Foad Kabinejadian Fangsen Cui Boyang Su Asawinee Danpinid Pei Ho Hwa Liang Leo

Transcription

1 Med Biol Eng Comput (215) 53: DOI 1.17/s ORIGINAL ARTICLE Effects of a carotid covered stent with a novel membrane design on the blood flow regime and hemodynamic parameters distribution at the carotid artery bifurcation Foad Kabinejadian Fangsen Cui Boyang Su Asawinee Danpinid Pei Ho Hwa Liang Leo Received: 29 July 213 / Accepted: 21 October 214 / Published online: 5 November 214 International Federation for Medical and Biological Engineering 214 Abstract We have recently developed a novel membrane design for carotid covered stents that prevents emboli while preserving the external carotid artery (ECA) branch flow. Our earlier in vitro studies have shown that this novel design can maintain more than 83 % of the original ECA flow and has the potential to considerably reduce the chance of emboli release as compared to bare metal stents. In the present study, utilizing computational fluid dynamics simulations and fluid structure interaction analyses, we further investigated the influence of this novel covered stent on the blood flow regime and distribution of hemodynamic parameters at the carotid artery bifurcation and within the branches. Simulation results of the effect of the covered stent on the flow division at the carotid bifurcation were F. Kabinejadian H. L. Leo (*) Department of Biomedical Engineering, National University of Singapore, 9 Engineering Drive 1, Block EA #3 12, Singapore , Singapore bielhl@nus.edu.sg F. Kabinejadian P. Ho Department of Surgery, National University of Singapore, 1E Kent Ridge Road, Singapore , Singapore F. Cui A. Danpinid Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore , Singapore B. Su Cardiac Mechanics Engineering and Physiology Unit, National Heart Center, 17 Third Hospital Avenue, National Heart Center, Mistri Wing, Singapore , Singapore P. Ho Department of Cardiac, Thoracic and Vascular Surgery, National University Health System, 1E Kent Ridge Road, Singapore , Singapore comparable with the earlier experimental results and further verified that this covered stent can considerably preserve the ECA flow. The results also showed that this covered stent may affect the flow regime and the distribution of hemodynamic parameters at the opening of the ECA branch and at the apex of the divider wall. These altered local hemodynamic characteristics may promote the post-stenting patency of the ECA branch. Evaluation of shear-induced platelet activation suggested that activation of platelets due to the blood flow through this membrane is unlikely. However, some slow-flow regions near the stent membrane around the ECA opening may induce platelet aggregation and thrombus formation. This study further demonstrated the potential of this novel covered-stent design for the treatment of carotid atherosclerotic stenosis. Future in vivo investigations of the biological effects and mechanical performance of this covered-stent design (e.g., its thrombogenicity potential and biocompatibility) are warranted. Keywords Fluid structure interaction (FSI) Computational fluid dynamics (CFD) Embolic protection Stroke Wall shear stress (WSS) 1 Introduction It is widely accepted that hemodynamics play an important role in the initiation, progression, and development of atherosclerosis, as strong correlations have been found between the sites of intimal thickening and variations in local hemodynamics [1]. The arterial sites exposed to low wall shear stress (WSS) [24], oscillating shear stress [11], and large WSS gradient (WSSG) [2] are particularly susceptible to development of atherosclerotic plaques and intimal thickening. Suggested underlying mechanisms include

2 166 Med Biol Eng Comput (215) 53: increased residence time of atherogenic particles near the vessel walls [3, 9], effects on endothelial function [6, 28], and alterations in mass transfer [27]. Complex geometry of carotid artery bifurcation (i.e., sudden increase in cross-sectional area, strong vessel wall curvatures, and bifurcation) causes flow disturbances (i.e., flow separation and reattachment, helical swirling flow, and recirculation) mainly near the outer walls of bifurcation. This leads to undesirable distribution of hemodynamic parameters, which in turn, results in atherosclerotic plaque formation and consequent stenosis. Although there is an increasing interest in carotid artery stenting for treatment of cervical carotid artery bifurcation atherosclerotic disease [5], currently available bare metal stents cannot provide an adequate protection against the detachment of the plaque fragments over diseased carotid artery, which could result in the formation of micro-emboli and subsequent stroke. The use of covered stents, on the other hand, carries the risk of compromising the perfusion of the external carotid artery (ECA) which is usually bridged in clinical applications. To address this issue, our research group has recently developed a novel covered-stent design for carotid artery with the aim of preventing friable fragments of atherosclerotic plaques from flowing into the cerebral circulation, and yet retaining the ability to preserve the flow of the ECA [14, 23]. This carotid covered stent comprises mainly of a bare stent coated with a membrane of a biocompatible