Basal metabolic rate scaled to body mass within species by the fractal dimension of the vascular system and body composition

Author: C.Z. Roux
Year: 2017
Issue: 4
Volume: 47
Page: 494 - 504

Previous investigations show that it is plausible that metabolic rates (MR) in all body organs and tissues scale with their own mass with exponent b = D/3, where D is the fractal dimension of the self-similar vascular whole body blood transport system. From the assumption that organ or tissue mass scale with body mass (BM) with exponent d, it follows that organ and tissue MR scale with BM exponents bd. By taking the median organ in vitro MR exponential scaling of 0.91 as an estimate of b, this principle is shown to be valid in porgy. With d = 0.89 and d = 1.04, the scaling exponents of viscera and white muscle are bd = 0.81 for viscera and bd = 0.95 for white muscle, respectively. The viscera value is very close to the porgy resting or basal metabolic rate (BMR) scaling exponent of c = 0.82, and white muscle is reasonably close to the average ectotherm maximum metabolic rate (MMR) scaling exponent 0.92. There are only two species, humans and crucian carp, with available scalings of MMR, BMR and viscera in terms of the exponents b, c and d. The postulate bd = c is shown to hold for both these species within the limits of experimental error, with the crucian carp evidence being especially convincing, since b, c and d are estimated from the same experimental situation. A collation of 19 ectotherm estimates of b shows highly significant differences between them. It is remarkable that the average values of b do not differ much between aquatics and terrestrials, while the average BMR exponents c differ to a remarkable extent, most likely caused by differences in d. Observed differences in d, with generally d ≥1 during early growth and d ≤1 or d ≤ b during later growth, coupled with 2/3 ≤b≤1, can explain the pattern of the BMR scaling with BM, with its often observed broken stick appearance during ontogeny. The examples from the literature confirm that the range of theoretical values 1, 14/15, 5/6 and 2/3 of b, when coupled with the observed values of d, is adequate to produce values of bd corresponding to c estimated from fasting experiments. An example is shown in humans that corrections for body fat percentage, exercise level and age give the same pattern in the relationship bd = c between mature individuals differing in size, as the one observed during growth.

Keywords: maximum metabolic rate, skeletal muscle, vascular distribution network, viscera
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