Computational modeling of low‐density lipoprotein accumulation at the carotid artery bifurcation after stenting

Restenosis typically occurs in regions of low and oscillating wall shear stress, which also favor the accumulation of atherogenic macromolecules such as low‐density lipoprotein (LDL). This study aims to evaluate LDL transport and accumulation at the carotid artery bifurcation following carotid artery stenting (CAS) by means of computational simulation. The computational model consists of coupled blood flow and LDL transport, with the latter being modeled as a dilute substance dissolved in the blood and transported by the flow through a convection‐diffusion transport equation. The endothelial layer was assumed to be permeable to LDL, and the hydraulic conductivity of LDL was shear‐dependent. Anatomically realistic geometric models of the carotid bifurcation were built based on pre‐ and post‐stent computed tomography (CT) scans. The influence of stent design was investigated by virtually deploying two different types of stents (open‐ and closed‐cell stents) into the same carotid bifurcation model. Predicted LDL concentrations were compared between the post‐stent carotid models and the relatively normal contralateral model reconstructed from patient‐specific CT images. Our results show elevated LDL concentration in the distal section of the stent in all post‐stent models, where LDL concentration is 20 times higher than that in the contralateral carotid. Compared with the open‐cell stents, the closed‐cell stents have larger areas exposed to high LDL concentration, suggesting an increased risk of stent restenosis. This computational approach is readily applicable to multiple patient studies and, once fully validated against follow‐up data, it can help elucidate the role of stent strut design in the development of in‐stent restenosis after CAS.


| INTRODUCTION
In recent years, the number of patients requiring carotid artery stenting (CAS) has increased compared to carotid artery endarterectomy (CAE).This is due to the nature of CAS treatment, which is less invasive, has a shorter recovery time, and is recommended to patients with high-risk surgery complications. 1,23][4][5] Data pertaining to the incidence of restenosis have shown the influence of stent characteristics with different designs and configurations. 6,7Previous studies reported different risks of peri-procedural incidents in patients treated with open-cell stents and closed-cell stents. 6,8,91][12] Differences in stent design may contribute to the disparity in wall shear stress distribution and subsequent development of neointimal hyperplasia; the latter involves platelet aggregation, smooth muscle cell proliferation and migration, and accumulation of inflammatory cells and fatty deposits.Several studies used wall shear stress as a hemodynamic risk indicator to identify potential regions of ISR 10,12,13 and to determine the optimal stent type for specific vessels.They found that post-stent models with a closed-cell type had a larger area of low and oscillating wall shear stress compared to the open-cell type.Similarly, Hussain et al. 9 collected clinical data that showed restenosis was higher in patients with closed-cell stents over a follow-up period of 20.2 ± 16.4 months.This finding was supported by Texakalidis et al. 14 that open-cell stents were associated with a lower risk of restenosis compared to closed-cell stents.
Different models of LDL transport through an arterial wall have been proposed in the literature. 43The simplest model is the wall-free model, where only the fluid domain is considered in the simulation, and the effects of the surrounding wall are incorporated through the imposed boundary conditions. 34,44,457][48] A more realistic wall model using an anatomically realistic multi-layered structure has also been proposed to model mass transport within the wall. 49Another advanced model combining a multi-layered wall with a multi-pore model for mass transfer of LDL has been applied to a stenosed coronary artery 27 and has shown improved prediction of LDL concentration in the local proximity of the endothelium, particularly for the initial progress of atherosclerosis.
Following these advancements, several computational models of atherosclerosis have been investigated by different research groups in order to characterize the onset of the disease. 19,24,50,51However, computational studies on the mass transport of macromolecules in post-stenting arteries are still lacking.Few studies have examined the altered hemodynamics caused by different post-stent geometry on neointimal hyperplasia (NIH). 42Understanding the effects of detailed stent cell geometry on the accumulation of atherogenic macromolecules such as LDL is essential for further future improvement and optimization of stent design.Modeling mass transport phenomena would also help elucidate the role of stent design and vascular curvature 52 in LDL clearance near the endothelial surface.
