Exercise-induced maximal metabolic rate scales with muscle aerobic capacity

The logarithmic nature of the allometric equation suggests that metabolic rate scaling is related to some fractal properties of the organism. Two universal models have been proposed, based on (1) the fractal design of the vasculature and (2) the fractal nature of the 'total effective surface' of mitochondria and capillaries. According to these models, basal and maximal metabolic rates must scale as M3/4. This is not what we find. In 34 eutherian mammalian species (body mass Mb ranging from 7 g to 500 kg) we found VO2max to scale with the 0.872 (+/-0.029) power of body mass, which is significantly different from 3/4 power scaling. Integrated structure-function studies on a subset of eleven species (Mb 20 g to 450 kg) show that the variation of VO2max with body size is tightly associated with the total volume of mitochondria and of the locomotor musculature capillaries. In athletic species the higher VO2max is linked to proportionally larger mitochondrial and capillary volumes. As a result, VO2max is linearly related to both total mitochondrial and capillary erythrocyte volumes, as well as to their surface areas. Consequently, the allometric variation of maximal metabolic rate is directly related to the scaling of the total effective surfaces of mitochondria and capillaries, thus confirming the basic conjecture of the second fractal models but refuting the arguments for 3/4 power scaling. We conclude that the scaling of maximal metabolic rate is determined by the energy needs of the cells active during maximal work. The vascular supply network is adapted to the needs of the cells at their working limit. We conjecture that the optimization of the arterial tree by fractal design is the result rather than the cause of the evolution of metabolic rate scaling. The remaining question is why the energy needs of locomotion scale with the 0.872 or 7/8 power of body mass.