The human brain ranks second amongst organs in absolute energy cost at rest only to the liver (Aschoff et al., 1971; Rolfe and Guy, 1997). Such high cost is commonly attributed to synaptic-mediated neuronal activity (Ames, 2000; Attwell and Laughlin, 2001; Harris et al., 2012), and is entirely met by molecules supplied from the blood and provided to neurons through glial cells whose metabolism is coupled to neuronal activity (Pellerin and Magistretti, 2004; Magistretti, 2006). The high energy cost of the brain, liver, and heart puts them at high risk of damage by diseases and conditions such as aging that compromise metabolism and oxygen supply (Leach and Treacher, 1998). Elucidating what determines the high energetic cost of the brain is thus central to understanding healthy and abnormal brain function.

Brain bioenergetics researchers consider that the high energetic cost of the brain is driven by a steep energetic requirement of neurons due to costs directly and indirectly related to synaptic activity and membrane repolarization (Attwell and Laughlin, 2001; Howarth et al., 2010; Harris et al., 2012). However, energetic use can be determined by demand only if it is matched dynamically by a non-limiting supply; otherwise, it is constrained by energetic supply that limits work. The former is the case of modern cities where the electricity that supplies homes is non-limiting, and demand is free to vary but is always met; the latter is the case in rural homes that already consume most of what little electricity they are supplied with and cannot sustain both an electric shower and air conditioning running simultaneously (Banavar et al., 2002). In biology, this is evident, for example, in hummingbirds, forced into torpor when food is insufficient (Hainsworth et al., 1977).

The brain is known to use a disproportionate amount of the body’s energy budget (Mink et al., 1981), but how much that use is limited by its energetic supply is a key open question. Importantly, there is good reason to suspect that brain energy use at rest is already close to the limits established by the blood supply. First, both local glucose use and blood flow at rest depend linearly on local capillary density in rat (Klein et al., 1986) and monkey (Noda et al., 2002). Task-related variations in local CBF are very small, in the order of 2%, and of at most 8% in primary sensory areas, such that total cerebral blood flow (CBF) remains remarkably constant throughout the day in healthy individuals (Schölvinck et al., 2008; Lin et al., 2010). These small local variations in CBF happen with hardly any capillary recruitment (Kuschinsky and Paulson, 1992; Hudetz, 1997). Additionally, blood flow rates in the brain are already as high at rest as they are in skeletal muscle during exercise (Madsen et al., 1993; Zheng et al., 2014).

Here we examine whether the distribution of capillaries in the brain is consistent with a supply-limiting or a demand-based scenario. To that end, we determine whether capillary density is homogeneous throughout the adult brain regardless of local variations in local neuronal density, which would be expected if capillary density were determined in a system-wide manner by physical scaling limitations (Banavar et al., 2002); or whether capillary density varies coordinately with local neuronal densities, which would be consistent with a plastic, demand-based reorganization of the capillary bed in response to use, whether because sites with more neurons have higher energy use simply because of the larger number of neurons, or because larger neurons (in sites of lower local neuronal densities) require more energy individually (Attwell and Laughlin, 2001). Further, to gain insight on the particular issue of energy availability per neuron, we calculate its proxy, the local endothelial-to-neuronal-cell (E/N) ratio, and examine how it varies locally in the mouse brain depending on local neuronal densities. Finally, we examine whether variations in energy availability per neuron might also be related to local variations in numbers of synapses per neuron, by combining our data with direct counts of synapse densities in identified locations in the mouse brain published recently (Zhu et al., 2018).