In order to investigate how the different stent designs could affect the transport of biologically active molecules dissolved in the blood, LDL transport was simulated in three post-stent carotid artery bifurcation models and a healthy contralateral carotid bifurcation, with the latter being used as a control.LDL transport was described using a convection-diffusion model accounting for trans-endothelial transport.

| Reconstruction of the carotid artery bifurcation and stents
A patient with asymptomatic chronic stenosis (90% according to NASCET grading) in the right internal carotid artery (ICA) was examined using contrast-enhanced computed tomography angiography (CTA).Due to the patient medical background, the patient was recommended for endovascular intervention using CAS. Figure 1 shows a self-expanding Wallstent (Carotid WALLSTENT 6-8 Â 37 mm, Boston Scientific, MA) deployed in the ICA and distal to the common carotid artery (CCA).According to the NHS Health Research Authority guidelines and regulations to the guidelines and regulations of the NHS Health Research Authority in England, formal ethical approval was not required for this limited retrospective and anonymized study.
The post-stent CTA images were acquired to reconstruct patient-specific models.The images were acquired using Philips Ingenuity CT machine with a slightly lower resolution: 100 slices of the carotid artery were taken with a thickness of 2 mm for each slice, interslice of 1 mm and pixel size of .549mm with a higher dose of 120 kV and 67.99 mAs.Two carotid bifurcation geometric models were built: (a) the post-stent model (reconstructed from post-stent CTA images of the right carotid) and (b) the contralateral carotid with low-grade stenosis (30%), reconstructed from CTA images of the left carotid.Both geometries were reconstructed with approximately similar dimensions-for CCA, the diameter is within .8 to 1.0 cm with the length of 7.0 to 7.2 cm.Similarly, for ICA length from the apex of bifurcation to the end is $6.2 to 6.5 cm.However, the diameter of the geometries differed in the area of distal and proximal to the bifurcation, that is, 1.12 cm is the largest diameter in the post-stent model compared with .81cm in the contralateral model.The post-stent model is larger than the contralateral model primarily due to the deployed stent shape.Another factor is the existence of low-grade stenosis in the contralateral model at the bulb area wall.The ICA length for both models was built way longer than the external carotid artery (ECA) as the region of interest for the flow pattern analysis comparison.
The reconstruction process begins with the segmentation of the inner surface of the carotid artery based on thresholding values and region-growing technique using MIMICS 16.0 (Materialise Inc., Leuven, Belgium).The sequence began with marking the region of interest, which was the lumen of the CCA, ICA, and ECA in the transverse plane.The region of interest was highlighted using pixel intensity, and the same procedure was repeated to all transverse plane images.The surface contours were then highlighted pixels and the smoothing criteria.The smoothing was done based on the prescribed measures to ensure the accuracy of the surface contours.Then, the 3D surface was created by superimposing and lofting these surface contours in the coronal plane, representing the 3D geometry of patient- specific carotid artery bifurcation.The smoothing level was controlled to ensure that none of the important physiological features were lost during the smoothing process.Polylines of the segmented post-stent geometry were also created together with the centerline path before being exported to SolidWorks (Dassault Systemes, Velizy, France) for lofting.
For stents creation in Figure 2, a generic approach to reconstruct the deployed stent was developed by making use of the following information: (1) geometry of the post-stent carotid bifurcation and (2) stent-specific properties including the number and width of cells, circumferential and longitudinal struts, as well as the overall stent length and diameter.To virtually deploy the stent, a series of Boolean operations were performed.Firstly, the stented region was separated from the post-stent model to undergo virtual stenting.The region was then wrapped with the parameterized sketch of the stent cell and hollowed to .12 mm thickness.An intersection Boolean operation was performed between the stent cell geometry and the stented region in order to remove the vessel and isolate the stent geometry.The stent geometry was then exported into a reconstructed post-stent carotid bifurcation.Lastly, a patient-specific stented carotid bifurcation model was obtained by subtracting the stent geometry from the post-stent model and removing the strut volume from the flow domain at the opening of the ECA.The inclusion of the stent struts at the opening of ECA is important in order to assess the effect of stent design and location on post-stent carotid hemodynamics.To investigate the influence of open-and closed-cell stent designs on blood flow patterns, models of two additional commercial stent designs were built.Stent B was created to represent another closed-cell stent design resembling an XACT stent, and Stent C was created for an open-cell design to resemble an ACCULINK stent (Figure 3).
