Numerical simulation of the stent expansion process based on the hemodynamic characteristics of bidirectional fluid-structure coupling

10 Hitherto, research on the fluid-structure coupling of coronary stents has mostly considered the state 11 after stent expansion following implantation. However, the factors and how they affect stent 12 expansion are as yet, unclear. To further investigate stent expansion, this paper proposes a model 13 combining balloon, stent, and blood using Solidworks. Thereafter, a co-simulation using ANSYS 14 Workbench is implemented using the methods of finite element and finite volume, to analyze 15 bidirectional fluid-structure coupling during the expansion of a balloon-expandable stent, for 16 periodically varying blood loads. By comparing the blood flow rate in the vessel, pressure on the 17 endovascular wall, and the pressure and stress on the stent system at different points in time, it can be 18 seen that the higher the blood flow rate, the greater the pressure on the endovascular wall and stent 19 system. Furthermore, the larger the volume of the implant, the greater the maximum blood flow rate 20 and maximum pressure on the endovascular wall, and the more drastic the change along the axis. In 21 summary, the results of the present study indicate that the stent expansion process has a significant 22 effect on the blood flow rate and pressure on the vascular wall; however, the impact of blood load on 23 stent stress can be ignored. This paper presents a simulation of the stent expansion process for a balloon-expandable coronary stent implanted for a vascular stenosis using finite element methods. The blood flow distribution and 249 velocity in the vessel at t = 0.8 s, 1.0 s, and 1.4 s during the stent expansion process were analyzed.


Introduction 25
Coronary heart disease is characterized by the narrowing or blockage of coronary artery lumina due 26 to atherosclerotic lesions and is currently one of the most common diseases affecting human health 27 (Lim et al.,2007;Koens et al.,2015). In recent years, coronary stent interventions have been 28 considered to be important in the treatment of coronary heart disease, since they are deemed as being  unidirectional coupling of the system during service, obtained pressure on the stent surface, and 62 assessed its mechanical properties. Hitherto most research on stent system hemodynamic 63 characteristics have only considered stents in service in a fully expanded state with no further 64 changes in geometry and position and with limited impact on blood flow. However, the stent 65 expansion process, during which the geometry of a stent changes in real-time and has a significant 66 impact on the periodically changing blood flow, requires further investigation. 67 The main contribution of this study is the proposition of a model combining a balloon, stent, and 68 blood, using Solidworks software. Thereafter, a co-simulation approach is presented using finite 69 element and finite volume methods to investigate the fluid-structure coupling of a balloon-70 expandable coronary stent subjected to a periodically changing blood load during the stent expansion 71 process. The blood flow rate and the pressure of the blood on both the stent and vascular wall during 72 the period of research were obtained. Furthermore, the distribution of blood in the stenotic artery in 73 the presence of an expanding stent was compared to that without an implant over the same temporal 74 cycle. The pressure on the stent system due to the impact of a blood load and the stress distribution of 75 the stent during the stent expansion process were also analyzed. From these studies on the changes in 76 blood flow due to stent expansion, a reference and guide for the clinical and surgical treatment of 77 coronary heart disease can be developed. 78

2
Materials and Methods 79

Geometric model 80
To address the research challenges described above, a balloon-expandable stent system model 81 consisting of a balloon, stent, and blood vessel, was built using the Solidworks 2020 3D modeling 82 platform (see Figure 1). The elements of the model were assembled and then imported into the finite 83 element simulation platform Ansys 2020 R2 for further analysis (Shi et al.,2015). The model for the 84 stent consisted of four groups of sinusoidal-shaped support rings and three sets of straight bridge 85 strips (see Figure 2), that have the advantages of providing better radial support and retraction 86 rates (Timmins et al.,2017). The inner and outer diameters of the stent were 3.3 mm and 3.6 mm, 87 respectively. The thickness of the stent was 0.15 mm with an axial length of 7.72 mm. Each support 88 ring had a length of 2.05 mm, while the length of the bridge strip was 1.67 mm. The balloon was 89 modeled as a thin-walled cylindrical shell with a thickness of 0.01 mm and an outer diameter of 3.3 90 mm, to fit within the inner diameter of the stent. The blood vessel was modeled as an axially 91 asymmetric segmented cylinder with a total length of 28 mm with a maximum diameter of 6 mm and 92 a minimum diameter of 5 mm. To account for blockages in the blood vessel, a model with a local 93 narrowing was built to simulate the effect of plaque on blood flow. Within the blood flow model, 94 Boolean operations were implemented to remove the corresponding parts of the balloon and stent, 95 with the remaining portion being the fluid model investigated in this study. 96  Table 1. Blood was assumed to be an incompressible Newtonian fluid with a density ρ = 105 1,050 kg /m 3 and a coefficient of viscosity of μ = 0.0035kg•m•s. 106 107 108

