Technology and Health Care 23 (2015) 9–21 DOI 10.3233/THC-140871 IOS Press
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Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm Futoshi Moria,b,∗, Makoto Ohtac and Teruo Matsuzawad a Interfaculty
Initiative in Information Studies, The University of Tokyo, Tokyo, Japan Research Institute, The University of Tokyo, Tokyo, Japan c Institute of Fluid Science, Tohoku-University, Sendai, Japan d Research Center for Simulation Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan b Earthquake
Received 1 September 2014 Accepted 19 October 2014 Abstract. BACKGROUND: Stent placement is thought to obstruct the inflow of blood to an aneurysm. However, we introduced parent artery expansion and demonstrated that this may reduce the blood flow by the stent. In our previous study using idealized shapes, the results showed that flow reduction was greater than 22.2%, even if the expansion rate was only 6%. Furthermore, the parent artery expansion is predominantly caused by the effect of flow reduction as compared to that of flow reduction due to the obstruction of flow under stent placement. However, a realistic shape is complex and the blood flow also becomes complex flow. It is not understood whether the results of flow in the idealized shape are reflective of flow from a realistic 3D model. Therefore, we examined the effect of parent artery expansion using a realistic model. OBJECTIVE: The aim is to clarify the effects of parent artery expansion on inflow rate, wall shear stress, and oscillatory shear index. METHODS: We used a patient-specific geometry of a human internal carotid artery with an aneurysm. The geometry of parent artery expansion due to oversized stent constructed based on the voronoi diagram. We performed calculations in the unsteady-state situations using constructed models. RESULTS: The complexity of the flow in the aneurysm decreases in case of expanded parent artery. The inflow rate decreases by 33.6% immediately after parent artery expansion alone without a stent. The effect of the parent artery expansion on flow reduction is larger than that of the obstruction flow by stent placement. In addition, wall shear stress and oscillatory shear index on the aneurysm wall decrease by change in blood flow due to the parent artery expansion. CONCLUSION: The effects of the parent artery expansion in a realistic aneurysm model with different stent lengths were evaluated on the basis of a numerical simulation. Although the flow was complex, the parent artery expansion with stent reduces the inflow to the aneurysm and wall shear stress and oscillatory shear index on the aneurysm. Therefore, we suggest that changes in the blood flow because of the parent artery expansion may be identified and, sometimes, is more effective than the obstruction flow due to the stent placement. Keywords: Parent artery expansion, stent, inflow rate, wall shear stress, oscillatory shear index, intracranial aneurysm
∗ Corresponding author: Futoshi Mori, Interfaculty Initiative in Information Studies, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan. Tel.: +81 3 5841 1768; Fax: +81 3 5841 1768; E-mail: [email protected].
c 2015 – IOS Press and the authors. All rights reserved 0928-7329/15/$35.00
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Fig. 1. Aneurysm treatment: before (left) and after pipeline embolization (right). This figure was reproduced with permission from Frontiers in Neurology; Zanaty et al., 2014. 10.3389/fneur.2014.00021.
1. Introduction Stents play major roles in stenosis and cerebral aneurysms. In stenosis, blood flow in the narrowed blood vessel lumen is improved by expanding the stent [1]. On the other hand, in cerebral aneurysms, the stent implanted in the aneurysm neck reduces the blood flow into the aneurysm, which is occluded by thrombosis [2]. Several clinical reports have indicated successful treatments for intracranial aneurysms [3,4]. This success is thought to be due to the reduction of flow following stent placement. Moreover, the selfexpandable stent is most often employed for the treatment of cerebral aneurysms and is thought to reduce flow due to its characteristics of low porosity and fine struts [5]. However, many reports have shown angiographic images following the stent treatment where the blood vessel expands due to the stent placement [5–7]. Zanaty et al. uses pipeline embolization to present an aneurysm before and after stent placement, as shown in Fig. 1 (originally published in Zanaty et al. Flow-Diversion Panacea or Poison? Front Neurol 5:21. doi. 10.3389/fneur.2014.00021). It was recently determined that flow reduction is caused by the following events: 1) the configuration of the parent artery [8,9], 2) stent placement [10,11] and 3) parent artery expansion [12]. We previously performed CFD simulations using idealized models and estimated the effect of expansion on flow reduction [12]. The results of these studies showed that the flow was reduced more than 22%, even when the expansion rate was only 6%. Furthermore, parent artery expansion is predominantly caused by flow reduction rather than stent placement. However, a limitation in our previous study was the use of idealized shapes when, in reality, the flow in a realistic shape is complex. Thus, the results obtained from the idealized shape may not occur or be reflected in the physiological context of an aneurysm. Because of these open questions, the aim of this study is to clarify the effect(s) of parent artery expansion using a realistic configuration of flow reduction. 2. Methods 2.1. Reconstruction of the parent artery for expansion shape In this study, we used a patient-specific geometry of a human internal carotid artery with an aneurysm as illustrated in Fig. 2(a). The geometries were provided by the Virtual Intracranial Stenting Challenge
F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
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Fig. 2. Realistic intracranial aneurysm model (a), Z-link stent (b) and stent position (c). The geometries and stent position were provided by VISC. In (c), the blue color indicates the stent at the aneurysm neck. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
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Fig. 3. The reconstructed parent artery expansion model from a realistic intracranial aneurysm model. (a) The Voronoi diagram and centerlines; (b) Clipping points A to D: A–D 25 mm, B–D 20 mm and C–D 15 mm; (c) Clipped Voronoi diagram, showing the Voronoi diagram and clipping point (C, D); (d) Voronoi points after interpolation; (e) reconstructed parent artery expansion. This reconstructed shape has expanded the diameter of the parent artery at the respective clipping points. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
(VISC) [13]. This aneurysm can be classified in relation to arterial dorsal curvature and the aneurysms were frequently found out in clinical features reported by Yoshimoto et al. [14]. The numerical data for the geometry is provided in the form of STL data. Stent geometry of the Z-link was used for this aneurysm, as shown in Fig. 2(b) and stent position is indicated in Fig. 2(c). Figure 3 shows an expansion procedure that was performed using libraries in the Vascular Modeling Toolkit (VMTK) for geometry reconstruction of the parent artery. Figure 3(a) illustrates the centerline and Voronoi diagram, which was constructed on the basis of centered points from the shape of the internal carotid artery with an aneurysm. The colors represent the radii of the maximal inscribed spheres. The centerlines, defined as centered paths traced on the Voronoi diagram, were made up of the locally largest spheres inscribed in the surface. As shown in Fig. 3(b), the clipping points are set on the centerline. The aneurysmal centerline segment and Voronoi points are clipped between planes normal to the centerline at these extents. The stent placement region is between points A and D (25 mm), B and D (20 mm), and C and D (15 mm). To study the effects of parent artery expansion in the region of stent placement, its diameter was increased. Three different diameter models were constructed: no expansion, 3% expansion and 6% expansion. Here the configurations of the stent placement region were denoted as Case 0 (no expansion case), Case 1 (parent artery expansion of C to D), Case 2 (parent artery expansion
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F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
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Fig. 4. Reconstructed parent artery expansion model with an aneurysm: (a) no expansion (Case 0) and (b) 6% expanded A to D clipping points (Case 3).
