Vulnerability analysis on the interaction between Asymmetric stent and arterial layer

Abstract

The utilization of Asymmetric stent for recovering atherosclerotic diseases, particularly non-symmetric obstruction, is a quite challenging breakthrough treatment. In terms of eccentric plaque, the non-uniform stiffness of arterial layer causes the increasingly complex issues of vulnerability. This study investigated the vulnerability of the interaction between the Asymmetric stent and the surrounding arterial layer using structural transient dynamic analysis in ANSYS. Four combinations of stent deployment, i.e. the Sinusoidal stent expanded by the offset balloon, the Sinusoidal stent expanded by the ordinary cylindrical balloon, the Asymmetric stent expanded by the offset balloon, and the Asymmetric stent expanded by the ordinary cylindrical balloon, are generated for this comparative study. Multilayer material properties from recent in vitro experiments are adopted for the surrounding arterial layer, such as a fibrous cap, lipid core, diseased-healthy intima, and diseased-healthy media. In order to address plaque vulnerability, the Cauchy stresses and Hencky strains are used for stress measure because of convenience in comparison with the uniaxial/biaxial tension test data. The location-specific threshold value from the diseased human carotid artery is adopted for rupture criteria. The simulation indicated that as regards the eccentric plaque, the plaque vulnerability is caused by the plaque shape and components rather than caused by the geometrical structure of the stent or balloon expansion method. Nevertheless, the non-symmetric inflation of balloon, which leads against the plaque, contributed to an increase in the vulnerability of fibrous cap of fibroatheroma plaque.

Keywords

Tissue rupture asymmetric eccentricity carotid artery stenting FEM

1. Introduction

The existence of plaque straitening arterial vessel is mostly created in the shape of the eccentric protrusion. In vivo studies found that the eccentric lesions were significantly more frequent than concentric ones [1–4], in which its tendency increases for the case of unstable angina [1]. The treatment of the eccentric plaque using an ordinary cylindrical balloon will lead to non-uniform stress distribution within the vessel wall [5]. The non-uniform stress distribution, which takes place at a plaque with a thin fibrous cap, could be beginning of the inflammatory cells activation. The inflammatory cells activation may contribute to rupture of the atherosclerotic plaque [6–8], and may cause a more severe problem such as carotid artery dissection [2]. Moreover, in vitro experimental studies showed that either plaque or underlying layer surrounding the stent has different material properties [9–11]. All soft atherosclerotic tissues are having non-linear material properties, and both media and fibrous cap are stiffer than either lipid core or thrombus [12]. Comparing with the healthy intima tissue, the diseased intima tissue can be expected to be stiffer as well as the underlying media tissue [13,14]. Therefore, it is necessary for the redesigning mesh structure of the stent to reduce non-uniform stress distribution due to the eccentric geometry of plaque. A new mesh structure design of stent that conforms eccentric protrusion has been developed, however, its interaction with the surrounding arterial layer is still unclear.

In the literature related to rupture analysis of the arterial tissue due to balloon expandable stent deployment, a limited number of supporting studies were found. Karimi et al. studied the effect of the plaque composition (calcified, cellular, and hypocellular) on the stresses induced in the arterial layers (intima, media, and adventitia), which was modeled using the isotropic hyperelastic behavior of Ogden parameters. It was reported that the stress on the stiffest calcified plaque wall was in the fracture level (2.38 MPa), whereas the cellular and hypocellular plaques remain stable due to the less stress on the walls. They also pointed out that the highest von Mises stresses were observed on the stiffest intima layer, while the lowest stresses were seen to be located in the less stiff media layer [15]. To find out the role of calcification in the plaque vulnerability and the wall rupture, Riyahi-Alam et al. evaluated preoperatively in silico analysis of atherosclerotic calcification vulnerability in carotid artery stenting. The in silico results showed that the average ultimate stresses of 55.7 ± 41.2 kPa and 171 ± 41.2 kPa, as well as the average plaque wall stresses of 19.03 ± 16.05 kPa and 64.3 ± 63.3 kPa, were obtained on calcifications [16].

