20.1 Introduction

Hemodynamic changes are known to play an important role in the etiology, growth, and rupture of cerebral aneurysms. The higher incidence of cerebral aneurysms in (1) patients with aortic coarctation, (2) vessels proximal to a stenosis, (3) feeding arteries of arteriovenous malformations, and (4) contralateral side of an occluded internal carotid artery are prime examples of the impact of altered fluid dynamics. However, the precise cause of cerebral aneurysm formation is still unknown. Complex interactions between the vessel wall and hemodynamic forces are believed to contribute to the process. ¹ Endovascular techniques allow modification of hemodynamic variables leading to a powerful means of therapy toward promoting thrombosis and eventual aneurysmal occlusion.

During the past two decades, coil embolization has been the most popular endovascular treatment for cerebral aneurysm repair. Recently, the endovascular treatment paradigm has shifted from intrasaccular therapies (where coils or liquid embolic agents are delivered into the aneurysm sac) to endoluminal therapies (where standalone stents are deployed along the parent vessel, across the aneurysm neck). Standalone stents, called flow-diverting stents (FDSs), change the flow between the aneurysm and parent vessel promoting stagnation. The stagnant flow within the aneurysm sac promotes gradual thrombosis which ultimately will occlude the aneurysm. Over time, endothelial growth within stent struts facilitates reconstruction of the parent vessels, ultimately resulting in permanent exclusion of the aneurysm from circulation. This chapter examines the impact of FDSs on cerebral aneurysm hemodynamics and the different methodologies used to analyze these changes.

20.2 In Vitro Techniques

Various in vitro techniques have demonstrated the effects of FDSs on cerebral aneurysm hemodynamics. ² , ³ , ⁴ One of the main advantages of in vitro techniques over in vivo techniques is the repeatability of the experimental process with different devices and configurations, vascular models, and flow conditions. Furthermore, idealized cerebral aneurysm models can be employed to investigate the effects of factors, such as aneurysm geometry and stent configuration, under controlled conditions to provide a fundamental understanding of the impact of different factors on treatment success. In general, in vitro experimentation involves (1) reconstructing or designing the computational aneurysm geometry, (2) translating the computational model to a physical model, (3) connecting the physical model to a flow loop with a blood analog as a circulating fluid, (4) measuring fluid flow through the model using techniques such as optical imaging, and (5) deploying FDS into the physical model to measure the effects of treatment on cerebral aneurysm flow.

Particle image velocimetry (PIV) is a popular flow visualization and analysis technique often used in cerebral aneurysm research. ² , ⁵ , ⁶ , ⁷ One of the methods for constructing the physical aneurysm model used for experimentation is the lost-core manufacturing technique ( Fig. 20.1). The optically clear model is connected to a flow loop for experimentation. The solution is seeded with reflecting particles that are illuminated by a laser, and then imaged by one or more cameras. Hemodynamic information, such as flow velocity, is calculated based on particle movement between subsequent images. Detailed information about PIV can be found in the study of Adrian and Westerweel. ⁸ The experimental process can be repeated to investigate the effects of different FDS on cerebral aneurysm hemodynamics ( Fig. 20.2).

20.3 Computational Techniques

Advances in computational modeling and simulation techniques have facilitated the use of computational fluid dynamics (CFD) in cerebral aneurysm research, which may be the most popular technique for investigating the effects of endovascular treatment on cerebral aneurysm hemodynamics. CFD models blood flow by solving the Navier-Stokes equations (governing equations of fluid flow), consisting of continuity and momentum equations, using numerical methods and algorithms. The Navier-Stokes equations for an incompressible fluid can be written as follows:

where , ρ, P, and v are the fluid velocity, density, pressure, and kinematic viscosity, respectively, and is the gravitational force acting on the fluid. One of the main advantages of CFD over in vivo and/or in vitro techniques is the flexibility to investigate large patient populations without the tedious and expensive process of physical model construction. CFD also allows virtual treatment with endovascular devices, and has the potential to be used as a treatment-planning tool. However, various assumptions have to be made to simplify the complexity of modeling blood flow. Blood is often modeled as an incompressible and Newtonian fluid, and the vessel walls are assumed to be rigid. There are techniques that can be used to overcome this, but at the cost of computational time.