of B to D) and Case 3 (parent artery expansion of A to D), respectively. Figure 3(c) shows the Voronoi diagram and the centerline between the clipped points C and D has been removed. Reconstruction of the parent artery begins by defining the path the vessel should follow through the missing segment. This is achieved by using a cubic spline to interpolate between the clipped centerline end points and interpolating the Voronoi points on the interpolated path line (Fig. 3(d)). Finally, the parent artery is reconstructed using the interpolated Voronoi diagram (pink color of Fig. 3(e)). Figure 4 shows the reconstructed geometry with the aneurysm of no expansion (a) and 6% expansion (b) described for Case 3. 2.2. Governing equations and calculation conditions A tetrahedral numerical mesh was generated using the Gambit 2.4.6 commercial software (ANSYS Inc., Canonsburg, PA). The mesh size was determined on the basis of the stent strut that is the smallest component in the model. We performed the calculation in the unsteady state situation. The governing equations used were the Navier-Stokes (Eq. (1)) and continuity (Eq. (2)): ∂u + (u · ∇)u = −∇p + μ∇2 u ρ (1) ∂t ∇·u=0
(2)
where u = (u v w) and is the flow vector, ρ = 1.05 × 103 kg/m3 is the density, p is the pressure and μ = 3.5 × 10−3 N· s/m2 is the viscosity. The calculation was performed with a commercial solver (Fluent 15.0, ANSYS Inc.) using the finite volume method. 2.3. Boundary conditions for the unsteady state The boundary conditions for the outlet, blood vessel, aneurysm wall, and stent were independent of time. The applied velocity inlet pulse wave for the unsteady state is shown in Fig. 5 [15]. The mean Reynolds number was 300 at pulsatile flow [16]. The outlet boundary condition was set to 0 Pa. A noslip condition was applied to the blood vessel, aneurysm wall, and stent. The wall boundary was set to rigid.
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Fig. 5. Pulsatile inlet velocity wave foam: inlet peak systolic flow occurs at t = 0.12 s. The mean Reynolds number is 300.
2.4. Quantitative evaluation of results The ratios of inflow rate, wall shear stress (WSS), and oscillatory shear index (OSI) were calculated to evaluate of the expansion effect using the following equations. These equations were already defined and used in our previous study [12]. In this study, these equations were maintained to find out the same effect of expansion as the idealized geometry: The inflow rate ratio equation comparison of the conditions without and with the stent: IR ratio =
IRw/o − IRw/_i × 100 IRw/o
(3)
where IR indicates the inflow rate, w/o indicates without the stent, w/ indicates with the stent and suffix i indicates each expansion rate WSS was determined form the velocity gradient, where τw is WSS, μ is viscosity of fluid and ∂u ∂y is the velocity gradient: τw = μ
∂u ∂y
(4)
The WSS ratio equation comparison of the conditions without and with the stent: WSS ratio =
WSSw/o − WSSw/_i × 100 WSSw/o
(5)
where WSS indicates the WSS, w/o indicates without the stent, w/ indicates with the stent and suffix i indicates each expansion rate OSI reflects the change of WSS within a cardiac cycle [17] and was calculated using Eq. (6) [18]. OSI would be 0.5 if the flow is highly oscillatory and 0 if the flow is unidirectional [19]. For calculating the mean OSI ratio with the stent than that without the stent, we used Eq. (7).