Nevertheless, the FE study for the non-symmetric expansion considering the rupture of arterial tissue has not been investigated yet. Therefore, the impact of non-symmetric stent expansion to the rupture of arterial tissue surrounding is not clearly explained. On the other hand, as a series of new stent development, the rupture analysis after the stent deployment is an essential problem. Using the finite element method in the analysis is quite helpful because FEM has transformed into an effective tool to observe the rupture tendency, which is difficult to accomplish through in vivo and in vitro experimental studies. The author had developed a new balloon expandable stent design having non-symmetric structural mesh, which is called Asymmetric stent [17,18]. It demonstrated an ability to inflate the stent towards the specific side of arterial layer, without any significant changes in surface roughness after expansion. This advantage becomes necessary in the treatment of atherosclerosis diseases, particularly in term of non-uniform obstruction. In this paper, the rupture analyses are performed considering the interaction between the Asymmetric stent and intact arterial layer (vessel wall), the dissection of plaque shoulder, and the inflammation tendency of the healthy intimal layer.

2. Methods

2.1. Computational model

To identify the deformation, the transient nonlinear structural analyses are built in ANSYS R17.0 (ANSYS Inc., Pennsylvania, USA). Two types of balloons and stents are utilized in the simulation: cylindrical and offset inflation type for the balloons [19,20], and Sinusoidal and Asymmetric structure types for the stents [18,21]. The Sinusoidal stent is a closed cell stent design and the same design is used with a flex-member, the Asymmetric stent. In total, four finite element models are developed for the comparison analysis, i.e. (a) Sinusoidal stent expanded by the offset balloon, (b) Sinusoidal stent expanded by the ordinary cylindrical balloon, (c) Asymmetric stent expanded by the offset balloon, and (d) Asymmetric stent expanded by the ordinary cylindrical balloon. The geometry of the stents is displayed in Fig. 1.

Fig. 1.

Geometry of the FE model. (a) Sinusoidal stent, (b) Asymmetric stent.

In this study, an idealized model of the internal carotid artery (ICA) developed by Syaifudin et al. is reused for the finite element simulation, as is shown in Fig. 2. The designed plaque is a little shorter than the stent, in which one side of the vessel wall surface is covered and another side is the free-lesion area (intact). Plaque-type is fibroatheroma, which is characterized by the large lipid pool and the thin fibrous cap. According to the American Heart Association (AHA), fibroatheroma is classified as type V of atherosclerotic plaque [22]. The thin fibrous cap also indicates the vulnerability of the plaque (unstable plaque) and the tendency to rupture [22–25]. In this simulation, the arterial layer under and surrounding the plaque is treated as the diseased intima and media. The length of the healthy carotid artery is built to be equal with that of the diseased carotid artery so that the effect of zero degrees of the freedom at the end of the carotid artery is neglected.

Fig. 2.

Exploded view of FE model for rupture analysis.

As a series of study, all material properties from previous investigations by Syaifudin et al. are reapplied in this simulation [18], i.e. stainless steel 316L for the stent; polyethylene terephthalate (PET) for the balloon; fibroatheroma for the plaque; and carotid artery for the vessel wall (including intima, media and adventitia layer). They are defined as isotropic multilinear for the stent and isotropic hyperelastic (nearly incompressible) for the balloon, plaque, and arterial tissue. To conform to material properties referred to in the literature, two layers of the healthy carotid artery are defined as the healthy media-intima and the healthy adventitia. As for the stenotic artery, the layers consist of a fibrous cap, lipid core, diseased intima, and diseased media. The fibrous cap and the diseased intima, in this case, were assumed to have the same material properties. The material properties are compiled in Table 1. The determined material constants of each tissue are obtained from the Cauchy stress–stretch ratio.

2.2. Loading conditions and solution

Boundary conditions applied in the model are displayed in Fig. 3. To maintain the dilatation shape of an offset balloon, the node coupling and constraint equations were subjected in the circumferential and radial direction. The coupling will cause only the prime degree of freedom (DOF) to be retained in analysis’ matrix equations and will cause all the other DOFs in a coupled set to be eliminated. The value calculated for the prime DOF will then be assigned to all the other DOFs in a coupled set [26]. This method is useful to maintain the inflated side of the offset balloon. The large deformation feature of ANSYS nonlinear transient analysis should be activated in order to obtain Cauchy (true) stress and Hencky (logarithmic) strain as native FEM results.

