Vascular dimensions of the cerebral arteries follow the principle of minimum work.

Abstract

This study demonstrates that the process of branching of the internal carotid artery system obeys the principle of minimum work, as the diameter exponent approximates 3. The principle of minimum work establishes strict functional relations between volumetric flow, flow velocity, and vessel radius. This model was extended to parametric optimization of branch angles, which has proved irrelevant in terms of functional optimization. Our results corroborate this finding. Shear stress-induced endothelial mediation seems to be the regulating mechanism for the maintenance of this optimum vessel design. The magnitude of wall shear stress is the same at every point in a vascular network obeying the principle of minimum work, because the flow rate influences the shear stress proportionally to the third power of the vessel radius. This observation has implications for understanding the remodeling of the cerebral vascular network in the presence of arteriovenous malformations and for the pathogenesis of saccular aneurysms.