Fluid–structure interaction simulation of a cerebral aneurysm: Effects of endovascular coiling treatment and aneurysm wall thickening

Author’s Accepted Manuscript Fluid–structure interaction simulation of a cerebral aneurysm: effects of endovascular coiling treatment and aneurysm wall thickening Amir Shamloo, Milad Azimi Nejad, Milad Saeedi www.elsevier.com/locate/jmbbm

PII: DOI: Reference:

S1751-6161(17)30209-6 http://dx.doi.org/10.1016/j.jmbbm.2017.05.020 JMBBM2338

To appear in: Journal of the Mechanical Behavior of Biomedical Materials Received date: 21 February 2017 Revised date: 9 May 2017 Accepted date: 12 May 2017 Cite this article as: Amir Shamloo, Milad Azimi Nejad and Milad Saeedi, Fluid– structure interaction simulation of a cerebral aneurysm: effects of endovascular coiling treatment and aneurysm wall thickening, Journal of the Mechanical Behavior of Biomedical Materials, http://dx.doi.org/10.1016/j.jmbbm.2017.05.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Fluid–structure interaction simulation of a cerebral aneurysm: effects of endovascular coiling treatment and aneurysm wall thickening Amir Shamlooa,*, Milad Azimi Nejada, Milad Saeedia a

Department of Mechanical Engineering, Sharif University of Technology

*Corresponding author: Dr. A. Shamloo, Department of Mechanical Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran, Email: [email protected]

Tel: 98-21-66165691, Fax: 98-21-66165599

In the present study, we investigate the effect of the hemodynamic factors of the blood flow on the cerebral aneurysms. To this end, a hypothetical geometry of the aneurysm in the circle of Willis, located in the bifurcation point of the anterior cerebral artery (ACA) and anterior communicating artery (ACoA) is modeled in a three-dimensional manner. Three cases are chosen in the current study: an untreated thin wall (first case), untreated thick wall (second case), and a treated aneurysm (third case). The effect of increasing the aneurysm wall thickness on the deformation and stress distribution of the walls are studied. The obtained results showed that in the second case, a reduction in the deformations of the walls was observed. It was also shown that the Von Mises stress has a 10 percent reduction in the untreated thick wall aneurysm compared to the untreated thin wall aneurysm. Thus, increasing the thickness of the aneurysm wall can be proposed as temporary remedial action. In the third case, an aneurysm that has been treated by endovascular coiling is investigated. The deformation and Von Mises stress in this case was decreased more than 43 and 87 percent compared to the first case, respectively. The wall shear stress distribution due to the fluid flow in the first and second cases showed small amounts of shear stress on the aneurysm sac. In these two cases, the oscillatory shear index was measured to have an approximate value of 0.47 in the aneurysm region, though, this value was measured to be about 0.1 for the third case. The hybrid effect of the wall shear stress and the oscillatory shear index on the relative residence time (RRT) was also studied. When this parameter reaches its maximum, the aneurysm rupture may occur. It was shown that by treating the aneurysm (the third case), RRT parameter can be decreased ~ 200 times relative to the first and second cases, which suggests an appropriate treatment of the aneurysm by choosing the coiling method. Keywords: cerebral aneurysm, aneurysm wall thickening, endovascular coiling treatment, vessel wall hyperelastic behavior, fluid-structure interaction, non-Newtonian properties of blood.

