Computers in Biology and Medicine 53 (2014) 1–8
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Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/cbm
The hemodynamic alterations induced by the vascular angular deformation in stent-assisted coiling of bifurcation aneurysms W. Jeong a, M.H. Han b, K. Rhee a,n a b
Department of Mechanical Engineering, Myongji University, San 38-2, Nam-dong, Cheoin-gu, Yongin, Gyeonggi-do, South Korea Department of Radiology, Seoul National University College of Medicine, Seoul, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 15 April 2014 Accepted 15 July 2014
The hemodynamic changes induced by stent deployment and vascular remodeling in bifurcation aneurysms were investigated using computational fluid dynamics. The stent deployment reduced the intra-aneurysmal flow activity by decreasing the mean velocity, mean kinetic energy, mean wall shear stress, and mean vorticity. These hemodynamic parameters increased with an increase in the branching angle because of the vessel deformation caused by stent straightening. The maximum wall shear stress and its spatial gradient occurred near the neck of the aneurysm in the stented left daughter vessel, whereas a maximum oscillatory shear index was detected near the neck of the right aneurysm of the right daughter vessel. Theses parameters, which might be related to the recurrence of aneurysms, were also increased by stent-induced vessel deformation. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Hemodynamics Coil Stent Computational fluid dynamics Bifurcation remodeling
1. Introduction An intracranial aneurysm is a cerebrovascular disorder in which the arterial wall weakens—resulting in localized dilation. Rupture of aneurysms causes sub-arachnoid hemorrhages, which are associated with high mortality and morbidity [1–3]. Interventional thromboembolization by endovascular insertion of coils is currently the most popular treatment to prevent the rupture of aneurysms. Thin platinum coils are inserted into the aneurysmal sac, where they form a thrombus that obliterates the aneurysm. Coil embolization of a wide neck aneurysm can be challenging and may not be effective [4] because of coil herniation. In recent years, stent-assisted coil embolization—in which the flexible stent acts as a supporting bridge to prevent herniation of aneurysm coils— has been widely used. The stent can divert flow into the aneurysmal sac and prevent coil herniation; therefore, stent-assisted coil embolization promotes the occlusion of incompletely coiled aneurysms and lowers the risk of recanalization compared with non-stenting embolization [5–9]. Various stent configurations have been used for bifurcation aneurysms [10], and deployment of a flexible stent may deform the host artery because of the mechanical interaction between stent and vessel. The bifurcation angle remodeling associated with stent placement has been
n
Corresponding author. E-mail address: [email protected] (K. Rhee).
http://dx.doi.org/10.1016/j.compbiomed.2014.07.006 0010-4825/& 2014 Elsevier Ltd. All rights reserved.
investigated in the carotid arteries [11], anterior communicating arteries [12], and intracranial arteries [13]. The immediate and delayed angular remodeling after stent deployment can affect thromboembolization efficacy and aneurysm recurrence because alterations of the vessel bifurcation geometry can alter the hemodynamics in aneurysms. Computational and experimental studies have been conducted using idealized or patient-specific models to investigate the intraaneurysmal hemodynamic changes caused by stents [10,14–21]. Meng et al. [17] and Wang et al. [21] investigated the hemodynamic alterations in idealized saccular aneurysm models—side wall and terminal aneurysm models—before and after stent placement using computational fluid dynamic (CFD) methods. Canton et al. [15] measured changes in flow dynamics using particle image velocimetry in bifurcating cerebral aneurysm models after a Neuroforms stent placement and concluded that the magnitude of the velocity of the jet entering the sac was reduced by up to 11%. Tateshima et al. [20] studied the hemodynamic effect of Neuroforms stent placement across the necks of patientspecific aneurysm models and concluded that the stents significantly altered flow velocity and flow structure in aneurysms. Tang et al. [19] studied the hemodynamic effects of aneurysm neck size after stenting and concluded that the volume flow rate of blood entering the aneurysm over the entire cardiac cycle could be reduced by 450% after the endovascular operation. Most of these studies focused on the intra-aneurysmal hemodynamic changes caused by the inserted stent; however, the hemodynamic
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alterations caused by vessel deformation after stenting—which may affect the efficacy of thromboembolization and recurrence of aneurysms—have not been studied to date. Recently, using patient-specific CFD analysis, Gao et al. [22,23] observed significant hemodynamic alterations near the neck of an intracranial bifurcation aneurysm caused by stent-induced angular remodeling. The authors virtually removed the aneurysm by using an aneurysm-capping method and showed that stent-induced angular remodeling resulted in the migration and narrowing of the flow impingement zone and a decrease in apical pressure. Given that the CFD study focused on the hemodynamic changes in completely thromboembolized aneurysms after long-term remodeling of stented aneurysms, it did not consider the deployed stent and coils inside an aneurysmal sac, which can have a significant influence on intra-aneurysmal hemodynamics. The immediate vascular remodeling caused by straightening of a stent after stent-assisted coiling treatment may affect the efficacy of thrombus formation inside the aneurysmal sac. However, the intraaneurysmal hemodynamic changes caused by vascular deformation have not been investigated. In the present study, we have modeled a deployed stent and coils inside an aneurysmal sac of the basilar bifurcation arteries, and investigated the hemodynamic changes induced by the angular deformation caused by straightening of the stent; the hemodynamic parameters in the wide neck aneurysms were computed, and the effect of bifurcation angle remodeling on the effectiveness of aneurysm embolization was discussed.
2. Methods 2.1. Aneurysm and stent modeling Two wide neck aneurysms located at the tip of a basilar arterial bifurcation were constructed using solid modeling software (SolidWorks, Dassault Systems, Concord, NH) to simulate a terminal aneurysm occurring at the tip of a basilar arterial bifurcation. The present study used 2 idealized aneurysm models. The wide neck basilar aneurysms from the patient angiograms were idealized as half-sphere aneurysms occurring at the tip of the symmetric Y-bifurcations. The aneurysm diameter, basilar artery diameter and neck width for the small and medium wide neck aneurysm model were obtained from the references [10,24]. The maximum diameters of the small and medium wide neck aneurysms were
4 mm and 8 mm, respectively, and the aspect ratios (ratio of dome height to neck width) of these models were kept constant at 0.75 (Fig. 1). The neck width (NW), dome diameter (DD), dome height (DH), and artery diameter (AD) of the small wide neck aneurysm with a maximum diameter of 4 mm measured 4 mm, 4 mm, 3 mm, and 2.7 mm, respectively. The NW, DD, DH, and AD of the medium wide neck aneurysm with a maximum diameter of 8 mm measured 8 mm, 8 mm, 6 mm, and 2.7 mm, respectively. A selfexpanding stent was assumed to be inserted into the left daughter branch of the bifurcation. The stent deployed in the left branch of the bifurcation was modeled as a mesh-like structure, where each closed cell assumed the shape of a rhombus. We modeled the closed cell stent because the stent with an open cell structure might generate the prolapse of the struts with cell opening, when it is located in a curved segment. Moreover, the sharp edges of the cell opening would generate singularities and instabilities in the computational analysis as well as require fine grids for stent modeling. Although the stent porosity might affect the hemodynamics of the aneurysms [25], the stent design (strut pattern) prevents the intra-aneurysmal flow from being noticeably affected [10,26]. The strut size was based on an intracranial self-expanding stent [27], and each cell was closed in order to facilitate strut modeling and computational stability. The stent had a length of 10 mm and an outer diameter of 2.7 mm, while the strut had a width of 0.06 mm and thickness of 0.065 mm (Fig. 1). The stent deployment inside the computational vessel model was performed using the simplified fast virtual stenting (FVS) method. Instead of analyzing the large deformation of the nitinol stent and the hyperelastic vessel using finite element methods, the simplex mesh was arranged as a virtual cylinder of 2.7 mm in diameter and aligned along the centerline of the bifurcating vessels. The stent was inserted in the cylinder and flexed, and the virtual cylinder was removed after positioning the stent in the vessel. The stent was radially expanded by manually repositioning the node points of stents outward to the vessel to account for nodes contact and smoothness. Although the mechanical properties of the stent and vessel deformability were neglected in FVS, the final configuration of the stent inside the vessel showed acceptable differences compared to the structural analysis based on FEM [28] and in vitro experiments [29]. Following insertion of the flexible coil wires into the aneurysmal sac, the randomly entangled wires formed a sponge-like volume inside the aneurysm. The intra-aneurysmal coil modeling was difficult because of the random geometry of the coils and the
Fig. 1. Bifurcation aneurysm and stent geometry. Abbreviations: AD, artery diameter; DD, dome diameter; DH, dome height; NW, neck width; and θ, branching angle. The coiled aneurysm sac is modeled as a porous domain and blood in the arteries is modeled as a fluid domain.