To guide the interpretation of our findings, the three main possible scenarios are depicted in Figure 3. The top row illustrates the results expected if the steady-state capillary density in the adult brain reflected local variations in neuronal density, and the average neuron was supplied with similar amounts of energy regardless of its size or location. In this case, local capillary density should be directly proportional to local neuronal density, and energy availability per neuron, indicated by the ratio of endothelial-associated (or simply “endothelial”) cells per neuron, should remain constant across brain sites. On the other hand, if larger neurons are supplied with more energy, then sites with larger neurons and thus lower neuronal densities should have higher E/N (Figure 3, rows 2 and 3). However, such finding of more energy availability where neurons are larger could occur in two different scenarios. In the first, higher E/N would happen due to reorganization of the capillary bed reflecting neuronal demand, in which case larger capillary densities would be expected in those sites with larger neurons (and therefore lower neuronal densities; row 3). In the second, higher E/N in those sites with larger neurons would be simply imposed by a lack of variation in capillary density across brain sites (row 2). The three particular cases in which numbers of synapses are constant per volume (left), constant per neuron (center) or larger in bigger neurons (right) are depicted separately for each scenario and illustrate the ensuing expected variation in energy availability per synapse as well as how energy availability per neuron would vary together with energy availability per synapse or not.

Across the ten brain structures examined, we find that the capillary area fraction is very small, amounting to no more than 3% of the tissue in any structure in 3D image stacks. While individual measurements of local capillary fraction vary 10x-fold across all brain sites, the average capillary fraction per structure varies only about twofold across structures, with 95% of measurements ranging around 1.29 ± 1.39% (Table 3). The average capillary fraction is highest in the GM of the cerebral cortex (2.22 ± 0.11%), and lowest in the granular layer of the dentate gyrus and subcortical WM (0.70 ± 0.07%; Table 3). In 2D images, we found similarly small variation in capillary fraction, as well as lower capillary fractions in WM than in GM, despite the artificially higher nominal capillary fractions measured with this method due to the larger optical thickness of the images (Table 4). The capillary fractions we report in 3D analyses are similar to vascular fractions between 2 and 6% reported in the mouse cerebral cortical gray matter (Tsai et al., 2009) and between 2.1 and 3.1% in the cat, macaque and human GM cortex (Pawlik et al., 1981; Borowsky and Collins, 1989; Boero et al., 1999).

Interestingly, capillary-associated (“endothelial” cells) typically constitute between 7 and 14% of all cells forming the brain structures examined (Tables 3, 4), a much larger percentage than could be expected from the average vascular fraction of 0.7–2.2% of the 3D volume that they occupy. This discrepancy indicates that endothelial cells are, on average, much smaller than neurons and glial cells in the tissue. Still, glial cells are consistently the majority (60–70%) of non-neuronal cells in all structures (Tables 3, 4). As expected from our previous studies (Herculano-Houzel et al., 2013, 2014), the percentage of cells that are neurons is highly variable across structures and sites within a structure; neurons are the vast majority of all cells in the granular layers of the dentate gyrus and cerebellum, a smaller percentage of all cells in other GM structures, and rare (but present) within the subcortical WM of both cerebral and cerebellar cortices (Tables 3, 4).

As expected for two different measurements of the same feature (capillary density), local endothelial cell density correlates well with local capillary area or volume fraction within and across the different brain structures, as well as across animals, especially in the 2D sample, which included a much larger number of sites and cells (Figure 4 and Table 5). Both capillary fraction and local endothelial cell density vary by a single order of magnitude across sites in the mouse brain, whether measured in 2D or 3D (Figure 4A). The two capillary density-related variables are correlated within each structure individually (Table 6), and there is good overlap in data points across structures and animals, especially in the larger 2D dataset (Figure 4A, right), where the overlapping power relationships (Table 6) indicate that the relationship between capillary fraction and cellular composition of capillaries is shared throughout the brain. This agreement suggests that endothelial cell density is a good proxy for the resting rates of blood flow and glucose use (Klein et al., 1986; Noda et al., 2002; Ventura-Antunes et al., 2022).

Neuronal densities, in contrast, vary over two orders of magnitude across sites in GM structures, from 31,250 to 3,843,750/mm³ (Figure 4B), and are not significantly correlated with local capillary fraction (Figure 4B) across brain sites and structures (Table 6). In fact, brain structures with enormously different neuronal densities have capillary fractions in the same restricted range (Figure 4B), and correlations, where significant, can be positive (cortical GM) or negative (cerebellar granular layer; Table 6).