polymer (e.g., polyurethane), with arrays of miniature flaps (U-shaped with width and total height of 5 µm) laser cut onto the polymer membrane in the stent cells (Fig. 1a). The utility of these miniature flaps is (1) to preserve the blood flow volume through the stent cover into side-branches (i.e., ECA), and (2) to confine the plaques at wall locations and prevent them from dislodging from the atherosclerotic plaques. In the former, the flaps are opened by the blood pressure gradient across the stent membrane between the common carotid artery (CCA) and ECA daughter branch, while in the latter the flaps adjacent to the vessel wall prevent the detachment of friable fragments from the carotid atherosclerotic plaques. We have earlier shown in vitro that this covered-stent design has a significantly higher emboli prevention capability than the corresponding bare metal stent, while preserving more than 83 % of the original flow of the ECA [23]. Also, a more uniform flow in the ECA through these covered stents was observed without evidence of undesirable flow recirculation and reversed flow. However, it is very difficult (if not impossible) to experimentally investigate the effects of this carotid covered-stent design on the distribution of hemodynamic parameters (such as WSS, WSSG, and OSI). Therefore, to further investigate the impact of this novel stent design on the flow regime and distribution of (c) (d) (e) 5µm 1mm 5µm Fig. 1 Schematic view of the covered stent and the deployment process. The covered stent was first bent according to the carotid artery geometry, and then only portion of that facing the ECA opening was maintained for FSI analysis, to reduce the computational overhead: a the carotid covered stent comprises of a bare stent coated with a polymeric membrane, with arrays of miniature flaps cut onto the membrane; b the stent before bending: the upstream side of the stent is placed in the CCA; c the stent after bending: the outer wall of the curvature of the covered stent is facing and covering the ECA opening; d only the portion of the covered stent facing the ECA opening is maintained for the FSI analysis; e one stent cell with the membrane and the dimensions of the flaps hemodynamic parameters (both qualitatively and quantitatively) at the carotid bifurcation, a computational flow study has been conducted, utilizing fluid structure interaction

3 Med Biol Eng Comput (215) 53: (FSI) analysis of the blood flow through the polymeric membrane of the covered stent in anatomically realistic geometries of human carotid artery. Following these, comparison of the flow field and calculated WSS parameters was made between the carotid models with and without the covered stent. This investigation constitutes another important step (prior to any in vivo evaluation) toward the clinical application of this novel carotid covered-stent design. 2 Materials and methods A two-way (bidirectional) fluid structure interaction (FSI) simulation of blood flow through the elastic polymer membrane of the covered stent was conducted in anatomically realistic geometric models of human carotid artery, using the commercial computational software ANSYS Workbench (ANSYS Inc.) for the coupling of the finite-elementbased software, ANSYS, with the finite-volume-based software, ANSYS CFX. Therein, the calculated displacements of the solid (polymer membrane) structure were transferred to the boundary walls of the fluid domain, and the computed forces in CFX were sent back to the solid domain at each stagger (coupling) iteration. In order to study the effects of the covered stent (Fig. 1a) on the flow field and distribution of hemodynamic parameters at the carotid artery bifurcation, the blood flow was studied in the model with the covered stent and compared with that in the corresponding model without stent. In order for the reduction of computational overhead, only the pertinent portion of the covered stent facing the ECA opening, and not the part of the covered stent in apposition to the artery walls, was modeled (Fig. 1d). The reason for this is that only the membrane flaps facing the blood stream at the ECA opening will open or close due to pressure gradient across the membrane, and not those flaps that are pressed against the vessel wall. The vessel walls and the stent struts were assumed to be rigid in the final model as their compliance and deformation are negligible in comparison with those of the polymeric membrane and the flaps (note that the arterial wall stiffness is increased due to both stent implantation and atherosclerosis) [29]. To be consistent with our earlier experimental study [23], the geometry of a self-expanding bare Nitinol stent (Protégé RX Carotid Stent: diameter 8 mm, length 6 mm; ev3 Inc, Plymouth, MN) was reconstructed and utilized as the scaffold of the covered stent (Fig. 1). 