The models were then exported and discretized into tetrahedral elements using ANSYS ICEM CFD 15.0.Initially, the 'octree' method was used before the volume mesh was regenerated using the 'delaunay' method to ensure the high-quality unstructured mesh.The skewness of the mesh elements and the mesh expansion factor were kept as small as possible.Figure 4 shows the mesh elements generated with local refinement around the stent struts, where the mesh density was much greater than in the rest of the model.A finer mesh strategy, including gradually finer elements toward the wall, was used to ensure convergence of the near wall transport equations and appropriate spatial resolution for LDL flux in the endothelial layer. 54Hence, the number of mesh elements increased by 15% more than the ones reported in our previous study. 53Mesh sensitivity tests were carried out for both models to ensure mesh-independent solutions.The final meshes for all post-stent models are approximately 8.2 million elements, while the contralateral model consists of approximately 3 million elements.Newtonian with a density of 1060 kg/m 3 , while its viscosity was described using the Quemada model. 55The Quemada viscosity model was adapted to incorporate regions of high shear rate with more than 100 s À1 with regions of stagnation, especially at the stent struts.The Quemada is appropriate for capturing the variability of viscosity characteristics at the low end of shear rates. 55In order to obtain clinically relevant numerical results, accurate boundary conditions need to be specified at the CCA inlet and the ICA and ECA outlets.For this purpose, Womersley 56 velocity profiles were applied at the CCA inlet, which was derived from the corresponding mean velocity waveforms of Doppler ultrasound.An instantaneous mean velocity (i.e., averaged across the Doppler beam) of a cardiac cycle was extracted for the calculation of the inlet flow rate by multiplying it with the cross-sectional area of the inlet CCA measured with CTA (Figure 5).Through the Womersleys method obtained using Matlab (Mathworks, Natick, MA), a harmonic patientspecific fully developed time-varying velocity profile was then specified at the CCA inlet.

| Flow and LDL transport modeling
Physiological pressure outflow boundary conditions were obtained using the 3-element Windkessel model (3-EWM).The 3-EWM has been proven to provide numerical results closer to in vivo, where the resistance of the downstream vasculature and arterial compliance determine the pressure at the outlet.The first resistance, R 1 is the proximal resistance which depends on the outlet diameter, C is the total wall compliance of the downstream vasculature, and R 2 is the distal resistance offered by the peripheral resistance of the vessel.Pressures and flowrates at each ICA and ECA outlets are related by the following Ordinary Differential Equation (ODE) 57 ; Schematic of the computational model employed in this study is similar to our previous report. 53 where Q out is the outlet flowrate that can be calculated from the Doppler ultrasound velocity waveform, while C, R 1 , and R 2 were fitted parameters and adjusted to match the maximum, minimum and cycle-averaged carotid blood pressures of 110, 90 and 70 mmHg, respectively (Table 1).Different values for these parameters were calculated for the contralateral and post-stent models based on the corresponding measured flow waveforms at the outlets.The walls were assumed to be rigid with no-slip conditions.LDL was modeled as a dilute substance dissolved in the blood and transported by the flow through a convectiondiffusion transport equation: where c is LDL concentration, u is blood velocity vector, and D is LDL diffusivity in blood.A physiological concentration of 1.2 mg/mL was applied at the inlet. 34The endothelial layer was assumed to be permeable to LDL, with LDL flux (Js) and transmural velocity (J v ) being described by the Kedem-Katchalsky equations: where L p is the hydraulic conductivity of the endothelium, ΔP is the pressure drop across the arterial wall, Δ Q is the oncotic pressure difference, σ D and σ f are respectively the osmotic and solvent reflection coefficients, k w is the LDL endothelial permeability, Δc is the LDL concentration difference across the endothelial wall and c is the average endothelial concentration. 58The shear-dependent equation for hydraulic conductivity L p proposed by Sun et al. 23 was adopted in order to incorporate the influence of local shear stress τ w on transmural flux: All parameter values have been taken from Sun et al. 23 In order to account for the early effects of smooth muscle cell proliferation, the strut thickness was reduced to half of its original size in the three post-stent models.