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large number of nodes required to model the coils in order to overcome the scale disparity between the coils and blood vessels. Therefore, the modeling required heavy computational resources and was less effective at yielding consistent computational results [30]. The intra-aneurysmal coils were assumed to have a porous structure, such as randomly-packed spheres and networks of capillaries and the aneurysm packed with platinum coils was computationally modeled as a porous medium [31–34]. A porous medium model could simulate the reduced flow within the aneurysm by inserting momentum sinks instead of modeling individual coils. The volume of the coiled aneurysmal sac was modeled as a porous zone, which consisted of approximately 150,000 and 650,000 tetrahedral elements for the small and medium wide neck aneurysms, respectively, and each element contained momentum sinks. This model might be suitable for modeling the packed coils immediately after coil insertion and before thrombus formation. The flow through the porous media depends on the permeability (k)—a measure of the fluid conductivity through the porous medium—and macroscopic properties— the porosity (φ), specific surface area (S), and tortuosity. The porosity represented the volume occupied by the pores with respect to the total volume, and the permeability represented the surface area to volume ratio. An aneurysm packed with 15 coils of 2.54 10 4 m in diameter produced a coil packing density of 26.5% or porosity of 0.735 [33]. The permeability of the porous zone was approximated as the layer of solid material with straight parallel tubes using a simplified expression based on the capillary theory of Kozeny [35]. The permeability was given as k¼
φ3 cS
ð1Þ
where c¼2 for circular cylinders. The permeability of the porous medium was estimated to be 1.54 10 8 m2 [36]. Gao et al. [13] measured the bifurcation angle before and after stent placement from the patient's angiograms. Changes in the branching angle caused by the straightening of a bifurcated vessel after stent deployment were modeled by tilting the symmetrical Y-bifurcation branch, and bifurcation angle alterations were based on data measured by using three-dimensional rotational angiography images of basilar tip arteries for 13 patients. The branching angle changed from 103.2 75.71–120.7 75.21 (Po 0.0001) after stenting. The angle between the parent artery and the left daughter branch was increased from 1001 to 1201 by straightening the stent immediately after intervention in the computational models.
2.2. Numerical methods Two bifurcation artery models were meshed into tetrahedral elements using the ICEM-CFD (ANSYS, Inc., Canonsburg, PA) program. The total number of grids was approximately 2,280,000 and 3,550,000 in the unstented and stented models, respectively. Grid dependency was determined and further refinement of the grid did not affect the converged solutions. The numerical analysis was performed using a commercial computational fluid dynamics (CFD) package (CFX, ANSYS, Inc., Canonsburg, PA) based on the finite volume method. Unsteady 3-dimensional incompressible laminar flow fields were obtained by solving the continuity and Navier–Stokes equations computationally. The coiled aneurysmal sac was modeled as a porous media zone, in which the momentum sink term (Si) was added as follows: η 1 Si ¼ ui þ C ρui jui j k 2
ð2Þ
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Fig. 2. Area mean velocity waveform at the inlet of a parent vessel.
where η is the viscosity, k is the permeability, C is the inertial resistance factor, ρ is the density, u is the velocity, and the subscript i represents the ith component of a momentum equation. A pulsatile flow waveform in the human basilar artery [37] was applied to the inlet of the parent vessel (Fig. 2). The periodic area mean velocity waveform is continuous at time 0 and 1 s, and the velocities have the same values of 0.2 m/s. Abrupt changes of the slopes at time 0 and 1 s are due to the sudden flow acceleration caused by ventricular contraction. Fully developed velocity profiles were applied at the inlet boundary, and zero pressure gradients across the normal outlet surface were applied at the outlet boundary. We assumed that the blood vessel had a rigid wall. Unsteady simulations were performed with a time step size of 0.01 s, and the solution converged after 3 flow cycles. All data were obtained as an output of the last cycle. The mean and maximum Reynolds numbers were 236 and 360, respectively, while the Womersley number was 1.86. The time-averaged mean velocity in the parent artery was 0.29 m/s. The blood density was assumed to be 1060 kg/m3. The non-Newtonian viscosity characteristics of the blood were incorporated using the Carreau model. The equation for the Carreau model was expressed as [38]: η ¼ η1 þ ðη0 η1 Þ½1 þ λ2 γ 2 ðq 1Þ=ð2Þ
ð3Þ
where the rheological parameters of human blood are η0 ¼ 0.056 Pa s, η1 ¼ 0.00345 Pa s, λ ¼3.313 s, q ¼0.356. η is the viscosity, and γ is the shear rate. Hemodynamics is a highly relevant physical factor for predicting the efficacy of thromboembolization [39,40] as well as the recurrence and regrowth of an aneurysm [41]. Thrombus formation in the early stage of coil insertion is affected by intraaneurysmal flow stasis caused by the packed coils; therefore, the intra-aneurysmal flow activity was represented by the spatial mean values of the time-averaged mean velocity (MVE) and kinetic energy (MKE) in the aneurysmal sac. The flow stasis near the aneurysm fundus was characterized by the spatial mean values of the time-averaged wall shear stress (MWS) and vorticity (MVO) in the dome region, which were defined as the half-spherical volume of an aneurysmal sac. Moreover, the oscillatory shear index (OSI), which measured the directional change of WSS during the cardiac cycle, was calculated [42] as follows: R 9 8 T 0 τw dt = 1< OSI ¼ 1 R T 2: jτw jdt ;
ð4Þ
0
where τw is the instantaneous wall shear stress and T is the cycle duration.
