INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Int. J. Numer. Meth. Biomed. Engng. (2014) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.2637
Proximal stenosis may induce initiation of cerebral aneurysms by increasing wall shear stress and wall shear stress gradient Kenichi Kono1,*,† , Takeshi Fujimoto2 and Tomoaki Terada1 1 Department 2 Department
of Neurosurgery, Wakayama Rosai Hospital, 93-1 Kinomoto, Wakayama 640-8505, Japan of Neurosurgery, Niigata Neurosurgical Hospital, 3057 Yamada, Niigata 950-1101, Japan
SUMMARY Hemodynamic parameters, such as wall shear stress (WSS), WSS gradient (WSSG), aneurysm formation indicator (AFI), or gradient oscillatory number (GON), have been proposed to be linked to initiation of cerebral aneurysms. However, how such conditions occur in humans is unclear. We encountered a rare and interesting case to address this issue. A patient had a newly formed aneurysm with proximal stenosis, which was confirmed by serial imagings. We made two pre-aneurysm models: one with stenosis and the other without stenosis. We performed computational fluid dynamics simulations for these models. Owing to jet flow caused by the stenosis, the maximum WSS and WSSG on the aneurysm initiation site were approximately doubled and tripled, respectively. However, the oscillatory shear index (OSI), AFI, and GON did not change substantially by the stenosis. Computer simulations using artificial vascular models with different degrees of proximal stenosis at different distances demonstrated that oscillatory shear index, AFI, and GON did not change substantially by the stenosis. These results showed that proximal stenosis caused high WSS and high WSSG at the aneurysm initiation site, possibly leading to aneurysm initiation. Proximal stenosis may be a potential factor to induce initiation of one class of cerebral aneurysms by increasing WSS and WSSG. Copyright © 2014 John Wiley & Sons, Ltd. Received 3 November 2013; Revised 2 February 2014; Accepted 10 March 2014 KEY WORDS:
aneurysm initiation; computational fluid dynamics simulations; hemodynamic stress; stenosis; wall shear stress; wall shear stress gradient
1. INTRODUCTION Hemodynamic factors play an important role in initiation of cerebral aneurysms. The combination of high wall shear stress (WSS) and a high positive WSS gradient (WSSG) has been proposed as a factor of aneurysm formation in computational and experimental studies [1, 2]. The aneurysm formation indicator (AFI) [3] and gradient oscillatory number (GON) [4] have also been proposed as hemodynamic parameters of aneurysm initiation. The oscillatory shear index (OSI) is regarded as an important hemodynamic parameter of aneurysm rupture [5]. However, it is unclear what kind of vascular anatomy in humans will make these hemodynamic values change so that aneurysms will be likely to form. We previously reported one newly formed (i.e., de novo) aneurysm and proposed that proximal stenosis could be a potential factor of aneurysm initiation [6]. In one de novo aneurysm, an angiogram taken 15 years ago showed no aneurysm or stenosis. Although we hypothesized that stenosis was formed before aneurysm initiation, the opposite situation was also possible. Therefore,
*Correspondence to: Kenichi Kono, Department of Neurosurgery, Wakayama Rosai Hospital, 93-1 Kinomoto, Wakayama 640-8505, Japan. † E-mail: [email protected] Copyright © 2014 John Wiley & Sons, Ltd.