Meshing and data transfer 111
The mesh used for the model was divided into two parts, i.e., a solid mesh and a fluid mesh. The 112 stent and balloon were modeled using the solid mesh with the unit type being SOLID186. The unit 113 size for the balloon portion was 0.1 mm, and the unit size for the stent portion was 0.05 mm (see 114 Figure 3(A)). Blood was modeled using the fluid mesh with an overall size of 1.0 mm and a local 115 size of 0.05 mm at the stent and balloon portions of the model (see Figure 3(B)). The coupled system 116 was computed using the Workbench 2020 R2 platform, in which the solid mesh of the balloon and 117 stent was calculated in the Transient Structural module, and the fluid mesh of blood was computed in 118 the Fluent module, with the data from both being exchanged using a system coupler named 'System 119 Coupling'. Additionally, the interface for data transfer was the outer surface of the stent and balloon, 120 and the inner surface of the blood vessel.

Boundary conditions and load application 124
To conform the model to the dynamics of the real situation, the following boundary conditions were 125 set: the solid portion had a cylindrical coordinate system with the axis along the centerline of the 126 balloon and stent which limited the axial and tangential displacements of the balloon to the 127 cylindrical coordinate system. Likewise, the axial and tangential displacements of the six vertices of 128 the support rings in the middle of the stent were also limited to the cylindrical coordinate system. The 129 boundary conditions were set for the fluid portion as follows: since the blood flow in the human body 130 has periodic peaks and troughs (Cebral et al.,2011), the period of the blood flow was set as T = 0.8 s 131 with an average blood flow velocity of v0 = 0.1 m/s. Moreover, the blood flow velocity at the 132 entrance was simulated as a sinusoidal function: = 0.1 + 0.07sin (7.85 )(m/s) and the relative 133 pressure at the outlet was set as P0 = 50 Pa with an inhibiting backflow function. Besides, the portion 134 of blood in contact with the solid part of the model was set as a fluid-structure coupling interface, 135 controlled by the active expansion of the stent and balloon. The outer surface of the blood was 136 considered to be static. The entire simulation process lasted 4s, during which the stent underwent a 137 radial expansion of 0.6 mm from its original size to the inner diameter of the vascular wall. During 138 this process, the blood flow incurred 5 cyclic changes. 139  Figure 4). Simultaneously, to study the effect of the stent system 159 on the blood flow rate and distribution, a stent-free blood vessel subjected to the same conditions was 160 used as the control group for the simulations (see Figure 5). Blood flow rate data was calculated at 20 161 time-points distributed evenly over 0.8~1.6s to obtain a line chart showing the trend of the maximum 162 flow rate with and without implants (see Figure 6). point is about 4 times that at the entrance due to the presence of the balloon and stent. Moreover, the 174 blood flow is disturbed over a small region downstream of the implant but returns to a normal 175 streamline flow thereafter. Comparing Figure 4 and Figure 5 shows that for a given time point with 176 the same inlet blood flow rate, the maximum blood flow rate at the stenosis is significantly increased 177

Solutions and configurations
in the presence of the balloon and stent. At the initial and peak time points, the maximum flow rate at 178 the stenosis is twice that without the implant when the blood flow rate is larger. From Figure 6 it is 179 observed that the maximum blood flow rate is consistent at the entrance, with or without an implant. 180

Pressure on endovascular wall 181
Changes in blood flow rates affect the pressure on endovascular walls, which in turn, affect the 182 internal environments of blood vessels and have a direct impact on human health. To further 183 investigate these effects, a cloud diagram of the pressure on a vascular wall at the initial time (0.8 s), 184 peak time (1.0 s), and trough time (1.4 s) of the second cycle has been analyzed in this section (see 185 Figure 7). Also, to study the effects of the stent system on vascular wall pressure, the corresponding 186 pressure on a vascular wall without a stent for the same conditions was used as the control during the 187 computational process (see Figure 8). To explore the trends in vascular wall pressures, the pressures 188 were calculated at 20 time-points distributed evenly during 0.8~1.6 s to obtain a line chart of the 189 maximum pressure with and without implants (see Figure 9). blood flow rate increases, which also leads to an increase in the pressure gradient, and the pressure 202 along the axis of the vascular wall drops rapidly. When the blood flow rate is high, a zone of negative 203 pressure develops at the junction of the stenotic and non-stenotic regions of the blood vessel. A 204 comparison of Figure 7 and Figure 8 shows that, for the same inlet blood flow rate, the presence of 205 an implant can lead to a sharp increase in pressure on the vascular wall due to the modified blood 206 flow. Moreover, this increase in endovascular wall pressure is of several orders of magnitude at the 207 entrance and the stenotic region. Besides, Figure 9 shows that the trend of the maximum pressure on 208 the endovascular wall is consistent with the trend of the blood load due to the implant. In the absence 209 of an implant, the pressure on the endovascular wall is smaller, without any observable changes in 210 the maximum pressure, due to a low blood flow rate. 211

