Optimality principles and flow orderliness at the branching points of cerebral arteries.

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Abstract
The cerebral arteries present an optimum blood flow/vessel radius relation. However, branch angles may vary widely in the cerebral arteries because the parametric optimization of branch angles is irrelevant in terms of energy cost. The position of the flow divider in extracranial arteries has been suggested to be optimum in flow orderliness. No data exist on the flow divider of cerebral arteries. Thus, we hypothesized that in the cerebral arteries the apex of the bifurcations, which is known to be the site of maximum hemodynamic stress in a vascular network, may normally lie in a non-optimum position relative to the dividing flow streamline in the parent vessel, leading to disturbed laminar flow and increased vessel wall shear stress at the apical region despite the optimum blood flow/vessel radius relation. The objective of this study was to test our hypothesis. We measured the branch angles and diameters of parent and branch segments of the anterior cerebral artery system from lateral projections to minimize the measurement error on angiographs chosen at random from normal sets. The position of the apex of the bifurcations in relation to the ostium of the parent artery (gamma) and the ratio of the branch diameters (d2/d1) were compared. Optimum curves for these parameters were calculated by a mathematical model. In addition, the separation of flow streamlines according to gamma was calculated for each bifurcation and related to the division of flow required by each branch according to the optimum blood flow/vessel radius relation. The data points on gamma and d2/d1 and the separation of flow according to gamma and the division of flow required by the branches were found to scatter around the optimum curves. However, a trend toward the theoretical optimum is discernible. The data points are suggested to be a random sample from a normal distribution around the optimum (.40 < P < .50). The bifurcations of the cerebral arteries appear to be optimized to avoid increased hemodynamic stresses both globally and locally in the same manner as extracranial arteries.