K. KONO, T. FUJIMOTO AND T. TERADA
we could not prove that the aneurysm was initiated after formation of proximal stenosis owing to a lack of serial images, which was a weakness of the previous study. In addition, we examined only WSS and WSSG and did not examine OSI, AFI, or GON. We recently encountered a rare and interesting case of a de novo anterior choroidal artery aneurysm with proximal stenosis and obtained serial images proving aneurysm formation, which could overcome the previous weakness. Using a patient-specific three-dimensional (3D) vascular model, we performed CFD simulations. We examined WSS, WSSG, OSI, AFI, and GON and investigated the relationship between proximal stenosis and an increased hemodynamic stress that is conducive for initiation of an aneurysm. We also performed CFD simulations using T-shaped vascular models with various degrees of stenosis at different distances from the apex as a parametric study. 2. METHODS 2.1. Clinical presentation A 63-year-old man suffered from subarachnoid hemorrhage because of a rupture of an anterior choroidal artery aneurysm. The anterior choroidal artery had 60% stenosis at its proximal end (Figure 1C). The stenosis was located at 2.1 mm proximal to the aneurysm. Magnetic resonance angiography (MRA) 3 years before the rupture showed the anterior choroidal artery with stenosis but there was no aneurysm (Figure 1B). Therefore, the aneurysm was de novo. We treated the aneurysm with coil embolization. Because of the stenosis, an SL-10 microcatheter (Stryker Neurovascular, Freemont, CA, USA) with an outer diameter of 0.57 mm (1.7 Fr) could not pass through the stenosis and we navigated a smaller microcatheter (Marathon; ev3, Irvine, CA, USA) with an outer diameter of 0.43 mm (1.3 Fr) into the aneurysm through the stenosis and embolized the aneurysm with coils. The patient died 2 weeks after the treatment because of severe initial damage of subarachnoid hemorrhage. 2.2. Image reconstruction A 3D image of the aneurysm was obtained by 3D rotational angiography with a spatial resolution of 0.2 mm (Philips Healthcare, Best, the Netherlands) and segmented using the Vascular Modeling Toolkit (vmtk; www.vmtk.org). The diameter of the stenotic lesion was 0.52 mm. Magnetic resonance imaging at the pre-aneurysm state was not of sufficient quality to reconstruct 3D geometry (Figure 1B). Using 3-matic software (Materialise NV, Leuven, Belgium), we manually created two pre-aneurysm models from the 3D aneurysm model: one with stenosis (Figure 2B and E) and another without stenosis (Figure 2A and D). In the process of removing the aneurysm from the original aneurysm model, we referred to the real pre-aneurysm image (Figure 1B) and determined the neck
Figure 1. (A) A schematic illustration shows the internal carotid artery with the anterior choroidal artery without stenosis (arrow) in the initial state. (B) Magnetic resonance angiography 3 years before subarachnoid hemorrhage shows stenosis at the proximal end of the anterior choroidal artery (arrow) in the intermediate state. (C) Three-dimensional rotational angiography after subarachnoid hemorrhage shows the ruptured anterior choroidal artery aneurysm with proximal stenosis (arrow) in the final state. Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
PROXIMAL STENOSIS MAY INDUCE INITIATION OF CEREBRAL ANEURYSMS
Figure 2. (A–C) Streamlines to the anterior choroidal artery at diastole colored according to flow velocity are shown in initial, intermediate, and final states. Jet flow can be seen only in the intermediate and final states (arrows in A, B, and C). (D–F) The contours of cycle-averaged wall shear stress (WSS) are shown in the three states. In the intermediate state, because of jet flow at the stenosis, WSS is elevated at the aneurysm initiation site (arrow in E).
of the aneurysm (Figure 1C) so that pre-aneurysm geometry would be similar to the real geometry. The three models corresponded to initial, intermediate, and final states (Figure 1A–C). The initial state had no stenosis and no aneurysm (Figure 1A). Although there was no image of this state, it was created to evaluate hemodynamic effects of the stenosis. On the two pre-aneurysm models, we defined a centerline on the aneurysm initiation site (Figure 3A and B). The centerline was selected among several parallel lines so that maximum WSS and WSSG on the line would be the highest. 2.3. CFD simulations We performed CFD simulations for the three models in a similar manner as described previously [7–9]. The fluid domains were extruded at the inlet to allow fully developed flow and meshed using ICEM software (Version 14.5, ANSYS Inc., Canonsburg, PA, USA) to create finite volume tetrahedral elements and five layers of wall prism elements. The number of elements was approximately 1,000,000–1,400,000, which was confirmed to be adequate to calculate WSS, WSSG, OSI, AFI, and GON by creating meshes of finer grid densities (i.e., grid independence was confirmed). Blood was modeled as a Newtonian fluid with a density of 1056 kg/m3 and a viscosity of 0.0035 kg/ms. A rigid-wall no-slip boundary condition was implemented at the vessel walls. We performed a pulsatile flow simulation with a commercial finite volume implicit solver, ANSYS CFX (Version 14.5, ANSYS Inc.), the accuracy of which was validated previously [8, 10]. For inlet flow conditions, we used the volumetric flow rate waveforms of the internal carotid artery of normal subjects given by Gwilliam et al. [11]. The flow rate was scaled so that cycle-averaged WSS at the parental artery would be 1.5 Pa, because a WSS of 1–7 Pa was considered as physiological in this study [12]. A zero pressure was imposed at the outlets. The time step for calculation was set at 0.005 s. Verification study of the time step was performed by using a smaller time step of 0.001 s. The differences of hemodynamic values at the aneurysm initiation site were 0.03% (WSS), 0.01% (WSSG), 0.9% (OSI), 0.004% (AFI), and 1.6% (GON). Therefore, we used 0.005 s as the time step. Calculations were performed for three cardiac cycles, and the result of the last cycle was used for analysis. We measured WSS and calculated WSSG on the centerlines based on cycle-averaged WSS. We determined Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
K. KONO, T. FUJIMOTO AND T. TERADA
Figure 3. (A and B) Cycle-averaged wall shear stress (WSS) and WSS gradient (WSSG) prior to aneurysm formation were evaluated for initial and intermediate states. In the intermediate state, the stenosis produces jet flow, resulting in elevation of WSS at the aneurysm initiation site (arrow in B). (C and D) WSS and WSSG along the centerlines were evaluated. Maximum WSS and WSSG are approximately doubled and tripled, respectively, because of stenosis.
