Struct 1997; 64: 1005–1011.

23.

Perry MD, Chang RT. Finite element analysis of Ni-Ti alloy stent deployment. The Second International Conference on Shape Memory and Superelastic Technology, Asilomar, CA: SMST Publications, 1997.

24.

Fontaine

Spigos

Eaton

et al.

Stent-induced intimal hyperplasia: are there fundamental differences between flexible and rigid stent designs?

J Vasc Interv Radiol 1994; 5: 739–744.

25.

Colombo

Stankovic

Moses

. Selection of coronary stents. J Am Coll Cardiol 2002; 40: 1021–1033.

26.

Etave

Finet

Boivin

et al.

Mechanical properties of coronary stents determined by using finite element analysis. J Biomech 2001; 34: 1065–1075.

27.

Perini

Migliavacca

Auricchio

et al.

Numerical investigation of the intravascular coronary stent flexibility. J Biomech 2004; 37: 495–501.

28.

Mori

Saito

. Effect of stent structure on stent flexibility measurements. Ann Biomed Eng 2005; 6: 733–742.

29.

Liu

Zhu

Yang

et al.

Bending behaviors of fully covered biodegradable polydioxanone biliary stent for human body by finite element method. J Mech Behav Biomed 2018; 77: 157–163.

30.

Zhang

Song

Dong

. Electrospinning preparation and luminescence properties of europium complex/polymer composite fibers. Phys Chem C 2008; 112: 9155–9162.

31.

Liu

Zhang

. Characterization of compression behaviors of bully covered biodegradable polydioxanone biliary stent for human body: A numerical approach by finite element model. J Mech Behav Biomed 2016; 62: 128–138.

32.

Que

Zhang

. Radial force analysis of polydioxanone coronary stent by finite element method. Journal of Donghua University 2013; 30: 375–377.

33.

Liu

Zhang

. Comparison of compression behaviors of fully covered biodegradable polydioxanone biliary stent for human body and uncovered biodegradable polydioxanone biliary stent: a numerical approach by finite element model. Text Res J 2017; 14: 1772–1783.