Scaling of Brain Metabolism and Blood Flow in Relation to Capillary and Neural Scaling

Abstract

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 as , brain capillary diameter increases as , and density of capillary length decreases as . It is predicted that velocity of capillary blood is almost invariant (), capillary transit time scales as , capillary length increases as , and capillary number as , where 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.

Scaling of cerebral blood perfusion in primates and marsupials

“…The large difference between the exponent of _ Q ICA on brain volume between haplorrhine primates (0.95) and diprotodont marsupials (0.73) almost exactly straddles the exponent of 0.86 for brain metabolic rate (Karbowski, 2007) and 0.84 for brain perfusion (Karbowski, 2011). ANCOVA shows that neither 0.95 nor 0.73 are significantly different from 0.86, based on the samples and relationships considered here.…”

“…Conversely, in diprotodonts, an increase in brain volume results in an increase in neuron size and a decrease in neuron density (Herculano-Houzel et al, 2006;Karbowski, 2007). Glucose and oxygen consumption per neuron is reported to be independent of neuron size (Herculano-Houzel, 2011c;Karbowski, 2011), so the diprotodonts scale lower, with an exponent close to the expected 0.75 value of 'Kleiber's Law'. It would be informative to determine whether or not other non-primate groups scale similar to diprotodonts.…”

“…The rate of oxygen uptake by the whole brain of seven mammalian species scales with V br 0.86 and the rate of glucose metabolism in ten species also scales with V br 0.86 (Karbowski, 2007). The scaling of cortical blood flow rate and cortical brain volume in up to seven species of mammals varies with exponents between 0.81 and 0.87, depending on the particular part of the cortex, but the overall exponent is 0.84 (Karbowski, 2011). This indicates that there is good matching of brain metabolic rate and blood flow rate and confirms the notion that blood flow rate can indicate metabolic rate.…”

“…On a tissue-mass-specific basis, brain metabolic rate in a resting mammal is about two-thirds of the rates of the most active organs (heart, liver, kidney) and more than 10-times higher than that of the rest of the body (Wang et al, 2001). Continuous cranial blood flow is required because of the aerobic nature of the brain and its inability to store glucose or glycogen (Karbowski, 2011;Weisbecker and Goswami, 2010). Blood flow rates in the internal carotid arteries are likely to indicate the levels of activity in the brain, because these vessels mainly supply the cerebrum (with minor supplies to the meninges, eyes and forehead scalp), whereas the vertebral arteries mainly supply the cerebellum in most mammals (Turnquist and Minugh-Purvis, 2012).…”

On the Normalization of Cerebral Blood Flow

“…Recent investigations have nevertheless challenged the CBF normalization by voxel volume and suggest an alternative scaling. 6 More precisely, based on allometric arguments associated with brain capillary length, diameter, and neuron density scalings, Karbowski 6 rather proposes to normalize the brain perfusion by the one-sixth power of the considered voxel volume V.…”