It is well known that the time scale of LDL transport is much greater than a cardiac cycle.In other words, LDL accumulation in atheroprone regions would take months or years to form.Within the current limitations of computational power, it is only feasible to simulate a limited number of cardiac cycles under pulsatile flow.While it is possible to observe differences in spatial distribution of LDL on the endothelial and sub-endothelial surfaces, it would be desirable to predict LDL accumulation over a longer time period.Clearly, simulating LDL accumulation over months/years in a real-time scale would be computationally prohibitive.This difficulty was circumvented by artificially accelerating the near wall processes.This artificial acceleration was achieved by multiplying the LDL flux by an enhancement coefficient, ϕ, which is related to the local time-averaged shear rate: where γ av is the time-averaged shear rate and γ t is a pre-defined threshold value for shear rate.The coefficient will be equal to 1 in regions where the local time-averaged shear stress is greater than .4(i.e., γ av >> γ t = 37 s À1 for Quemada viscosity model), and it will be equal to 10 4 in regions of particularly low shear.The .4 value is based on Malek et al. 59 that suggested the wall area with TAWSS <.4 Pa is considered to be atheroprone, in which atherosclerotic lesions colocalize with regions of low wall shear stress.In regions where the local time-averaged shear stress is below .4Pa, the wall flux will be enhanced by 10 4 -fold, so that LDL accumulation over a much longer time scale can be predicted by only simulating a few cardiac cycles: This methodology allows us to de-couple the time scales of solute and blood transport, simulating a wall transport process occurring over a time scale of the order of 10 4 s ($3 h) per cardiac cycle.

| Computational details
In ANSYS CFX 15.0, a high-resolution advection strategy was utilized to spatially discretize the Navier-Stokes equation, while a second order implicit backward Euler scheme was employed to temporally discretize the equation.The model was first to run for three cardiac cycles to get a periodic flow solution and to initialize the model variables.Then the LDL model was included starting with the fourth cardiac cycle.For temporal advancement, a uniform time-step of .001s was employed, with a maximum root-mean-square (RMS) residual of 10 À5 manually specified to regulate the solution's precision.Around 15-20 iterations were required to attain convergence at each time step.Overall, CFD simulations including the LDL transport simulations for all post-stent models, require an average of 3 h of computer processing time per cardiac cycle using an Intel Xeon E5-2697 workstation with 24 cores and 96 GB RAM.

| RESULTS AND DISCUSSION
Figure 6 shows the local sub-endothelial LDL concentration with normal near-wall transport in the four models.For the contralateral carotid (Figure 6A), the normalized LDL concentration is concentrated around the bifurcation wall, especially at the outer wall of CCA to ICA.Elevated LDL concentrations of about 3.4% are observed in this area which is the entrance of the carotid bulb.The increase of LDL in this area was reported earlier by Kenjeres and Loor, 60 with a maximum increase of 3.5% in the healthy patient-specific carotid bifurcation model.The variation of LDL concentration distribution can be interpreted through observation of time-averaged wall shear stress (TAWSS) gradients.As reported in References 38,53,60, low TAWSS corresponds to the recirculation flow structure within the carotid bulb.The area of high LDL concentration is limited to the connection of CCA and ICA, which corresponds to the area of low TAWSS in the geometry.The computed area for both low TAWSS and high LDL is similar to Kim and Giddens, 38 who applied realistic wall thickness to represent wall structure in their FSI simulations.The local flow fields are highly dependent upon individual or patient-specific lumen and wall geometry as well as the blood flowrates, thus making the reconstruction of actual hemodynamic environment is crucial since the wall shear stress is used as the basis to measure local LDL transport parameters.