Introduction Aneurysm is a disease which affects the blood vessels and makes the artery walls become vulnerable; It causes thinning and bulging in the vessel walls [1]. About 5 to 8 percent of the cerebral aneurysms are unknown until the full outbreak because there is no symptom for them. The aneurysm rupture is the main cause of subarachnoid hemorrhage inside the brain and leads to many problems, such as mortality, morbidity and disability [2]. Rupture of a cerebral aneurysm is also one of the main causes of stroke [2, 3], and has obtained much attention among many researchers [4]. Among cerebral aneurysms, the ones that are made within the circle of Willis have the highest number and ~ 85% of saccular aneurysms are formed in the vessels of the circle of Willis [5]. About 35 percent of the aneurysms formed in the circle of Willis are related to the anterior cerebral artery (ACA) [6]. There are different methods to cure aneurysm, such as clipping, endovascular coiling and balloon placement [7]. The decision about choosing a specific treatment method depends on the shape, position and width of the neck (dome-neck ratio) of the aneurysms [8]. Depending on the location of aneurysm, it can be cured by sending a catheter through the vessel and injecting a substance made of platinum; this method is called coiling [9, 10]. For aneurysm treatment, understanding about the behavior of aneurysm, the important factors causing its growth and burst is necessary [11]. The hemodynamic factors of the blood flow and particularly the flow shear stress may have many effects on the dysfunction of endothelial cells resulting in the destruction of the vessel walls [12, 13]. Defects and weaknesses in the vessel walls of the patients can exacerbate these factors which finally may lead to the formation, growth and rupture of the aneurysms [14, 15]. Computational Fluid Dynamics (CFD) can be a very helpful method to study and understand the mechanism of aneurysm growth and burst [16]. The numerical modeling of the blood flow and its influence on the aneurysm and vessel walls can be a powerful tool for prediction of the growth and rupture time of aneurysm with no cost and morbidity [17]. Regarding the soft nature of the vessel walls, it is necessary to investigate the interaction of blood flow and the vessel walls, and thus, fluid-structure interaction (FSI) simulation method should be implemented [1622]. Some previous studies had focused on investigating the biological systems of the human body as well as the animal body [23]. Many experimental and theoretical studies are conducted to understand the effect of hemodynamic properties of blood flow on the aneurysm especially by analyzing the shear stress and deformation in the blood vessel walls [2, 16-22, 24-26]. The tensile stress and shear stress have a great effect on the blood vessels reconstruction [27]. In most of these studies, it has been shown that the aneurysm is most probable to happen in the vessels bifurcation points. In the bifurcation points, the risk of rupture increases due to the great magnitude of the wall shear stress. The aim of mathematical studies is to investigate the amount of wall deformation which can be performed by numerical simulation [16-22, 24-26, 28]. The aneurysm formation has been modeled by Sheidaei et al. [29]. However, it is not yet possible to precisely predict the aneurysm formation in the human body [16]. To study blood flow in the vessels and also within the cerebral aneurysm, FSI simulation is widely used. In previous studies, the blood flow in the cerebral aneurysms has been simulated considering various geometries of

the vessels and using different hypotheses [2, 6, 14-22, 24-26]. Torii et al. [16, 26] investigated the effects of the wall thickness on the aneurysm using the FSI simulation. They showed that the aneurysm has a significant influence on the induced shear stress and deformations of the blood vessel walls. Mitsos et al. [30] applied a patient-specific geometry to investigate the endovascular effect on the aneurysm treatment. Acevedo-Bolton et al. [31] simulated the aneurysm treatment by CFD and compared CFD results with the experiment. The results showed that CFD can elucidate the effect of hemodynamic parameters of the blood flow on the aneurysm treatment. It should be mentioned that the blood is a non-Newtonian fluid [32, 33] and the vessel walls have a behavior similar to the hyperelastic materials [34]. In the current study, the ideal geometry of the ACA and anterior communicating artery (ACoA) are used for aneurysm modeling at the bifurcation point. FSI analysis of the vessel walls was implemented by using the five-parameter hyper-elastic Mooney-Rivilin model and the blood viscous modeling was performed by using the Herschel-bulky non-Newtonian model. In all of the cases studied, the vessel wall thickness was considered to be 0.3 mm. In the first case, the aneurysm wall thickness was assumed to be 0.15 mm thinner than the normal vessel walls while in the second case, in order to investigate the effect of thickening of the aneurysm wall, the thickness of these walls was selected to be 0.3 mm. Finally, in the third case, the filled sac aneurysm model was investigated which was not simulated in previous studies. Therefore, the third case is selected for the investigation of the effectiveness of the coiling remedial action on the extent of the wall deformation, induced stresses on the vessel walls, flow patterns, wall shear stress (WSS), oscillatory shear index (OSI) and relative residence time (RRT). Moreover, in the second case, the effect of aneurysm wall thickening relative to the first case is studied using the aforementioned parameters. Computational model Geometry In this study, the MRI base models are not used for the geometry of simulation owing to their complicated tortuosities. Arteries are normally straight to transport blood to distal organs in an efficient manner [35]. However, arteries may become tortuous as a result of abnormal development or vascular disease [35, 36]. Several forms of the vessel tortuosity have been reported including, curving/curling, angulation, twisting, looping and kinking [35]. Since these tortuosities do not have a significant effect on fluid-structure interaction (FSI), we utilized a simplified geometry for our study which is defined as “ideal geometry”. The only difference between our ideal model and the Willis anatomy is some minor tortuosities of Willis anatomy, whereas other characteristics of the Willis anatomy has been taken into account in our ideal model. Ideal geometry was delineated by Solidworks according to the geometry of the anterior part of the circle of Willis in anatomy (figure 1.a, b) which is shown with a red highlight in figure 1.b. In this geometry, aneurysm sac is modeled by a sphere with 2.8 mm in diameter that is located in the bifurcation point of the anterior cerebral artery (ACA) and anterior communicating artery (ACoA). There are two main reasons for choosing this diameter. First, the aneurysm size is lower than 4 mm in 90 percent of unruptured aneurysms [2]. Second, Kataoka et al. [37] reported that in the aneurysms with the size of less than 5 mm, the aneurysm wall is

