Computation of Hemodynamics in the Circle of Willis

Abstract

Background and Purpose-Wall shear stress (WSS) and pressure are important factors in the development of cerebral aneurysms. We aimed to develop a computational fluid dynamics simulator for flow in the complete circle of Willis to study the impact of variations in vessel radii and bifurcation angles on WSS and pressure on vessel walls. Methods-Blood flow was modeled with Navier-Stokes equations as an incompressible newtonian fluid within rigid vessel walls. A model of the circle of Willis geometry was approximated as a network of tubes around cubic curves. Pulsatile inlet flow rates and constant outlet pressure were used as boundary conditions. Results-The simulations confirmed that differences in vessel radii and asymmetric branch angles influence WSS magnitude and spatial distribution. High WSS occurred at locations where aneurysms are frequent and in anatomic variants known to be associated with an increased risk for aneurysm development. Conclusions-Computational fluid dynamics analysis can be applied to the complete circle of Willis and should be used to study the pathophysiology of this complex vascular structure, including risk factors for aneurysm development. Key Words: aneurysm Ⅲ computational fluid dynamics Ⅲ circle of Willis Ⅲ hemodynamics Ⅲ wall shear stress D isruption of the internal elastic lamina is required for the creation of saccular aneurysms. Hemodynamic factors play an important role in this process. Saccular aneurysms usually arise at the distal carina of bifurcations, where vessels are exposed to the maximum impact of wall shear stress (WSS). 1 The amount of WSS depends on the geometry of the bifurcation. 2-5 WSS is minimized when the relation between vessel radii and bifurcation angles follows optimality principles of minimum work. 6 -8 In the circle of Willis, there is a confluence of flow from 3 vessels: both internal carotid arteries and the basilar artery (BA). Therefore, the hemodynamics in the circle of Willis is anatomically significantly different from the hemodynamics in normal branching situations addressed by the optimality principle. Accordingly, the normal physiology of flow and the likely impact of deviation from normality in the circle of Willis are not fully understood.In a previous study, we analyzed 3-dimensional digital subtraction angiography images of cerebral vessels with respect to vessel radii and bifurcation angles and concluded that bifurcations beyond the circle of Willis approximated optimality principles, whereas those within the circle of Willis did not. 9 In addition, we observed an increased prevalence of aneurysms at bifurcations with large branch angles. Furthermore, studies of this complex vascular structure in patients, animal models, or experimental in vitro models are difficult. Therefore, simulations with computational fluid dynamics (CFD) may contribute to the understanding of this problem. In the present study, we aimed to develop a CFD simulator for flow in the complete circle of Willis to study the impact of variations in vessel radii and bifu...

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