Roger S. Seymour, Qiaohui Hu, Edward P. Snelling, and Craig R. White

This meta-study investigated the relationships between blood flow rate (Q; cm3 s–1), wall shear stress (w; dyn cm–2) and lumen radius (ri; cm) in 20 named systemic arteries of nine species of mammals, ranging in mass from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varied between 3.7 µm in a cremaster artery of a rat and 11.2 mm in the aorta of a human. The 92 logged data points of
and ri are described by a single second-order polynomial curve with the equation:
. The slope of the curve increased from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci’s rule (
) applies to the main arteries and Murray’s law (
) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which
is fairly constant, yielded the allometric power equation:
. These empirical equations allow calculation of resting perfusion rates from arterial lumen size alone, without reliance on theoretical models or assumptions on the scaling of wall shear stress in relation to body mass. As expected,
of individual named arteries is strongly affected by body mass; however,
of the common carotid artery from six species (mouse to horse) is also sensitive to differences in whole-body basal metabolic rate, independent of the effect of body mass.

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