Table 1
Material properties used in the rupture analysis

Component Material Material behavior Poisson’s ratio Density (tonne/mm³) Material constants

Balloon Polyethylene terephthalate Hyperelastic nearly incompressible 0.49 1.38E-9 Mooney-Rivlin 2 parameters: C₁₀ = 1.0318 MPa; C₀₁ = 3.6927 MPa d = 0.004261

Stent SS 316 Multilinear isotropic 0.33 7.99E-9 Fitting stress-strain curve resulted from tensile test

FC/Diseased intima Hypo cellular Hyperelastic nearly incompressible 0.49 1.07E-9 Mooney-Rivlin 3 parameters C₁₀ = −1.3192 MPa; C₀₁= 1.4533 MPa C₁₁ = 3.8801 MPa; d = 0.1501

Lipid Hypo cellular Hyperelastic nearly incompressible 0.49 1.07E-9 Mooney-Rivlin 3 parameters C₁₀ = −0.1362 MPa; C₀₁ = 0.1729 MPa C₁₁ = 0.2816 MPa; d = 0.5477

Diseased media Carotid artery Hyperelastic nearly incompressible 0.49 1.07E-9 Mooney-Rivlin 3 parameters C₁₀ = −1.4174 MPa; C₀₁ = 1.5274 MPa C₁₁ = 3.2808 MPa; d = 0.1830

Healthy intima-media Carotid artery Hyperelastic nearly incompressible 0.49 1.07E-9 Ogden 1 parameter𝜇₁ = 0.00042369 MPa;𝛼₁ = 17.539 MPa d ₁ = 10.8382

Diseased adventitia Carotid artery Hyperelastic nearly incompressible 0.49 1.07E-9 Ogden 1 parameter𝜇₁ = 0.00024647 MPa;𝛼₁ = 40.561 MPa d ₁ = 8.0563

Component	Material	Material behavior	Poisson’s ratio	Density (tonne/mm³)	Material constants
Balloon	Polyethylene terephthalate	Hyperelastic nearly incompressible	0.49	1.38E-9	Mooney-Rivlin 2 parameters: C₁₀ = 1.0318 MPa; C₀₁ = 3.6927 MPa d = 0.004261
Stent	SS 316	Multilinear isotropic	0.33	7.99E-9	Fitting stress-strain curve resulted from tensile test
FC/Diseased intima	Hypo cellular	Hyperelastic nearly incompressible	0.49	1.07E-9	Mooney-Rivlin 3 parameters C₁₀ = −1.3192 MPa; C₀₁= 1.4533 MPa C₁₁ = 3.8801 MPa; d = 0.1501
Lipid	Hypo cellular	Hyperelastic nearly incompressible	0.49	1.07E-9	Mooney-Rivlin 3 parameters C₁₀ = −0.1362 MPa; C₀₁ = 0.1729 MPa C₁₁ = 0.2816 MPa; d = 0.5477
Diseased media	Carotid artery	Hyperelastic nearly incompressible	0.49	1.07E-9	Mooney-Rivlin 3 parameters C₁₀ = −1.4174 MPa; C₀₁ = 1.5274 MPa C₁₁ = 3.2808 MPa; d = 0.1830
Healthy intima-media	Carotid artery	Hyperelastic nearly incompressible	0.49	1.07E-9	Ogden 1 parameter𝜇₁ = 0.00042369 MPa;𝛼₁ = 17.539 MPa d ₁ = 10.8382
Diseased adventitia	Carotid artery	Hyperelastic nearly incompressible	0.49	1.07E-9	Ogden 1 parameter𝜇₁ = 0.00024647 MPa;𝛼₁ = 40.561 MPa d ₁ = 8.0563

By considering the residual stresses inclusion, the stresses generated after balloon removal are taken into account. As a result, multiple load step of pressure loading consists of the inflation, deflation and steady phases are considered in this simulation. To obtain a similar nominal diameter for both stent models, the same pressures scheme of 1.6 MPa for the ordinary balloon and 1.75 MPa for the offset balloon were subjected to the inner surface of the balloon. After reaching 130% of its nominal diameter, the balloon deflated steadily for half second to secede from the stent completely and to neglect the impact effect after balloon removal.