Flow analysis using CFD usually entails (1) construction of the three-dimensional (3D) computational model; (2) discretization of the computational model into mesh elements; (3) applying suitable boundary conditions to the inflow(s), outflow(s), and vessel walls; and (4) simulation of blood flow ( Fig. 20.3).

20.4 Effects of Flow-Diverting Stents on Hemodynamics

One of the main factors that plays an important role in the success of FDSs is the stent porosity. ⁹ Specifically, a correlation exists between aneurysm occlusion rates and stent porosity. ¹⁰ Porosity is defined as the ratio of the metal-free surface area to the total (equivalent to the preoperative condition). Therefore, reducing the porosity of an FDS would improve the likelihood of flow reduction and diversion. This would in turn lead to increased stagnation within the aneurysm sac promoting thrombosis, and ultimately aneurysm occlusion. However, stent porosities less than 65% can occlude neighboring perforating vessels, thereby compromising cerebral perfusion. ¹¹ Higher metal coverage (i.e., lower porosity) has also been found to cause in-stent stenosis, secondary to intimal hyperplasia. ¹² Furthermore, low porosity stents can lack the flexibility needed to navigate through cerebral vasculature. Another important consideration during the deployment of an FDS is that aneurysms often occur in the greater curvature of curved vessels. Deploying an FDS in such geometries would “open up” the stent pores at the aneurysm neck, increasing the porosity at the ostium. Fortunately, emerging technologies in CFD and modeling have enabled assessment of treatment effectiveness prior to clinical deployment of FDSs, such as effects of the stent on (1) flow diversion, (2) neighboring vasculature, and (3) parent vessel morphology, as well as the impact of different stent deployment strategies, including the use of multiple telescoping stents.

Quantitative hemodynamic responses include intra-aneurysmal velocities, aneurysmal inflow, intra-aneurysmal pressure, wall shear stress (WSS) and WSS gradients, vorticity, and turnover time. Qualitative responses include flow complexity and impingement zones. The remainder of this subsection details the effects of FDSs on hemodynamics.

20.4.1 Intra-aneurysmal Velocity and Aneurysmal Inflow

The amount of blood crossing the aneurysm neck per second, or aneurysmal inflow, and velocities inside the aneurysm can serve as indicators for FDS treatment effectiveness. In general, FDSs have proven to be superior to other stents in terms of reducing aneurysmal flow velocities, correlating with favorable clinical outcomes. ¹⁰ , ¹³ , ¹⁴ , ¹⁵ Intra-aneurysmal flow velocities in an untreated cerebral aneurysm are sometimes up to 70% of the parent vessel velocity at the end of systole. ⁹ Various clinical trials, along with experimental and computational studies, have demonstrated the effectiveness of a FDS in cerebral aneurysm treatment. In a PIV-based study, previously conducted by our group, reductions in aneurysmal velocities were observed when comparing the effects of cerebral aneurysm hemodynamics after treatment with the Pipeline Embolization Device (PED) and the Flow Redirection Endoluminal Device (FRED). Intra-aneurysmal velocity reductions of more than 55 and 65% were observed after treatment with PED and FRED, respectively, under steady and pulsatile flow conditions ( Fig. 20.4). In another CFD-based study, Kulcsár et al analyzed eight patients with para-ophthalmic aneurysms treated with SILK flow diversion (not available in the United States). ¹⁶ Velocity reductions of 44% were observed after virtually treating the aneurysm with this device. Roszelle et al have also compared the effects of PED with those of telescoping high porosity stents showing that PED treatment was associated with the greatest reductions in intra-aneurysmal flow. ²

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