an aneurysm initiation area on the two pre-aneurysm models (Figure 4) and calculated the OSI [13], AFI [3], and GON [4] as defined in each reference. The AFI was calculated at diastole. 2.4. T-shaped bifurcation models with proximal stenosis To further clarify the relationship between hemodynamic stresses at an impingement zone and the degree and location of a proximal stenosis, we conducted a parametric study using idealized vascular models. We created 12 idealized T-shaped bifurcation vascular models with different degrees of stenosis at different proximal distances from the apex using the 3-matic software. Although our clinical case was a sidewall aneurysm, the vessel was acutely bent just distal to the stenosis and the jet flow through the stenosis impinged on the vessel wall (Figure 2B and E). Therefore, we considered that these T-shaped models were applicable to simulate hemodynamic stress by proximal stenosis, which was similar to the clinical case. The diameters of the vessels were all 3 mm. Six models had a fixed 50% diameter stenosis at different locations (3.5, 4.5, 6.5, 9, 11.5, and 16.5 mm) from the apex. Five models had stenosis located at a fixed distance of 6.5 mm with degree of stenosis increasing from 30% to 70% with 10% intervals. One model had no stenosis. We defined an area on the top surface of the horizontal vessels. CFD simulations were performed in the same fashion as previously mentioned. We evaluated OSI, AFI, and GON on the top surface area. An illustrative model is shown in Figure 5. We did not examine WSS and WSSG because we previously examined these parameters using the same vascular models and showed that WSS and WSSG on the apex were increased when the degree of stenosis became higher or the distance from the apex became closer [6]. 3. RESULTS 3.1. Patient-specific model In the intermediate and final models, proximal stenosis caused jet flow (Figure 2B and C). In the intermediate model, the jet flow increased WSS on the aneurysm initiation site (Figure 2E). The Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
PROXIMAL STENOSIS MAY INDUCE INITIATION OF CEREBRAL ANEURYSMS
Figure 4. (A–C) The contours of the oscillatory shear index (OSI), aneurysm formation indicator (AFI), and gradient oscillatory number (GON) are shown in the initial state. The aneurysm initiation site (arrow in A) is encircled in white. (D–F). The contours of OSI, AFI, and GON are shown in the intermediate state with stenosis (arrow in D). OSI and AFI at the initiation site was not changed by the stenosis. GON at the initiation site was slightly increased by the stenosis. The AFI was calculated at diastole in both states.
Figure 5. The results of simulations of a T-shaped vascular model with 50% stenosis at 6.5 mm proximal to the apex are shown. (A) Streamlines at diastole colored according to flow velocity are shown. Jet flow through the stenosis is observed. (B–D) The contours of the oscillatory shear index (OSI), aneurysm formation indicator (AFI), and gradient oscillatory number (GON) are shown. The apex is encircled in white (arrow in B).
Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
K. KONO, T. FUJIMOTO AND T. TERADA
maximum WSS and WSSG on the centerline were 6.6 Pa and 8.5 Pa/mm in the initial model and 12.2 Pa and 24.8 Pa/mm in the intermediate model, respectively, (Figure 3). Owing to the stenosis, the maximum WSS and WSSG were approximately doubled and tripled, respectively. Area-averaged OSI, AFI, and GON at the aneurysm initiation site were measured in the initial and intermediate states (Figure 4 and Table I). Changes in these parameters by the stenosis were little, and absolute values of these parameters were not enough for aneurysm initiation, referring to the previous reports: 0.016 (unruptured) versus 0.0035 (ruptured) in OSI [5], 0.4 to 0.5 in AFI at aneurysm initiation sites [3], and 0.8 to 0.9 in GON at aneurysm initiation sites [4]. 3.2. T-shaped bifurcation models with proximal stenosis The results were shown in Figure 6. Changes in or absolute values of OSI, AFI, and GON were negligible for aneurysm initiation, referring to the previous reports [3–5]. There were no trends between these values and the distances from the apex to the 50% stenosis probably because changes in these values were little (Figure 6A–C). In the models with various degrees of stenosis at 6.5 mm from the apex (Figure 6D–F), the highest stenosis (70%) increased OSI and GON and decreased AFI, which were directed to aneurysm initiation. However, the absolute values were also negligible.
Table I. Hemodynamic values at the aneurysm initiation area in the initial and intermediate states.
Initial state Intermediate state
OSI
AFI
GON
0.0001 0.0021
0.9994 0.9886
0.026 0.061
OSI, Oscillatory shear index; AFI, aneurysm formation indicator; GON, gradient oscillatory number.
Figure 6. A–C) The relationships between hemodynamic values and the distances from the 50% stenosis to the apex in the T-shaped vascular models are shown. (D–F) The relationships between hemodynamic values and the degrees of stenosis at 6.5 mm from the apex are shown. Oscillatory shear index (OSI), aneurysm formation indicator (AFI), and gradient oscillatory number (GON). Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
PROXIMAL STENOSIS MAY INDUCE INITIATION OF CEREBRAL ANEURYSMS
4. DISCUSSION 4.1. De novo aneurysms The annual incidence of de novo aneurysm formation is in the range of 0.3–1.8% [14–17]. Because aneurysm formation is rarely encountered, there is a shortage of knowledge on what situation might cause it. Therapeutic carotid occlusion is known to cause an increase in compensatory flow in the contralateral arteries. The resulting increased hemodynamic stress may result in formation of de novo aneurysms on the contralateral side [18]. In the current case, there was no contralateral internal carotid artery occlusion. Therefore, formation of the aneurysm was not associated with occlusion of other vessels but was potentially associated with proximal stenosis of the feeding artery. 4.2. CFD and experimental study on aneurysm initiation Several reports have described that high WSS combined with high positive WSSG is associated with initiation of de novo aneurysms, as shown by CFD studies, animal experiments, and in vitro experiments [1, 2, 19, 20]. Kulcsár et al [20] showed that high WSS and high positive WSSG were associated with de novo aneurysms in three patients, and these aneurysms had no proximal stenosis. Carotid occlusion produces high WSS and high positive WSSG at the basilar terminus in rabbits [2], and may be associated with initiation of aneurysms in humans [18]. Besides carotid occlusion, we demonstrated that proximal stenosis could produce high WSS and high positive WSSG. Measurements using different modalities show that WSS is in the range of 1–7 Pa in the arterial vascular network [12, 21, 22]. Therefore, we defined unphysiologically high WSS as >7 Pa in this study. In the current case, we found that WSS was nearly doubled and increased at >7 Pa because of stenosis. Therefore, it is possible that the proximal stenosis produced unphysiologically high WSS combined with high positive WSSG and led to initiation of aneurysms. The threshold of 7 Pa is not definitive. In addition, WSS magnitude would change by