Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Abstract

Blood flow rate ((Formula presented.)) in relation to arterial lumen radius (ri) is commonly modelled according to theoretical equations and paradigms, including Murray’s Law ((Formula presented.) ∝ (Formula presented.)) and da Vinci’s Rule ((Formula presented.) ∝ (Formula presented.)). Wall shear stress (τ) is independent of ri with Murray’s Law (τ ∝ (Formula presented.)) and decreases with da Vinci’s Rule (τ ∝ (Formula presented.)). These paradigms are tested empirically with a meta-analysis of the relationships between (Formula presented.) and ri in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that (Formula presented.) ∝ (Formula presented.) and τ ∝ (Formula presented.), more consistent with da Vinci’s Rule than Murray’s Law. This meta-analysis provides standard values for (Formula presented.), ri and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.