Like endothelial cell densities, variation in glial cell densities is restricted to within one order of magnitude across sites in the mouse brain (Figure 5A). Within the cortical GM, local glial cell densities vary significantly in positive correlation with local neuronal density, as previously observed across sites within both human (Lauwers et al., 2008) and mouse cortices (Herculano-Houzel et al., 2013; Figure 5A and Table 6). In contrast, there is no universal correlation between local neuronal and glial cell densities across brain structures; if anything, there is a modest negative correlation across all sites (Figure 5A), which is due to the slightly more elevated glial cell densities in WM sites.

Importantly, a large range of neuronal densities occurs with similar endothelial cell densities across structures in the mouse brain, with only a weak overall trend toward higher endothelial cell densities where neuronal densities are higher (Figure 5B). A significant increase in local endothelial cell density in sites with increasing local neuronal density is found only in the cortical GM, thalamus and striatum (Figure 5B and Table 6). Similarly, we find significant correlations between local densities of endothelial cells and glial cells within some structures, but no strong systematic correlation across locations (Figure 5C).

Consistently with the larger variation of neuronal densities than glial cell densities across locations, the glia/neuron (G/N) ratio is highly variable within the mouse brain, and is universally and inversely related to local neuronal densities across all sites and structures, as we described previously (Mota and Herculano-Houzel, 2014; Figures 6A,B). That is, there are more glial cells per neuron in those sites with lower neuronal densities, in a relationship that applies both across and within structures, regardless of their identity (Table 6). In contrast, the relationship between local glia/neuron ratio and glial cell density is specific to each structure, with different ranges of glia/neuron ratios sharing similar glial cell densities across structures (Figures 6C,D). Importantly, although higher G/N ratios where neuronal densities are smaller (and therefore neurons are larger) have been proposed to accompany the presumably higher energetic demands of larger neurons (Attwell and Laughlin, 2001), the entire 10,000-fold range of G/N ratios occurs within the same restricted range of endothelial cell densities, with no consistent correlation across brain structures and sites (Figures 6E,F). That is, endothelial cell densities are not significantly higher in those locations where each neuron is accompanied by a larger number of glial cells.

Because of the much larger variation in neuronal densities than in endothelial cell densities across sites, the local ratio of endothelial cells per neuron is inversely proportional to local neuronal density across all sites and structures examined (Figure 7). Importantly, this relationship is universal across brain locations, as the power function that applies across structures contains all structures and almost all data points within its 95% CI (Figures 7A,B). That is, each neuron is accompanied by more endothelial cells at sites with lower neuronal densities than at sites with higher neuronal densities. In contrast, the ratio of endothelial cells per neuron does not vary consistently with local glial cell density neither across nor within brain structures (Figures 7C,D and Table 6). As expected for the quantity in the numerator of the ratio, local endothelial cell density is very strongly correlated with the E/N ratio in each brain structure in the mouse brain, but there is hardly any overlap across structures: because of the widely different neuronal densities across structures, brain sites with similar densities of endothelial cells have very different E/N ratios across structures (Figures 7E,F). As could be expected of two quantities that are heavily dependent on variation in neuronal density, the E/N ratio is strongly and linearly correlated with the G/N ratio across all sites and structures (Figure 8). That is, where more endothelial cells supply energy per neuron (i.e., in structures and sites with low neuron density), there are also more glial cells per neuron. Importantly, the relationship that applies across structures includes most data points for every structure, indicating that this relationship is universal.