2.1 Mechanical models and boundary conditions Although the stent struts were assumed to be rigid in the final simulations, in order to model the deployed covered stent within the CCA and ICA, the metal stent was initially 167 given the properties of Nitinol (i.e., linear elastic with E = 5 GPa and ν =.33). This stent with the PU membrane fixed within each cell was bent by fixing (i.e., zerodisplacement constraint) one end in the CCA (Fig. 1b) and applying.35 radian (~2 ) rotation on the other end in the ICA (Fig. 1c) to match the geometry of the carotid artery, utilizing commercial FEA software Abaqus (version 6.11). Subsequently, the portion of the deformed stent facing the ECA opening was cut and maintained for FSI simulation (in which the stent struts were set as rigid) and was fixed to the rigid arterial walls by additional rigid material (Fig. 1d), in order to constrain the stent and to prevent flow from surrounding of this portion of the stent into the ECA Polymeric membrane model Polyurethane (PU) was assumed as the membrane material in this study, to be consistent with our earlier experimental (in vitro) study [23]. A small strain (large deformation) approximation of the polymeric membrane mechanics was utilized. The transient structural equilibrium equation is { } } { } F(t) = [M] {ü(t) + [K] u(t) (1) where {F} is the load vector, [M] is the structural mass matrix, [K] is the structural stiffness matrix, {u} is the nodal displacement vector, and { ü } is the nodal acceleration vector. The equilibrium equations for the PU membrane structure were solved with stress boundary conditions (the calculated pressure and WSS values from the fluid domain) at the fluid structure interface and constraint conditions at their connection to the stent struts, in order to estimate the PU flap displacements. The PU membrane was assumed to be isotropic, incompressible, and homogeneous with a density of 1,2 kg/m 3 and modeled as a linearly elastic, geometrically non-linear shell structure [15, 3] with a thickness of 8 µm (to be consistent with the prototypes [23]). Poisson s ratio was regarded as ν.5 to express the incompressibility of the isotropic PU membrane, and the Young s modulus of PU (ChronoFlex AR, AdvanSource Biomaterials Corporation, Wilmington, MA) was measured by tensile test to be 1 MPa. The tensile test demonstrated an almost constant value (~1 MPa) of elastic modulus for strain values of up to.7, which validates the assumption of linear elastic behavior for the PU membrane in this study Blood flow model Blood flow in the carotid artery was assumed to be a threedimensional, time-dependent, incompressible, isothermal, Newtonian, and laminar flow. In FSI models, the modified equations of motion for fluid mechanics computations

4 168 Med Biol Eng Comput (215) 53: Fig. 2 CCA flow waveform and the pressure difference between the CCA inlet and the outlets of the daughter branches (ICA and ECA). The labels indicate the time instants at which the velocity field has been discussed Flow rate (L/min) Flow and Pressure Waveforms CCA Flow (ECAoutlet-CCAinlet) Pressure (ICAoutlet-CCAinlet) Pressure t t 3-6 t t 1-15 t 5-12 Pressure (Pa) Time (s) (with corrected convective velocity due to moving boundaries [18]), which are obtained by applying the Leibnitz Rule on the integral conservation equations, are as follows. d ρ dv + ρ ( ) U j W j dnj = dt (2) V(t) S d ρ U i dv + ρ ( ) U j W j Ui dn j dt V(t) S ( Ui = Pdn i + µ + U ) j dn j x j x i S S where U j and W j are the components of the flow velocity and the velocity of the control volume boundary (mesh velocity), respectively, ρ is density (assumed to be 1,5 kg/m 3 for blood in this study [21, 22]), P is pressure, and µ is the dynamic viscosity of the fluid (taken as.35 Pa s for blood [4]). V and S denote volume and surface regions of integration, respectively, and dn j are the differential Cartesian components of the outward normal surface vector. The mesh velocity at the inner points of the fluid domain (near the moving flaps) was calculated from the wall movement by a Displacement Diffusion mesh motion model, in which the displacements applied on the boundaries were diffused to other mesh points in a way that the relative mesh distribution of the initial mesh was preserved. For instance, as the initial mesh was fine in boundary layers and near the flap openings, it remained comparatively fine after the mesh motion model was applied. A fully developed pulsatile flow was applied at the CCA inlet. The CCA flow waveform with the time period of T = 1 s, used in this study (Fig. 2), is based on (3) measurements by phase-contrast magnetic resonance imaging within common carotid arteries of older adults with little or no carotid artery disease [16]. The systolic peak flow rate is Q max = 9 ml/min, and the maximum Reynolds and Womersley numbers are calculated to be Re max = 499 and α max = 4.58, respectively, based on the CCA inlet diameter of 8 mm. The Womersley solution [36] is assumed for the inlet axial velocity profile, which is derived as a fully developed pulsatile flow and implemented as the inlet boundary condition. In order to set proper boundary conditions at the outlets of the carotid artery branches (ICA and ECA), initially the flow simulation in the model with no stent was conducted with outflow boundary conditions (assuming a zero normal gradient for all flow variables except pressure) constraining the flow rate ratio between the internal and external carotid artery branches to Q ICA :Q ECA = 7:3. Subsequently, the pressure waveforms at the outlets of the carotid artery branches obtained from this solution were used as the actual boundary conditions in the simulations for both the no-stent and covered-stent models (Fig. 2). The governing equations were solved numerically by a finite volume method and the computational fluid dynamic (CFD) software, ANSYS CFX, using a fully implicit second-order backward Euler differencing scheme. The convergence criterion (a normalized residual, obtained based on the imbalance in the linearized system of discrete equations) was set to 1 6 in this study. The mesh sensitivity was tested on the velocity and WSS, by varying the number of grid cells. The computational fluid domain with 5.3 million cells was considered to be sufficient for this study, when further mesh refinement could only result in less than 2 % change in velocity and 1 % change in WSS at some examined sections. The large number of elements required was due to the need for fine

