Numerical Models of Auto-regulation and Blood Flow in the Cerebral Circulation

Abstract

A two-dimensional time-dependent computational fluid dynamics model of the Circle of Willis has been developed. To simulate, not only the peripheral resistance of the cerebrovascular tree but also its auto-regulation function, a new "active" boundary condition has been defined and developed using control theory to provide a model of the feedback mechanism. The model was then used to simulate different common abnormalities of the Circle of Willis while a pressure drop, simulating a rapid compression of the right internal carotid artery, was imposed. Test results using a simple tube compared excellently with experiment. The total time-dependent flux for each efferent artery was tabulated and showed the important relationship between geometrical variations in the Circle of Willis and the auto-regulation of blood flow by vascular vaso-dilation and contraction. From this study, it was found that the worst case seemed to be that of a missing or dysfunctional right A1 segment of the anterior cerebral artery. The use of valid physiological models of the peripheral resistance allows for more realistic models of the blood flow in the Circle whilst allowing an easy extension to 3D patient specific simulations.

3D models of blood flow in the cerebral vasculature

“…To represent the effects of the arteriole, venous and capillary beds, eliminated from the model by the choice of efferent artery termination, the approach of using a porous block, proposed by (Ferrandez et al 2002;David et al 2003), at the termination of each efferent artery has been implemented. The permeability of the porous blocks can be set to provide a resistance to the flow in much the same way as the vascular beds, hence realistic representations of the hemodynamics can still be achieved.…”

“…These effects are of particular importance when investigating how blood is redistributed via the circle of Willis. It should be noted that there have been numerous cerebral autoregulation models proposed (Ursino and Giulioni 2003;Ursino 1991;Olufsen et al 2002), including models incorporated with a circle of Willis (Moorhead et al 2004;Ferrandez et al 2002;David et al 2003). However, the combination of autoregulation with the more realistic 3D circle of Willis geometries remains a relatively unexplored field.…”

“…This approach however cannot capture the effects of the complex arterial geometry, in particular the effects of blood vessel junctions. Subsequent 2D models of the circle of Willis (Ferrandez et al 2002;David et al 2003) have improved the definition of the geometry, however to obtain more realistic hemodynamic data 3D models must be considered. Studies have been performed on 3D models of the circle of Willis (Cebral et al 2003) generated from Magnetic Resonance Imaging (MRI) data, however, the 3D models neglected the effects of autoregulation on cerebral blood flow.…”

Computational challenges of viscous incompressible flows

“…To account for the large arterial network, Quarteroni and his colleagues have developed a circuit analog, which has been applied to more inclusive circulatory systems modeling such as the cardiovascular system and the Circle of Willis in the brain (see [ 5 5 ] among many publications). An alternative way of imposing downstream boundary conditions has been developed by Tim David and his colleagues [56] in their computation of the Circle of Willis (Cow).…”

Modelling of flow through the circle of Willis and cerebral vasculature

“…Computational Fluid Dynamics (CFD) models of the CoW include a 2D nonlinear model with time varying resistances [14,15]. There have been several CFD studies on 3D patient-specific models of the CoW that considered anatomical variations.…”