Background and Purpose: The principle of minimum work is a parametric optimization model for the growth and adaptation of arterial trees. It establishes a balance between energy dissipation due to frictional resistance of laminar flow (shear stress) and the minimum volume of the vascular system, implying that the radius of the vessel is adjusted to the cube root of the volumetric flow. The purpose of this study is to verify whether the internal carotid artery system obeys the principle of minimum work.

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

Susceptibility-weighted GRE imaging at 1.5 T is highly sensitive to both hyperacute hemorrhage in the brain parenchyma and to subarachnoid and intraventricular hemorrhage.

Arteries supplying cerebral arteriovenous malformations (AVMs) are known to dilate with time. These changes are reversible, and the feeders have been shown to slowly decrease in calibre after removal of the AMV. There is evidence that arteries alter their internal diameters in response to sustained changes of blood flow so that shear stress is kept constant. This implies that blood flow-induced shear stress might be the driving force for remodelling of the cerebral vascular network in the presence of an AVM, and for reversion of these changes after radical operation. The objective of this study is to examine the hypothesis that the shear stress in cerebral arteries supplying AMVs is of the same magnitude as in arteries supplying normal brain tissue in spite of larger blood flow rate. Fifteen patients with supratentorial cerebral AVMs admitted for endovascular treatment were examined with transcranial Doppler ultrasound in the distal Willisian vessels. Vessel calibres were measured in angiograms with magnification correction. Shear stress was estimated assuming a constant value for blood viscosity. Corresponding arteries in the cerebral hemisphere with AVM and in the contralateral one were compared in pairs. Thirty-four pairs of homonymous arteries were studied. The arteries on the AVM side presented larger calibres, higher axial blood flow velocities, lower pulsatility index and larger blood flow rates than the contralateral side. There was a clear positive correlation between blood flow velocities and vessel calibres. The estimates of shear stress did not differ significantly in corresponding arteries of both hemispheres (p = 0.18). The results indicate a precise adjustment of cerebral arterial calibre and blood flow-induced shear stress that presumably induces the progressive dilation of AVM feeders, and the slow regression of the vessel calibres to average dimensions after removal of the lesion. Each vessel seems to remodel itself in response to long-term changes in blood flow rate so that the vessel calibre is reshaped to maintain a constant level of wall shear stress.

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