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Optmality principles and flow orderliness at the branching points of cerebral arteries. Stroke
, 1993
"... Background and Purpose: 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 extracra ..."
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Background and Purpose: 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 nonoptimum 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 ('y) and the ratio of the branch diameters (d2/dl) were compared. Optimum curves for these parameters were calculated by a mathematical model. In addition, the separation of flow streamlines according to v 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 yand d2/dl and the separation of flow according to 'yand 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. (Stroke
Energetic and Spatial Constraints of Arterial Networks
 Arquivos de NeuroPsiquiatria
, 1995
"... SUMMARY The principle of minimum work (PMW) is a parametric optimization model for the growth and adaptation of arterial trees. A balance between energy dissipation due to frictional resistance of laminar flow (shear stress) and the minimum volume of the blood and vessel wall tissue is achieved whe ..."
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SUMMARY The principle of minimum work (PMW) is a parametric optimization model for the growth and adaptation of arterial trees. A balance between energy dissipation due to frictional resistance of laminar flow (shear stress) and the minimum volume of the blood and vessel wall tissue is achieved when the vessel radii are adjusted to the cube root of the volumetric flow. The PMW is known to apply over several magnitudes of vessel calibers, and in many different organs, including the brain, in humans and in animals. Animal studies suggest that blood flow in arteries is approximately proportional to the cube of the vessel radius, and that arteries alter their caliber in response to sustained changes of blood flow according to PMW. Remodelling of the retinal arteriolar network to longterm changes in blood flow was observed in humans. Remodelling of whole arterial networks occurs in the form of increase or diminishing of vessel calibers. Shear stress induced endothelial mediation seems to be the regulating mechanism for the maintenance of this optimum blood flow/vessel diameter relation. Arterial trees are also expected to be nearly space filing. The vascular system is constructed in such a way that, while blood vessels occupy only a small percentage of the body volume leaving the bulk to tissue, they also crisscross organs so tightly that every point in the tissue lies on the boundary between an artery and a vein. This review describes how the energetic optimum principle for least energy cost for blood flow is also compatible with the spatial constraints of arterial networks according to concepts derived from fractal geometry.
Numerical investigation for the effect of blood flow rate and asymmetric bifurcation angle on the anterior circulation aneurysm formation. ASMEJSMEKSME Joint Fluids Engineering Conference
, 2011
"... ABSTRACT Most of aneurysms in the cranial cavity occur at the bifurcation of anterior circulation system. A cerebral aneurysm is easily ruptured, and it is fatal for most patients. Generally it is known that aneurysm occurs when arterial wall is deformed by high pressure or high wall shear stress(W ..."
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ABSTRACT Most of aneurysms in the cranial cavity occur at the bifurcation of anterior circulation system. A cerebral aneurysm is easily ruptured, and it is fatal for most patients. Generally it is known that aneurysm occurs when arterial wall is deformed by high pressure or high wall shear stress(WSS). A blood flow pattern and the geometry and the blood vessel are important factors for aneurysm formation and the location. The transient interaction between blood flow and the arterial wall affects for simulating deformation of the blood vessel. Thus, numerical analysis is performed for various bifurcation angles and flow rate ratio in bifurcation artery with different diameters to predict the location of aneurysm by hemodynamic characteristics of blood flow. A bifurcation angle between the internal carotid artery and the anterior cerebral artery(ACA) increased, a region of high pressure moved to the bifurcated artery with larger bifurcation angle when ratio of blood flow rate is constant case. When the ratio of blood flow increased, the region of high wall shear stress moved to the side of large flow rate ratio. Our results showed that the high WSS or high pressure region occur at the location of aneurysm as mentioned in the clinical research. Thus, this indicates that the geometry of blood vessel and blood flow rate affect the location of the anterior circulation aneurysm.
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MS AJNR Am J Neuroradiol 20:1079–1089, June/July 1999 An Analysis of the Geometry of Saccular
, 1998
"... BACKGROUND AND PURPOSE: Our goal was to characterize the geometry of simplelobed cerebral aneurysms and to find the absolute size of these lesions from angiographic tracings. METHODS: Measurements of angiographic neck width (N), dome height (H), dome diameter (D), and semiaxis height (S) were obta ..."
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BACKGROUND AND PURPOSE: Our goal was to characterize the geometry of simplelobed cerebral aneurysms and to find the absolute size of these lesions from angiographic tracings. METHODS: Measurements of angiographic neck width (N), dome height (H), dome diameter (D), and semiaxis height (S) were obtained from tracings of 87 simplelobed lesions located at the basilar bifurcation (BB), middle cerebral (MCA), anterior communicating (AcomA), posterior communicating (PcomA), superior cerebellar (SCA), and posterior cerebral (PCA) arteries. The following ratios were analyzed as subgroups according to location and as a collective sample: dome diameter/dome height (D/H), dome height/neck width (H/N), dome diameter/ neck width (D/N), and dome height/semiaxis height (H/S). Using the parent artery as a reference, aneurysm dimensions were normalized to absolute in vivo size. Estimations were validated using angiographic markers. RESULTS: For the entire sample, mean ratios were D/H 5 1.11, D/N 5 1.91, and H/N 5 1.86. For the H/S ratio, the value was 1.98 for BB, MCA, and PcomA lesions and significantly smaller for the AcomA subgroup, at 1.52. The average sizes (in mm) for these dimensions were N 5 3.4 for MCA, 3.0 for AcomA, 3.1 for PcomA, and 6.5 for BB; D 5 6.1 for MCA, 5.9 for