5 Med Biol Eng Comput (215) 53: Fig. 3 Stent membrane deformation: contours of total mesh displacement of the polymeric membrane of the covered stent at peak flow rate (t 2 ) and late diastole (t 5 ). Magnified (2.7 ) images of the flaps with maximum displacements are presented at the bottom for better illustration Total Mesh Displacement µm 2.7x 2.7x mesh (1) near the stent membrane and the flaps to facilitate the mesh motion in this FSI region and (2) within the small gap around each flap to secure the continuity of the fluid domain between the both sides of the stent membrane through the flap openings. The time-step size was taken to be.1 s, and the results were recorded at the end of each time-step. In order to eliminate the start-up effects of transient flow, the computation was carried out for 3 periods, and the third period results are presented. The FSI methodology used in this study was validated by comparison of the computational results of a simple sinusoidal flow in a straight compliant tube with the corresponding analytical solution. The same process has been elaborated in the study by Kabinejadian and Ghista [2]. A good agreement was observed between the analytical solution and the obtained numerical solution with an average relative error of 5 %, based on which the applied FSI method was considered to be accurate for this study. 3 Results 3.1 Stent membrane deformation Contours of mesh displacement of the stent membrane (only due to the interaction with the fluid flow after the deployment, and excluding the deformation due to the bending and deployment) at the ECA opening at peak systole (t 2 ) and late diastole (t 5 ) are shown in Fig. 3. The deformation pattern remains qualitatively unchanged during the cardiac cycle (i.e., the flap tips consistently have higher displacement, and flap bases have lower displacement values). The maximum mesh displacement is about 1 µm, occurring at time t 2 at the tip of the flaps near the apex where the high-momentum flow from the CCA impinges onto the curved stent membrane and the fluid flow pressure due to centrifugal forces applies moment on the flaps (about their bases) on the outer wall of curvature on the stent membrane. Likewise, at time t 5, the maximum displacement occurs at the tip of the flaps, but with a lower magnitude. The considerable deformation observed on the middle part of some cells is due to the stent deformation as a result of the bending of the stent, rather than to the fluid flow pressures. Figure 4a demonstrates the deformed state of a flap and its total mesh displacement contour at peak systole (t 2 ) to better illustrate the flap deformation. Figure 4b presents the excursion of the tip of the flap (with the maximum displacement) along with the pressure gradient immediately across the flap, as well as the pressure gradient between the CCA inlet and ECA outlet. As expected, the flap tip displacement is in phase with the immediate pressure gradient across the flap, while a phase difference can be observed between the (P inlet P outlet ) and the flap tip movement, due to the pressure waveform propagation along the CCA and ECA. 3.2 Flow division between the branches The simulation results showed that the flow rate into the external carotid artery branch reduced to 26 % (from the original 3 %) of the CCA flow rate upon the deployment of the covered stent at the carotid artery bifurcation (i.e., 13.3 % reduction of the ECA flow). This is consistent with the earlier in vitro observations [23]. This flow reduction was due to the increase of the resistance against the flow through the ECA after stenting, which was caused by the flapped stent membrane. Figure 5a demonstrates the total resistance against the flow through the ECA over the cardiac cycle. The resistance after stenting was higher than that of the no-stent case all over the cardiac cycle. The overall resistance against the flow through the ECA, calculated by Eq. (4) [8], was increased by 2.8 times after

