## Abstract

This meta-study investigated the relationships between blood flow rate (Q̇; cm3 s-1), wall shear stress (τw; 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 [Formula: see text] and ri are described by a single second-order polynomial curve with the equation: [Formula: see text] 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 ([Formula: see text]) applies to the main arteries and Murray's law ([Formula: see text]) applies to the microcirculation. A subset of the data, comprising only cephalic arteries in which [Formula: see text] is fairly constant, yielded the allometric power equation: [Formula: see text] 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, [Formula: see text] of individual named arteries is strongly affected by body mass; however, [Formula: see text] 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.

Original language | English |
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Article number | jeb199554 |

Number of pages | 10 |

Journal | Journal of Experimental Biology |

Volume | 222 |

DOIs | |

Publication status | Published - 3 Apr 2019 |

## Keywords

- Artery
- Blood flow rate
- Circulation
- Da Vinci's rule
- Murray's law
- Wall shear stress