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3. Results The effectiveness of thromboembolization by insertion of a stent and coils was estimated by examining the reduction in intraaneurysmal flow activity. Both MVE and MKE were reduced by
insertion of a stent, which showed a flow diversion effect of a stent in the small and medium aneurysm models (Fig. 3). The percent reductions of MVE and MKE were 8.2% and 12.7%, respectively, for a small aneurysm model, and 7.9% and 13.1%, respectively, for a medium aneurysm model. The MVE and MKE increased by 6.1%
Fig. 3. Mean velocity (MV) and mean kinetic energy (MKE) inside an aneurysm sac. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle: 1001) and after deformation (branching angle: 1201), respectively. (a) MV in a small aneurysm, (b) MKE in a small aneurysm, (c) MV in a medium aneurysm, and (d) MKE in a medium aneurysm.
Fig. 4. Mean vorticity (MVO) and time-averaged wall shear stress (MWS) inside an aneurysm sac. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle: 1001) and after deformation (branching angle: 1201), respectively. (a) MWS in a small aneurysm, (b) MVO in a small aneurysm, (c) MWS in a medium aneurysm, and (d) MVO in a medium aneurysm.
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and 4.1%, respectively, for the deformed small aneurysm model and by 6.8% and 9.7%, respectively, for the deformed medium aneurysm, compared with those in the pre-deformed models. The MWS and MVO in the dome region were computed to estimate the flow stasis near the aneurysm fundus. Stent insertion decreased
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the MWS and MVO by 28.7% and 29.3%, respectively, in a small aneurysm model and by 20.1% and 25.5%, respectively, in a medium aneurysm model. The MWS and MVO increased by 21.3% and 37.8%, respectively, for a small aneurysm model and by 21.4% and 33.6%, respectively, for a medium aneurysm model,
Fig. 5. Wall shear stress (WSS) contours at peak flow. (a) A pre-deformed small aneurysm, (b) a pre-deformed small aneurysm with a stent, (c) a deformed small aneurysm with a stent, (d) a pre-deformed medium aneurysm, (e) a pre-deformed medium aneurysm with a stent, and (f) a deformed medium aneurysm with a stent.
Fig. 6. Spatially averaged time-averaged wall shear stress (MWS) in the left and right daughter vessels. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle 1001) and after deformation (branching angle 1201), respectively. (a) Spatially averaged MWS of a left daughter vessel in a small aneurysm, (b) spatially averaged MWS of a right daughter vessel in a small aneurysm, (c) spatially averaged MWS of a left daughter vessel in a medium aneurysm, and (d) spatially averaged MWS of a right daughter vessel in a medium aneurysm.
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because of the angular deformation caused by stent straightening (Fig. 4). Aneurysm recurrence is frequently observed after endovascular coil treatment [43]; moreover, elevated WSS and high spatial gradients are suspected to be related to aneurysm formation by inducing a destructive remodeling of the internal elastic lamina [44,45]. The WSS contours at peak flow are shown in Fig. 5. The maximum WSS at peak flow and the spatial gradient of WSS (WSSG) were observed near the aneurysm neck in the left daughter vessel. The maximum WSS and WSSG values were increased by 23% and 19%, respectively, as the vessel is deformed in a small aneurysm; however, they did not show a noticeable increase in a medium aneurysm. After aneurysm formation, low and oscillatory shear can lead to further aneurysmal growth because of its association with endothelium permeability changes and a deteriorating phenotype associated with inflammation [46,47]. Although the vessel wall remodeling during aneurysm
growth may be different from atherosclerotic wall remodeling [48,49], the inflammatory responses caused by low and oscillatory WSS may affect aneurysm growth and rupture via degenerative vascular wall remodeling [50]. The MWS and OSI distributions in the daughter vessels were examined. The MWS was spatially averaged over the left and right daughter vessels. Although the MWS in the left and right daughter vessels decreased slightly as the vessel deformed, the decrease was not noticeable except for the right branch of the small aneurysm bifurcation (Fig. 6). As shown in Fig. 7, the stenting and subsequent angular deformation increased the OSI in the left and right daughter vessels in the small and medium aneurysm models. The maximum OSI occurred near the distal neck of the right daughter branch. Although the stenting and angular deformation increased the maximum OSI in the small aneurysm model, the increase in the maximum OSI was not noticeably affected in the medium aneurysm by the stenting and angular deformation (Fig. 8).
Fig. 7. Oscillatory shear index (OSI) contour. (a) A pre-deformed small aneurysm, (b) a pre-deformed small aneurysm with a stent, (c) a deformed small aneurysm with a stent, (d) a pre-deformed medium aneurysm, (e) a pre-deformed medium aneurysm with a stent, and (f) a deformed medium aneurysm with a stent.
Fig. 8. Maximum oscillatory shear index (OSI) in a right daughter vessel. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle 1001) and after deformation (branching angle 1201), respectively. (a) Small aneurysm, and (b) medium aneurysm.
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4. Discussion Stent-assisted coil embolization has been successfully used in the treatment of intracranial aneurysms, and Y-stenting has been frequently used to treat wide neck aneurysms at arterial bifurcations [24]. Stent placement prevents coil protrusion into the parent artery, with the additional inflow blocking effects of the flow diversion. Once a stent is deployed inside an artery, a selfexpanding stent exerts a force that resists bending, as confirmed by the bifurcation angular changes observed during follow-up angiography [12,13]. Although the hemodynamics of completely thromboembolized aneurysms have been analyzed, the hemodynamic alterations after stent-induced vascular deformation have not been examined. In the present study, the novel intraaneurysmal hemodynamic changes occurring immediately after stent-assisted coiling were analyzed to elucidate the thromboembolization efficacy resulting from the vascular remodeling induced by a stent. The thromboembolization process involves many biochemical reaction pathways and associated biochemical factors for platelet activation and fibrin gel formation. As the hemodynamics are believed to affect thrombus formation, several studies have investigated the role of hemodynamic variables—such as the shear rate, shear stress and flow stagnation—on thromboembolization process [51,52]. Although the hemodynamics may not be the only factor affecting the thromboembolization process, it may be an important determinant of the physical environment in which the thrombus forms. The MVE, MKE, MWS, and MVO decreased in the stented aneurysms, which showed reduced flow activities caused by the flow diversion effect of the stent. These hemodynamic parameters increased in the deformed vessels. Angular remodeling caused by stent insertion may provide an unfavorable hemodynamic environment because the increased flow activity inside the coiled aneurysm should delay thrombus formation. The maximum WSS at the peak flow was observed near the neck of the aneurysm in the left daughter branch where the stent was deployed, and it increased in the deformed vessels. The maximum OSI occurred near the distal neck of the right daughter branch, which could be related to an abrupt change in flow direction in the right branch resulting from branching angle deformation. The MWS decreased and the maximum OSI increased in the daughter vessels as a result of the angular deformation; these changes were more prominent in the small aneurysm model. Because a high WSS and WSSG are suspected to be related to aneurysm formation [44,45] and a low MWS and high OSI might be correlated with aneurysm growth and rupture [46,47], angular remodeling may provide a hemodynamic environment that promotes aneurysm recurrence. The changes in the hemodynamic variables were more noticeable in the small than in the medium aneurysms. The major finding of the present study—the hemodynamic alteration caused by angular remodeling might provide an unfavorable environment for thromboembolization—contradicts the previously reported preliminary conclusions. Huang et al. [12] reported that changes in the stent-related vascular angle might reduce the secondary flow by decreasing the vessel curvature [50,53] and could promote aneurysm healing; however, this hypothesis was not confirmed because the hemodynamics were not analyzed in this study, and the decreased vessel curvature in the stented branch caused by the angular deformation was associated with an increase in the vessel curvature in the other branch. In the pioneering work of Gao et al. [23] on the hemodynamic changes associated with angular remodeling, the authors concluded that stent-induced angular remodeling significantly altered hemodynamics in a favorable direction by blunting apical pressure and causing the migration of the flow impingement zone at the bifurcation apex. Moreover, they observed a narrowing of