To establish additional correlations between the local flow and LDL concentration distributions, an arbitrarily selected '0 to 1' line profile along the lumen wall of the carotid bulb is extracted (Figure 7A).The resulting profiles of TAWSS and normalized LDL concentration along the '0 to 1' line are plotted the Figure 7B for comparison.It can be seen that a local minimum of the TAWSS takes place at L/L o = .2before gradually increasing toward the end of the profile line.At the same location, profiles of normalized LDL concentration reached local maximum and gradually decreased, respectively.This means that many areas with low WSS also have high LDL concentrations along the endothelium layer.Similar findings were also recorded in References 44,60 where the area of lowest WSS and highest LDL concentration mostly coincide.
For the post-stent models, elevated LDL concentrations are observed in the proximal portion of the stent along the outer wall, especially at the sharp corners of the struts, with less pronounced LDL accumulation in the distal region (Figure 6A).The highest normalized concentration found in these regions is up to 2.34, about 80% higher than the contralateral carotid.The elevated LDL concentration was observed around the stent struts in all post-stent models, with the highest LDL is at the outer wall of CCA to ICA.As the geometry shapes of the post-stent models are identical, the spatial pattern of LDL is observed following the stent design.A marginally larger area of elevated LDL concentration occurs in the Wallstent model compared to the other two models (Figure 6B).Since the geometrical feature of the Wallstent has a higher number of stent cells, it causes a larger area of complex flow patterns near the wall, especially between the struts.Similar to the contralateral model, these areas are dominantly covered by low TAWSS which directly correspond to local flow recirculation close to the struts (Figure 8).This abnormal hemodynamic environment leads to larger areas of low TAWSS.Similar results were also recorded by Santis et al. 13 in the study of restenosis prediction using wall shear stress and indices computed from CFD simulations on ideal open-and closed-cell stents.
The LDL concentrations in the contralateral carotid are not affected by the artificial acceleration of its near wall transport as shown in Figure 9.A similar location of elevated LDL concentrations is recorded in the carotid bulb.However, the accelerated LDL concentration in the contralateral model may not be compared directly with previous studies.Kenjeres and Loor 60 used steady laminar flow profile with identical Re = 105, while Kim and Giddens 38 only performed simulations in three cardiac cycles.However, all post-stent models observed notable changes in accelerated LDL concentrations.First, there is a substantial increase in LDL accumulation in different regions of the stented geometries where concentrations are more than 20 times higher than in the contralateral carotid.Second, LDL accumulation is most pronounced in the distal region of the stent, with Stent C showing the least coverage of high LDL hot spots.Finally, LDL accumulation in the proximal region only occurs at a few isolated spots.According to previous studies, restenosis occurs mostly within the first year after CAS, 61,62 and the accelerated near-wall transport simulation is indeed useful to approach realistic LDL accumulation duration.
While LDL concentrations in the contralateral carotid are not affected by the artificial acceleration of its near-wall transport, obvious changes are noted for the post-stent models.Significant LDL accumulation toward the distal end of the stent could be attributed to the combined effect of bending at both ends of the stent, slightly enlarged local diameter, and a mild constriction in the middle of the stent.Isolated spots of LDL accumulation were also observed at the F I G U R E 8 Recirculation flows in free cell area between the stent struts.This figure has been reported in the previous study by our group. 53roximal end of the stent, but these were limited to the sharp corners around the struts.Based on our results, LDL accumulation appeared to be more pronounced in Wallstent and Stent B-both are closed-cell stents.Nonetheless, it should be borne in mind that our simulation results were based on the assumption that the plaque was pushed back uniformly by the stent so that any possible protrusion of the plaque through the free cell area of the stent was not taken into account.
