Allometric scaling of brain energetics and hemodynamics in relation to capillary scaling.

Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales
with brain volume raised to a power of around 5/6. This value is significantly higher than the more
common exponent 3/4 relating whole body resting metabolism with body mass and several other
physiological variables in animals and plants. This article investigates the reasons for brain
allometric distinction on a level of its microvessels. Based on collected empirical data it is
found that regional cerebral blood flow CBF across gray matter scales with cortical volume V with
an exponent -1/6, brain capillary diameter scales with V with an exponent 1/12, and density of
capillary length decreases with V with an exponent -1/6. It is predicted that velocity of capillary
blood is almost invariant, capillary transit time scales with exponent 1/6, capillary length increases
with V with power 1/6+epsilon, and capillary number with power 2/3-epsilon, where epsilon is typically
a small correction for medium and large brains, due to blood viscosity dependence on capillary radius.
It is shown that the amount of capillary length and blood flow per cortical neuron are essentially
conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular
coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular
variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which
suggests that brain metabolism is more similar to the metabolism of aerobic than resting body.
Relation of these findings to brain functional imaging studies involving the link between cerebral
metabolism and blood flow is also discussed.

References:
1) Karbowski J (2007) Global and regional brain metabolic scaling and its functional consequences.
    BMC Biology 5: 18. http://dx.doi.org/10.1186/1741-7007-5-18

2) Karbowski J (2011) Scaling of brain metabolism and blood flow in relation to capillary and neural scaling.
    PLoS ONE 6(10): e26709. http://dx.doi.org/10.1371/journal.pone.0026709