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the high pressure zone and movement of WSS peak bands to the bifurcation apex, which might result in the movement of the destructive remodeling vessel wall zone to the inert coil mass zone [22]. The vessel geometry from the patients' angiograms may accurately represent the vessel angular deformation caused by stenting; however, the vascular geometry near the bifurcation sites might not be realistic because the aneurysm is virtually removed. These models could represent the vessel model during long-term follow-up, when the aneurysm is completely embolized—although the hemodynamics in the aneurysm immediately after coil treatment could not be analyzed using these models. The present study had several limitations. The main limitation of the study is related to the geometry of the aneurysm models. Idealized terminal aneurysm geometries are based on the sizes of the artery and aneurysm obtained from angiograms of basilar tip aneurysms [10,24]. However, the simplified geometries in the present study may not be realistic representations of the wide neck aneurysms occurring at basilar bifurcations. Furthermore, the ideal angular deformation was assessed in the anteroposterior plane, whereas a stent might deform the bifurcated vessels in other planes. Because the aneurysm geometry can significantly affect the intra-aneurysmal hemodynamics [53,54], the CFD results for the idealized model may not be applicable to aneurysms with different geometries. However, the idealized model could separate the effects of in-plane angular geometrical changes from those of other remodeling events (vessel wall, aneurysmal sac, other planar deformation) caused by stent deployment. Although the present CFD results might not be applicable to aneurysms showing noticeably different bifurcation geometries, they could be applied to simple wide neck aneurysms with a symmetric bifurcation because the intra-aneurysmal flow is not significantly affected by the aneurysm geometry in coiled aneurysms. Patient-specific models have been used for hemodynamic analysis [33,36], and CFD analysis using aneurysm images from real patients should be performed in the future. Another limitation of the present computational study is related to the assumptions of rigid vessel walls. Although the radial wall motion inside the embolized cerebral aneurysm and bifurcated vessels was low compared with that of the large arteries [55–57], the vessel wall compliance could alter the local hemodynamics. Fluid–solid interaction algorithms could be applied to assess the effect of vessel wall elasticity on hemodynamics [58]. Moreover, bending and compression of the vessel wall caused by stent deployment may increase stress and affect the vessel wall function, which are related to the recurrence of an aneurysm; however, these factors were not examined in the present study. Finite element methods have been used to analyze the stress in stents and vessel walls and to simulate stent deployment and vessel deformation [59–61]. Moreover, the effects of the branching angle on hemodynamic changes for various bifurcating angles and asymmetry would be interesting. Although these analyses should provide insight into the physics of stented arteries, they are beyond the scope of this study. Despite these limitations and the assumptions adopted in the present study, the computational analysis suggests that the vessel deformation after stent-assisted coil intervention results in novel hemodynamic changes.
5. Summary Stent-assisted coil embolization is used for the treatment of wide neck aneurysms to prevent coil herniation into the parent arteries. A self-expanding stent causes immediate and delayed angular remodeling of the arteries, which may affect thromboembolization efficacy and aneurysm recurrence. Computational flow dynamics analysis was performed using coiled basilar tip
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aneurysm models to elucidate the hemodynamic alterations caused by stenting and stent-induced vessel deformation. The hemodynamic parameters characterizing intra-aneurysmal flow activity—the mean velocity, mean kinetic energy, mean wall shear stress, and mean vorticity—decreased after stenting, which showed the flow diversion effect of a stent. Moreover, the hemodynamic parameters increased as the branching angle increased because of the vessel deformation caused by stent straightening. The maximum wall shear stress and its spatial gradient were observed near the neck of the left daughter vessel, whereas the maximum oscillatory shear index occurred near the neck of the right daughter vessel; moreover, these parameters increased following vessel deformation. The vessel deformation induced by stenting increased the intra-aneurysmal flow activity and localized high and oscillatory shear stress near the aneurysm neck, which might provide an unfavorable hemodynamic environment for thrombus formation and ultimately prevent the recurrence of aneurysms. Conflict of interest statement None Source of funding The present study was supported by the 2014 Research Fund at Myongji University. Ethical Approval: No human subjects were involved in the present study. Acknowledgment This work was supported by 2014 Research Fund of Myongji University. References [1] M. Kaminogo, M. Yonekura, S. Shibata, Stroke 34 (2003) 16–21. [2] F. Linn, G. Rinkel, A. Algra, J. Van Gijn, Stroke 27 (1996) 625–629. [3] H.R. Winn, J.A. Jane, J. Taylor, D. Kaiser, G.W. Britz, J. Neurosurg. 96 (2002) 43–49. [4] M. Hayakawa, Y. Murayama, G.R. Duckwiler, Y.P. Gobin, G. Guglielmi, F. Viñuela, J. Neurosurg. 93 (2000) 561–568. [5] N. Chalouhi, P. Jabbour, L.F. Gonzalez, A.S. Dumont, R. Rosenwasser, R.M. Starke, D. Gordon, S. Hann, S. Tjoumakaris, Neurosurgery 71 (2012) 785–794. [6] B. Izar, A. Rai, K. Raghuram, J. Rotruck, J. Carpenter, PloS One 6 (2011) e24875. [7] M.F. Lawson, W.C. Newman, Y.-Y. Chi, J. Mocco, B.L. Hoh, Neurosurgery 69 (2011) 598–604. [8] M. Piotin, R. Blanc, L. Spelle, C. Mounayer, R. Piantino, P.J. Schmidt, J. Moret, Stroke 41 (2010) 110–115. [9] A. Wakhloo, I. Linfante, C. Silva, E. Samaniego, G. Dabus, V. Etezadi, G. Spilberg, M. Gounis, Am. J. Neuroradiol. 33 (2012) 1651–1656. [10] M.H. Babiker, L.F. Gonzalez, J. Ryan, F. Albuquerque, D. Collins, A. Elvikis, D.H. Frakes, J. Biomech. 45 (2012) 440–447. [11] J. Berkefeld, J. Martin, J. Théron, F. Zanella, L. Guimaraens, M. Treggiari-Venzi, H. Rosendahl, D. Rüfenacht, Neuroradiology 44 (2002) 67–76. [12] Q.-H. Huang, Y.-F. Wu, Y. Xu, B. Hong, L. Zhang, J.-M. Liu, Am. J. Neuroradiol. 32 (2011) 1721–1725. [13] B. Gao, M. Baharoglu, A. Cohen, A. Malek, Am. J. Neuroradiol. 33 (2012) 649–654. [14] S. Appanaboyina, F. Mut, R. Löhner, E. Scrivano, C. Miranda, P. Lylyk, C. Putman, J. Cebral, Int. J. Comput. Fluid Dyn. 22 (2008) 669–676. [15] G. Cantón, D.I. Levy, J.C. Lasheras, J. Neurosurg. 103 (2005) 146–155. [16] F. Dorn, F. Niedermeyer, A. Balasso, D. Liepsch, T. Liebig, Neuroradiology 53 (2011) 267–272.