The methodology presented in this study allows us to replicate stent apposition from the post-CAS patientspecific geometry, maintaining the complex shape of the stent struts such as floating struts at the ECA entrance and a small constriction downstream of the bifurcation; all of these influence the local hemodynamics. 4,5The results clearly show that the patient-specific geometry and stent design in post-stent models affects the distribution of LDL concentration.Low endothelial shear stress, flow recirculation, and stagnation are known to be associated with weak convective clearance near the endothelial surface, which could result in local accumulation of biologically active compounds like LDL. 28,63 Through artificial acceleration of the near wall processes, we were able to simulate LDL accumulation over a much longer time period than a few cardiac cycles.Using a low TAWSS threshold of .4Pa to trigger the accelerated transport, 59 our computational results predicted a potential risk for LDL accumulation in the distal segment of the stent in all post-stent models, although the coverage of LDL accumulation was less in Stent C (open-cell).
Figure 10  ranging between 0 and a maximum .5.RRT predicts the likelihood of cell deposition on the arterial wall. 64Low TAWSS, elevated OSI, and high RRT have been reported being correlated with neointimal thickening, which could potentially lead to ISR.The LDL simulation presented in this study revealed the same spots of high LDL concentration with the hemodynamic features, especially at the area toward the distal end of the stent.The unfavorable hemodynamic features and LDL accumulation in post-stent models were consistent with Texakalidis et al., 14 who found that open-cell stents were associated with a statistically lower risk of restenosis compared to closed-cell stents.
By artificially accelerating the wall transport process, this study has demonstrated the feasibility of simulating LDL accumulation in the wall over a much longer timescale than several cardiac cycles.Since the buildup of LDL is involved in the initial stage of intimal thickening, the current findings can be used to predict the risk of intimal thickening based on the distribution of LDL accumulation in the carotid artery.
This method can be applied to multiple patient cases to elucidate further stent design's role in the development of ISR after CAS.There are four limitations of this study.First, the model for LDL transport was limited to luminal and trans-endothelium transport without accounting for the multi-layered structure of the arterial wall.The initial condition of LDL concentration was also assumed with a constant value (C C 0 ), proving by a previous study 65 that different LDL concentrations may produce different patterns of LDL distributions in the artery.However, the present study aims to compare the LDL distribution between different stent designs with the normal contralateral carotid.The purpose is to identify which stent design is predicted to have a higher risk of stent restenosis.Hence, we believe our initial condition of constant LDL concentration profiles diluted in blood flow is reasonable to meet the study's purpose.Nonetheless, the recommendation by Reference 65 is beneficial for future studies.
Second, the vessel wall and the stent were assumed to be rigid in the CFD simulations; nevertheless, as the study aimed to observe the pattern of LDL distribution in the stented region, the rigid wall assumption is expected to have a minor influence on the results. 66To account for the potential influence of remodeling on the hemodynamics, the strut thickness was also reduced to half of its original size in all post-stent models.This adjustment attempts to partially consider the remodeling of the stent's geometry and its effects on the flow patterns and LDL distribution.The findings reported by Corti et al. 67 are in line with the assumptions made in the current study regarding stent remodeling.They observed that most of the restenosis occurred in the first post-operative month, and subsequent remodeling affected the hemodynamics, leading to a slowing down of the restenosis process over time.While the current study did not explicitly simulate the long-term follow-up and remodeling process as performed by Corti et al., 67 the inclusion of the stent strut thickness reduction aimed to consider the potential effects of remodeling on the results.However, it is important to note that the specific influence of remodeling on the results was not extensively investigated in the current study.