different inlet conditions. Therefore, we consider that the increase of WSS and WSSG by two to threefolds was more essential for aneurysm initiation than the absolute values of WSS. We previously reported four cases of aneurysms with proximal stenosis, including one de novo aneurysm [6]. In the one de novo aneurysm, we could not prove that the aneurysm was initiated after formation of proximal stenosis owing to a lack of serial images. In the current case, serial imaging showed that proximal stenosis existed before aneurysm formation, which strengthens our hypothesis that proximal stenosis causes aneurysm initiation. The other three aneurysms in the four aneurysms had proximal stenosis but were not de novo. Therefore, we could only presume that these three aneurysms might be initiated by the proximal stenosis. In our previous report [6], using a parametric study of aneurysm models, we demonstrated that a stenosis diameter >40% located
Proximal stenosis may induce initiation of cerebral aneurysms by increasing wall shear stress and wall shear stress gradient Kenichi Kono1,*,† , Takeshi Fujimoto2 and Tomoaki Terada1 1 Department 2 Department
of Neurosurgery, Wakayama Rosai Hospital, 93-1 Kinomoto, Wakayama 640-8505, Japan of Neurosurgery, Niigata Neurosurgical Hospital, 3057 Yamada, Niigata 950-1101, Japan
SUMMARY Hemodynamic parameters, such as wall shear stress (WSS), WSS gradient (WSSG), aneurysm formation indicator (AFI), or gradient oscillatory number (GON), have been proposed to be linked to initiation of cerebral aneurysms. However, how such conditions occur in humans is unclear. We encountered a rare and interesting case to address this issue. A patient had a newly formed aneurysm with proximal stenosis, which was confirmed by serial imagings. We made two pre-aneurysm models: one with stenosis and the other without stenosis. We performed computational fluid dynamics simulations for these models. Owing to jet flow caused by the stenosis, the maximum WSS and WSSG on the aneurysm initiation site were approximately doubled and tripled, respectively. However, the oscillatory shear index (OSI), AFI, and GON did not change substantially by the stenosis. Computer simulations using artificial vascular models with different degrees of proximal stenosis at different distances demonstrated that oscillatory shear index, AFI, and GON did not change substantially by the stenosis. These results showed that proximal stenosis caused high WSS and high WSSG at the aneurysm initiation site, possibly leading to aneurysm initiation. Proximal stenosis may be a potential factor to induce initiation of one class of cerebral aneurysms by increasing WSS and WSSG. Copyright © 2014 John Wiley & Sons, Ltd. Received 3 November 2013; Revised 2 February 2014; Accepted 10 March 2014 KEY WORDS:
aneurysm initiation; computational fluid dynamics simulations; hemodynamic stress; stenosis; wall shear stress; wall shear stress gradient
1. INTRODUCTION Hemodynamic factors play an important role in initiation of cerebral aneurysms. The combination of high wall shear stress (WSS) and a high positive WSS gradient (WSSG) has been proposed as a factor of aneurysm formation in computational and experimental studies [1, 2]. The aneurysm formation indicator (AFI) [3] and gradient oscillatory number (GON) [4] have also been proposed as hemodynamic parameters of aneurysm initiation. The oscillatory shear index (OSI) is regarded as an important hemodynamic parameter of aneurysm rupture [5]. However, it is unclear what kind of vascular anatomy in humans will make these hemodynamic values change so that aneurysms will be likely to form. We previously reported one newly formed (i.e., de novo) aneurysm and proposed that proximal stenosis could be a potential factor of aneurysm initiation [6]. In one de novo aneurysm, an angiogram taken 15 years ago showed no aneurysm or stenosis. Although we hypothesized that stenosis was formed before aneurysm initiation, the opposite situation was also possible. Therefore,
*Correspondence to: Kenichi Kono, Department of Neurosurgery, Wakayama Rosai Hospital, 93-1 Kinomoto, Wakayama 640-8505, Japan. † E-mail: [email protected] Copyright © 2014 John Wiley & Sons, Ltd.