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Fig. 6. Isovelocity surface (v = 0.4 m/s) (first row), flow using streamlines (second row) and WSS distribution using contour (third row) with no expansion and each 6% expansion of samples with and without stent: Case 0 (no expansion), Case 1 (stent length 15 mm), Case 2 (stent length 20 mm) and Case 3 (stent length 25 mm). The black arrow is the remarkable point. In flow using streamlines, the blue and red colors indicate slow and high speed, respectively. In WSS distribution using contour, the blue and red colors indicate low and high distribution, respectively. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
OSI equation is as follows: ⎞ T 0 WSS dt ⎠ OSI = 0.5 × ⎝1.0 − T | WSS | dt 0 ⎛
(6)
where OSI indicates OSI, |WSS| is the instantaneous WSS magnitude and T is the pulse period. The OSI ratio equation comparison of the conditions without and with the stent: OSI ratio =
OSIw/o − OSIw/_i × 100. OSIw/o
(7)
where OSI indicates OSI, w/o indicates without the stent, w/ indicates with the stent and suffix i indicates each expansion rate 3. Results: The effects of parent artery expansion on blood flow without and with the stent Figure 6 shows the isovelocity surface (v = 0.4 m/s), flow using streamlines and WSS using contour comparison between Case 0 and the 6% expansion of Cases 1–3 with and without the stent at the peak
F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
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Fig. 7. Inflow rate (a), inflow rate ratio (b), mean WSS (c) and mean WSS ratio (d). Horizontal axes indicate each case and vertical axes indicate the inflow rate, the inflow rate ratio, the mean WSS and the mean WSS ratio for panels (a) to (d), respectively. Blue and red bars represent conditions without and with the stent, respectively. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
systole of flow (t = 0.12). The first row of Fig. 6 illustrates the isovelocity surface. Without the stent, the isovelocity surfaces in the expansion cases (Cases 1–3) are smaller than that without expansion (Case 0). The isovelocity surface increased after stent treatment (compare “Case 0 without stent” with “Case 0 with stent”). The isovelocity surface with stent (Cases 1–3) decreases more than Case 0 with stent. Together, these results show the effect of expansion on inflow. Moreover, the isovelocity surface tends decrease in stent length (Cases 1–3). The second row of Fig. 6 shows the flow using streamlines. The flow pattern in the aneurysm is complex and a high speed flow is observed up to the top of aneurysm in the no expansion case (Case 0). Upon the parent artery expansion, the flow speed in the aneurysm decreases (Cases 1–3). The flow pattern in the aneurysm is changed after stent placement, as it becomes simple due to parent artery expansion after stent placement. This suggests that the vortex decreases. The flow speed in Case 3 shows a more drastic decrease than those of the other expansion cases and its flow pattern becomes the most simple in the aneurysm. The third row of Fig. 6 shows WSS. The range of WSS distribution serves to emphasize the distribution of the aneurysm. A high WSS distribution area is observed in the center of the aneurysm wall with no expansion. In contrast, the high WSS distribution area on the aneurysm disappeared after parent artery expansion. WSS of Case 3 on the aneurysm is the smallest among all the expansion cases.
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F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm (a) (b)
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Fig. 8. OSI distribution using contour in all cases without and with stent (a), mean OSI value (b) and mean OSI value ratio. Horizontal axes indicates each case and vertical axes indicate the mean OSI value and the mean OSI ratio for panels (c) and (d), respectively. Blue and red bars indicate conditions without and with the stent, respectively. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
Figure 7 shows the inflow rate (a), the inflow rate ratio (b), mean WSS (c), and the mean WSS ratio (d) at the peak systole (t = 0.12). When focusing on the without stent cases, the parent artery expansion led to a decreased inflow rate (compare Case 0 with Cases 1–3). The maximum reductions of the inflow rates of Case 3 without and with stent are 33.6% and 37.9%, respectively. As such, the role of flow reduction by stenting can be estimated as only 4.3%. Therefore, we can conclude that flow reduction by parent artery expansion is occupied mostly in this stent position. A similar trend is also seen in Case 2, although the inflow rate was lowered by parent artery expansion. The mean WSS is also decreased upon parent artery expansion. When we compare Case 0 and Case 3 without the stent, the difference of the mean WSS ratio is 46.0%, which means only expansion can reduce the flow. From the viewpoint of with and without the stent in Case 0, the reduction of the mean WSS ratio is 4.5%, which means the role of stenting in flow reduction is very low as compared to the expansion. In Cases 1–3, Case 3 demonstrates the greatest effect on parent artery expansion. The expansion also affects WSS as well as the inflow rate.
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Fig. 9. Flow pattern using streamlines (a) and the secondary flow in the slice section (b) in Case 0 without the stent (left side) and 6% expansion of Case 3 without the stent (right side): In (a), blue and red colors indicate low and high speed, respectively. In vector of (b), blue and red colors indicate low and high speed, respectively. In schematic flow direction of (b), blue arrow is the flow via the parent artery and red arrow is the inflow to aneurysm. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
Figure 8(a) shows the OSI distribution in Case 0–3 (without and with stent) represented as the backside view using contour. In Case 0 without the stent, a high OSI area was observed in the center of the aneurysm wall, which was decreased by stent placement. In the expansion cases without stent, OSI increases locally as compared to Case 0 without the stent. Figures 8(b) and (c) respectively show the mean OSI values and ratios of the aneurysm wall in all levels of expansion. When we compare Case 0 and Case 3 without the stent, the difference of the mean OSI ratio is 17.0%, which is the effect of the parent artery expansion. Furthermore, when we estimate the effect of stent placement on OSI, we calculate 28.0% as the difference of Case 0 with and without stent. However, when the differences between Case 0 without stent and Cases 1, 2 or 3 with stent are calculated (i.e., the effect of the stent together with expansion), all of the mean OSI values are exactly similar and only approximately 30%. Anzai et al. advocates that BOI, which is visualized as a region of streamlines entering an aneurysm, is the region affecting circulation in an aneurysm [11]. We regard BOI as being associated with inflow rate ratio, WSS ratio and mean OSI ratio. To explain the effect of expansion on the flow reduction using BOI, Fig. 9 shows the BOI (a) and the secondary flow (b) of Case 0 (no expansion) and Case 3 (expansion) without stent at peak systole (t = 0.12). In Case 0 (Fig. 9 left (a)), the main flow to the aneurysm is along the parent artery wall. On the other hand, the main flow in the 6% expansion of Case 3 (Fig. 9 right (a)) is not along the parent artery wall, but flows through the center of the parent artery. We can conclude that the artery expansion causes this difference in flow. In Case 3, the starting point (clipping point A) of expansion, shown in Fig. 3(b), is in part of the curvature of the parent artery, which will