2.3. Stress measure

The evaluation of stress level provides two choices in assessing the magnitude of critical stresses, i.e. using the maximum principal stresses [27–32] or using the von Mises stress [33–38]. The von Mises stress is well known as a classical equivalent stress in the engineering analyses of yielding due to excessive shear stresses, however, an experimental study on the aortic tissue indicated that the maximum normal stress governs the failure [39]. In addition, as mentioned by Kock et al. [30], the tensile and compressive stresses are not distinguishable by the von Mises stresses [30]. Holzapfel et al. [40] also addressed the rupture-potential of atherosclerotic plaques without the von Mises stress. The normal and shear stress measures, compiled with experimental data could identify new failure criteria, preferably in terms of failure properties of the plaque components. The failure criteria developed for the atherosclerotic plaques are used in FE studies to serve the basis for a better comparison of all future atherosclerotic plaque models. Without the appropriate failure criteria, the plaque models remain incapable of addressing the issue of rupture-potential [40].

Fig. 3.

Boundary conditions used in the simulation. The global coordinate system is the cylindrical coordinate system, in which X, Y and Z axis are the radial, circumferential and longitudinal directions, respectively. The blue triangles show the applied constraints.

This study is in line with the studies by Kock et al. [30] and Holzapfel et al. [40] with regards to utilizing the tensile stresses to address plaque vulnerability, because these measures are easy to compare with the uniaxial/biaxial tension test data. From the experimental data, the circumferential and axial true stresses are obtained, as well as the circumferential and axial stretches. These data can be compared with the Cauchy stresses and Hencky strains, which are as native FEM results from the post-processing stage of computational analyses.

In order to analyze the plaque and the intimal layer rupture tendency, the normal stress in the circumferential and axial direction from each simulation is compared. The simulation results used in the analysis are the normal Cauchy (true) stresses and Hencky (logarithmic) strains in both circumferential and axial direction after balloon removal, namely residual Cauchy stresses and stretches. We used the residual stresses rather than the maximum/peak stresses within the arterial layer (induced stresses after balloon removal rather than that before balloon removal). This approach is consistent with a number of idealized FE studies, which have reported that the inclusion of the residual stresses/strains in the arterial models is important for more accurate evaluations of the stress distribution within the atherosclerotic plaque [38,41–44]. These studies also pointed out that the inclusion of the residual stresses has a significant effect on the resultant stress values [45] and would eliminate overestimation of stress within the atherosclerotic plaque [40]. Besides, the vessel wall tissue consists of many smooth muscle cells in its medial layer, which is capable to stretch under supraphysiological loading [46]. The trauma of endothelial cells is mainly caused by the surface profile of the stent rather than the peak of pressure loading.

2.4. Rupture criterion

The plaque rupture represents the plaque components failure due to the existance of high stress level [40]. Currently, the most used threshold value within FE studies is 300 kPa (0.3 MPa) that causes the lethal myocardial infarction (at a pressure of 110 mmHg) [47]. However, it should not be assumed that all plaques rupture at this stress level. Hence, a more location-specific threshold value is required to adapt the differences of morphological and geometrical stenotic artery. Therefore, individual material and structural properties are needed [48–50].

In this study, the location-specific threshold values are derived from the works of Teng et al. [51], Mulvihill et al. [53], and Holzapfel et al. [40]. Teng et al. determined that the rupture (engineering) stresses of the human carotid artery sections containing type II and III lesions (AHA classifications). A mean of 1996 ± 867 and 1802 ± 703 kPa for the adventitia in the axial and circumferential directions and corresponding mean values of 519 ± 270 and 1230 ± 533 kPa for the media were used for the analysis. The rupture stretches in both the axial and circumferential directions were 1.50 ± 0.22 [51]. The mean ultimate strength of adventitia was about 280% and 50% higher than that of media in the axial and circumferential directions, respectively. The mean ultimate strength of media in the axial direction (520 kPa) was considered as a reference threshold value for the assessment schemes of the plaque vulnerability. According to Schmermund and Erbel, type II and III lesions according to AHA classification are not potential to rupture [52]. Therefore, this study used the result of Teng et al. merely to represent the arterial layer (media and adventitia) of the diseased carotid artery or the arterial tissue surrounding the plaque. The rupture criteria for the human atherosclerotic plaque appplied in the simulation are collected in Fig. 4.