K. KONO, T. FUJIMOTO AND T. TERADA
we could not prove that the aneurysm was initiated after formation of proximal stenosis owing to a lack of serial images, which was a weakness of the previous study. In addition, we examined only WSS and WSSG and did not examine OSI, AFI, or GON. We recently encountered a rare and interesting case of a de novo anterior choroidal artery aneurysm with proximal stenosis and obtained serial images proving aneurysm formation, which could overcome the previous weakness. Using a patient-specific three-dimensional (3D) vascular model, we performed CFD simulations. We examined WSS, WSSG, OSI, AFI, and GON and investigated the relationship between proximal stenosis and an increased hemodynamic stress that is conducive for initiation of an aneurysm. We also performed CFD simulations using T-shaped vascular models with various degrees of stenosis at different distances from the apex as a parametric study. 2. METHODS 2.1. Clinical presentation A 63-year-old man suffered from subarachnoid hemorrhage because of a rupture of an anterior choroidal artery aneurysm. The anterior choroidal artery had 60% stenosis at its proximal end (Figure 1C). The stenosis was located at 2.1 mm proximal to the aneurysm. Magnetic resonance angiography (MRA) 3 years before the rupture showed the anterior choroidal artery with stenosis but there was no aneurysm (Figure 1B). Therefore, the aneurysm was de novo. We treated the aneurysm with coil embolization. Because of the stenosis, an SL-10 microcatheter (Stryker Neurovascular, Freemont, CA, USA) with an outer diameter of 0.57 mm (1.7 Fr) could not pass through the stenosis and we navigated a smaller microcatheter (Marathon; ev3, Irvine, CA, USA) with an outer diameter of 0.43 mm (1.3 Fr) into the aneurysm through the stenosis and embolized the aneurysm with coils. The patient died 2 weeks after the treatment because of severe initial damage of subarachnoid hemorrhage. 2.2. Image reconstruction A 3D image of the aneurysm was obtained by 3D rotational angiography with a spatial resolution of 0.2 mm (Philips Healthcare, Best, the Netherlands) and segmented using the Vascular Modeling Toolkit (vmtk; www.vmtk.org). The diameter of the stenotic lesion was 0.52 mm. Magnetic resonance imaging at the pre-aneurysm state was not of sufficient quality to reconstruct 3D geometry (Figure 1B). Using 3-matic software (Materialise NV, Leuven, Belgium), we manually created two pre-aneurysm models from the 3D aneurysm model: one with stenosis (Figure 2B and E) and another without stenosis (Figure 2A and D). In the process of removing the aneurysm from the original aneurysm model, we referred to the real pre-aneurysm image (Figure 1B) and determined the neck
Figure 1. (A) A schematic illustration shows the internal carotid artery with the anterior choroidal artery without stenosis (arrow) in the initial state. (B) Magnetic resonance angiography 3 years before subarachnoid hemorrhage shows stenosis at the proximal end of the anterior choroidal artery (arrow) in the intermediate state. (C) Three-dimensional rotational angiography after subarachnoid hemorrhage shows the ruptured anterior choroidal artery aneurysm with proximal stenosis (arrow) in the final state. Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
PROXIMAL STENOSIS MAY INDUCE INITIATION OF CEREBRAL ANEURYSMS
Figure 2. (A–C) Streamlines to the anterior choroidal artery at diastole colored according to flow velocity are shown in initial, intermediate, and final states. Jet flow can be seen only in the intermediate and final states (arrows in A, B, and C). (D–F) The contours of cycle-averaged wall shear stress (WSS) are shown in the three states. In the intermediate state, because of jet flow at the stenosis, WSS is elevated at the aneurysm initiation site (arrow in E).
of the aneurysm (Figure 1C) so that pre-aneurysm geometry would be similar to the real geometry. The three models corresponded to initial, intermediate, and final states (Figure 1A–C). The initial state had no stenosis and no aneurysm (Figure 1A). Although there was no image of this state, it was created to evaluate hemodynamic effects of the stenosis. On the two pre-aneurysm models, we defined a centerline on the aneurysm initiation site (Figure 3A and B). The centerline was selected among several parallel lines so that maximum WSS and WSSG on the line would be the highest. 2.3. CFD simulations We performed CFD simulations for the three models in a similar manner as described previously [7–9]. The fluid domains were extruded at the inlet to allow fully developed flow and meshed using ICEM software (Version 14.5, ANSYS Inc., Canonsburg, PA, USA) to create finite volume tetrahedral elements and five layers of wall prism elements. The number of elements was approximately 1,000,000–1,400,000, which was confirmed to be adequate to calculate WSS, WSSG, OSI, AFI, and GON by creating meshes of finer grid densities (i.e., grid independence was confirmed). Blood was modeled as a Newtonian fluid with a density of 1056 kg/m3 and a viscosity of 0.0035 kg/ms. A rigid-wall no-slip boundary condition was implemented at the vessel walls. We performed a pulsatile flow simulation with a commercial finite volume implicit solver, ANSYS CFX (Version 14.5, ANSYS Inc.), the accuracy of which was validated previously [8, 10]. For inlet flow conditions, we used the volumetric flow rate waveforms of the internal carotid artery of normal subjects given by Gwilliam et al. [11]. The flow rate was scaled so that cycle-averaged WSS at the parental artery would be 1.5 Pa, because a WSS of 1–7 Pa was considered as physiological in this study [12]. A zero pressure was imposed at the outlets. The time step for calculation was set at 0.005 s. Verification study of the time step was performed by using a smaller time step of 0.001 s. The differences of hemodynamic values at the aneurysm initiation site were 0.03% (WSS), 0.01% (WSSG), 0.9% (OSI), 0.004% (AFI), and 1.6% (GON). Therefore, we used 0.005 s as the time step. Calculations were performed for three cardiac cycles, and the result of the last cycle was used for analysis. We measured WSS and calculated WSSG on the centerlines based on cycle-averaged WSS. We determined Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
K. KONO, T. FUJIMOTO AND T. TERADA
Figure 3. (A and B) Cycle-averaged wall shear stress (WSS) and WSS gradient (WSSG) prior to aneurysm formation were evaluated for initial and intermediate states. In the intermediate state, the stenosis produces jet flow, resulting in elevation of WSS at the aneurysm initiation site (arrow in B). (C and D) WSS and WSSG along the centerlines were evaluated. Maximum WSS and WSSG are approximately doubled and tripled, respectively, because of stenosis.