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induce the change of blood flow. In addition, the width and speed of flow streamlines to the aneurysm in Case 3 without stent is smaller than that in Case 0 without stent. In addition, Fig. 9(b) shows velocity distribution in the slice section. The schematic diagram of the secondary flows of Case 0 without stent (no expansion) and Case 3 without stent (expansion) are also shown in Fig. 9(b). The flow in Case 0 without stent has two flow patterns, one is the flow to parent artery and the other is inflow to aneurysm. On the other hand, the inflow of Case 3 without stent separates to two flow directions at the aneurysm neck. Then, the inflow point is moved to the center of neck. Finally, the flow pattern at the neck wall is changed. The change of the flow is induced by the parent artery expansion. And this change will lead the OSI reduction, because the OSI is affected by the flow pattern. 4. Discussion 4.1. Effect of the parent artery expansion on flow reduction, WSS and OSI In the present study, we investigated the effect of the parent artery expansion by the stent on inflow decrease and WSS in a realistic geometry. In our previous study [12], we studied the expansion effect using idealized shapes in the unsteady state and the results showed that the effect of the parent artery expansion occupied for total flow and WSS reduction. On the basis of these results, we could conclude that the main effect of stenting on the flow reduction is mainly due to the expansion when a coarse mesh stent is used. However, changes of the flow patterns after the expansion rarely occurred in the previous study because we used idealized shapes. Therefore, in this study, we used a patient-specific geometry and the results showed that it induced a complex flow. As a result, the effect of expansion on the flow reduction is drastic, although the flow is complex. This result indicates that a reduction will be found in the patient artery. In addition, the results showed quantitative reduction. The stent without expansion (Case 0) had almost no effect on the flow reduction and the results showed that the flow rate with a stent and without expansion slightly increased. This finding was demonstrated in a previous study [20]. However, in the present study, the outcome of “only expansion and without stent” showed the reduction of the flow. The maximum effect of the parent artery expansion alone was 33.6% in the 6% expansion for Case 3 (longest stent) and the minimum effect was 6.43% in the 6% expansion for Case 1 (shortest stent). These results showed that although using a stent increases the flow, it can still be reduced under the expansion effect by stenting and the expansion should be longer. Therefore, the parent artery expansion is a key parameter to decrease the inflow to the aneurysm. Moreover, we found that the mean WSS and OSI value on the aneurysm wall decreases after the expansion in a realistic model. WSS will be changed, in case that the following events happen; 1) the change of flow direction to the aneurysm and then, 2) the change of flow gradient on the aneurysm. When comparing the expansion case with the no expansion case, the flow direction in the aneurysm neck is changed to the parent artery side from the aneurysm side due to the parent artery expansion, as shown in the schematic diagram of Fig. 9(b). This changes leads that the stress on the aneurysm wall decreases. Moreover, the flow speed in the aneurysm wall proximity after parent artery expansion is smaller than no expansion case and the flow gradient is small. This result also leads the decreasing mean WSS. The mean OSI presents the time-variable of the gradient. In case of no change of the flow direction to the aneurysm, the change of gradient is very small and the mean OSI is increased or constant. In our previous study using the idealized shape, we presented that the mean OSI increased because the flow direction is not changed after parent artery expansion [12]. On the other hand, in this study using the
F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
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realistic shape, the flow is decreasing due to the parent artery expansion and is inducing the change of flow direction to the aneurysm, as shown in Fig. 9(b). In the realistic shape, a similar trend is not only the result of slow speed but also of the change of the flow pattern due to the expansion. 4.2. Clinical aspect from the results in comparison with those of other studies Jou et al., using the data from 14 aneurysms, statistically described that oversized artery by stenting may lead to the incomplete occlusion [21]. They showed that artery oversized by 1 mm did not yield occlusion. However, our oversized artery was approximately only 0.2 mm and the data of previous study showed that this oversizing amount could cause occlusion. In addition, Mut et al. used the data from 3 aneurysms and pointed out that the oversized artery and larger stent cells lead to the increasing inflow [10]. However, in that study, the range of the oversizing was 0.5 mm–1.0 mm. In the case of our oversized artery, the inflow reduction occurred at an oversizing of less than 0.5 mm. Moreover, Jou et al. and Mut et al. focused only on the stent oversizing and increasing flow [10,21]. However, in the study by Jou et al., 50% of the cases showed that the occlusion occurred at an oversizing of less than 1 mm. This result cannot be explained only with the increasing flow as Jou et al. and Mut et al. suggested. According to our results, one possibility could be the reduction of the inflow upon artery oversizing. However, we only focused on the artery oversize and neglected the stent oversize. Therefore, this explanation could be compromised and should be discussed in the light of future results. 4.3. Difference between steady state and unsteady state in CFD simulation Radaelli et al. analyzed the steady state model and demonstrated that the flow reduction can range from 3%–16% after stenting [13]. This value was different from our results in the unsteady state and the flow reduction changes only minimally after stent placement. This difference could be explained with the data from Zeng et al., who indicated that the flow pattern in an aneurysm in the unsteady state is different from that in the steady state [22]. In addition, this difference of the flow pattern between the steady state and unsteady state could influence the flow reduction. 4.4. Limitations The present study has some limitations. First, we used only one realistic shape. Then, we found that the expansion effect is larger than that of the stenting and the mechanism of this phenomenon was already described in the previous study [12]. However, it is necessary to determine the effect of the parent artery expansion using various realistic shapes to determine the dependence of the blood flow on the geometry of the shapes. Moreover, the stent position and design influence the flow to an aneurysm [10] and the realistic position and expansion may be necessary. However, the exact position and expanded design are currently not clear and further studies are necessary.
5. Conclusion The effects of the parent artery expansion in a realistic aneurysm model with different stent lengths were evaluated on the basis of a numerical simulation. Although the flow was complex, the parent artery
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expansion with stent reduces the inflow to the aneurysm and WSS and OSI on the aneurysm. Therefore, we suggest that changes in the blood flow because of the parent artery expansion may be identified and, sometimes, is more effective than the obstruction flow due to the stent placement. Although this is the first study shedding light on the possibility of reducing the inflow by expanding the parent artery using a realistic geometry, we need to examine the possibility of using other geometries.
Acknowledgements We are grateful to the Japan Advanced Institute of Science and Technology, Japan, for allowing us to use their super computer and the VISC committee for providing the arterial and stent geometry data through the VISC 2006 project. Moreover, we are grateful for support of Professor Furumura at The University of Tokyo.
