AN OPTIMIZATION PRINCIPLE FOR VASCULAR RADIUS INCLUDING THE EFFECTS OF SMOOTH-MUSCLE TONE

An optimization principle is proposed for the regulation of vascular m orphology. This principle, which extends Murray's law, is based on the hypothesis that blood vessel diameter is controlled by a mechanism th at minimizes the total energy required to drive the blood flow, to mai ntain the blood supply, and to support smooth muscle tone. A theoretic al analysis reveals that the proposed principle predicts that the opti mum shear stress on the vessel wall due to blood flow increases with b lood pressure. This result agrees qualitatively with published finding s that the fluid shear stress in veins is significantly smaller than i t is in arteries.