6 17 Med Biol Eng Comput (215) 53: Total Mesh Displacement [µm] Total Mesh Displacement (µm) Flap Tip Excursion vs. Pressure Gradient Time (s) Pressure gradient (Pa) Flap Tip Displacement Immediate Pressure Gradient P - P (CCA-inlet) (ECA-outlet).2.4 (m).1.3 Fig. 4 a Total mesh displacement contour of the flap with the maximum displacement; b excursion of the tip of the flap with the maximum displacement along with the pressure gradient immediately across the flap and the pressure gradient between the CCA inlet and ECA outlet. The flap tip displacement is in phase with the immediate pressure gradient across the flap, while a phase difference can be observed between the (P inlet P outlet ) and the flap tip movement, due to the pressure waveform propagation along the CCA and ECA 12 Total Resistance (ECA) 6 Total Resistance (ICA) Resistance (M Pa s / m 3 ) Resistance (ECA) - Stented Resistance (ECA) - No-Stent Resistance (M Pa s / m 3 ) Resistance (ICA) - Stented Resistance (ICA) - No-Stent Time (s) Time (s) Fig. 5 The total resistance against the flow through the a ECA and b ICA over the cardiac cycle; the ECA resistance after stenting is higher than that of the no-stent case all over the cardiac cycle; however, no remarkable change is observed in the resistance against the flow through the ICA after stenting stenting. Figure 5b shows the total resistance against the flow through the ICA over the cardiac cycle. As expected, no remarkable change was observed in the resistance against the flow through the ICA after stenting. T (P inlet P outlet ) Q dt R = T (4) Q 2 dt 3.3 Flow patterns The flow fields were studied at 5 different time points, including early systolic acceleration (t 1 ), peak flow rate (t 2 ), mid-systolic deceleration (t 3 ), dicrotic notch (t 4 ), and late diastolic deceleration (t 5 ), as shown on the flow waveform in Fig. 2. During the mid-systolic acceleration phase (t 1 ), in the no-stent model, the flow bifurcated smoothly into the

7 Med Biol Eng Comput (215) 53: Fig. 6 Flow streamlines at peak flow (t 2 ) in the nostent carotid bifurcation model and covered-stent carotid bifurcation model. Flow separation and recirculation can be observed in the ICA sinus at this time instant Fig. 7 Flow streamlines at time t 3 during systolic deceleration phase in the a no-stent carotid bifurcation model and b covered-stent carotid bifurcation model. Flow disturbances are present in the whole ICA sinus at this time instant. The flow recirculation at the ECA opening is vanished in the coveredstent model daughter branches, forming a stagnation line on the apex of the divider wall. As the flow accelerated to its peak (t 2 ), flow separation occurred at the CCA ICA adjoining wall due to the strong adverse pressure gradient caused by the wall curvature of the ICA bulb. This resulted in the diversion of the flow from the lateral sides into the ICA bulb forming secondary flows in this region, as shown by the flow streamlines in Fig. 6a. Similar flow patterns were observed in the covered-stent model during these time phases, except that the stagnation line on the apex of the divider wall vanished (Fig. 6b); this is because the blood which flows through the flap openings of the covered stent passes over the apex and into the ECA branch without stagnation. In the no-stent model, as the flow decelerated (t 3 ), the secondary flow region (flow recirculation zone) in the ICA bulb increased in size with more flow disturbances. A recirculation zone was observed at the ECA opening near the outer wall with partial flow reverted into the bifurcation region toward the ICA, as shown in Fig. 7a. At this instance (t 3 ), the flow field in the ICA of the covered-stent model (which is actually the zone within the covered stent) is similar to that in the no-stent model; however, the flow in the ECA (after passing through the flap openings of the covered stent) is smooth with no recirculation (Fig. 7b). Similar flow trends are observed at dicrotic notch (t 4 ) and during late diastolic deceleration (t 5 ). 3.4 Distribution of hemodynamic parameters It has been shown that (1) localized distribution of low WSS and high-oscillatory shear index (OSI) strongly correlates with the focal locations of atheroma [11], (2) large spatial WSSG contributes to the elevated wall permeability

8 172 Med Biol Eng Comput (215) 53: TAWSS (Pa) Y TAWSSG (Pa/m) Z X Z Y X Fig. 8 TAWSS distribution in the a no-stent carotid bifurcation model and b covered-stent carotid bifurcation model and atherosclerotic lesions [7], (3) combination of highshear stress and large exposure times may induce platelet activation [12, 31, 37, 38], and (4) stagnant and recirculation flow regions can cause platelet aggregation and thrombogenesis (especially for activated platelets). Hence, in this study, the distributions of hemodynamic parameters, including time-averaged WSS (TAWSS), TAWSSG [2], and OSI [11], and relative residence time (RRT) [26] are calculated according to Eqs. (5 8), respectively, and compared in the no-stent and covered-stent models. TAWSS = 1 T TAWSSG = 1 T T T τ W dt ( τx ) 2 + x T OSI = 1 τ W dt 2 1 T τ W dt ( ) 2 τy + y 1 RRT = (1 2 OSI) TAWSS = 1 1 T T τ W dt ( ) 2 τz dt z where τ W is the WSS vector (traction) and T is the time period of the flow cycle. Figure 8 shows the contour of the TAWSS distribution in the no-stent and covered-stent models. In the no-stent model (Fig. 8a), the TAWSS is low (<1 Pa) in the CCA, majority of the bifurcation region, and (<2 Pa) on the flow stagnation line on the apex of the divider wall. However, higher values of up to 3 Pa were observed on both (5) (6) (7) (8) Fig. 9 TAWSSG distribution in the a no-stent carotid bifurcation model and b covered-stent carotid bifurcation model. The TAWSSG is higher at the apex of the divider wall in the no-stent model as a result of the moving stagnation line at this location sides of the