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Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm Futoshi Moria,b,∗, Makoto Ohtac and Teruo Matsuzawad a Interfaculty
Initiative in Information Studies, The University of Tokyo, Tokyo, Japan Research Institute, The University of Tokyo, Tokyo, Japan c Institute of Fluid Science, Tohoku-University, Sendai, Japan d Research Center for Simulation Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan b Earthquake
Received 1 September 2014 Accepted 19 October 2014 Abstract. BACKGROUND: Stent placement is thought to obstruct the inflow of blood to an aneurysm. However, we introduced parent artery expansion and demonstrated that this may reduce the blood flow by the stent. In our previous study using idealized shapes, the results showed that flow reduction was greater than 22.2%, even if the expansion rate was only 6%. Furthermore, the parent artery expansion is predominantly caused by the effect of flow reduction as compared to that of flow reduction due to the obstruction of flow under stent placement. However, a realistic shape is complex and the blood flow also becomes complex flow. It is not understood whether the results of flow in the idealized shape are reflective of flow from a realistic 3D model. Therefore, we examined the effect of parent artery expansion using a realistic model. OBJECTIVE: The aim is to clarify the effects of parent artery expansion on inflow rate, wall shear stress, and oscillatory shear index. METHODS: We used a patient-specific geometry of a human internal carotid artery with an aneurysm. The geometry of parent artery expansion due to oversized stent constructed based on the voronoi diagram. We performed calculations in the unsteady-state situations using constructed models. RESULTS: The complexity of the flow in the aneurysm decreases in case of expanded parent artery. The inflow rate decreases by 33.6% immediately after parent artery expansion alone without a stent. The effect of the parent artery expansion on flow reduction is larger than that of the obstruction flow by stent placement. In addition, wall shear stress and oscillatory shear index on the aneurysm wall decrease by change in blood flow due to the parent artery expansion. CONCLUSION: The effects of the parent artery expansion in a realistic aneurysm model with different stent lengths were evaluated on the basis of a numerical simulation. Although the flow was complex, the parent artery expansion with stent reduces the inflow to the aneurysm and wall shear stress and oscillatory shear index on the aneurysm. Therefore, we suggest that changes in the blood flow because of the parent artery expansion may be identified and, sometimes, is more effective than the obstruction flow due to the stent placement. Keywords: Parent artery expansion, stent, inflow rate, wall shear stress, oscillatory shear index, intracranial aneurysm
∗ Corresponding author: Futoshi Mori, Interfaculty Initiative in Information Studies, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan. Tel.: +81 3 5841 1768; Fax: +81 3 5841 1768; E-mail: [email protected].
c 2015 – IOS Press and the authors. All rights reserved 0928-7329/15/$35.00
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F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
Fig. 1. Aneurysm treatment: before (left) and after pipeline embolization (right). This figure was reproduced with permission from Frontiers in Neurology; Zanaty et al., 2014. 10.3389/fneur.2014.00021.
1. Introduction Stents play major roles in stenosis and cerebral aneurysms. In stenosis, blood flow in the narrowed blood vessel lumen is improved by expanding the stent [1]. On the other hand, in cerebral aneurysms, the stent implanted in the aneurysm neck reduces the blood flow into the aneurysm, which is occluded by thrombosis [2]. Several clinical reports have indicated successful treatments for intracranial aneurysms [3,4]. This success is thought to be due to the reduction of flow following stent placement. Moreover, the selfexpandable stent is most often employed for the treatment of cerebral aneurysms and is thought to reduce flow due to its characteristics of low porosity and fine struts [5]. However, many reports have shown angiographic images following the stent treatment where the blood vessel expands due to the stent placement [5–7]. Zanaty et al. uses pipeline embolization to present an aneurysm before and after stent placement, as shown in Fig. 1 (originally published in Zanaty et al. Flow-Diversion Panacea or Poison? Front Neurol 5:21. doi. 10.3389/fneur.2014.00021). It was recently determined that flow reduction is caused by the following events: 1) the configuration of the parent artery [8,9], 2) stent placement [10,11] and 3) parent artery expansion [12]. We previously performed CFD simulations using idealized models and estimated the effect of expansion on flow reduction [12]. The results of these studies showed that the flow was reduced more than 22%, even when the expansion rate was only 6%. Furthermore, parent artery expansion is predominantly caused by flow reduction rather than stent placement. However, a limitation in our previous study was the use of idealized shapes when, in reality, the flow in a realistic shape is complex. Thus, the results obtained from the idealized shape may not occur or be reflected in the physiological context of an aneurysm. Because of these open questions, the aim of this study is to clarify the effect(s) of parent artery expansion using a realistic configuration of flow reduction. 2. Methods 2.1. Reconstruction of the parent artery for expansion shape In this study, we used a patient-specific geometry of a human internal carotid artery with an aneurysm as illustrated in Fig. 2(a). The geometries were provided by the Virtual Intracranial Stenting Challenge
F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
(a)
(b)
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(c)
Fig. 2. Realistic intracranial aneurysm model (a), Z-link stent (b) and stent position (c). The geometries and stent position were provided by VISC. In (c), the blue color indicates the stent at the aneurysm neck. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
(a)
(b)
(c)
(d)
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Fig. 3. The reconstructed parent artery expansion model from a realistic intracranial aneurysm model. (a) The Voronoi diagram and centerlines; (b) Clipping points A to D: A–D 25 mm, B–D 20 mm and C–D 15 mm; (c) Clipped Voronoi diagram, showing the Voronoi diagram and clipping point (C, D); (d) Voronoi points after interpolation; (e) reconstructed parent artery expansion. This reconstructed shape has expanded the diameter of the parent artery at the respective clipping points. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
(VISC) [13]. This aneurysm can be classified in relation to arterial dorsal curvature and the aneurysms were frequently found out in clinical features reported by Yoshimoto et al. [14]. The numerical data for the geometry is provided in the form of STL data. Stent geometry of the Z-link was used for this aneurysm, as shown in Fig. 2(b) and stent position is indicated in Fig. 2(c). Figure 3 shows an expansion procedure that was performed using libraries in the Vascular Modeling Toolkit (VMTK) for geometry reconstruction of the parent artery. Figure 3(a) illustrates the centerline and Voronoi diagram, which was constructed on the basis of centered points from the shape of the internal carotid artery with an aneurysm. The colors represent the radii of the maximal inscribed spheres. The centerlines, defined as centered paths traced on the Voronoi diagram, were made up of the locally largest spheres inscribed in the surface. As shown in Fig. 3(b), the clipping points are set on the centerline. The aneurysmal centerline segment and Voronoi points are clipped between planes normal to the centerline at these extents. The stent placement region is between points A and D (25 mm), B and D (20 mm), and C and D (15 mm). To study the effects of parent artery expansion in the region of stent placement, its diameter was increased. Three different diameter models were constructed: no expansion, 3% expansion and 6% expansion. Here the configurations of the stent placement region were denoted as Case 0 (no expansion case), Case 1 (parent artery expansion of C to D), Case 2 (parent artery expansion
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F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
(a)
(b)
Fig. 4. Reconstructed parent artery expansion model with an aneurysm: (a) no expansion (Case 0) and (b) 6% expanded A to D clipping points (Case 3).