an aneurysm initiation area on the two pre-aneurysm models (Figure 4) and calculated the OSI [13], AFI [3], and GON [4] as defined in each reference. The AFI was calculated at diastole. 2.4. T-shaped bifurcation models with proximal stenosis To further clarify the relationship between hemodynamic stresses at an impingement zone and the degree and location of a proximal stenosis, we conducted a parametric study using idealized vascular models. We created 12 idealized T-shaped bifurcation vascular models with different degrees of stenosis at different proximal distances from the apex using the 3-matic software. Although our clinical case was a sidewall aneurysm, the vessel was acutely bent just distal to the stenosis and the jet flow through the stenosis impinged on the vessel wall (Figure 2B and E). Therefore, we considered that these T-shaped models were applicable to simulate hemodynamic stress by proximal stenosis, which was similar to the clinical case. The diameters of the vessels were all 3 mm. Six models had a fixed 50% diameter stenosis at different locations (3.5, 4.5, 6.5, 9, 11.5, and 16.5 mm) from the apex. Five models had stenosis located at a fixed distance of 6.5 mm with degree of stenosis increasing from 30% to 70% with 10% intervals. One model had no stenosis. We defined an area on the top surface of the horizontal vessels. CFD simulations were performed in the same fashion as previously mentioned. We evaluated OSI, AFI, and GON on the top surface area. An illustrative model is shown in Figure 5. We did not examine WSS and WSSG because we previously examined these parameters using the same vascular models and showed that WSS and WSSG on the apex were increased when the degree of stenosis became higher or the distance from the apex became closer [6]. 3. RESULTS 3.1. Patient-specific model In the intermediate and final models, proximal stenosis caused jet flow (Figure 2B and C). In the intermediate model, the jet flow increased WSS on the aneurysm initiation site (Figure 2E). The Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
PROXIMAL STENOSIS MAY INDUCE INITIATION OF CEREBRAL ANEURYSMS
Figure 4. (A–C) The contours of the oscillatory shear index (OSI), aneurysm formation indicator (AFI), and gradient oscillatory number (GON) are shown in the initial state. The aneurysm initiation site (arrow in A) is encircled in white. (D–F). The contours of OSI, AFI, and GON are shown in the intermediate state with stenosis (arrow in D). OSI and AFI at the initiation site was not changed by the stenosis. GON at the initiation site was slightly increased by the stenosis. The AFI was calculated at diastole in both states.
Figure 5. The results of simulations of a T-shaped vascular model with 50% stenosis at 6.5 mm proximal to the apex are shown. (A) Streamlines at diastole colored according to flow velocity are shown. Jet flow through the stenosis is observed. (B–D) The contours of the oscillatory shear index (OSI), aneurysm formation indicator (AFI), and gradient oscillatory number (GON) are shown. The apex is encircled in white (arrow in B).
Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
K. KONO, T. FUJIMOTO AND T. TERADA
maximum WSS and WSSG on the centerline were 6.6 Pa and 8.5 Pa/mm in the initial model and 12.2 Pa and 24.8 Pa/mm in the intermediate model, respectively, (Figure 3). Owing to the stenosis, the maximum WSS and WSSG were approximately doubled and tripled, respectively. Area-averaged OSI, AFI, and GON at the aneurysm initiation site were measured in the initial and intermediate states (Figure 4 and Table I). Changes in these parameters by the stenosis were little, and absolute values of these parameters were not enough for aneurysm initiation, referring to the previous reports: 0.016 (unruptured) versus 0.0035 (ruptured) in OSI [5], 0.4 to 0.5 in AFI at aneurysm initiation sites [3], and 0.8 to 0.9 in GON at aneurysm initiation sites [4]. 3.2. T-shaped bifurcation models with proximal stenosis The results were shown in Figure 6. Changes in or absolute values of OSI, AFI, and GON were negligible for aneurysm initiation, referring to the previous reports [3–5]. There were no trends between these values and the distances from the apex to the 50% stenosis probably because changes in these values were little (Figure 6A–C). In the models with various degrees of stenosis at 6.5 mm from the apex (Figure 6D–F), the highest stenosis (70%) increased OSI and GON and decreased AFI, which were directed to aneurysm initiation. However, the absolute values were also negligible.
Table I. Hemodynamic values at the aneurysm initiation area in the initial and intermediate states.
Initial state Intermediate state
OSI
AFI
GON
0.0001 0.0021
0.9994 0.9886
0.026 0.061
OSI, Oscillatory shear index; AFI, aneurysm formation indicator; GON, gradient oscillatory number.
Figure 6. A–C) The relationships between hemodynamic values and the distances from the 50% stenosis to the apex in the T-shaped vascular models are shown. (D–F) The relationships between hemodynamic values and the degrees of stenosis at 6.5 mm from the apex are shown. Oscillatory shear index (OSI), aneurysm formation indicator (AFI), and gradient oscillatory number (GON). Copyright © 2014 John Wiley & Sons, Ltd.
Int. J. Numer. Meth. Biomed. Engng. (2014) DOI: 10.1002/cnm
PROXIMAL STENOSIS MAY INDUCE INITIATION OF CEREBRAL ANEURYSMS
4. DISCUSSION 4.1. De novo aneurysms The annual incidence of de novo aneurysm formation is in the range of 0.3–1.8% [14–17]. Because aneurysm formation is rarely encountered, there is a shortage of knowledge on what situation might cause it. Therapeutic carotid occlusion is known to cause an increase in compensatory flow in the contralateral arteries. The resulting increased hemodynamic stress may result in formation of de novo aneurysms on the contralateral side [18]. In the current case, there was no contralateral internal carotid artery occlusion. Therefore, formation of the aneurysm was not associated with occlusion of other vessels but was potentially associated with proximal stenosis of the feeding artery. 4.2. CFD and experimental study on aneurysm initiation Several reports have described that high WSS combined with high positive WSSG is associated with initiation of de novo aneurysms, as shown by CFD studies, animal experiments, and in vitro experiments [1, 2, 19, 20]. Kulcsár et al [20] showed that high WSS and high positive WSSG were associated with de novo aneurysms in three patients, and these aneurysms had no proximal stenosis. Carotid occlusion produces high WSS and high positive WSSG at the basilar terminus in rabbits [2], and may be associated with initiation of aneurysms in humans [18]. Besides carotid occlusion, we demonstrated that proximal stenosis could produce high WSS and high positive WSSG. Measurements using different modalities show that WSS is in the range of 1–7 Pa in the arterial vascular network [12, 21, 22]. Therefore, we defined unphysiologically high WSS as >7 Pa in this study. In the current case, we found that WSS was nearly doubled and increased at >7 Pa because of stenosis. Therefore, it is possible that the proximal stenosis produced unphysiologically high WSS combined with high positive WSSG and led to initiation of aneurysms. The threshold of 7 Pa is not definitive. In addition, WSS magnitude would change by different inlet conditions. Therefore, we consider that the increase of WSS and WSSG by two to threefolds was more essential for aneurysm initiation than the absolute values of WSS. We previously reported four cases of aneurysms with proximal stenosis, including one de novo aneurysm [6]. In the one de novo aneurysm, we could not prove that the aneurysm was initiated after formation of proximal stenosis owing to a lack of serial images. In the current case, serial imaging showed that proximal stenosis existed before aneurysm formation, which strengthens our hypothesis that proximal stenosis causes aneurysm initiation. The other three aneurysms in the four aneurysms had proximal stenosis but were not de novo. Therefore, we could only presume that these three aneurysms might be initiated by the proximal stenosis. In our previous report [6], using a parametric study of aneurysm models, we demonstrated that a stenosis diameter >40% located
