Data on the in vivo
specific utilization rates of glucose (CMRglc) and oxygen (CMRO2
) by the brain of unanesthetized adult animals are available for six mammalian species 
for which we have determined total numbers of brain neurons: three rodents (mouse, rat, and squirrel 
) and three primates (macaque monkey, baboon, and human 
). Across these species, brain mass varies by 3627-fold, and the number of neurons in the brain varies by 1213-fold (although at different scaling rates across rodents and primates 
Total of glucose and oxygen by the whole brain, cerebral cortex and cerebellum are shown in and , calculated as the product of the published specific rates 
and structure mass (our data). Across the six species, whole brain total glucose use increases with brain mass raised to the power of 0.873 (p<0.0001, 95% CI 0.830–0.915), significantly below linearity, which means that glucose use per gram of tissue decreases with brain mass raised to the power of −0.127, in agreement with the literature 
. Similarly, whole brain use of oxygen increases with brain mass raised to the power of 0.862 (p
0.0037, 95% CI 0.635–1.088). In the cerebral cortex and cerebellum, total glucose use also scales with structure mass raised to similar powers of 0.850 and 0.844, respectively (p<0.0001, 95% CI 0.824–0.876 and 0.768–0.919; ).
Glucose consumption averaged per neuron.
Oxygen consumption averaged per neuron.
Scaling of total glucose use by the whole brain, cerebral cortex and cerebellum.
Remarkably, however, a direct comparison with numbers of neurons shows that total glucose use by the brain as a whole, by the cerebral cortex and also by the cerebellum alone vary with the number of neurons in the structures in a manner that is best described as a linear function across the 6 species (all p<0.0001; ), despite the different relationships between structure mass and number of neurons that apply to rodents and to primates 
. Indeed, the variation in total glucose use by the whole brain or cerebral cortex matches closely the variation in numbers of neurons in these structures across species (), although not as closely in the cerebellum. Further evidence of the linear scaling of tissue metabolism with its number of neurons is the finding that glucose use per gram of brain tissue increases linearly with neuronal density in the brain (r2
0.0034; power exponent, 0.986, p
0.0041; ). The apparent scaling of glucose use per gram of brain tissue with brain size raised to an exponent of −0.127 in the present sample can therefore be explained by a similar apparent scaling of neuronal density in the whole brain with brain size raised to an exponent of −0.116 (). Similarly, the slightly larger exponent of −0.15 that relates specific brain metabolism to brain mass across larger mammalian samples 
can be accounted for by an apparent scaling of neuronal density with brain mass raised to an exponent that varies depending on the choice of species. Across the mammals that we have examined so far, the apparent exponent for the whole sample is −0.172, close to the exponent of −0.15 for brain metabolism, but notice that there is no universal scaling of neuronal density in the brain with brain mass across all species (). The scaling of brain metabolism, therefore, is best described as a function of the total number of neurons in the brain, regardless of how that relates to brain mass or neuronal density across species.
Scaling of average specific glucose use in the brain and neuronal density.
Consistently with the linear variation in total glucose use depending on the number of neurons in the structure, the estimated average glucose use per neuron within each structure is remarkably constant across species (), as is the average oxygen use per neuron for the whole brain (), considering that the small 0.4-fold variations in average glucose use per neuron occur across a 1,000-fold variation in numbers of neurons and total glucose use and a 3-fold variation in neuronal density for the whole brain. Moreover, the small variations in average energy use per neuron do not correlate with structure mass nor with number of neurons in the structure (Spearman correlation, glucose: cerebral cortex, p
0.2301; cerebellum, p
0.1615; whole brain, p
0.8480. Spearman correlation, oxygen: whole brain, p
0.2987). This indicates that the average energy use per neuron does not scale with number of neurons or brain size. The small variations in the estimated average glucose use per neuron are not correlated with variations in neuronal density across species in any structure (Spearman correlation: cerebral cortex, p
0.3173; cerebellum, p
0.6892; whole brain, p
0.5653), nor with the ratio between non-neuronal and neuronal cells (which approximates the glia/neuron ratio in the tissue; Spearman correlation, cerebral cortex, p
0.2301; cerebellum, p
0.5485; whole brain, p
0.8480). Given that non-neuronal cell density is remarkably constant across these species 
, the inverse of neuronal density can be considered to provide a direct estimate of how average neuronal size varies in the structures. Therefore, the finding that variations in the estimated average glucose use per neuron are not correlated with variations in neuronal density across species suggests that the average energy use per neuron does not scale with average neuronal size (including the soma and all arborizations).
The relatively stable average energy requirement per neuron, whether in the cerebral cortex or cerebellum, allows one to estimate the energy requirement of these structures as a simple linear function of their numbers of neurons (). Interestingly, the average glucose consumption per neuron is nearly 20× higher in the cerebral cortex (1.50×10−8
µmol glucose/neuron.min) than in the cerebellum (0.87×10−9
µmol glucose/neuron.min; see for a comparison within species). Because about 80% of all brain neurons are in the cerebellum, the average glucose use per neuron for the whole brain (5.79×10−9
) is lower than the average glucose use by cortical neurons. However, the coordinate scaling of the numbers of neurons in the cerebral cortex and cerebellum, such that the ratio between numbers of cortical and cerebellar neurons remains fairly constant across mammalian species 
, warrants the use of the average glucose consumption per neuron in the whole brain to estimate how the total energy requirement of a mammalian brain depends on the total number of neurons that it contains. As the average brain neuron is estimated to cost 5.79×10−9
µmol glucose/min, with no significant difference between rodents and primates, the overall metabolic cost of a brain can be inferred from its number of neurons. Notice that the total glucose use per minute estimated by this method () is a very good approximation of the actual measurements made in the available species (). The similarity between the predicted and measured values validates the calculation of the total energy requirement of a mammalian brain as a linear function of its total number of neurons. Thus, a mammalian brain with 100 million neurons would be predicted to consume 0.579 µmol glucose/min, requiring 0.6 kCal/day; a brain with 1 billion neurons would use 5.79 µmol glucose/min, or 6 kCal/day; and a brain with 100 billion neurons would use 579 µmol glucose/min, or 600 kCal/day, regardless of the volume of these brains ().
Estimated cost of mammalian cerebral cortex and cerebellum.
Estimated cost of mammalian brains.