thinned about 48 percent. In contrast, the formation of aneurysms with the size larger than 5 mm is usually due to atherosclerosis which is not the aim of this study. The applied geometry for the fluid domain has been shown in figure 1.b. The vessel lengths and the diameter of ACA and ACoA are summarized in table 1. In this study, we have chosen three cases to study the effect of aneurysm treatment on the hemodynamic parameters of the blood flow by endovascular coiling method and aneurysm wall thickening. In all cases, the vessels wall thickness excluding aneurysm wall has been assumed to be 0.3 mm [26]. Abruzzo et al. [38] have stated that the lowest thickness of an aneurysm wall is 0.05 mm before its rupture occurs and one of the aims of this investigation is to study the untreated thin wall aneurysm. So the thickness of 0.15 mm [39] is used for the aneurysm wall in the first case (untreated thin wall) and 0.3 mm for the second case (untreated thick wall). In the third case, aneurysm sac has been considered to be fully filled to explore the effect of endovascular coiling treatment. In this study, these cases are defined as an untreated thin wall, untreated thick wall, and a treated aneurysm, respectively. Table 1- The diameter and length of the vessels[40, 41]

Length (mm) Diameter (mm) Anterior communicating artery 2 2 Anterior cerebral artery - A1 12.5 2.2 Anterior cerebral artery - A2 23 2.3 For analyzing the simulations, some hemodynamic parameters of the blood flow are reported which have a strong effect on the endothelial cells function and vessel diseases. In this study, the hemodynamic parameters such as flow pattern, wall shear stress (WSS), oscillatory shear index (OSI) and relative residence time (RRT) will be stated and analyzed. OSI and RRT parameters can be utilized to show their effects on the aneurysm and its progression or treatment. Oscillatory shear index and relative residence time Equations 1 and 2 define the oscillatory shear index (OSI) and time-averaged wall shear stress (TAWSS), respectively. In these equations, T and  w are the cardiac cycle duration and the vector of instantaneous wall shear stress [42]. T

 1 OSI  (1  2   0

w

)

T

0

 TAWSS 

T

(t )dt

w

(1)

(t ) dt

 w (t ) dt

(2) T OSI value varies from 0 for steady flow to 0.5 for completely oscillatory flows. Meng et al. [2] have reported that a low WSS and a high OSI can trigger inflammatory-cell-mediated destructive remodeling. Moreover, high and low wall shear stress can affect the extracellular matrix (ECM) degradation and cell death. Consequently, the aneurysm growth and rupture risk will increase 0

[2]. Also, a low WSS (or TAWSS) and a high OSI have strong effects on the growth and rupture risk of aneurysm, therefore it is desirable to choose and analyze a parameter that considers both the aforementioned parameters. Thereby, the relative residence time (RRT) can be chosen for this purpose. This parameter is mathematically defined according to the equation 3. RRT can attribute to much more distinction between the oscillatory phenomena because it does not have an upper limit as opposed to OSI [43].

RRT 

1 (1  2OSI )  TAWSS

(3)

Computational model for the fluid domain The regime of blood flow in the arteries is considered to be laminar due to the low Reynolds number. The governing equations of blood flow are continuity and Navier–Stokes which have the following forms:

.v  0 v    v.v  P  .( v) t Blood is an incompressible fluid, hence its density is constant and equals to 1050 kg / m3 .

(4) (5)

Viscose properties of blood Rheology studies show that the blood is a non-Newtonian fluid owing to its viscoelastic, shear thinning, and yield stress properties [44]. Blood mainly consists of plasma which has a Newtonian behavior, but the existence of the cells, causes the deviation of blood from Newtonian to non-Newtonian behavior. The amount of this deviation depends on the hematocrit percent, adhesion of blood cells, and plasma viscosity [32]. The non-Newtonian properties of blood are considered in this research and Herschel-bulky model is employed for this purpose. CampoDeaño et al. [32] have experimentally studied the viscous properties of blood and compared the experimental results with the non-Newtonian conventional models. Their comparison showed that Herschel-bulky model has a good agreement with the experimental data. Carreau-Yasuda and Quemada models also showed a good agreement with those data, as well, but, the Herschelbulky model had a better agreement with experimental data in comparison to other models based on this report [32]. The main equation of Herschel-bulky model is expressed in equation (6) in which  ,  , k , n and  0 are defined effective viscosity, shear strain rate, consistency factor, power-law index and yield shear stress, respectively [32].