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Contents lists available at ScienceDirect
Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/cbm
The hemodynamic alterations induced by the vascular angular deformation in stent-assisted coiling of bifurcation aneurysms W. Jeong a, M.H. Han b, K. Rhee a,n a b
Department of Mechanical Engineering, Myongji University, San 38-2, Nam-dong, Cheoin-gu, Yongin, Gyeonggi-do, South Korea Department of Radiology, Seoul National University College of Medicine, Seoul, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 15 April 2014 Accepted 15 July 2014
The hemodynamic changes induced by stent deployment and vascular remodeling in bifurcation aneurysms were investigated using computational fluid dynamics. The stent deployment reduced the intra-aneurysmal flow activity by decreasing the mean velocity, mean kinetic energy, mean wall shear stress, and mean vorticity. These hemodynamic parameters increased with an increase in the branching angle because of the vessel deformation caused by stent straightening. The maximum wall shear stress and its spatial gradient occurred near the neck of the aneurysm in the stented left daughter vessel, whereas a maximum oscillatory shear index was detected near the neck of the right aneurysm of the right daughter vessel. Theses parameters, which might be related to the recurrence of aneurysms, were also increased by stent-induced vessel deformation. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Hemodynamics Coil Stent Computational fluid dynamics Bifurcation remodeling
1. Introduction An intracranial aneurysm is a cerebrovascular disorder in which the arterial wall weakens—resulting in localized dilation. Rupture of aneurysms causes sub-arachnoid hemorrhages, which are associated with high mortality and morbidity [1–3]. Interventional thromboembolization by endovascular insertion of coils is currently the most popular treatment to prevent the rupture of aneurysms. Thin platinum coils are inserted into the aneurysmal sac, where they form a thrombus that obliterates the aneurysm. Coil embolization of a wide neck aneurysm can be challenging and may not be effective [4] because of coil herniation. In recent years, stent-assisted coil embolization—in which the flexible stent acts as a supporting bridge to prevent herniation of aneurysm coils— has been widely used. The stent can divert flow into the aneurysmal sac and prevent coil herniation; therefore, stent-assisted coil embolization promotes the occlusion of incompletely coiled aneurysms and lowers the risk of recanalization compared with non-stenting embolization [5–9]. Various stent configurations have been used for bifurcation aneurysms [10], and deployment of a flexible stent may deform the host artery because of the mechanical interaction between stent and vessel. The bifurcation angle remodeling associated with stent placement has been
n
Corresponding author. E-mail address: [email protected] (K. Rhee).
http://dx.doi.org/10.1016/j.compbiomed.2014.07.006 0010-4825/& 2014 Elsevier Ltd. All rights reserved.
investigated in the carotid arteries [11], anterior communicating arteries [12], and intracranial arteries [13]. The immediate and delayed angular remodeling after stent deployment can affect thromboembolization efficacy and aneurysm recurrence because alterations of the vessel bifurcation geometry can alter the hemodynamics in aneurysms. Computational and experimental studies have been conducted using idealized or patient-specific models to investigate the intraaneurysmal hemodynamic changes caused by stents [10,14–21]. Meng et al. [17] and Wang et al. [21] investigated the hemodynamic alterations in idealized saccular aneurysm models—side wall and terminal aneurysm models—before and after stent placement using computational fluid dynamic (CFD) methods. Canton et al. [15] measured changes in flow dynamics using particle image velocimetry in bifurcating cerebral aneurysm models after a Neuroforms stent placement and concluded that the magnitude of the velocity of the jet entering the sac was reduced by up to 11%. Tateshima et al. [20] studied the hemodynamic effect of Neuroforms stent placement across the necks of patientspecific aneurysm models and concluded that the stents significantly altered flow velocity and flow structure in aneurysms. Tang et al. [19] studied the hemodynamic effects of aneurysm neck size after stenting and concluded that the volume flow rate of blood entering the aneurysm over the entire cardiac cycle could be reduced by 450% after the endovascular operation. Most of these studies focused on the intra-aneurysmal hemodynamic changes caused by the inserted stent; however, the hemodynamic
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alterations caused by vessel deformation after stenting—which may affect the efficacy of thromboembolization and recurrence of aneurysms—have not been studied to date. Recently, using patient-specific CFD analysis, Gao et al. [22,23] observed significant hemodynamic alterations near the neck of an intracranial bifurcation aneurysm caused by stent-induced angular remodeling. The authors virtually removed the aneurysm by using an aneurysm-capping method and showed that stent-induced angular remodeling resulted in the migration and narrowing of the flow impingement zone and a decrease in apical pressure. Given that the CFD study focused on the hemodynamic changes in completely thromboembolized aneurysms after long-term remodeling of stented aneurysms, it did not consider the deployed stent and coils inside an aneurysmal sac, which can have a significant influence on intra-aneurysmal hemodynamics. The immediate vascular remodeling caused by straightening of a stent after stent-assisted coiling treatment may affect the efficacy of thrombus formation inside the aneurysmal sac. However, the intraaneurysmal hemodynamic changes caused by vascular deformation have not been investigated. In the present study, we have modeled a deployed stent and coils inside an aneurysmal sac of the basilar bifurcation arteries, and investigated the hemodynamic changes induced by the angular deformation caused by straightening of the stent; the hemodynamic parameters in the wide neck aneurysms were computed, and the effect of bifurcation angle remodeling on the effectiveness of aneurysm embolization was discussed.
2. Methods 2.1. Aneurysm and stent modeling Two wide neck aneurysms located at the tip of a basilar arterial bifurcation were constructed using solid modeling software (SolidWorks, Dassault Systems, Concord, NH) to simulate a terminal aneurysm occurring at the tip of a basilar arterial bifurcation. The present study used 2 idealized aneurysm models. The wide neck basilar aneurysms from the patient angiograms were idealized as half-sphere aneurysms occurring at the tip of the symmetric Y-bifurcations. The aneurysm diameter, basilar artery diameter and neck width for the small and medium wide neck aneurysm model were obtained from the references [10,24]. The maximum diameters of the small and medium wide neck aneurysms were
4 mm and 8 mm, respectively, and the aspect ratios (ratio of dome height to neck width) of these models were kept constant at 0.75 (Fig. 1). The neck width (NW), dome diameter (DD), dome height (DH), and artery diameter (AD) of the small wide neck aneurysm with a maximum diameter of 4 mm measured 4 mm, 4 mm, 3 mm, and 2.7 mm, respectively. The NW, DD, DH, and AD of the medium wide neck aneurysm with a maximum diameter of 8 mm measured 8 mm, 8 mm, 6 mm, and 2.7 mm, respectively. A selfexpanding stent was assumed to be inserted into the left daughter branch of the bifurcation. The stent deployed in the left branch of the bifurcation was modeled as a mesh-like structure, where each closed cell assumed the shape of a rhombus. We modeled the closed cell stent because the stent with an open cell structure might generate the prolapse of the struts with cell opening, when it is located in a curved segment. Moreover, the sharp edges of the cell opening would generate singularities and instabilities in the computational analysis as well as require fine grids for stent modeling. Although the stent porosity might affect the hemodynamics of the aneurysms [25], the stent design (strut pattern) prevents the intra-aneurysmal flow from being noticeably affected [10,26]. The strut size was based on an intracranial self-expanding stent [27], and each cell was closed in order to facilitate strut modeling and computational stability. The stent had a length of 10 mm and an outer diameter of 2.7 mm, while the strut had a width of 0.06 mm and thickness of 0.065 mm (Fig. 1). The stent deployment inside the computational vessel model was performed using the simplified fast virtual stenting (FVS) method. Instead of analyzing the large deformation of the nitinol stent and the hyperelastic vessel using finite element methods, the simplex mesh was arranged as a virtual cylinder of 2.7 mm in diameter and aligned along the centerline of the bifurcating vessels. The stent was inserted in the cylinder and flexed, and the virtual cylinder was removed after positioning the stent in the vessel. The stent was radially expanded by manually repositioning the node points of stents outward to the vessel to account for nodes contact and smoothness. Although the mechanical properties of the stent and vessel deformability were neglected in FVS, the final configuration of the stent inside the vessel showed acceptable differences compared to the structural analysis based on FEM [28] and in vitro experiments [29]. Following insertion of the flexible coil wires into the aneurysmal sac, the randomly entangled wires formed a sponge-like volume inside the aneurysm. The intra-aneurysmal coil modeling was difficult because of the random geometry of the coils and the
Fig. 1. Bifurcation aneurysm and stent geometry. Abbreviations: AD, artery diameter; DD, dome diameter; DH, dome height; NW, neck width; and θ, branching angle. The coiled aneurysm sac is modeled as a porous domain and blood in the arteries is modeled as a fluid domain.