A further study by Mulvihill et al. provided the rupture criterion for the human carotid plaque in the circumferential direction only as shown in Fig. 4(a) [53]. They found that the average rupture stress and average rupture stretch values for the lipid-dominant plaques are 0.342 ± 0.16 MPa and 1.927 ± 0.26 stretches, respectively. To the best knowledge of the authors, there are no rupture stresses and stretches criteria for the human carotid plaque in the axial direction. Therefore, the mechanical response of the fibrous plaque caps from the study of Holzapfel et al. [54] regarding the human stenotic iliac arteries is adopted in this work. They found that the average rupture stress and average rupture stretch values for fibrous plaque caps in the circumferential direction are 0.221 ± 0.14 MPa and 1.251 ± 0.176 stretches, respectively, and 0.354 ± 0.27 MPa and 1.14 ± 0.0875 stretches, respectively, in the axial direction. Addressing the different rupture stretch criteria between Mulvihill et al. and Holzapfel et al., the rupture stretch criterion provided by Holzapfel et al. has a much lower stretch at rupture (1.251 ± 0.176 stretches) in comparison with Mulvihill et al. (1.927 ± 0.26 stretch). This is caused by the difference of the atherosclerotic plaque type, for which Holzapfel et al. used calcified-dominant plaque [53].

Fig. 4.

Rupture criterion for diseased carotid artery and for the human carotid plaque: (a) Circumferential direction, (b) Axial direction.

3. Results and discussion

Figure 5 shows a comparative chart between the simulation results and the rupture stress/stretch data in the circumferential direction, while Fig. 6 shows those comparisons in the axial direction. The adventitia and media in Fig. 5 and Fig. 6 refer to the diseased adventitia and diseased media surrounding the plaque, while the intact refers to the free-lesion area of the arterial tissue opposite the plaque.

It can be seen from Fig. 5(a) that there is no significant effect of the combination of expansion, except for the residual Cauchy stress generated by the stents within the intact layer. It is indicated that for Asymmetric stent, the offset balloon combination produced the highest residual Cauchy stress within the free-lesion area in front of the plaque, whereas for the Sinusoidal stent, the ordinary cylindrical balloon combination produced the smallest one. Furthermore, the residual Cauchy stress within the diseased adventitia and media was quite small which caused the edge dissection/fissure of the arterial layer. This result affirmed the FE studies of Li et al. [34,35] in that the higher stress concentration area took place in the vicinity of the plaque shoulder.

Fig. 5.

Comparative chart in circumferential direction: (a) Cauchy stresses, (b) Stretches ratio.

On the contrary, the carotid plaque and arterial tissue around the free-lesion area stored a large amount of the residual stress. The high residual stress stored in the arterial tissue of the free-lesion area was still around the critical limit of rupture. However, this phenomenon is an initial symptom that causes the inflammation of the free-lesion area of the vessel wall. Moreover, the residual stress within the carotid plaque should get more attention because of both rupture criterions; even the carotid plaque quantitatively stored the lower amount of the residual Cauchy stress.

Fig. 6.

Comparative chart in axial direction: (a) Cauchy stresses, (b) Stretches ratio.

Comparative chart for the stretches ratio in the circumferential direction is shown in Fig. 5(b). It is clearly indicated that the stretch ratio in the circumferential direction tends to be similar for each expansion combination and its values remain under all rupture criteria, except for minimum limit of the rupture stretches data of Holzapfel et al. It means that all combination models of expansion used in the simulation can be applied in the treatment. It is noted that the stretches ratio of the plaque was slightly lower than that of the other arterial tissues. This is an interesting phenomenon as the direction of the balloon inflation is directly on the plaque surface. However, because its stiffness is higher than the arterial tissue of the free-lesion area, the lower stretch value becomes a result.

Figure 6 shows the relationship between the residual Cauchy stresses and stretches ratio in the axial direction for each expansion combination. In the case of the Cauchy stresses, the tendency is equal to the simulation results in the circumferential direction, though the intact has lower residual stress than the carotid plaque. Nevertheless, the Cauchy stress stored within the carotid plaque both in the circumferential and axial direction has comparable values. It is caused by the thickness of the fibrous plaque cap that is thinner than that of the intact. In the case of the stretch ratio, the simulation result in both directions represented a similar tendency for each layer though the stretch ratio in the axial direction was slightly lower than that in the circumferential direction.