  k n 1 

0 

Coefficients of equation (6) have been given as following [32]:

(6)

k  8.9721103

Ns n m2

 0  0.0175

n  0.8601

N m2

Boundary condition In this study, velocity and pressure profiles in ACA have been used as the inlet and outlet boundary condition, respectively. Pressure and velocity profiles have been derived from the experimental works of Abdi et al. [45] and Liu et al. [46] which are shown in figure 2. In a short distance from the inlet, the flow becomes fully developed due to the small diameter of the vessel and the viscosity dominant effects. Based on the Liu et al [47] report, the inlet effects are minimized at axial distances greater than 5 times of the vessel diameter downstream. According to table 1, the inlet effects are negligible before the aneurysm sac and bifurcation point which are considered to be the critical points in this study. No-slip boundary condition has been imposed for the vessel and aneurysm walls. ANSYS Fluent software has been employed to solve three-dimensional equations of continuity and momentum. The convergence value for these equations was set to 7 106 (RMS). This software executes the SIMPLE algorithm for discretization and solving of equations. Total solving time has been considered to be 1.8 s (two cardiac cycles). The time step independency analysis was performed for the time steps of 0.01 and 0.005 s. The obtained results showed that the relative difference between the wall shear stress area averaged (WSSAA) parameter for these time steps is lower than 0.6 percent. So, the time step of 0.01 s has been utilized for all cases. Moreover, the simulation was performed for three cycles and WSSAA for each cycle was calculated. A relative difference of 0.1 percent was obtained for WSSAA of the second and third cycles. Thereby, the results have been collected from the second cycle. Mesh In this research, the mesh for the fluid and solid domains has been explicitly generated by ANSYS solver. The number of elements and nodes for each domain are presented in table 2 for three mentioned cases. Six mesh layers were used adjacent to the vessel and aneurysm walls to increase the accuracy of calculations. The utilized mesh is sufficiently fine for the independency of the results from the mesh. The mesh sensitivity analysis was done for the first case fluid domain and with the number of elements mentioned in table 2 while comparing the result with the one obtained using a finer mesh. The finer mesh had about 220000 elements. The difference of the obtained WSSAA for these meshes was almost one percent. Accordingly, we used the data of table 2 for simulations. The solid domain mesh has been shown in figure 3.a. Table 2. The node and element number of utilized mesh

Type of simulation Untreated thin wall aneurysm (First case) Untreated thick wall aneurysm (Second case) Treated aneurysm

Fluid/Solid Domain Fluid Solid Fluid Solid Fluid

Number of elements

Number of nodes

158176 59221 155832 74703 124175

51632 28837 51208 36140 45357

(Third case)

Solid

41474

19907

The computational model for solid domain The arteries are dilated by blood pressure due to the soft and flexible structure of vessels. Their radius change is mostly higher in low blood pressure compared to the high blood pressure. In other words, the relation between the blood pressure and the artery radius change is not linear. This type of behavior observed in the rat carotid artery which has been reported by Martin et al. [48], is also true for other brain arteries. This behavior deviates from the behavior of linear elastic materials and has a more adaptation with the behavior of hyperelastic materials. Thereby, the 5-parameter Mooney-Rivlin model has been employed to simulate the hyperelastic behavior of the vessel walls. The strain energy function of this model has the following form: 1 ( J  1) 2 (7) d In this equation, W is a second order combination of two invariants of the left Cauchy–Green deformation tensor and J is the determinant of the gradient matrix of the deformation which equals to 1 for incompressible material. C coefficients or material constants were obtained from non-axial true strain-stress curve of the vessel wall which has been illustrated in figure 3.b. These coefficients have been derived from this curve by using the software curve fitting tool. These constants are used to calculate the shear and bulk modulus of the vessel wall [49]. The vessel wall is assumed to be compressible. Its density is 1060 kg/m3 and has been fixed at the inlet and outlet locations. W  C10 ( I 1  3)  C01 ( I 2  3)  C11 ( I 1  3)( I 2  3)  C20 ( I 1  3) 2  C02 ( I 2  3) 2 

