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Research Article

Relating Structure and Function in the Human Brain: Relative Contributions of Anatomy, Stationary Dynamics, and Non-stationarities

* E-mail: [email protected]

Affiliation Laboratoire d'Imagerie Fonctionnelle, UMR678, Inserm/UPMC Univ Paris 06, Paris, France

• Arnaud Messé, 
• David Rudrauf, 
• Habib Benali, 
• Guillaume Marrelec

• Published: March 20, 2014
• https://doi.org/10.1371/journal.pcbi.1003530
• Reader Comments

Investigating the relationship between brain structure and function is a central endeavor for neuroscience research. Yet, the mechanisms shaping this relationship largely remain to be elucidated and are highly debated. In particular, the existence and relative contributions of anatomical constraints and dynamical physiological mechanisms of different types remain to be established. We addressed this issue by systematically comparing functional connectivity (FC) from resting-state functional magnetic resonance imaging data with simulations from increasingly complex computational models, and by manipulating anatomical connectivity obtained from fiber tractography based on diffusion-weighted imaging. We hypothesized that FC reflects the interplay of at least three types of components: (i) a backbone of anatomical connectivity, (ii) a stationary dynamical regime directly driven by the underlying anatomy, and (iii) other stationary and non-stationary dynamics not directly related to the anatomy. We showed that anatomical connectivity alone accounts for up to 15% of FC variance; that there is a stationary regime accounting for up to an additional 20% of variance and that this regime can be associated to a stationary FC; that a simple stationary model of FC better explains FC than more complex models; and that there is a large remaining variance (around 65%), which must contain the non-stationarities of FC evidenced in the literature. We also show that homotopic connections across cerebral hemispheres, which are typically improperly estimated, play a strong role in shaping all aspects of FC, notably indirect connections and the topographic organization of brain networks.

Author Summary

By analogy with the road network, the human brain is defined both by its anatomy (the ‘roads’), that is, the way neurons are shaped, clustered together and connected to each others and its dynamics (the ‘traffic’): electrical and chemical signals of various types, shapes and strength constantly propagate through the brain to support its sensorimotor and cognitive functions, its capacity to learn and adapt to disease, and to create consciousness. While anatomy and dynamics are organically intertwined (anatomy contributes to shape dynamics), the nature and strength of this relation remain largely mysterious. Various hypotheses have been proposed and tested using modern neuroimaging techniques combined with mathematical models of brain activity. In this study, we demonstrate the existence (and quantify the contribution) of a dynamical regime in the brain, coined ‘stationary’, that appears to be largely induced and shaped by the underlying anatomy. We also reveal the critical importance of specific anatomical connections in shaping the global anatomo-functional structure of this dynamical regime, notably connections between hemispheres.

Citation: Messé A, Rudrauf D, Benali H, Marrelec G (2014) Relating Structure and Function in the Human Brain: Relative Contributions of Anatomy, Stationary Dynamics, and Non-stationarities. PLoS Comput Biol 10(3): e1003530. https://doi.org/10.1371/journal.pcbi.1003530

Editor: Claus C. Hilgetag, Hamburg University, Germany

Received: August 14, 2013; Accepted: February 8, 2014; Published: March 20, 2014

Copyright: © 2014 Messé et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This work is supported by the Inserm and the University Pierre et Marie Curie (Paris, France). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Coherent behavior and cognition involve synergies between neuronal populations in interaction [1] – [3] . Even at rest, in the absence of direct environmental stimulations, these interactions drive the synchronization of spontaneous activity across brain systems, shedding light on the large-scale anatomo-functional organization of the brain [4] . The study of such patterns of synchronization has known important developments due to recent methodological advances in brain imaging data acquisition and analysis. These advances have enabled investigators to estimate interactions in the brain by measuring functional connectivity (FC) from resting-state functional MRI (rs-fMRI). Analyses of FC at rest have supported the hypothesis that the brain is spatially organized into large-scale intrinsic networks [5] – [7] , e.g. the so-called resting-state networks [8] , [9] , such as the default mode network, which have been linked to central integrative cognitive functions [10] – [13] . The study of large-scale intrinsic networks from rs-fMRI has become a central and active area for neuroscience research. However, the mechanisms and factors driving FC, as well as their relative contribution to empirical data, are still highly debated [14] and remain to be elucidated.