of B to D) and Case 3 (parent artery expansion of A to D), respectively. Figure 3(c) shows the Voronoi diagram and the centerline between the clipped points C and D has been removed. Reconstruction of the parent artery begins by defining the path the vessel should follow through the missing segment. This is achieved by using a cubic spline to interpolate between the clipped centerline end points and interpolating the Voronoi points on the interpolated path line (Fig. 3(d)). Finally, the parent artery is reconstructed using the interpolated Voronoi diagram (pink color of Fig. 3(e)). Figure 4 shows the reconstructed geometry with the aneurysm of no expansion (a) and 6% expansion (b) described for Case 3. 2.2. Governing equations and calculation conditions A tetrahedral numerical mesh was generated using the Gambit 2.4.6 commercial software (ANSYS Inc., Canonsburg, PA). The mesh size was determined on the basis of the stent strut that is the smallest component in the model. We performed the calculation in the unsteady state situation. The governing equations used were the Navier-Stokes (Eq. (1)) and continuity (Eq. (2)): ∂u + (u · ∇)u = −∇p + μ∇2 u ρ (1) ∂t ∇·u=0
(2)
where u = (u v w) and is the flow vector, ρ = 1.05 × 103 kg/m3 is the density, p is the pressure and μ = 3.5 × 10−3 N· s/m2 is the viscosity. The calculation was performed with a commercial solver (Fluent 15.0, ANSYS Inc.) using the finite volume method. 2.3. Boundary conditions for the unsteady state The boundary conditions for the outlet, blood vessel, aneurysm wall, and stent were independent of time. The applied velocity inlet pulse wave for the unsteady state is shown in Fig. 5 [15]. The mean Reynolds number was 300 at pulsatile flow [16]. The outlet boundary condition was set to 0 Pa. A noslip condition was applied to the blood vessel, aneurysm wall, and stent. The wall boundary was set to rigid.
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Fig. 5. Pulsatile inlet velocity wave foam: inlet peak systolic flow occurs at t = 0.12 s. The mean Reynolds number is 300.
2.4. Quantitative evaluation of results The ratios of inflow rate, wall shear stress (WSS), and oscillatory shear index (OSI) were calculated to evaluate of the expansion effect using the following equations. These equations were already defined and used in our previous study [12]. In this study, these equations were maintained to find out the same effect of expansion as the idealized geometry: The inflow rate ratio equation comparison of the conditions without and with the stent: IR ratio =
IRw/o − IRw/_i × 100 IRw/o
(3)
where IR indicates the inflow rate, w/o indicates without the stent, w/ indicates with the stent and suffix i indicates each expansion rate WSS was determined form the velocity gradient, where τw is WSS, μ is viscosity of fluid and ∂u ∂y is the velocity gradient: τw = μ
∂u ∂y
(4)
The WSS ratio equation comparison of the conditions without and with the stent: WSS ratio =
WSSw/o − WSSw/_i × 100 WSSw/o
(5)
where WSS indicates the WSS, w/o indicates without the stent, w/ indicates with the stent and suffix i indicates each expansion rate OSI reflects the change of WSS within a cardiac cycle [17] and was calculated using Eq. (6) [18]. OSI would be 0.5 if the flow is highly oscillatory and 0 if the flow is unidirectional [19]. For calculating the mean OSI ratio with the stent than that without the stent, we used Eq. (7).