FSI simulation In this research, the realistic FSI is used to solve both the fluid and solid domains simultaneously. For coupling of the fluid and solid domains, Dynamic Mesh method has been used, which results in the two-way data transfer of the fluid and solid domain solvers. By solving the fluid domain, the stress distribution on the interface of the fluid and solid regions is computed and this distribution on the vessel wall are considered as the input for the solid domain solver. Likewise, by solving the solid domain, the wall displacement, radius and lumen volume changes are specified. These values are considered as the input for the fluid domain solver, so that, this solver changes the fluid domain mesh based on these values and uses this modified mesh for the next iteration. This data transfer between the fluid and solid solvers is repeated as far as the data transfer reaches the convergence. This solving process is called the two-way FSI simulation. If only the fluid solver data is given to the solid domain, and no output data is given from the solid to the fluid domain, this solution process is called one-way FSI simulation. From the aforementioned explanations, it is obvious that the two-way FSI simulation is more accurate than the one-way one. Therefore, the two-way FSI or the realistic FSI simulation has been employed in this study. Based on the report of Siamak et al. [50], this method is complicated and numerically expensive. The finer mesh and smaller time steps results in more complications. Thereby, we used the time step of 0.01 and the reported meshes in table 2 for all cases to reduce the time and calculation cost.

Results Wall displacement Figure 4 shows the solid wall displacement contour for all cases during the systolic phase. The maximum displacement equals to 0.67, 0.66 and 0.37 mm for the first, second and third cases, respectively. In the first and the second case, the maximum displacement occurs in the aneurysm neck. Overall, in the third case, the displacement (figure 4.c) is lower relative to the first and second cases (figures 4.a and 4.b). The main reason for this difference is related to the particular pattern of blood flow in comparison to the first and second cases. The maximum displacement for the treated aneurysm is 43 percent less than the other two cases. So, the aneurysm treatment by endovascular coiling method can decrease its wall displacement and rupture risk. The maximum displacement of the vessel wall has been plotted in figure 5.a at each time step for the first and second cases. In reality, the effect of wall thickness on the displacement is given in this figure. There is a slight difference between the displacement of the first and second cases. The displacement difference in these two cases becomes bigger at the systolic phase. It should be noted that the displacement decreases by aneurysm wall thickening. Von Mises stress Von Mises stress is defined as the effective stress and this parameter is a combination of the normal and shear stresses that are exerted on the solid substance elements. The comparison of this parameter with material strength can predict the failure of the material. Here, the material failure is interpreted as the aneurysm wall rupture. The plot of maximum Von Mises stress that occurs at the aneurysm neck has been depicted in figure 5.b for the first and second cases. The relative difference of Von Mises stress is negligible during the solving time excluding the systole time. During the systole, the relative difference of 10 percent is observed between the first and second cases. This difference is related to the aneurysm wall thickness which in the first case is 0.15 mm and in the second case is 0.3 mm. Time averaged of Von Mises stress was calculated to be 0.266 and 0.241 MPa for these cases, respectively. The Von Mises stress distribution for these cases at the systole phase have been presented in figure 6. The maximum stress for the first, second and third cases are 0.9919, 0.8869 and 0.1274 MPa, respectively. In the treated aneurysm, the relative reduction of the maximum stress is equal to 87 percent whereas this value is 10 percent for the untreated thick wall aneurysm when comparing the results with the untreated thin wall aneurysm. The stress in the normal vessels is much smaller than the stress in the aneurysm dome, as can be seen in figure 6.a and 6.b. It should be noted that the aneurysm rupture risk in the first case is higher than the second and third cases. Velocity contour and velocity vector In figure 7.a the velocity contour has been shown in x-y midplane for the first case at the systolic phase. From this figure, it is clear that a low amount of blood flow enters to the aneurysm sac and this low flow inserts a slight amount of shear stress on the aneurysm wall. In figure 7.b, the velocity vectors are presented in the aneurysm sac and the bifurcation region for the first case, in which the vectors have a normal size and are illustrated with the same distance from each other.