Finally, by comparing our measurements of local cell densities and capillary fraction in cortical gray matter sites matching those with recently published data on local synaptic densities in the mouse cerebral cortex (Zhu et al., 2018), we could examine whether there is evidence of higher energy availability in sites of higher synaptic densities, even at rest, to support the expectation that energy supply responds to local demands due to synaptic activity by self-reorganization of capillary densities (Attwell and Laughlin, 2001; Harris et al., 2012). Densities of synapses (measured as synapses that express PSD and/or SAP according to data in Zhu et al., 2018) vary 1.5-fold across cortical sites, while densities of endothelial cells vary 2.5-fold and neuronal densities vary a similar 2.2-fold. However, we find no significant correlation between local endothelial cell density and synaptic density (Figure 9A) or neuronal density (Figure 9B) across areas within the mouse cerebral cortex (Spearman, p = 0.4133 and 0.7047), indicating that cortical areas with more synapses or more neurons receive as much capillary supply as sites with fewer synapses or neurons. Higher local synaptic densities are only modestly associated with higher local neuronal densities (Figure 9C; Spearman, p = 0.0414), such that the ratio of synapses per neuron is concentrated in the 6,500–9,500 range (Figure 9E; Spearman, p = 0.0129 due to a single data point above 12,500), compatible with previous estimates of ca. 8,000 synapses per cortical neuron in the mouse (Schüz and Palm, 1989; Braitenberg and Schüz, 1998). We find that the average number of synapses per neuron is not higher where there are more synapses (Figure 9D; Spearman, p = 0.0775), and is also not significantly correlated with the local number of glial cells per neuron (Spearman, p = 0.3177; Table 6). Indeed, local densities of synapses are not correlated with local glial cell densities (Spearman, p = 0.6488), and the higher the local glial cell density, the fewer the synapses per glial cell (Spearman rho = -0.831, p < 0.0001; Table 6). Crucially, the average number of synapses per neuron is not significantly correlated with the local ratio of endothelial cells per neuron (Figure 9F; Spearman, p = 0.4717): the E/N ratio varies about four-fold across cortical sites with similar average numbers of synapses per neuron, and at a similar capillary supply per neuron, local neurons may have variable average numbers of synapses. Instead, the most striking pattern is, again, that at cortical sites where each neuron has more capillary cells available to it, there are also more capillary cells available per synapse (E/S; Figure 9G; Spearman, p = 0.0001).

These data thus indicate that higher E/S is associated with higher E/N, even though there are not more endothelial cells where there are more synapses (or more neurons; Figures 9A,B), and there are also not more E/N where there are more S/N (Figure 9F). Rather, higher E/S occurs with higher E/N (Figure 9G) simply due to small variations in endothelial cell densities that are not correlated with variations in densities of neurons or synapses (Figures 9A,B) in the presence of significant local variations in neuronal densities that are only somewhat correlated with smaller variations in densities of synapses (Figure 9C). A principal component analysis supports this conclusion. We find that three factors are required to account for the variance in all six variables, with capillary density loading only in the first factor [explaining 42.9% of the variance; factor loading, 0.996, associated with E/N (0.816) and E/S (0.926)], neuronal density loading only in the second factor [total variance explained, 78.8%; loading, –0.943, associated with E/N (0.557) and S/N (0.976)], and synaptic density as the sole contributor to the third factor (explaining a total of 99.3% of the variance; factor loading, 0.981).

Finally, while the glia/neuron ratio is locally higher in cortical sites where the endothelial cell/neuron ratio is also higher (Spearman, p = 0.0118), the number of endothelial cells per synapse is not correlated with the local glia/neuron ratio (p = 0.2868; Table 6). Thus, a higher proportion of glial cells per neuron is not associated with a larger capillary supply per synapse.

The brain is an expensive organ and, at rest, already uses nearly as much energy as during sensory activation (Leithner and Royl, 2014). The high energy cost of the brain has traditionally been regarded as driven by an unusually high energy demand by neurons, leading to the expectation that sites with more neurons, or larger neurons, or more synapses use more energy and thus have more capillary supply. Instead, here we find that capillary density is relatively homogeneous across brain structures despite a 100-fold variation in local neuronal densities. We propose that in the adult steady-state measured in a fixed brain, neurons are constrained to using what energy is made available by the relatively homogeneous capillary supply, with little evidence for plastic, self-organizing adjustments according to local demand (see Herculano-Houzel and Rothman, 2022). Such a supply-limited view of brain metabolism explains its high risk of ischemia and vulnerability to states of compromised metabolism, including normal aging.