stagnation line, attributed to the fact that the flow velocity profiles are highly skewed toward the divider wall at the bifurcation [3, 39], resulting in higher velocity gradients (i.e., shear rates) at these locations. The TAWSS gradually increased in magnitude with the concomitant reduction of the lumen diameter along the ICA and ECA branches. Higher TAWSS values were recorded on the outer walls of the curvatures when compared to those along the inner walls, because the flow velocity profiles were skewed toward the outer walls of the lumen curvatures due to centrifugal forces, resulting in higher shear rates. Similar patterns of TAWSS distribution were observed in the CCA, ICA, and ECA of the covered-stent model (Fig. 8b); however, the magnitude of the TAWSS values recorded in the ICA and ECA was higher than those observed in the no-stent model. The increase of TAWSS magnitude in the ICA can be attributed to the change in the flow division between the two branches caused by the covered stent (Q ICA :Q ECA of 74:26 versus 7:3) resulting in higher flow rate in the ICA when compared to the nostent model, and the increase of TAWSS magnitude in the ECA can be attributed to the absence of the flow recirculation and reversed flow (which were observed in the no-stent model) which leads to a relatively higher forward WSS along the ECA wall in the covered-stent model. Further, the TAWSS pattern at the apex of the divider wall is different between the two models. As the flow stagnation line did not exist in the covered-stent model, the low-tawss line and its neighboring high-tawss zones, which were present in the no-stent model, were replaced by a low-tawss zone in the covered-stent model (located between the stent membrane and the apex of the divider wall). The distributions of TAWSSG are shown in Fig. 9. The TAWSSG was generally low ( 5 Pa/m) in both models

9 Med Biol Eng Comput (215) 53: Fig. 1 OSI distribution in the a no-stent carotid bifurcation model and b covered-stent carotid bifurcation model. The high-osi region at the ECA opening is vanished in the covered-stent model OSI (no stent and covered stent). However, the magnitude of the TAWSSG increased to up to 9 kpa/m at the apex of the divider wall in the no-stent model (Fig. 9a), where the vicinity of the stagnation line (low WSS) and its two neighboring high-wss regions resulted in high spatial gradients of WSS. In the covered-stent model (Fig. 9b), there were small zones with TAWSSG values of up to 3 kpa/m within the bifurcation region near the stent membrane. This can be partly attributed to the jet-alike flows through the flaps of the covered stent impinging onto the vessel wall and forming small stagnation points which result in relatively high spatial WSSG at these locations. The highest magnitude of TAWSSG in the covered-stent model was observed at the apex of the divider wall with values of 4 kpa/m. For better illustration, the contours of the OSI are shown from different angles in Fig. 1. In the no-stent model (Fig. 1a), high-osi (>.3) regions were observed on the outer walls of bifurcation, covering a considerable portion of the ICA bulb. This is because the expansion of the cross-sectional area and the wall curvatures at these locations led to flow separation and recirculation with moving vortices during the cardiac cycle, thus resulted in high OSI values. Further, higher magnitudes of OSI were recorded along the moving stagnation line at the apex of the divider wall. This could be due to the different flow directions on the lateral sides of the stagnation line and also due to the movement of the stagnation line during the cardiac cycle, which resulted in an oscillating flow at this location. However, in the covered-stent model (Fig. 1b), there was no high-osi zone outside the stented region (neither on the outer wall of the ECA nor at the apex of the divider wall). This is because the flow in this area was uniform and unidirectional with no oscillations, as observed in Figs. 6b and 7b. Although the OSI in the ICA bulb of the covered-stent model was higher than that of the no-stent model, since the ICA bulb in a stented carotid artery bifurcation would be covered with the stent membrane in the real case, the blood is not directly in contact with the vessel wall at this location and the WSS parameters are not affecting the intima. Hence, the variation of the hemodynamic parameters in this region is neither discussed nor compared between the two models in this paper. As the combination of high-shear stress (>1 Pa) and large exposure times may induce platelet activation [12, 31, 37, 38], the fluid shear through the flap openings was investigated. Bluestein et al. [1], based on experiments on platelet deposition in stenosis models, formulated a platelet activation parameter as the integral of shear stress and time. The highest fluid shear stress through the flap openings calculated over the cardiac cycle was 9.16 Pa, and the time for a blood particle to pass through the flap region was <.33 s. This resulted in a shear stress time product of <.31 Pa s, which is far below the threshold value of 3.5 Pa s suggested for procoagulant platelet factor 3 release [31], indicative of platelet activation. Hence, it is not likely

