This meta-study investigates the relationships between blood flow rate (Q̇ ; cm3 s−1), wall shear stress (τ; dyne cm−2) and lumen radius (ri; cm) in 20 named systemic arteries of nine species of mammals, weighing from 23 g mice to 652 kg cows, at rest. In the dataset, derived from 50 studies, lumen radius varies between 3.7 µm in a cremaster artery of a rat to 11.2 mm in the aorta of a human. The 92 logged data points of Q̇ and ri are described by a single second-order polynomial curve with the equation, log Q̇=−0.20 log ri2 +1.91 log ri+1.82. The slope of the curve increases from approximately 2 in the largest arteries to approximately 3 in the smallest ones. Thus, da Vinci's Rule (Q̇ ∝ ri2) applies to the main arteries and Murray's Law (Q̇ ∝ ri3) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which Q̇ is fairly constant, yielded the allometric power equation, Q̇=155 ri2.49. 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, Q̇ of individual named arteries is strongly affected by body mass, however, Q̇ 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.
Interspecific scaling of blood flow rates and arterial sizes in mammals
Currently Viewing Accepted Manuscript - Newer Version Available
Roger S. Seymour, Qiaohui Hu, Edward P. Snelling, Craig R. White; Interspecific scaling of blood flow rates and arterial sizes in mammals. J Exp Biol 2019; jeb.199554. doi: https://doi.org/10.1242/jeb.199554
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