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large number of nodes required to model the coils in order to overcome the scale disparity between the coils and blood vessels. Therefore, the modeling required heavy computational resources and was less effective at yielding consistent computational results [30]. The intra-aneurysmal coils were assumed to have a porous structure, such as randomly-packed spheres and networks of capillaries and the aneurysm packed with platinum coils was computationally modeled as a porous medium [31–34]. A porous medium model could simulate the reduced flow within the aneurysm by inserting momentum sinks instead of modeling individual coils. The volume of the coiled aneurysmal sac was modeled as a porous zone, which consisted of approximately 150,000 and 650,000 tetrahedral elements for the small and medium wide neck aneurysms, respectively, and each element contained momentum sinks. This model might be suitable for modeling the packed coils immediately after coil insertion and before thrombus formation. The flow through the porous media depends on the permeability (k)—a measure of the fluid conductivity through the porous medium—and macroscopic properties— the porosity (φ), specific surface area (S), and tortuosity. The porosity represented the volume occupied by the pores with respect to the total volume, and the permeability represented the surface area to volume ratio. An aneurysm packed with 15 coils of 2.54 10 4 m in diameter produced a coil packing density of 26.5% or porosity of 0.735 [33]. The permeability of the porous zone was approximated as the layer of solid material with straight parallel tubes using a simplified expression based on the capillary theory of Kozeny [35]. The permeability was given as k¼
φ3 cS
ð1Þ
where c¼2 for circular cylinders. The permeability of the porous medium was estimated to be 1.54 10 8 m2 [36]. Gao et al. [13] measured the bifurcation angle before and after stent placement from the patient's angiograms. Changes in the branching angle caused by the straightening of a bifurcated vessel after stent deployment were modeled by tilting the symmetrical Y-bifurcation branch, and bifurcation angle alterations were based on data measured by using three-dimensional rotational angiography images of basilar tip arteries for 13 patients. The branching angle changed from 103.2 75.71–120.7 75.21 (Po 0.0001) after stenting. The angle between the parent artery and the left daughter branch was increased from 1001 to 1201 by straightening the stent immediately after intervention in the computational models.
2.2. Numerical methods Two bifurcation artery models were meshed into tetrahedral elements using the ICEM-CFD (ANSYS, Inc., Canonsburg, PA) program. The total number of grids was approximately 2,280,000 and 3,550,000 in the unstented and stented models, respectively. Grid dependency was determined and further refinement of the grid did not affect the converged solutions. The numerical analysis was performed using a commercial computational fluid dynamics (CFD) package (CFX, ANSYS, Inc., Canonsburg, PA) based on the finite volume method. Unsteady 3-dimensional incompressible laminar flow fields were obtained by solving the continuity and Navier–Stokes equations computationally. The coiled aneurysmal sac was modeled as a porous media zone, in which the momentum sink term (Si) was added as follows: η 1 Si ¼ ui þ C ρui jui j k 2
ð2Þ
3
Fig. 2. Area mean velocity waveform at the inlet of a parent vessel.
where η is the viscosity, k is the permeability, C is the inertial resistance factor, ρ is the density, u is the velocity, and the subscript i represents the ith component of a momentum equation. A pulsatile flow waveform in the human basilar artery [37] was applied to the inlet of the parent vessel (Fig. 2). The periodic area mean velocity waveform is continuous at time 0 and 1 s, and the velocities have the same values of 0.2 m/s. Abrupt changes of the slopes at time 0 and 1 s are due to the sudden flow acceleration caused by ventricular contraction. Fully developed velocity profiles were applied at the inlet boundary, and zero pressure gradients across the normal outlet surface were applied at the outlet boundary. We assumed that the blood vessel had a rigid wall. Unsteady simulations were performed with a time step size of 0.01 s, and the solution converged after 3 flow cycles. All data were obtained as an output of the last cycle. The mean and maximum Reynolds numbers were 236 and 360, respectively, while the Womersley number was 1.86. The time-averaged mean velocity in the parent artery was 0.29 m/s. The blood density was assumed to be 1060 kg/m3. The non-Newtonian viscosity characteristics of the blood were incorporated using the Carreau model. The equation for the Carreau model was expressed as [38]: η ¼ η1 þ ðη0 η1 Þ½1 þ λ2 γ 2 ðq 1Þ=ð2Þ
ð3Þ
where the rheological parameters of human blood are η0 ¼ 0.056 Pa s, η1 ¼ 0.00345 Pa s, λ ¼3.313 s, q ¼0.356. η is the viscosity, and γ is the shear rate. Hemodynamics is a highly relevant physical factor for predicting the efficacy of thromboembolization [39,40] as well as the recurrence and regrowth of an aneurysm [41]. Thrombus formation in the early stage of coil insertion is affected by intraaneurysmal flow stasis caused by the packed coils; therefore, the intra-aneurysmal flow activity was represented by the spatial mean values of the time-averaged mean velocity (MVE) and kinetic energy (MKE) in the aneurysmal sac. The flow stasis near the aneurysm fundus was characterized by the spatial mean values of the time-averaged wall shear stress (MWS) and vorticity (MVO) in the dome region, which were defined as the half-spherical volume of an aneurysmal sac. Moreover, the oscillatory shear index (OSI), which measured the directional change of WSS during the cardiac cycle, was calculated [42] as follows: R 9 8 T 0 τw dt = 1< OSI ¼ 1 R T 2: jτw jdt ;
ð4Þ
0
where τw is the instantaneous wall shear stress and T is the cycle duration.
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3. Results The effectiveness of thromboembolization by insertion of a stent and coils was estimated by examining the reduction in intraaneurysmal flow activity. Both MVE and MKE were reduced by
insertion of a stent, which showed a flow diversion effect of a stent in the small and medium aneurysm models (Fig. 3). The percent reductions of MVE and MKE were 8.2% and 12.7%, respectively, for a small aneurysm model, and 7.9% and 13.1%, respectively, for a medium aneurysm model. The MVE and MKE increased by 6.1%
Fig. 3. Mean velocity (MV) and mean kinetic energy (MKE) inside an aneurysm sac. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle: 1001) and after deformation (branching angle: 1201), respectively. (a) MV in a small aneurysm, (b) MKE in a small aneurysm, (c) MV in a medium aneurysm, and (d) MKE in a medium aneurysm.