10 174 Med Biol Eng Comput (215) 53: Fig. 11 RRT distribution in the a no-stent carotid bifurcation model and b covered-stent carotid bifurcation model. The RRT distribution in the ICA bulb is similar to the two models. There is no high-rrt region on the outer wall of the ECA in the covered-stent model, due to the unidirectional flow and elimination of the flow recirculation in the ECA after deployment of the covered stent; however, a high-rrt strip is present around the ECA opening at the connection of the deployed covered stent with the arterial wall which may increase the risk of thrombogenesis at this location RRT (1/Pa) for the platelets to get activated by passing through the flap openings of the covered stent under carotid flow conditions. It has been shown that the near-wall residence time of blood particles is proportional to a combination of TAWSS and OSI [13], and a metric termed relative residence time (RRT) has accordingly been put forward to quantify that (Eq. 8) [26]. Figure 11 demonstrates the contour of RRT distribution in the no-stent and covered-stent models. In the no-stent model (Fig. 11a), regions of high residence time were observed on the outer walls of bifurcation, covering a significant part of the ICA bulb. This is due to the flow recirculation and vortices formed at these locations as shown earlier in Figs. 6 and 7, which enhance the blood particles residence time. In the covered-stent model (Fig. 11b), the RRT distribution in the ICA bulb was similar to that of the no-stent model, but different RRT patterns were observed opposite the ICA bulb. There was no high-rrt region on the outer wall of the ECA, due to the smooth unidirectional flow and elimination of the flow recirculation in the ECA after deployment of the covered stent; however, a high-rrt strip was observed around the ECA opening at the connection of the deployed covered stent with the arterial wall (on the outer side of the stent membrane). This revealed a stagnant/slow-flow region at this location downstream the stent membrane. Since stagnant and recirculation flow regions can cause platelet aggregation and thrombogenesis (especially for activated platelets), this neighboring region of the stent membrane can potentially be a thrombosis high-risk zone, especially if platelets get activated while passing through the flap openings of the membrane. 4 Discussion In the present study, the hemodynamic characteristics of a novel covered stent were thoroughly investigated by means of FSI analyses. Simulation results showed that the effect of the covered stent on the flow division between the daughter branches at the carotid artery bifurcation was comparable with the earlier experimental results [23], further demonstrating the fact that this novel covered stent can considerably preserve the ECA flow. The computational simulation results and the obtained flow streamlines provided the hemodynamic characteristics at the vicinity of the novel covered stent, shedding light on the impact of such stent on the local flow regimes. Smooth flow profiles during the systolic acceleration phase and flow disturbances during the deceleration and diastolic phases were observed in the anatomical model of carotid artery bifurcation (no stent). These flow disturbances include flow recirculation, vortices, and reversed flows in the ICA bulb and the ECA opening near the outer walls of bifurcation, and flow impingement on the vessel wall along with flow stagnation at the apex of the divider wall, that might predispose these vessel walls to atherosclerotic lesions [7], plaque formation, and intimal thickening [24, 28]. However, the flow disturbances at the apex and the ECA opening were no longer evident in the covered-stent model, because the covered stent forms a curved lumen from the CCA into the ICA which locates the functional flaps (i.e., the flow passage into the ECA) on the outer wall of this curvature. The resultant centrifugal forces caused

11 Med Biol Eng Comput (215) 53: by the altered flow pattern give rise to a pressure gradient toward the outer wall of the curvature on the inner surface of the cover membrane of the stent at the ECA opening (i.e., on the upstream surface of the functional flaps) during the cardiac cycle. In addition, the small flap openings led to a significant pressure drop through the membrane of the covered stent (about 5 times that of the no-stent case). Therefore, during the deceleration phase, the low-pressure wave from the CCA was not able to create an adverse pressure gradient across the functional flaps. These resulted in the elimination of the reversed flow and the flow recirculation (at the ECA opening of the covered-stent model) which was evident in the no-stent model during the same time phases. The absence of flow recirculation and reversal at the opening of the ECA in the covered-stent model leads to a relatively higher forward WSS along the artery wall. This altered flow patterns may help to reduce the residence time of the blood cells and the likelihood of platelet activation [17]. Significant correlations have been reported between the preferred sites of intimal thickening and the regions of slow flow recirculation with low WSS [19, 32, 34, 35], as such the observed altered flow patterns through the covered stent may be perceived as a beneficial feature of the stent, which may positively impact