While neuroscientists often frame the energy cost of the brain in terms of high neuronal demand for energy, we prefer to reframe metabolism simply as energy use, a term that implies nothing about what defines it, whether supply or demand, and instead leaves these open to investigation (Herculano-Houzel and Rothman, 2022). The issue of energetic use by neurons can then be separated into the more tractable questions of (a) whether there is evidence that larger neurons demand and thus are provided with more energy, depending on their intrinsic biophysical properties (Lin et al., 2010), and (b) whether there is evidence that larger neurons are supplied with more energy than smaller neurons, regardless of (a). Our finding that local capillary area fraction or density of capillary cells does not accompany the enormous variation in neuronal densities across sites in the mouse brain nor synaptic densities in the mouse cerebral cortex provides evidence against (a) and in support of (b), against several intuitive, but so far untested, central tenets of neurophysiology and functional brain imaging. These untested tenets are, namely: that neurons demand energy, and larger neurons demand (and receive) more energy than smaller neurons; that sites with more synapses use more energy; that because larger neurons have more synapses, they demand (and receive) more energy; and that the steady-state density of the adult capillary bed reflects self-organized adjustments across brain sites according to variations in local energy demand by neurons and synapses.

Instead, given our main finding of a comparatively constant capillary density, we interpret our data to indicate that, with the 100× larger variation in neuronal densities throughout the mouse brain, larger neurons get access to more energy simply because where neurons are larger, as indicated by lower neuronal densities, fewer neurons compete for the capillary density-restricted blood supply. Although neuronal networks are by definition distributed, thanks to the far-reaching dendrites and axons that define neurons, the neuronal cell body is the site of massive macromolecule synthesis that constitutes a major destination of resources; thus, the E/N ratio, defined here as the number of capillary cells supplying an individual neuronal cell body, is a physiologically relevant variable, although individual neurons will undoubtedly receive partial energetic support from other capillary cells that supply territories where their neurites extend.

Similarly to larger neurons having less competition for blood supply that is limited by capillary density, and given the small but significant variation in densities of synapses with densities of neurons within the cerebral cortex, we propose that there is a restricted range of numbers of synapses per neuron, and, where neurons are larger, more endothelial cells provide energy both per neuron and per synapse (highlighted middle panel in Figure 3). These findings suggest the intriguing possibility that, whereas cell sizes in mammalian bodies are constant across species for all other cell types, increasing neuronal sizes in evolution may have brought neurons the advantage of not decreasing energy availability per neuronal unit (with its surrounding glial cells), and possibly holding that constant, as body size increases and total metabolic rate scales more slowly than body mass (Herculano-Houzel, 2011), a possibility that we are now ready to address by extending the present analysis to other species.

Within the cerebral cortex, in particular, a previous detailed study of variation in fractional volume of the microvasculature across layers found that it varies little, and does not reflect variations in neuronal density across cortical layers (Tsai et al., 2009). When compiling data across layers, that study did find a significant positive correlation between neuronal density and microvasculature volume fraction across sites, which our analysis corroborates when restricted to the cerebral cortical GM alone (Table 6). Importantly, while this variation of capillary density with neuronal density is significant across cortical sites, it is by no means large enough to maintain a constant E/N ratio across cerebral cortical sites within the mouse brain: even within the cerebral cortical GM, the E/N ratio still decreases with increasing neuronal density (Figures 7A,B and Table 6), which is indicative of less energy availability per neuron in these sites. Therefore, it remains true for the cerebral cortex alone that our data suggest that energy availability per neuron is supply-limited.

There are presently no direct data available on rates of energy use per neuron, whether in different structures or species, to test the hypothesis that larger neurons use more energy (whether due to supply or demand); all measurements so far have been of energy use per gram of tissue (Mink et al., 1981; Karbowski, 2007), not per neuron. A necessary first step to establishing whether larger neurons use more energy, be it due to increased demand, supply, or both, is comparing average energy use per neuron where neurons have different sizes, both within and across species. The practical impediment here is that measuring energy use requires bringing live animals to the lab. We propose that local capillary density, which can be measured readily and efficiently in 2D images of thin brain sections, is a good proxy and viable alternative to estimating energy availability per volume as well as per neuron in fixed brain tissue. What makes it a good proxy is that local capillary density in fixed brain tissue correlates very well, and linearly, with resting blood flow and local rate of glucose use in both rat (Klein et al., 1986; Borowsky and Collins, 1989) and macaque brains (Noda et al., 2002). A direct validation of the correspondence between local capillary density and resting metabolic rate is reported in the accompanying study (Ventura-Antunes et al., 2022), in which we find that the small variations in the local vascular fraction measured as in the present study across sites in the rat brain are a very good approximation of measurements of local energy cost at rest in each structure. We thus expect that systematic analyses of local capillary densities will provide a powerful tool to circumvent the limitations to studying energy use per neuron in living animals, and open the way to comparative studies of energy availability per neuron in brains of species that are unlikely ever to be brought alive to laboratory settings.