According to this figure, the flow enters from the right ACA-A1 to ACoA and the same pressure of the both branches of ACA prevents this flow to enter into the left part of the ACA branch, thereby, this flow enters the aneurysm sac and its impingement to the front wall causes the formation of two vortex flows inside the aneurysm sac. Furthermore, two vortex flows are created in ACoA. The existence of the vortex flows in the vessel causes the creation of areas with low shear stress and high intensity of oscillation [51]. The impingement of the flow to the wall creates a stagnation point on the aneurysm wall. The stagnation points have a higher pressure than the other points and the stagnation of the flow around these points leads to the creation of areas with low shear stress. High pressure and low shear stress make the stagnation points more vulnerable to the aneurysm rupture than the other points. Flow patterns and velocity vectors in the second case are similar to the first case owing to the little thickness change of the aneurysm wall. Consequently, flow patterns and velocity vectors have not been reported for the second case. For the third case, velocity contour is shown in figure 8.a and velocity vectors at the bifurcation and treated aneurysm locations are presented in figure 8.b. It can be seen from figure 8.a and figure 8.b that two vortex flows are created in ACoA. These two vortex flows are created due to the specific geometry of this part of the circle of Willis that can also be seen in the first case. The areas with vortex flow have the lower shear stress than the other areas and are prone to endothelial cells destruction. Therefore, the majority of aneurysms of the circle of Willis are created in the bifurcation of ACA and ACoA. Finlay et al. [52], have also reported that the bifurcation regions are potential areas for the formation of the aneurysm sacs. Wall shear stress WSS contours are presented for the first and third cases during the systolic phase in figure 9.a and 9.b, respectively. In both figures, the upper limit of the instantaneous wall shear stress is about 30 Pa, which is in agreement with the numerical studies done in this field. There are some higher values reported by other studies, e.g. Torri et al. [16] and Castro et al. [53] calculated this value as 40 and 65 Pa, respectively. The maximum wall shear stress location in the first and third cases has been marked in figure 9. In these regions, the wall shear stress has a larger amount due to the existence of bifurcation and the impingement of the blood flow to the wall. A relatively low wall shear stress occurs on the aneurysm and ACoA wall. In figure 9.a, the range of wall shear stress on the aneurysm region varies from 0.05 Pa to 2.5 Pa. In figure 9.b, the low wall shear stress area on aneurysm sac is removed by endovascular treatment. Oscillatory shear index and relative residence time In figure 10, OSI parameter is presented for all three cases at the systolic phase. As shown in figure 10.a and 10.b, the maximum of OSI parameter for the first and second cases equals to the ~ 0.47 which occurs on the aneurysm sac. Moreover, the maximum value of this index for the third case (figure 10.c) equals to 0.12. In this case, the hemodynamic parameter of the blood flow that caused cell inflation and destruction becomes very weak. This could be the reason for the effectiveness and permanency of aneurysm treatment by endovascular coiling method. The bifurcation regions have larger values of OSI than the other areas as seen in figure 10.c. Can and

Du [54] reported that the aneurysm formation is significantly related to high values of OSI and the regions of aneurysm formation usually have a high oscillatory shear index. These areas have been marked in figure 10.c. In figure 11, RRT contour has been shown for each of the three cases at the systolic phase. In figure 11.a and 11.b, the location of the maximum RRT has been marked with a red arrow. In the first and second cases, RRT parameter reaches its maximum on the aneurysm sac. High values of RRT related to this case, show the low wall shear stress and high oscillatory index at the same time on the aneurysm sac. The red arrow in these two cases can be the region that the aneurysm rupture occurs. From figure 11.c it can be seen that RRT value has been decreased compared to the first and second cases by filling the aneurysm sac. This value is reduced up to 200 times for the treated case in comparison with the first and second cases. This shows the permanent treatment of the aneurysm by endovascular coiling method that makes the rupture probability to become negligible. Discussion: Computational fluid dynamic (CFD) can be a robust tool for analyzing and interpreting the cerebral vessel diseases such as ruptured and unruptured cerebral aneurysms. With the aid of this tool, valuable information about effective parameters in this field is achievable without any risk. Performing CFD analysis before the surgery can decrease the mortality and morbidity risk of the surgery. Implementing simulation data for surgical treatments can strongly improve the quality of the operation. Moreover, methods that are proposed as the surgical operation can be validated with the CFD tool. The researchers report their CFD findings according to the hemodynamic and morphological parameters. Hemodynamic parameters used in aneurysm studies are as follows: Wall shear stress (WSS), maximum intra-aneurysmal wall shear stress (MWSS), low WSS area, WSS gradient (WSSG), OSI, the number of vortices (NV), relative residence time (RRT) and pressure [55, 56]. The NV is defined as the number of vortices that are formed in the cross-sectional plane of the aneurysm sac. This parameter exhibits the complexity of flow structure. Xiang et al. [56] have reported that the formation of vortices in the aneurysm sac is correlated with aneurysm rupture because of increasing the cell inflammatory behavior of aneurysm wall. Moreover, their obtained results showed that the ruptured aneurysm had multiple vortices and unruptured aneurysms had a single vortex. In our results as shown in figure 7.b, two vortices formed in the aneurysm sac for the untreated thin and thick wall aneurysm, so the probability of aneurysm rupture increases in these cases. But, these vortices in the third case is removed due to the endovascular treatment. Hoi et al. [57] reported that the blood flow enters the aneurysm sac from distal neck and by forming a vortex, it exits from the proximal neck. This pattern of flow also has been observed in our study (figure 7.b). Another hemodynamic parameter is the wall shear stress. The low wall shear stress targets the cellular regeneration and by destruction of extracellular matrix (ECM) intensifies the cell death and aneurysm growth [2]. Lu et al. [58] analyzed patient-specific aneurysm models by using CFD. In these patient-base geometries, the stated range for WSS distribution varies from 0 to 30