Pressure on stent system and stress distribution 212
When flowing blood initially encounters an implanted stent, the resulting pressure generated on its 213 surface causes the stent to expand. This expansion of the stent can also deform its structure and alter 214 the internal stress. In this section, cloud diagrams of the pressure on the stent system at the initial 215 time (0.8 s), peak time (1.0 s), and trough time (1.4 s) in the second cycle have been analyzed (see 216 Figure 10). Also, the Von-Mises effective stress is obtained for the stent, from which the effect of the 217 blood load on the internal force of the stent is evaluated (see Figure 11). The maximum, minimum, 218 and average stress of the stent during 0.8~1.6 s are shown in Figure 12. 219 It can be seen from Figure 10 that the pressure of blood on the stent and balloon increases as the 220 blood flow rate increases, and that the pressure gradient increases as well, while the pressure along 221 the axis drops rapidly. This phenomenon is similar to the effect of blood pressure on the 222 endovascular wall. Furthermore, the expansion distance of the stent is proportional to time. It can be 223 seen from Figure 11 that, as time increases, the stent expansion becomes progressively larger, and 224 that its internal stress increases accordingly. For the same time point, the maximum stress appears at 225 the bend with the most change in the geometric angle, while the minimum stress appears at the 226 straight bridge strip. Figure 12 shows that the maximum, minimum, and average stress of the stent 227 are proportional to time, during the stent expansion process. 228 To obtain more accurate results, the blood flow distribution and velocity in a vessel without an 251 implant was used as the control. The results show that at the same time point and the same inlet blood 252 flow rate, the maximum blood flow rate at the stenosis increases significantly due to the effect of 253 balloon and stent. Moreover, the blood flow in a small region downstream of the implant is disturbed 254 and the blood flow returns to normal after passing through this region. 255 Due to the effect of the blood flow rate and its distribution, the pressure distribution on the 256 endovascular wall varies accordingly. By analyzing the cloud diagrams of the pressure on the 257 endovascular wall at t = 0.8 s, 1.0 s, and 1.4 s, the following conclusions were drawn: as blood flow 258 rate increases, the maximum pressure of blood on the endovascular wall increases, while the pressure 259 drops rapidly along the axis of the vascular wall; due to the presence of an implant, the pressure on 260 the endovascular wall changes sharply at both the entrance and the stenotic region. 261 When the blood flow encounters the stent, pressure is generated on the surface of the stent. To 262 analyze the mutual effects, cloud diagrams for the pressure on the stent system at t = 0.8 s, 1.0 s, and 263 1.4 s have been analyzed and compared with the internal stress of the stent. The results show that the 264 blood load produces a maximum pressure of hundreds of Pascals on the surface of the stent, but this 265 pressure is 10 6 times different from the equivalent stress of several hundred MPa, at the same time 266 point. Therefore, the internal stress analysis of the stent should first consider its geometric bends, 267 where the maximum stress usually occurs. In the limiting condition, the blood load can be ignored 268 when analyzing the internal stress of the stent. 269 The expansion of the balloon-stent system can affect the blood flow distribution in a vessel, which in 270 turn affects the pressure on the endovascular wall. By comparing the blood flow distribution and 271 pressure on the vascular wall at t = 0.8 s and t = 4.0 s, the following results were obtained: the more  272  space the implant occupies, the faster the blood flow rate at the stenosis, and the greater the pressure  273  on the vascular wall; the pressure on the vascular wall changes drastically along the axis of the blood  274 vessel. Therefore, in the process of clinical stent implantation, the duration of the surgery should be 275 shortened as much as possible to reduce the effects of the implant on the blood vessel, and the harm 276 to the human body from the resulting elevation in blood pressure. In particular, for patients with 277 arteriosclerosis and greater than normal calcification of blood vessel walls, the higher blood pressure 278 resulting from stent implantation increases the risk of rupturing the vascular wall. 279

Conflict of Interest 280
The authors declare that the research was conducted in the absence of any commercial or financial 281 relationships that could be construed as a potential conflict of interest. 282

Author Contributions 283
SB, and HL presented the concept of the work. SB performed the FEA and CFD computations and 284 drafted the manuscript. LL analyzed the data and drew the figures. HL provided suggestion and 285 editing assistance. 286

Data availability statement 287
All datasets generated in the study are included in the article, further inquiries can be directed to the 288 corresponding authors. 289

Ethics statements 290
No animal studies are presented in this manuscript. 291 No human studies are presented in this manuscript. 292 No potentially identifiable human images or data is presented in this study.