It is important to note that both the diseased adventitia and the diseased media store high residual stress within both the circumferential and axial direction, which leads to a rupture. The rupture occurs in the fibrous plaque cap rather than in the intact. We reckon that the large size of the lipid core and the quite thin fibrous cap are the major causes of the high residual stress stored in the plaque. Considering the thickness of the fibrous cap used in the simulation model, it is classified as in vivo critical fibrous cap thickness as shown by Yonetsu et al. [25]. The thinner fibrous cap thickness leads to the higher residual stress store in it. Further simulation model with the thicker fibrous cap may be useful to identify the real effect of the asymmetric expansion. All simulation models generated an almost similar amount of residual stress within it except for the high residual stress stored in fibrous cap, which is equal to 200% of plaque rupture threshold (0.342 ± 0.16 MPa). This condition may be more severe compared with the in vivo rupture stress values predicted by Maldonado et al. [55], who suggested that non-calcified tissue ruptures at 0.107 MPa. Moreover, the studies by Cheng et al. and Huang et al. confirmed that the lipid component of the plaque specimens is the main contributor to the rupture of plaque and a key factor in plaque vulnerability [27,47].

4. Conclusion and outlook

The finite element analysis on the development of the Asymmetric stent to treat the eccentric plaque of the human carotid artery considering the plaque vulnerability and the arterial wall rupture was carried out in this chapter. Four combinations of expansion consist of the Asymmetric stent, Sinusoidal stent, offset balloon, and ordinary cylindrical balloon was analyzed. The following conclusions were obtained:

Four types of expansion combination did not cause the major influence to produce the residual Cauchy stress and stretch within the diseased adventitia, the diseased media, and the fibrous plaque cap. A little influence of the residual Cauchy stress was observed on the intact of the arterial wall opposite the plaque in both directions. In this case, the combination of an Asymmetric stent – offset balloon generates the highest residual Cauchy stress in the circumferential direction, while the combination of the Sinusoidal stent – offset balloon generates the highest one in the axial direction.

The residual Cauchy stresses within the plaque in both directions are the most critical location because the observed high residual stress always exceeds all rupture criteria. However, the stretch of the plaque remains under the safety region. This result suggests that the eccentric plaque obstruction with the large lipid core and the thin fibrous cap is a reason for the rupture.

For the plaque geometry studied here (the large lipid core, thin fibrous cap, and eccentric plaque obstruction), the residual Cauchy stresses in both directions are comparable. The reversed result was observed on the intact of the arterial wall opposite the plaque.

The Asymmetric stent is specifically developed for treating the eccentric plaque. The development is based on the phenomenon that the material properties of the plaque or arterial layers surrounding the plaque vary. Several experimental studies found that the fibrous cap of fibroatheroma plaque has a high stiffness, whereas the healthy intima layer has a high flexibility. These two layers are often found in terms of fibroatheroma eccentric plaques. In this case, the Asymmetric stent is expected to be used in the treatment, in order to provide a proportional pressure to the stiffness of the surrounding layer.

In general, this study was unable to demonstrate the advantages of Asymmetric stents in application. The direction of balloon inflation is suspected to cause increasing the vulnerability level of the plaque, especially by applying the combination of Asymmetric stent and offset balloon. The authors assumed that it is also affected by the single model used for the eccentric plaque and the similar direction of Asymmetric stent expansion (merely against the plaque). Considering the direction of balloon expansion, the balloon expansion against the intact of the arterial wall would become an interesting investigation. Besides, the position of the critical plaque when correlated with the changes in stent surface roughness would be a trigger to a larger problem [17,56]. Therefore, to uncover the most effective manner for the Asymmetric stent in the deployment process, further studies are needed.

On the other hand, the isotropic material model used in the analyses enacts a lack of this study. Many researchers suggest considering the anisotropic material model in the FE studies on the atherosclerotic diseases [45,48,50,54]. Nevertheless, a simple adjustment can be made to compare the simulation results between the isotropic and anisotropic material model, so one could interpret the result of the anisotropic model from the isotropic model [50].

Footnotes

Acknowledgements

This research work is partially supported by Program Percepatan Publikasi Internasional 2018, LPPM Institut Teknologi Sepuluh Nopember (ITS). The authors gratefully acknowledge the support.

Conflict of interest

There is no actual or potential conflict of interest.

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