the post-stenting patency of the ECA branch. This conclusion has been verified by the comparison of the calculated hemodynamic parameters between the two models. As illustrated in Figs. 8 and 1, the TAWSS is lower than.3 Pa and the OSI is higher than.25 in significant areas on the outer wall of the bifurcation along the ECA in the no-stent model; however, these hemodynamic parameters have more favorable values of TAWSS >.5 Pa and OSI <.5 in the corresponding regions of the covered-stent model. The deployment of the covered stent within the CCA and ICA ensures a smoother division of flow at the apex of the divider wall that effectively eliminates the stagnation at the apex of the divider wall while retaining adequate blood flow volume through the functioning flaps into the ECA. A moving (due to the pulsatile flow) stagnation point/ line is always associated with a region of low WSS, high spatial WSSG, and high OSI, contributing to intimal thickening and atherosclerosis development and increasing the risk of the aggregation of red blood cells [7, 19, 24, 28, 32]. Hence, the absence of the flow stagnation in the coveredstent model can be considered as another positive feature of this covered stent. This finding has been further verified by the comparison of the calculated hemodynamic parameters between the two models. As shown in Figs. 8a, 9 and 1a, considerable part of the apex of the divider wall in the no-stent model experiences low TAWSS (<1.5 Pa), high TAWSSG (>8.5 kpa/m), and somewhat high values of OSI (>.2), while in the covered-stent model (Figs. 8b, 175 9, 1b) these vulnerable areas are smaller in size, and they typically experience higher TAWSS (>1.5 Pa) and lower TAWSSG (<7.3 kpa/m) and OSI (<.5) values than the no-stent model (note that these values have been obtained from the calculations and may not be discernible in the figures, due to the limited number of ranges and coloring of the contours). The investigation of the fluid shear stress through the flap openings showed a maximum shear stress value of <1 Pa and a shear stress time product of about.3 Pa s which suggest that platelet activation due to the blood flow through the flap openings is unlikely. However, some high- RRT regions around the stent membrane at the ECA opening may predispose this zone to platelet aggregation and thrombus formation. 4.1 Evaluation of methods and limitations As the focus of this investigation was on the effects of the covered stent on the flow fields and the distribution of hemodynamic parameters rather than the structural analysis of the covered stent, a small strain (large deformation) approximation of the mechanics of the polymeric membrane was utilized. The membrane of the covered stent was assumed to be isotropic and homogeneous and modeled as a linearly elastic, geometrically nonlinear shell structure [15, 3]. Our tensile test of the PU membrane showed an almost constant Young s modulus of about 1 MPa for strain values of up to.7, which justifies the assumption of linear elastic for the PU membrane in this study. Although earlier comparisons of rigid and elastic carotid wall models have shown lower WSS values in elastic models [25, 3], the main objective of this comparative study was to understand the effects of the covered stent on the flow field and distribution of hemodynamic parameters (as compared with the no-stent case). Hence, for simplicity, the artery walls were assumed to be rigid in this study. For the same reason, the non-newtonian rheology of blood was not considered in this investigation either. In this study, only the portion of the covered stent facing the ECA opening was simulated and not the part along the artery walls. This simplification is due to the fact that the covered stent flaps do not open or close when they are in apposition to the artery walls, and they only open and close when they are in the blood stream at the side branch openings. Moreover, in the evaluation of shear-induced platelet activation, only shear stress and time were considered, and variations in shear loading rates were not taken into account. Recently, more comprehensive predictive platelet activation models have been developed [33] that account for variations in shear loading rates too, to characterize blood flow through medical devices.

12 176 Med Biol Eng Comput (215) 53: Conclusions In this paper, CFD and FSI analyses of the blood flow through the polymeric membrane of a recently developed carotid covered stent have been implemented and the influence of this novel carotid covered stent on the flow regime and distribution of hemodynamic parameters has been investigated. This covered stent has been found to have some positive effects on the flow regime and distribution of hemodynamic parameters at the opening of the ECA branch and at the apex of the divider wall which can benefit the poststenting patency of the ECA. Platelet activation due to the blood flow through this covered stent seems to be unlikely. However, some slow-flow regions around the stent membrane at the ECA opening may predispose this zone to platelet aggregation and thrombus formation. This study has further demonstrated the potential of this novel covered-stent design for the treatment of carotid atherosclerotic stenosis. 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