Nevertheless, the vessels participating in (or immediately proximal to) the circle of Willis may not follow the geometric model as it is generally applied and this must also be investigated. The authors hypothesized that normal bifurcations of cerebral arteries beyond the circle of Willis would follow optimality principles of minimum work and that the presence of aneurysms would be associated with deviations from optimum bifurcation geometry. This must have an impact on understanding of the relationship between shear stress and aneurysm formation. The circle of Willis changes this relationship because the vessels proximal to the ring of vessels have additional factors that determine work minimization compared with more distal branches. Nevertheless, the model is predicated on an absence of significant communication between these branches. This determines the relationship between the angle of a bifurcation and the radii of the vessels. The angles of arterial bifurcations are governed by principles of work minimization (optimality principle).
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