It is possible that blood flow rates through capillaries vary across sites depending on factors such as network geometry and branch order, and also vary over time, according to variations in blood pressure in arterioles. However, red blood cell transit times in the brain have been shown to be relatively uniform across resting awake and stimulated conditions, with rates of oxygen transfer determined primarily by capillary length density (Jesperson and Ostergaard, 2012). Most importantly, the demonstration that local rates of blood flow in the awake brain are strongly, and linearly, correlated with both capillary density and rates of glucose use (Klein et al., 1986; Borowsky and Collins, 1989) provides the necessary evidence that local capillary density is a useful proxy for local rates of energy supply and use at rest.

While we examine fixed tissue and can make no claims about physiological properties and dynamic changes in neurovascular coupling (Leithner and Royl, 2014), the relatively homogeneous distribution of the capillary bed in the perfused tissue compared to highly variable neuronal densities, in the presence of constant overall blood flow in the brain (Mintun et al., 2001; Sato et al., 2011; Smith and Ainslie, 2017), does inform that, per neuronal cell body, there is more energy available in those sites with lower neuronal densities (with few and larger neurons; Mota and Herculano-Houzel, 2014) than in sites of high neuronal density. These findings are compatible with a scenario where neurons compete for limited energy supply, rather than the usually presumed scenario in which larger neurons and/or neurons with more synapses demand more energy, which is then provided as the capillary bed adapts to those demands during development. A limited energy supply constrained by the density of the capillary bed would have direct consequences for the level of neuronal and synaptic activity that can be sustained across brain sites, in line with our previous suggestion that fundamental aspects of neuronal structure and function are constrained by energy supply across species (Herculano-Houzel, 2011). It remains to be determined whether these constraints manifest themselves during development, for instance through the self-regulation of the numbers of synapses that can form and remain active, or simply through self-regulation of levels of activity (as in synaptic homeostasis; Turrigiano, 2012).

The present findings have fundamental implications for brain health and normal and diseased aging. First, they suggest that the heightened vulnerability of the human WM to ischemia (Wang et al., 2016) may be primarily due to its low capillary density compared to GM structures, and not simply to its large relative volume. Second, as cortical locations with high neuron densities have far less blood supplied per neuron than locations with low neuronal densities, individual neurons in “crowded” cortical areas are likely to be much more vulnerable to aging and pathologies that compromise circulation and/or metabolic capacity. Most remarkably, the hippocampus, whose granular layer contains most of its neurons and exhibits some of the lowest values of E/N found here, is one of the brain structures most highly vulnerable to hypoxia (Hossmann, 1999). Finally, some of the regions first and most vulnerable to Alzheimer’s disease are cortical areas with high resting metabolism (Buckner et al., 2005). While that might be indicative of higher capillary densities that would increase energy availability as a whole, it is possible that this is offset by very high neuronal densities, such as those found in the entorhinal cortex and hippocampus here, leading to low values of E/N and thus particularly high vulnerability to hypoxic insults. We are currently investigating the effects of aging on capillary density in the brain, and the possibility that local variation in E/N correlates with brain tissue vulnerability in normal and diseased aging.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

All animal use in this project was approved by the Committee on Ethical Animal Use of the Health Sciences Center (CEUA-CCS), Federal University of Rio de Janeiro (UFRJ), with protocol number 01200.001568/2013-87.

SH-H conceived the study. LV-A executed all data acquisition. Both authors analyzed the data and wrote the manuscript.