Fig. 4. Mean vorticity (MVO) and time-averaged wall shear stress (MWS) inside an aneurysm sac. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle: 1001) and after deformation (branching angle: 1201), respectively. (a) MWS in a small aneurysm, (b) MVO in a small aneurysm, (c) MWS in a medium aneurysm, and (d) MVO in a medium aneurysm.
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and 4.1%, respectively, for the deformed small aneurysm model and by 6.8% and 9.7%, respectively, for the deformed medium aneurysm, compared with those in the pre-deformed models. The MWS and MVO in the dome region were computed to estimate the flow stasis near the aneurysm fundus. Stent insertion decreased
5
the MWS and MVO by 28.7% and 29.3%, respectively, in a small aneurysm model and by 20.1% and 25.5%, respectively, in a medium aneurysm model. The MWS and MVO increased by 21.3% and 37.8%, respectively, for a small aneurysm model and by 21.4% and 33.6%, respectively, for a medium aneurysm model,
Fig. 5. Wall shear stress (WSS) contours at peak flow. (a) A pre-deformed small aneurysm, (b) a pre-deformed small aneurysm with a stent, (c) a deformed small aneurysm with a stent, (d) a pre-deformed medium aneurysm, (e) a pre-deformed medium aneurysm with a stent, and (f) a deformed medium aneurysm with a stent.
Fig. 6. Spatially averaged time-averaged wall shear stress (MWS) in the left and right daughter vessels. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle 1001) and after deformation (branching angle 1201), respectively. (a) Spatially averaged MWS of a left daughter vessel in a small aneurysm, (b) spatially averaged MWS of a right daughter vessel in a small aneurysm, (c) spatially averaged MWS of a left daughter vessel in a medium aneurysm, and (d) spatially averaged MWS of a right daughter vessel in a medium aneurysm.
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because of the angular deformation caused by stent straightening (Fig. 4). Aneurysm recurrence is frequently observed after endovascular coil treatment [43]; moreover, elevated WSS and high spatial gradients are suspected to be related to aneurysm formation by inducing a destructive remodeling of the internal elastic lamina [44,45]. The WSS contours at peak flow are shown in Fig. 5. The maximum WSS at peak flow and the spatial gradient of WSS (WSSG) were observed near the aneurysm neck in the left daughter vessel. The maximum WSS and WSSG values were increased by 23% and 19%, respectively, as the vessel is deformed in a small aneurysm; however, they did not show a noticeable increase in a medium aneurysm. After aneurysm formation, low and oscillatory shear can lead to further aneurysmal growth because of its association with endothelium permeability changes and a deteriorating phenotype associated with inflammation [46,47]. Although the vessel wall remodeling during aneurysm
growth may be different from atherosclerotic wall remodeling [48,49], the inflammatory responses caused by low and oscillatory WSS may affect aneurysm growth and rupture via degenerative vascular wall remodeling [50]. The MWS and OSI distributions in the daughter vessels were examined. The MWS was spatially averaged over the left and right daughter vessels. Although the MWS in the left and right daughter vessels decreased slightly as the vessel deformed, the decrease was not noticeable except for the right branch of the small aneurysm bifurcation (Fig. 6). As shown in Fig. 7, the stenting and subsequent angular deformation increased the OSI in the left and right daughter vessels in the small and medium aneurysm models. The maximum OSI occurred near the distal neck of the right daughter branch. Although the stenting and angular deformation increased the maximum OSI in the small aneurysm model, the increase in the maximum OSI was not noticeably affected in the medium aneurysm by the stenting and angular deformation (Fig. 8).
Fig. 7. Oscillatory shear index (OSI) contour. (a) A pre-deformed small aneurysm, (b) a pre-deformed small aneurysm with a stent, (c) a deformed small aneurysm with a stent, (d) a pre-deformed medium aneurysm, (e) a pre-deformed medium aneurysm with a stent, and (f) a deformed medium aneurysm with a stent.
Fig. 8. Maximum oscillatory shear index (OSI) in a right daughter vessel. SAneu and MAneu denote a small and medium aneurysm, _St denotes a stented vessel, and _100 and _120 denote bifurcation before deformation (branching angle 1001) and after deformation (branching angle 1201), respectively. (a) Small aneurysm, and (b) medium aneurysm.
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4. Discussion Stent-assisted coil embolization has been successfully used in the treatment of intracranial aneurysms, and Y-stenting has been frequently used to treat wide neck aneurysms at arterial bifurcations [24]. Stent placement prevents coil protrusion into the parent artery, with the additional inflow blocking effects of the flow diversion. Once a stent is deployed inside an artery, a selfexpanding stent exerts a force that resists bending, as confirmed by the bifurcation angular changes observed during follow-up angiography [12,13]. Although the hemodynamics of completely thromboembolized aneurysms have been analyzed, the hemodynamic alterations after stent-induced vascular deformation have not been examined. In the present study, the novel intraaneurysmal hemodynamic changes occurring immediately after stent-assisted coiling were analyzed to elucidate the thromboembolization efficacy resulting from the vascular remodeling induced by a stent. The thromboembolization process involves many biochemical reaction pathways and associated biochemical factors for platelet activation and fibrin gel formation. As the hemodynamics are believed to affect thrombus formation, several studies have investigated the role of hemodynamic variables—such as the shear rate, shear stress and flow stagnation—on thromboembolization process [51,52]. Although the hemodynamics may not be the only factor affecting the thromboembolization process, it may be an important determinant of the physical environment in which the thrombus forms. The MVE, MKE, MWS, and MVO decreased in the stented aneurysms, which showed reduced flow activities caused by the flow diversion effect of the stent. These hemodynamic parameters increased in the deformed vessels. Angular remodeling caused by stent insertion may provide an unfavorable hemodynamic environment because the increased flow activity inside the coiled aneurysm should delay thrombus formation. The maximum WSS at the peak flow was observed near the neck of the aneurysm in the left daughter branch where the stent was deployed, and it increased in the deformed vessels. The maximum OSI occurred near the distal neck of the right daughter branch, which could be related to an abrupt change in flow direction in the right branch resulting from branching angle deformation. The MWS decreased and the maximum OSI increased in the daughter vessels as a result of the angular deformation; these changes were more prominent in the small aneurysm model. Because a high WSS and WSSG are suspected to be related to aneurysm formation [44,45] and a low MWS and high OSI might be correlated with aneurysm growth and rupture [46,47], angular remodeling may provide a hemodynamic environment that promotes aneurysm recurrence. The changes in the hemodynamic variables were more noticeable in the small than in the medium aneurysms. The major finding of the present study—the hemodynamic alteration caused by angular remodeling might provide an unfavorable environment for thromboembolization—contradicts the previously reported preliminary conclusions. Huang et al. [12] reported that changes in the stent-related vascular angle might reduce the secondary flow by decreasing the vessel curvature [50,53] and could promote aneurysm healing; however, this hypothesis was not confirmed because the hemodynamics were not analyzed in this study, and the decreased vessel curvature in the stented branch caused by the angular deformation was associated with an increase in the vessel curvature in the other branch. In the pioneering work of Gao et al. [23] on the hemodynamic changes associated with angular remodeling, the authors concluded that stent-induced angular remodeling significantly altered hemodynamics in a favorable direction by blunting apical pressure and causing the migration of the flow impingement zone at the bifurcation apex. Moreover, they observed a narrowing of
