Optimality principles and flow orderliness at the branching points of cerebral arteries. 1993

S Rossitti, and J Löfgren
Department of Neurosurgery, University of Göteborg, Sahlgrenska Hospital, Sweden.

OBJECTIVE 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. METHODS 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. RESULTS 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). CONCLUSIONS 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.

UI MeSH Term Description Entries
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D012039 Regional Blood Flow The flow of BLOOD through or around an organ or region of the body. Blood Flow, Regional,Blood Flows, Regional,Flow, Regional Blood,Flows, Regional Blood,Regional Blood Flows
D001921 Brain The part of CENTRAL NERVOUS SYSTEM that is contained within the skull (CRANIUM). Arising from the NEURAL TUBE, the embryonic brain is comprised of three major parts including PROSENCEPHALON (the forebrain); MESENCEPHALON (the midbrain); and RHOMBENCEPHALON (the hindbrain). The developed brain consists of CEREBRUM; CEREBELLUM; and other structures in the BRAIN STEM. Encephalon
D002536 Cerebral Arteries The arterial blood vessels supplying the CEREBRUM. Arteries, Cerebral,Artery, Cerebral,Cerebral Artery
D002560 Cerebrovascular Circulation The circulation of blood through the BLOOD VESSELS of the BRAIN. Brain Blood Flow,Regional Cerebral Blood Flow,Cerebral Blood Flow,Cerebral Circulation,Cerebral Perfusion Pressure,Circulation, Cerebrovascular,Blood Flow, Brain,Blood Flow, Cerebral,Brain Blood Flows,Cerebral Blood Flows,Cerebral Circulations,Cerebral Perfusion Pressures,Circulation, Cerebral,Flow, Brain Blood,Flow, Cerebral Blood,Perfusion Pressure, Cerebral,Pressure, Cerebral Perfusion
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000783 Aneurysm Pathological outpouching or sac-like dilatation in the wall of any blood vessel (ARTERIES or VEINS) or the heart (HEART ANEURYSM). It indicates a thin and weakened area in the wall which may later rupture. Aneurysms are classified by location, etiology, or other characteristics. Saccular Aneurysm,Fusiform Aneurysm,Aneurysm, Fusiform,Aneurysms,Aneurysms, Fusiform,Fusiform Aneurysms
D013314 Stress, Mechanical A purely physical condition which exists within any material because of strain or deformation by external forces or by non-uniform thermal expansion; expressed quantitatively in units of force per unit area. Mechanical Stress,Mechanical Stresses,Stresses, Mechanical

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