Geometric similarity of aorta, venae cavae, and certain of their branches in mammals

Abstract

The diameters of the aorta and venae cavae at various points throughout their lengths, the diameters of their major branches, and the lengths of various aortic and vena caval segments were measured in plastic corrosion casts of the arterial and venous systems of the normal adult mouse, rat, rabbit, dog, goat, horse, and cow, extending over a body weight range of 38,000-fold (arterial) and 1,100-fold (venous). It is shown that the diameters and lengths of these vessels are described by power-law equations relating the particular diameter or length to body weight (BW) raised to a particular diameter or length to body weight (BW) raised to a particular power, i.e., diameter = a BWb. Equations for the diameters and lengths of the vessels are given for slightly distended vessels and for vessels distended in the physiological range.

Exercise-induced maximum metabolic rate scaled to body mass by the fractal dimension of the vascular distribution network

“…This is almost identical to the estimate of Holt et al (1981) ( Weibel et al (2004) and of 0.879±0.020 for birds and mammals of Bishop (1999), obtained with adjustment to a standard mammalian relative heart size scaling with body mass and haemoglobin concentration.…”

“…This is confirmed from an estimate from Holt et al (1981), to excellent approximation. Furthermore, it could be assumed that .…”

“…Maximum aerobic metabolic rate exponents from aorta cross-section scaling There are two estimates of in the literature, the first by Clark (1927), and the second by Holt et al (1981). For mature mammals of various species, Clark (1927) found a consistent relationship between and heart mass with exponent of 0.8 in agreement with the 95% confidence interval (CI) 0.80±0.047, calculated from his appendices II and III.…”

Internal carotid arterial canal size and scaling in Euarchonta: Re-assessing implications for arterial patency and phylogenetic relationships in early fossil primates

“…We hypothesize that evolutionary increases in brain and body size lead to a diminished stapedial size because of a negatively allometric relationship between the stapes size and both body mass and brain volume. Under this scenario, as lineages evolve larger body sizes, the stapes will increasingly impinge on blood flow requirements, which e all else being equal e appear to require that canal cross sectional area scales with positive allometry to body mass (Holt et al, 1981;Schmidt-Nielsen, 1984;Sutera, 1993;Dawson, 2014). While allometric exponents of ossicular elements are not available for broad comparative samples, Braga et al (2015) show that the area of the oval window (that tightly fits the stapes footplate) scales with an exponent of 0.330 to body mass for catarrhine primates.…”

Testing Metabolic Theories

“…The assumption that the network tips are invariant with size has been argued to be inconsistent with the space-filling assumption, although the branching network model still predicts three-fourths power scaling if blood flow velocity increases with M 1/12 (Banavar et al 2010). Given that cardiac output of mammals scales as the product of heart rate ∝ M Ϫ0.23 (Seymour and Blaylock 2000) and stroke volume ∝ M 1.03 (Seymour and Blaylock 2000) and that aorta diameter scales with M 0.36 (Holt et al 1981), flow velocity through the aorta should scale as M 0.08 , which is very close to M 1/12 . WBE argued that, if cells were the terminal units of the circulatory system and not capillaries, metabolically active tissue density would have to vary with mass to the onefourth to match the observed mass-specific scaling of metabolic rate .…”