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Fig. 6. Isovelocity surface (v = 0.4 m/s) (first row), flow using streamlines (second row) and WSS distribution using contour (third row) with no expansion and each 6% expansion of samples with and without stent: Case 0 (no expansion), Case 1 (stent length 15 mm), Case 2 (stent length 20 mm) and Case 3 (stent length 25 mm). The black arrow is the remarkable point. In flow using streamlines, the blue and red colors indicate slow and high speed, respectively. In WSS distribution using contour, the blue and red colors indicate low and high distribution, respectively. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
OSI equation is as follows: ⎞ T 0 WSS dt ⎠ OSI = 0.5 × ⎝1.0 − T | WSS | dt 0 ⎛
(6)
where OSI indicates OSI, |WSS| is the instantaneous WSS magnitude and T is the pulse period. The OSI ratio equation comparison of the conditions without and with the stent: OSI ratio =
OSIw/o − OSIw/_i × 100. OSIw/o
(7)
where OSI indicates OSI, w/o indicates without the stent, w/ indicates with the stent and suffix i indicates each expansion rate 3. Results: The effects of parent artery expansion on blood flow without and with the stent Figure 6 shows the isovelocity surface (v = 0.4 m/s), flow using streamlines and WSS using contour comparison between Case 0 and the 6% expansion of Cases 1–3 with and without the stent at the peak
F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
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Fig. 7. Inflow rate (a), inflow rate ratio (b), mean WSS (c) and mean WSS ratio (d). Horizontal axes indicate each case and vertical axes indicate the inflow rate, the inflow rate ratio, the mean WSS and the mean WSS ratio for panels (a) to (d), respectively. Blue and red bars represent conditions without and with the stent, respectively. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
systole of flow (t = 0.12). The first row of Fig. 6 illustrates the isovelocity surface. Without the stent, the isovelocity surfaces in the expansion cases (Cases 1–3) are smaller than that without expansion (Case 0). The isovelocity surface increased after stent treatment (compare “Case 0 without stent” with “Case 0 with stent”). The isovelocity surface with stent (Cases 1–3) decreases more than Case 0 with stent. Together, these results show the effect of expansion on inflow. Moreover, the isovelocity surface tends decrease in stent length (Cases 1–3). The second row of Fig. 6 shows the flow using streamlines. The flow pattern in the aneurysm is complex and a high speed flow is observed up to the top of aneurysm in the no expansion case (Case 0). Upon the parent artery expansion, the flow speed in the aneurysm decreases (Cases 1–3). The flow pattern in the aneurysm is changed after stent placement, as it becomes simple due to parent artery expansion after stent placement. This suggests that the vortex decreases. The flow speed in Case 3 shows a more drastic decrease than those of the other expansion cases and its flow pattern becomes the most simple in the aneurysm. The third row of Fig. 6 shows WSS. The range of WSS distribution serves to emphasize the distribution of the aneurysm. A high WSS distribution area is observed in the center of the aneurysm wall with no expansion. In contrast, the high WSS distribution area on the aneurysm disappeared after parent artery expansion. WSS of Case 3 on the aneurysm is the smallest among all the expansion cases.
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F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm (a) (b)
(c)
Fig. 8. OSI distribution using contour in all cases without and with stent (a), mean OSI value (b) and mean OSI value ratio. Horizontal axes indicates each case and vertical axes indicate the mean OSI value and the mean OSI ratio for panels (c) and (d), respectively. Blue and red bars indicate conditions without and with the stent, respectively. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
Figure 7 shows the inflow rate (a), the inflow rate ratio (b), mean WSS (c), and the mean WSS ratio (d) at the peak systole (t = 0.12). When focusing on the without stent cases, the parent artery expansion led to a decreased inflow rate (compare Case 0 with Cases 1–3). The maximum reductions of the inflow rates of Case 3 without and with stent are 33.6% and 37.9%, respectively. As such, the role of flow reduction by stenting can be estimated as only 4.3%. Therefore, we can conclude that flow reduction by parent artery expansion is occupied mostly in this stent position. A similar trend is also seen in Case 2, although the inflow rate was lowered by parent artery expansion. The mean WSS is also decreased upon parent artery expansion. When we compare Case 0 and Case 3 without the stent, the difference of the mean WSS ratio is 46.0%, which means only expansion can reduce the flow. From the viewpoint of with and without the stent in Case 0, the reduction of the mean WSS ratio is 4.5%, which means the role of stenting in flow reduction is very low as compared to the expansion. In Cases 1–3, Case 3 demonstrates the greatest effect on parent artery expansion. The expansion also affects WSS as well as the inflow rate.
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(a)
(b)
Fig. 9. Flow pattern using streamlines (a) and the secondary flow in the slice section (b) in Case 0 without the stent (left side) and 6% expansion of Case 3 without the stent (right side): In (a), blue and red colors indicate low and high speed, respectively. In vector of (b), blue and red colors indicate low and high speed, respectively. In schematic flow direction of (b), blue arrow is the flow via the parent artery and red arrow is the inflow to aneurysm. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140871)
Figure 8(a) shows the OSI distribution in Case 0–3 (without and with stent) represented as the backside view using contour. In Case 0 without the stent, a high OSI area was observed in the center of the aneurysm wall, which was decreased by stent placement. In the expansion cases without stent, OSI increases locally as compared to Case 0 without the stent. Figures 8(b) and (c) respectively show the mean OSI values and ratios of the aneurysm wall in all levels of expansion. When we compare Case 0 and Case 3 without the stent, the difference of the mean OSI ratio is 17.0%, which is the effect of the parent artery expansion. Furthermore, when we estimate the effect of stent placement on OSI, we calculate 28.0% as the difference of Case 0 with and without stent. However, when the differences between Case 0 without stent and Cases 1, 2 or 3 with stent are calculated (i.e., the effect of the stent together with expansion), all of the mean OSI values are exactly similar and only approximately 30%. Anzai et al. advocates that BOI, which is visualized as a region of streamlines entering an aneurysm, is the region affecting circulation in an aneurysm [11]. We regard BOI as being associated with inflow rate ratio, WSS ratio and mean OSI ratio. To explain the effect of expansion on the flow reduction using BOI, Fig. 9 shows the BOI (a) and the secondary flow (b) of Case 0 (no expansion) and Case 3 (expansion) without stent at peak systole (t = 0.12). In Case 0 (Fig. 9 left (a)), the main flow to the aneurysm is along the parent artery wall. On the other hand, the main flow in the 6% expansion of Case 3 (Fig. 9 right (a)) is not along the parent artery wall, but flows through the center of the parent artery. We can conclude that the artery expansion causes this difference in flow. In Case 3, the starting point (clipping point A) of expansion, shown in Fig. 3(b), is in part of the curvature of the parent artery, which will
