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Over the past few decades, different therapeutic methods for the treatment of intracranial aneurysms have been developed. During recent years, novel standalone intrasaccular Woven EndoBridge (WEB) technique has paved the way for efficient therapy and reduced some deficiencies in prior procedures. Blood hemodynamics plays a crucial role in occurrence and perpetuating of aneurysm; therefore, understanding of relevant parameters can lead to a better treatment and evolution of design. Objectively, this paper has established the first mathematical framework to explore hemodynamic parameters for WEB-treated saccular aneurysms by employing Computational Fluid Dynamics (CFD). Two ideal models of artery — one is suffered by a bifurcation aneurysm at Basilar Artery (BA) and another Posterior Cerebral Artery (PCA) aneurysm — are selected. Simulations are performed for an untreated and three WEB-treated aneurysms by Dual Layer (DL), Single Layer (SL) and Single Layer Sphere (SLS) WEBs. Results demonstrate that, generally, the WEB reduces flow intrusion and circulation inside the aneurysm sac, which leads to lowering WSS; however, the infiltrated flow to the WEB causes slight increase in intrasaccular pressure. Moreover, the numerical results show that the WEB DL reduces velocity and WSS, and elevates pressure inside the sac more than the WEBs SL and SLS. Among the explored WEB models (DL, SL and SLS), by assuming thorough binding at the aneurysm neck, the WEB DL demonstrates much efficient performance in flow diversion from the aneurysm, while despite the different structure of WEBs SL and SLS, they perform similarly.

In recent decades, cardiovascular disease and stroke are recognized as the most important reason for the high death rate. Irregular bloodstream and the circulatory system are the main reason for this issue. In this paper, Computational Fluid dynamic method is employed to study the impacts of the flow pattern inside the cerebral aneurysm for detection of the hemorrhage of the aneurysm. To achieve a reliable outcome, blood flow is considered as a non-Newtonian fluid with a power-law model. In this study, the influence of the blood viscosity and velocity on the pressure distribution and average wall shear stress (AWSS) are comprehensively studied. Moreover, the flow pattern inside the aneurysm is investigated to obtain the high-risk regions for the rupture of the aneurysm. Our results indicate that the wall shear stress (WSS) increases with increasing blood flow velocity. Furthermore, the risk of aneurysm rupture is considerably increased when the AWSS increases more than 0.6. Indeed, the blood flow with high viscosity expands the high-risk region on the wall of the aneurysm. Blood flow indicates that the angle of the incoming bloodstream is substantially effective in the high-risk region on the aneurysm wall. The augmentation of the blood velocity and vortices considerably increases the risk of hemorrhage of the aneurysm.

The morbidity and mortality of aneurysm rupture have raised significantly in current years. In this research, numerical investigations have been performed to disclose the impacts of hemodynamic on the breach and growth of the Intracranial Aneurysms (IA) in the middle cerebral artery (MCA). To perform this research, computational fluid dynamic (CFD) methodology is employed to model the non-Newtonian blood stream through the IA. 3D model of IA is chosen for the analysis blood flow. Wall shear stress (WSS) was evaluated and compared at the high-risk region, where the probability of rupture is high. This study offers precise information and insight about the influence of blood viscosity and velocity on the danger of the aneurysm rupture in the MCA. Our outcomes show that the location and orientation of the aneurysm have direct impacts on the growth of the aneurysm. The main attention of this research is to reveal more vibrant facts about the primary reasons for the rupture of the aneurysm and present connection among the rupture points and the local hemodynamic features. This work tries to demonstrate the critical area on the aneurysm surface by analyzing the WSS and pressure distribution.