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the high pressure zone and movement of WSS peak bands to the bifurcation apex, which might result in the movement of the destructive remodeling vessel wall zone to the inert coil mass zone [22]. The vessel geometry from the patients' angiograms may accurately represent the vessel angular deformation caused by stenting; however, the vascular geometry near the bifurcation sites might not be realistic because the aneurysm is virtually removed. These models could represent the vessel model during long-term follow-up, when the aneurysm is completely embolized—although the hemodynamics in the aneurysm immediately after coil treatment could not be analyzed using these models. The present study had several limitations. The main limitation of the study is related to the geometry of the aneurysm models. Idealized terminal aneurysm geometries are based on the sizes of the artery and aneurysm obtained from angiograms of basilar tip aneurysms [10,24]. However, the simplified geometries in the present study may not be realistic representations of the wide neck aneurysms occurring at basilar bifurcations. Furthermore, the ideal angular deformation was assessed in the anteroposterior plane, whereas a stent might deform the bifurcated vessels in other planes. Because the aneurysm geometry can significantly affect the intra-aneurysmal hemodynamics [53,54], the CFD results for the idealized model may not be applicable to aneurysms with different geometries. However, the idealized model could separate the effects of in-plane angular geometrical changes from those of other remodeling events (vessel wall, aneurysmal sac, other planar deformation) caused by stent deployment. Although the present CFD results might not be applicable to aneurysms showing noticeably different bifurcation geometries, they could be applied to simple wide neck aneurysms with a symmetric bifurcation because the intra-aneurysmal flow is not significantly affected by the aneurysm geometry in coiled aneurysms. Patient-specific models have been used for hemodynamic analysis [33,36], and CFD analysis using aneurysm images from real patients should be performed in the future. Another limitation of the present computational study is related to the assumptions of rigid vessel walls. Although the radial wall motion inside the embolized cerebral aneurysm and bifurcated vessels was low compared with that of the large arteries [55–57], the vessel wall compliance could alter the local hemodynamics. Fluid–solid interaction algorithms could be applied to assess the effect of vessel wall elasticity on hemodynamics [58]. Moreover, bending and compression of the vessel wall caused by stent deployment may increase stress and affect the vessel wall function, which are related to the recurrence of an aneurysm; however, these factors were not examined in the present study. Finite element methods have been used to analyze the stress in stents and vessel walls and to simulate stent deployment and vessel deformation [59–61]. Moreover, the effects of the branching angle on hemodynamic changes for various bifurcating angles and asymmetry would be interesting. Although these analyses should provide insight into the physics of stented arteries, they are beyond the scope of this study. Despite these limitations and the assumptions adopted in the present study, the computational analysis suggests that the vessel deformation after stent-assisted coil intervention results in novel hemodynamic changes.
5. Summary Stent-assisted coil embolization is used for the treatment of wide neck aneurysms to prevent coil herniation into the parent arteries. A self-expanding stent causes immediate and delayed angular remodeling of the arteries, which may affect thromboembolization efficacy and aneurysm recurrence. Computational flow dynamics analysis was performed using coiled basilar tip
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aneurysm models to elucidate the hemodynamic alterations caused by stenting and stent-induced vessel deformation. The hemodynamic parameters characterizing intra-aneurysmal flow activity—the mean velocity, mean kinetic energy, mean wall shear stress, and mean vorticity—decreased after stenting, which showed the flow diversion effect of a stent. Moreover, the hemodynamic parameters increased as the branching angle increased because of the vessel deformation caused by stent straightening. The maximum wall shear stress and its spatial gradient were observed near the neck of the left daughter vessel, whereas the maximum oscillatory shear index occurred near the neck of the right daughter vessel; moreover, these parameters increased following vessel deformation. The vessel deformation induced by stenting increased the intra-aneurysmal flow activity and localized high and oscillatory shear stress near the aneurysm neck, which might provide an unfavorable hemodynamic environment for thrombus formation and ultimately prevent the recurrence of aneurysms. Conflict of interest statement None Source of funding The present study was supported by the 2014 Research Fund at Myongji University. Ethical Approval: No human subjects were involved in the present study. Acknowledgment This work was supported by 2014 Research Fund of Myongji University. References [1] M. Kaminogo, M. Yonekura, S. Shibata, Stroke 34 (2003) 16–21. [2] F. Linn, G. Rinkel, A. Algra, J. Van Gijn, Stroke 27 (1996) 625–629. [3] H.R. Winn, J.A. Jane, J. Taylor, D. Kaiser, G.W. Britz, J. Neurosurg. 96 (2002) 43–49. [4] M. Hayakawa, Y. Murayama, G.R. Duckwiler, Y.P. Gobin, G. Guglielmi, F. Viñuela, J. Neurosurg. 93 (2000) 561–568. [5] N. Chalouhi, P. Jabbour, L.F. Gonzalez, A.S. Dumont, R. Rosenwasser, R.M. Starke, D. Gordon, S. Hann, S. Tjoumakaris, Neurosurgery 71 (2012) 785–794. [6] B. Izar, A. Rai, K. Raghuram, J. Rotruck, J. Carpenter, PloS One 6 (2011) e24875. [7] M.F. Lawson, W.C. Newman, Y.-Y. Chi, J. Mocco, B.L. Hoh, Neurosurgery 69 (2011) 598–604. [8] M. Piotin, R. Blanc, L. Spelle, C. Mounayer, R. Piantino, P.J. Schmidt, J. Moret, Stroke 41 (2010) 110–115. [9] A. Wakhloo, I. Linfante, C. Silva, E. Samaniego, G. Dabus, V. Etezadi, G. Spilberg, M. Gounis, Am. J. Neuroradiol. 33 (2012) 1651–1656. [10] M.H. Babiker, L.F. Gonzalez, J. Ryan, F. Albuquerque, D. Collins, A. Elvikis, D.H. Frakes, J. Biomech. 45 (2012) 440–447. [11] J. Berkefeld, J. Martin, J. Théron, F. Zanella, L. Guimaraens, M. Treggiari-Venzi, H. Rosendahl, D. Rüfenacht, Neuroradiology 44 (2002) 67–76. [12] Q.-H. Huang, Y.-F. Wu, Y. Xu, B. Hong, L. Zhang, J.-M. Liu, Am. J. Neuroradiol. 32 (2011) 1721–1725. [13] B. Gao, M. Baharoglu, A. Cohen, A. Malek, Am. J. Neuroradiol. 33 (2012) 649–654. [14] S. Appanaboyina, F. Mut, R. Löhner, E. Scrivano, C. Miranda, P. Lylyk, C. Putman, J. Cebral, Int. J. Comput. Fluid Dyn. 22 (2008) 669–676. [15] G. Cantón, D.I. Levy, J.C. Lasheras, J. Neurosurg. 103 (2005) 146–155. [16] F. Dorn, F. Niedermeyer, A. Balasso, D. Liepsch, T. Liebig, Neuroradiology 53 (2011) 267–272.
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