It would be more interesting to evaluate the qualitative comparison of LDL concentration between the different sizes of the stenotic model (pre-stent) and post-stent models.The absence of follow-up data has limited the study for any direct comparison between the predicted LDL accumulation and restenosis, especially the LDL concentration values around the stent strut.A few previous articles simulated the LDL transport in the other parts of the stented artery, such as Gai et al., 68 Liu et al., 69 and Escuer et al. 70 However, none of the articles proposed the LDL concentration values in the stented area.Nonetheless, the similarity of the three articles is that the normalized LDL concentration around the stent struts is way higher than in the other endothelium wall, which is also predicted in the present study.The studies are not focusing on the stent strut shape and size, as they mentioned difficulties in reproducing the complex geometry of the stent; hence, the simplified circular stent area was employed in the study.Besides, the clinical observation study by 68 recommends further analysis for possible LDL concentration values in the specific stent area.Finally, regarding the influence of different acceleration factors on the areas of high LDL concentration, it is to note that the specific influence of other acceleration factors was not addressed in this particular study.Instead, the focus was on assessing LDL influx in a longer time period and providing preliminary results.Further evaluation and validation of the computational technique used in this study, including performing sensitivity analyses with different acceleration factors would be useful in the future studies for a more comprehensive understanding of the model's behavior.

| CONCLUSION
In this study, we investigated the accumulation of LDL in patient-specific post-stent carotid bifurcation models reconstructed from CTA images to predict the potential of restenosis.The predicted LDL accumulation was compared between the closed-and open-cell stents models and the normal contralateral model.Our results clearly show that LDL accumulation is more pronounced in Wallstent and Stent B-both are closed-cell stents.This computational technique is readily applicable to various patient data.Once fully validated against follow-up data, it can help elucidate the role of stent strut design in the development of in-stent restenosis after CAS.Future studies of more patient-specific models using our methodology will be beneficial to assess the impact of more stent designs and vessel curvatures, especially with specific post-stenting follow-up information.This will facilitate a similar analysis to determine key factors in the progression of restenosis.
image of post-stent carotid artery bifurcation showing metallic artifact due to the presence of stent metal.(B) Volume rendering and segmentation of the model from CT images before generation (C) polylines.(D) Both polylines and centerlines were exported to CAD files to reconstruct the lumen surface.
Laminar and pulsatile blood flows were simulated by numerically solving the governing equations for an incompressible fluid using a finite volume-based CFD code (ANSYS CFX 15.0).Blood was treated as incompressible and non-F I G U R E 2 (from left to right) The stented area in the dotted square is wrapped with a parameterized sketch of stent cells.Using Boolean operation, the intersection of the stent cells and solid surface yields the realistic expanded Wallstent before subtracting it from the post-stent model to create a stented carotid artery bifurcation model (post-stent model) for CFD simulation.

F
I G U R E 3 Three stent designs geometries in the deployed configuration.(From left) WALLSTENT, XACT (Stent B), and Acculink (Stent C). Figure adapted from the previous study. 53F I G U R E 4 The tetrahedral elements mesh used in the post-stent carotid bifurcation model with high-density concentration in the stented region, especially in the vicinity of stent struts.
(A) The carotid bifurcation model together with the RCR network model at the ECA and ICA outlets and (B) the inflow waveform prescribed at the CCA inlet section based on (C) Doppler ultrasound measurements.

F
I G U R E 6 Sub-endothelial LDL concentration in the post-stent models and in the contralateral carotid obtained with normal wall transport.(A) Comparison between the contralateral carotid and the Wallstent carotid showing the exact location of high concentration of LDL accumulation, (B) all three different post-stent models showing similar pattern of high LDL accumulation distribution at the proximal region.
U R E 7 (A) The contours of normalized LDL concentration and TAWSS at the bifurcation area and location of the lines (L/L 0 ) for extraction of the characteristic profiles.(B) The profiles along the L/L 0 lines compare LDL concentration and TAWSS (Pa).
shows a comparison of local hemodynamic features, that is, TAWSS, oscillatory shear index (OSI) and relative residence time (RRT) reported in Johari et al.'s Reference 53, with LDL accumulation in the least potential risk of ISR model, Stent C. As blood flow may change its direction, many studies have used OSI to quantify the cyclic motion, F I G U R E 9 LDL concentrations in the contralateral carotid (top) and the post-stent carotids (bottom) obtained with accelerated nearwall transport.

F I G U R E 1 0
Comparison of hemodynamic simulations (top) reported by Johari et al. 2020 53 with LDL concentrations in post-stent model, Stent C (bottom).

1
Windkessel parameters for each outlet.