In the recent decades, the main reason for the high death rate is related to cardiovascular disease and stroke. In this paper, numerical studies have been done to investigate the hemodynamic effects on the rupture of middle cerebral artery (MCA) in different working conditions. In this work, the effects of the blood viscosity and velocity on the pressure distribution and average wall shear stress (AWSS) are fully investigated. Also, the flow pattern inside the aneurysm is investigated to obtain the high-risk regions for the rupture of the aneurysm. Our findings show that the wall shear stress increases with increasing the blood flow velocity. Meanwhile, the risk of aneurysm rupture is considerably increased when the AWSS increases more than 0.6. In fact, the blood flow with high viscosity expands the high-risk region on the wall of the aneurysm. Blood flow indicates that the angle of the incoming bloodstream is substantially effective in the high-risk region on the aneurysm wall. The augmentation of the blood velocity and vortices considerably increases the risk of hemorrhage of the aneurysm.

This study provides comprehensive information about the impact of the parent vessel’s shape on the risk of cerebral aneurysm rupture. It focuses on internal carotid artery (ICA) aneurysms with varying parent vessel sizes, analyzing different aspects of blood flow dynamics. By comparing various hemodynamic factors such as wall shear stress (WSS), oscillatory shear index (OSI) and pressure distribution, the researchers aim to establish a meaningful relationship between the parent vessel’s mean diameter and these significant hemodynamic parameters.

In the present paper a one-dimensional mathematical model of a cerebral aneurysm is considered. The model combines the interaction between the arterial wall structure, blood pressure and the cerebral spinal fluid (CSF) that is around the aneurysm. CSF is considered electrically conducting in the presence of a uniform magnetic field. Therefore, it may be possible to control pressure and its flow behavior by using an appropriate magnetic field. Hence, such studies have potential for the treatment of Cerebral aneurysms, diseases of heart and blood vessels. The modeled mathematical equations are solved algebraically and the displacement of the arterial wall is plotted to visualize the wall movement. It is evident from the graphs the inclusion of magnetic field reduce the movement of the arterial wall and in turn prevent the rupture of the cerebral aneurysm. The solution is also investigated using computational tools for various other parameters involve in the model.

A fractional-order model is proposed to describe the dynamic behaviors of the velocity of blood flow in cerebral aneurysm at the circle of Willis. The fractional-order derivative is used to model the blood flow damping term that features the viscoelasticity of the blood flow behaving between viscosity and elasticity, unlike the existing fractional models that use fractional-order derivatives to replace the integer-order derivatives as mathematical/logical generalization. A numerical analysis of the nonlinear dynamic behaviors of the model is carried out, and the influence of the damping term and the external power supply on the nonlinear dynamics of the model is investigated. It shows that not only chaos via period-doubling bifurcation is observed, but also two additional small period-doubling-bifurcation-like diagrams isolated from the big one are observed, a phenomenon that needs further investigation.

A mathematical model for the rupture of cerebral saccular aneurysms is developed through the analysis of three-dimensional stress distribution in the aneurysm wall. We assume in this paper that a saccular aneurysm resembles a thin spherical shell (a spherical membrane), and then develop a strain-energy function valid for finite strain to analyze three-dimensional stress distribution in the aneurysm wall. We find that rupture occurs when the ratio of the wall thickness to the radius of the aneurysm is 6.1 × 10^-3. We also conclude from our analysis that rupture can occur when the ratio of thickness to radius of the parent aneurysm equals the ratio of thickness to radius of the daughter aneurysm. These findings may be helpful to the neurosurgeon for predicting the rupture potential in patients presenting with unruptured aneurysms.

The mechanics of cerebral aneurysm pathogenesis, evolution and rupture are not yet well understood. This paper presents a numerical analysis of the formation of a saccular cerebral aneurysm in for the first time in a 3D model of the basilar artery bifurcation under normal and hypertensive blood pressure. Due to the excessive endothelium derived nitric oxide produced in high wall shear stress, we assumed that smooth muscle cell relaxation is the origin of the aneurysm formation. Arterial wall remodeling under constant tension was considered to be the other mechanism of disease evolution. The wall was constructed from two elastic and hyperelastic isotropic regions. The flow was considered steady, laminar, Newtonian, and incompressible. The fully coupled fluid and structure models were solved with the finite elements package ADINA 8.5. The wall shear stress, effective stress and deformation distributions under normal and hypertensive blood pressure were compared to a healthy bifurcation. The model shows that although the malfunction of the endothelial cell layer and the corresponding smooth muscle cell-related loss of vascular tone is important to the inception of the disease; A saccular aneurysm may not be formed by this mechanism alone, and also requires the fiber-related arterial wall remodeling for further development.