pascal at the systole time. This range is in adaptation with the reported range in our ideal geometry. In addition to the WSS, the regions with high OSI are mainly located on the aneurysm wall, in these patient-based geometries. These regions are also seen in figure 10.a and 10.b in our simulations. Studying the interaction of the blood flow and the vessel walls is much more complex in patientspecific geometries, unlike the ideal geometry, so, for analyzing the aneurysm treatment models such as endovascular coiling, at the first step, the ideal geometry can be utilized to determine the overall effect of the treatment on the hemodynamic parameters that results in the deterioration or improvement of these parameters. In the next step, a patient-based geometry can be utilized to obtain more details. It is clear that the simulation cost is lower in the ideal geometry compared to the patient-based geometry. Generally, patient-specific geometry reconstruction is cumbersome and time-consuming [50]. One of the reported limitations by Lu et al. [58] and Xiang et al. [56] is the rigid wall assumption for their patient-based geometries that has been solved in our research. The changes of area averaged WSS over time are depicted in figure 12.a for the first case, the range of these changes is from 2 to 9 Pa. Rossitti et al. [59] have experimentally reported the range of 2.66 Pa to 9.232 Pa for WSS of cerebral arteries, and according to the report of Cheng et al. [60] this range is from 2 to 16 Pa, which confirms the results of our study which is in an acceptable consistency with experimental data. In this study, time averaged of mean shear stress is 4.6 pascal. This value is within the reported range for the normal artery (i.e. 1-7 pascal) by Malek et al. [51]. Yagi et al. [61] studied cerebral aneurysms experimentally by stereoscopic particle image velocimetry, and it was reported that the aneurysmal dome occupied by the separated flow exhibited a smaller WSS of the order of 3 Pa. This value is in accordance with the value obtained by current study. The average of WSS versus time in aneurysm neck is depicted in figure 12.b for the first case. Authors proposed the low wall shear stress as a risk factor for aneurysm rupture [58, 62, 63]. Xiang et al. [56] showed that WSS in intracranial aneurysms is lower than WSS in their parent vessels. This low WSS is seen in figure 9.a at the aneurysm sac while comparing it with the parent vessel. At the systole time, the upper limit of WSS is 2.5 pascal for aneurysm sac while this value is 30 pascal for the parent vessel. Moreover, the obtained WSS range varies from 1 to 3.5 and 2 to 9 pascal for aneurysm neck and parent vessel that is illustrated in figure 12.a and 12.b, respectively. The phenotype of endothelial cells in oscillatory flows is specified with the rounded shape. This shape increases the proliferation rate and permeability. Moreover, the endothelial dysfunction by the oscillatory shear stress is related to the increased Endothelin-1 (ET-1) and decreased NO production and finally can cause the cellular toxicity and smooth muscle cell proliferation and atherogenesis [64]. This dysfunction, owing to oscillatory flow, is measured by OSI. As seen in figure 10, this parameter has a high value equal to the 0.47 on the aneurysm wall for the first and second cases. In the third case, this value reaches to the 0.1. Thereby, endothelial dysfunctions can be significantly decreased in this case compared to the first and second cases. When the complex flow with multiple vortices is created in the aneurysm sac, the flow adjacent to the walls tends to be recirculating, slow and oscillatory. So, in these regions WSS has a low