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induce the change of blood flow. In addition, the width and speed of flow streamlines to the aneurysm in Case 3 without stent is smaller than that in Case 0 without stent. In addition, Fig. 9(b) shows velocity distribution in the slice section. The schematic diagram of the secondary flows of Case 0 without stent (no expansion) and Case 3 without stent (expansion) are also shown in Fig. 9(b). The flow in Case 0 without stent has two flow patterns, one is the flow to parent artery and the other is inflow to aneurysm. On the other hand, the inflow of Case 3 without stent separates to two flow directions at the aneurysm neck. Then, the inflow point is moved to the center of neck. Finally, the flow pattern at the neck wall is changed. The change of the flow is induced by the parent artery expansion. And this change will lead the OSI reduction, because the OSI is affected by the flow pattern. 4. Discussion 4.1. Effect of the parent artery expansion on flow reduction, WSS and OSI In the present study, we investigated the effect of the parent artery expansion by the stent on inflow decrease and WSS in a realistic geometry. In our previous study [12], we studied the expansion effect using idealized shapes in the unsteady state and the results showed that the effect of the parent artery expansion occupied for total flow and WSS reduction. On the basis of these results, we could conclude that the main effect of stenting on the flow reduction is mainly due to the expansion when a coarse mesh stent is used. However, changes of the flow patterns after the expansion rarely occurred in the previous study because we used idealized shapes. Therefore, in this study, we used a patient-specific geometry and the results showed that it induced a complex flow. As a result, the effect of expansion on the flow reduction is drastic, although the flow is complex. This result indicates that a reduction will be found in the patient artery. In addition, the results showed quantitative reduction. The stent without expansion (Case 0) had almost no effect on the flow reduction and the results showed that the flow rate with a stent and without expansion slightly increased. This finding was demonstrated in a previous study [20]. However, in the present study, the outcome of “only expansion and without stent” showed the reduction of the flow. The maximum effect of the parent artery expansion alone was 33.6% in the 6% expansion for Case 3 (longest stent) and the minimum effect was 6.43% in the 6% expansion for Case 1 (shortest stent). These results showed that although using a stent increases the flow, it can still be reduced under the expansion effect by stenting and the expansion should be longer. Therefore, the parent artery expansion is a key parameter to decrease the inflow to the aneurysm. Moreover, we found that the mean WSS and OSI value on the aneurysm wall decreases after the expansion in a realistic model. WSS will be changed, in case that the following events happen; 1) the change of flow direction to the aneurysm and then, 2) the change of flow gradient on the aneurysm. When comparing the expansion case with the no expansion case, the flow direction in the aneurysm neck is changed to the parent artery side from the aneurysm side due to the parent artery expansion, as shown in the schematic diagram of Fig. 9(b). This changes leads that the stress on the aneurysm wall decreases. Moreover, the flow speed in the aneurysm wall proximity after parent artery expansion is smaller than no expansion case and the flow gradient is small. This result also leads the decreasing mean WSS. The mean OSI presents the time-variable of the gradient. In case of no change of the flow direction to the aneurysm, the change of gradient is very small and the mean OSI is increased or constant. In our previous study using the idealized shape, we presented that the mean OSI increased because the flow direction is not changed after parent artery expansion [12]. On the other hand, in this study using the
F. Mori et al. / Changes in blood flow due to stented parent artery expansion in an intracranial aneurysm
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realistic shape, the flow is decreasing due to the parent artery expansion and is inducing the change of flow direction to the aneurysm, as shown in Fig. 9(b). In the realistic shape, a similar trend is not only the result of slow speed but also of the change of the flow pattern due to the expansion. 4.2. Clinical aspect from the results in comparison with those of other studies Jou et al., using the data from 14 aneurysms, statistically described that oversized artery by stenting may lead to the incomplete occlusion [21]. They showed that artery oversized by 1 mm did not yield occlusion. However, our oversized artery was approximately only 0.2 mm and the data of previous study showed that this oversizing amount could cause occlusion. In addition, Mut et al. used the data from 3 aneurysms and pointed out that the oversized artery and larger stent cells lead to the increasing inflow [10]. However, in that study, the range of the oversizing was 0.5 mm–1.0 mm. In the case of our oversized artery, the inflow reduction occurred at an oversizing of less than 0.5 mm. Moreover, Jou et al. and Mut et al. focused only on the stent oversizing and increasing flow [10,21]. However, in the study by Jou et al., 50% of the cases showed that the occlusion occurred at an oversizing of less than 1 mm. This result cannot be explained only with the increasing flow as Jou et al. and Mut et al. suggested. According to our results, one possibility could be the reduction of the inflow upon artery oversizing. However, we only focused on the artery oversize and neglected the stent oversize. Therefore, this explanation could be compromised and should be discussed in the light of future results. 4.3. Difference between steady state and unsteady state in CFD simulation Radaelli et al. analyzed the steady state model and demonstrated that the flow reduction can range from 3%–16% after stenting [13]. This value was different from our results in the unsteady state and the flow reduction changes only minimally after stent placement. This difference could be explained with the data from Zeng et al., who indicated that the flow pattern in an aneurysm in the unsteady state is different from that in the steady state [22]. In addition, this difference of the flow pattern between the steady state and unsteady state could influence the flow reduction. 4.4. Limitations The present study has some limitations. First, we used only one realistic shape. Then, we found that the expansion effect is larger than that of the stenting and the mechanism of this phenomenon was already described in the previous study [12]. However, it is necessary to determine the effect of the parent artery expansion using various realistic shapes to determine the dependence of the blood flow on the geometry of the shapes. Moreover, the stent position and design influence the flow to an aneurysm [10] and the realistic position and expansion may be necessary. However, the exact position and expanded design are currently not clear and further studies are necessary.
5. Conclusion The effects of the parent artery expansion in a realistic aneurysm model with different stent lengths were evaluated on the basis of a numerical simulation. Although the flow was complex, the parent artery
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expansion with stent reduces the inflow to the aneurysm and WSS and OSI on the aneurysm. Therefore, we suggest that changes in the blood flow because of the parent artery expansion may be identified and, sometimes, is more effective than the obstruction flow due to the stent placement. Although this is the first study shedding light on the possibility of reducing the inflow by expanding the parent artery using a realistic geometry, we need to examine the possibility of using other geometries.
Acknowledgements We are grateful to the Japan Advanced Institute of Science and Technology, Japan, for allowing us to use their super computer and the VISC committee for providing the arterial and stent geometry data through the VISC 2006 project. Moreover, we are grateful for support of Professor Furumura at The University of Tokyo.
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