Intracranial saccular aneurysms tend to be thin walled and stiffer compared with a normal artery. The current work describes computational structural dynamics (CSD) in an anatomically realistic model of a cerebral aneurysm located in the ophthalmic region, using different wall thickness, model data for the artery and aneurysm, and geometry size. The model was obtained from three-dimensional rotational angiography image data. The wall was assumed three-dimensional hyperelastic solid with different thickness in the artery and in the aneurysm regions. The effects of carotid siphon length are reported. The CSD was solved with the finite elements package ADINA. The predictions of stress and strain on the aneurysm wall were compared.

The risk of rupture of intracranial saccular aneurysms is one of the leading dilemmas for patients and neurologists. Although the probability of rupture is small, the consequences of rupture are usually fatal or crippling, and a concern for the patient is whether or not to treat an existing aneurysm. In this paper, an idealized model of saccular aneurysms with assumed Fung material behavior was investigated for rupture potential when the stresses exceeded the maximum wall strength of the aneurysm wall. Numerical simulations used various levels of blood pressure, from normal to hypertensive, in order to determine correlations of aneurysm size and risk of rupture. Results showed that hypertensive individuals harboring cerebral aneurysms with a size of at least 6 mm are at risk.

The walls of the blood vessels involved with cerebral aneurysms present different mechanical properties, when compared with those of normal artery. Consequently the models which may describe then predict an aneurysm rupture need as input their mechanical properties. This paper describes the experimental determination of the mechanical properties of the tissues of the blood vessels affected with a cerebral aneurysm. In particular, we determine and discuss the critical elongation and the rupture strength. The affected tissues were obtained from surgical clipping and extraction; six specimens were tested. The mechanical tests were performed in a tensile device. The experimental data was fitted numerically with a Mooney–Rivlin hyper elastic model. The model was compared with previous published data.

Fluid–structure interaction (FSI) simulations were carried out in a human cerebral aneurysm model with the objective of quantifying the effects of hypertension and pressure gradient on the behavior of fluid and solid mechanics. Six FSI simulations were conducted using a hyperelastic Mooney–Rivlin model. Important differences in wall shear stress (WSS), wall displacements, and effective von Mises stress are reported. The hypertension increases wall stress and displacements in the aneurysm region; however, the effects of hypertension on the hemodynamics in the aneurysm region were small. The pressure gradient affects the WSS in the aneurysm and also the displacement and wall stress on the aneurysm. Maximum wall stress with hypertension in the range of rupture strength was found.

Flow-diverting stent is an ongoing embolization device to treat cerebral aneurysms, and it diverts the flow direction to reduce the flow velocity inside the aneurysmal sacs and promote the thrombus formation. However, its effect for aneurysm embolization is controversial. A hemodynamic-biomedical coupling model was constructed to describe the generation and transport of thrombin in arteries, and the model was applied to investigate the variation of thrombin concentration, which plays a key role in thrombus formation, in two patient-specific cerebral aneurysm models when they are treated with Pipeline flow diverting stents. It is observed from computational fluid dynamics simulations that thrombin concentration in the aneurysmal sac without collateral artery increases significantly after Pipeline implantation, however, it has hardly any variation in the aneurysmal sac without collateral artery or in the giant aneurysmal sac after Pipeline implantation. Therefore, we believe that single Pipeline is very effective to embolize a small aneurysm without collateral artery, but cannot embolize a giant aneurysm or a small aneurysm with a collateral artery on its sac effectively.

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