amount and OSI has a high value and fluid particles tend to spend a longer time near the wall [58]. RRT parameter can quantify this time and it is clear that the high amount of this parameter is related to the regions that the movement of blood particles is very slow and almost quiescent. As seen in figure 11, RRT value on the aneurysm wall is very high for the first and second cases compared to the third case. Ohta et al. [65] and Valencia et al. [66] have reported that non-Newtonian effects of the blood should be considered in cerebral aneurysms due to the existence of the slow flow in the aneurysm dome and the small diameter of the cerebral vessels. So, the non-Newtonian effects of the blood were taken into account in our simulations. Xiang et al. [67] investigated the effect of blood viscosity on the cerebral aneurysm hemodynamic parameters by using the Newtonian, Casson and Herschel-Bulky models. They stated that the Newtonian model is acceptable for CFD simulation of cerebral aneurysm hemodynamics, but it may underestimate the viscosity and overestimate the shear rate and WSS in the slowly recirculating flow regions. These regions are typically found at the dome of the saccular aneurysms as well as in the aneurysms following endovascular treatment. Thereby, we applied the Herschel-Bulky model to study the aneurysm treatment by endovascular coiling method and achieved more accurate results. When the aneurysm rupture occurs, the effective stress (flow-induced stress) exceeds the strength of aneurysmal wall (tissue strength). Therefore, the effective stress is a remarkable factor for predicting the aneurysm rupture that is analyzed in this research. Although, the accurate determination of the tissue strength is a problematic issue [68], it has been found that the wall strength is correlated with the collagen fibers strength and their orientation in the aneurysm wall [69]. Previous studies has shown that the assumption of the rigid wall for modeling the elastic properties of the vessels wall overestimates WSS [39]. So, we utilized the hyperelastic model to simulate the vessel wall elastic characteristics. In this study, the maximum effective stress occurred at the aneurysm neck that is consistent with the Valencia et al. [69] and Isaksen et al. [39] reports. Valencia et al. [69] stated that the high values of the effective stress in this region is related to the high curvature in this area. As seen in figure 4, the displacement also reaches its maximum at aneurysm neck. Thus, the high wall tension and displacement in this area increases the risk of rupture particularly in the first case but these quantities decrease with aneurysm wall thickening in the second case. In the third case, the displacement decreases in comparison to the first and second cases. According to Macdonald et al. [70] report, the breaking stress of the cerebral aneurysm tissue varies approximately between 1.09 MPa and 1.91 MPa. Since the calculated wall stresses in our model are 0.9919 MPa, 0.8869 MPa and 0.1274 MPa for the untreated thin wall, untreated thick wall and treated aneurysm, respectively, it should be stated that the first case condition is critical and its rupture probability is high. But, by thickening the aneurysm wall, the rupture probability is reduced and in the third case, this probability reaches its lowest amount by endovascular coiling treatment. So, aneurysm wall thickening can be proposed as a short-term treatment against the endovascular coiling method. Lee et al. [71] stated that the biological and mechanical wall weakening mechanism plays a more significant role compared to the high wall tension in aneurysm rupture. Conclusion

In this research, we investigated an untreated thin wall, untreated thick wall, and a treated aneurysm to study the effects of aneurysm wall thickening and endovascular treatment on the hemodynamic and structural parameters. The biological mechanisms of the aneurysm wall weakening, Von Mises stress and wall displacement showed a high reduction in the treated aneurysm when the endovascular treatment was applied. In the untreated thick wall aneurysm, only Von Mises stress and displacement showed a reduction compared to the untreated thin wall aneurysm. So the aneurysm wall thickening can be proposed as a temporary treatment. It should be noted that the endovascular coiling method can be proposed as a permanent treatment of the aneurysm according to the obtained results. To achieve these results, the non-Newtonian effects of the blood and the hyperelastic behavior of the vessel walls were taken into account in our simulations. References: [1] [2]

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Figures:

(a) (b) Figure 1. (a) Utilized geometry for the simulation. (b) Circle of Willis anatomy[34].

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Figure 2. Velocity and pressure waveforms: (a) Velocity profile for the inlet boundary condition. (b) Pressure profile for the outlet boundary condition.

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Figure 3. (a) Solid domain mesh. (b) Vessel wall material ( stress-strain curve)

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Figure 4. The displacement contour (a) Untreated thin wall aneurysm (first case) (b) Untreated thick wall aneurysm (second case) (c) Treated aneurysm

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Figure 5. (a) Maximum displacement (b) Maximum Von Mises stress for the first and second case.

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Figure 6. The Von Mises stress contour (a) Untreated thin wall aneurysm (first case) (b) Untreated thick wall aneurysm (second case) (c) Treated aneurysm

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Figure 7. (a) Velocity contour (b) velocity vectors in the bifurcation point and aneurysm sac in systolic phase of the first case.

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Figure 8. (a) Velocity contour (b) velocity vectors in the bifurcation and aneurysm sac at systole in the third case.

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Figure 9. Wall shear stress contour at the systole (a) first case. (b) third case

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Figure 10. Stress oscillatory index contour: (a) for the first case. (b) For the second case. (c) For the third case.

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Figure 11. RRT contour in systole phase: (a) the first case. (b) The second case. (c) The third case

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Figure 12. Area averaged of WSS, (a) in the whole solution domain, (b) in the neck of the aneurysm