Theoretical rationale and empirical findings support the hypothesis that FC is driven and shaped by structural connectivity (SC) between brain systems, i.e., by the actual bundles of white matter fiber connecting neurons [15] . As a first approximation, SC can be inferred from fiber tractography based on diffusion-weighted imaging (DWI) [16] – [19] . A recent study [20] , which focused on a small subset of robustly estimated structural connections, demonstrated the existence of a statistical, yet complex, correspondence between FC and specific features of SC (e.g., low vs. high fiber density, short vs. long fibers, intra vs. interhemispheric connections). However, a large part of FC cannot be explained by SC alone [21] . There appears that FC is the result of at least two main contributing factors: (i) the underlying anatomical structure of connectivity, and (ii) the dynamics of neuronal populations emerging from their physiology [3] . A key issue is to better understand the relative contributions of these two components to FC. Besides, recent studies using windowed analyses have suggested that FC estimated over an entire acquisition session (referred to as ‘stationary FC’ in the literature) breaks down into a variety of reliable correlation patterns (also referred to as ‘dynamic FC’ or ‘non-stationarities’) when estimated over short time windows (30 s) [14] , [22] . The authors advocated that FC estimated over short time windows (or windowed FC, for short) mostly reflects recurrent transitory patterns that are aggregated when estimating FC over a whole session. They further suggested that whole-session FC may only be an epiphenomenon without clear physiological underpinning, and not the reflection of an actual process with stationary FC [14] . This perspective remains to be reconciled with the fact that whole-session FC has been found to be highly reproducible, functionally meaningful and a useful biomarker in many pathological contexts [23] , [24] . Note that, in the recent literature of fMRI data analysis, stationarity implicitely refers to a stationary FC (i.e., the invariance of FC over time), to be contrasted with the more general notion of (strong) stationarity, where a model or process is stationary if its parameters remain constant over time [25] , [26] . SC being temporally stable at the scale of a whole resting state fMRI session (typically 10 min), we could expect SC to drive a stationary process (in the strong sense). Since SC is furthermore expected to drive FC, we can hypothesize that this stationary process contributes to generate a stationary FC.

In order to bring together the structural and dynamical components underlying FC, some studies have used computational models that incorporate SC together with biophysical models of neuronal activity to generate coherent brain dynamics [27] – [32] . This approach has yielded promising results for the understanding of the relationship between structure and function [17] , [33] , [34] . Here, we used a testbed of well-established generative models simulating neuronal dynamics combined with empirical measures, to investigate the relative contributions of anatomical connections, stationary dynamics, and non-stationarities to the emergence of empirical functional connectivity. In particular, we considered the following hypotheses: (H1) part of FC directly reflects SC; (H2) models of physiological mechanisms added to SC increase predictive power all the more as they are complex; (H3) part of the variance of FC that is unexplained by models is due to issues in the estimation of SC, e.g., problems with measuring homotopic connections; (H4) there is an actual stationary process reflected in whole-session FC that is not merely an artifact but substantially reflects the driving of the dynamics by SC.

In order to test these hypotheses and estimate the relative contribution of anatomy, stationary dynamics and non-stationarities to FC, we relied on the following approach. After T 1 -weighted MRI based parcellation of the brain ( N  = 160 regions), SC was estimated using the proportion of white matter fibers connecting pairs of regions, based on probabilistic tractography of DWI data [35] . FC was measured on rs-fMRI data using Pearson correlation between the time courses of brain regions. We quantified the correlation between SC alone and FC as a reference, and also fed SC to generative neurodynamical models of increasing complexity: a spatial autoregressive (SAR) model [36] , analytic models with or without conduction delays [28] – [31] , [37] , and biologically constrained models [29] , [32] . Importantly, all these models were used in their stationary regime in the strong sense, since their parameters were not changed during the simulations. Of these models, only the SAR is explicitely associated with a stationary FC; other, more complex models, generate dynamics that are compatible with a non-stationary FC. We computed FC from data simulated by these models and compared the results to empirical FC. For each model, performance was quantified using predictive power [29] , for each subject as well as on the ‘average subject’ (obtained by averaging SC and empirical FC across subjects). Values for the model parameters were based on the literature, except for the structural coupling strength that was optimized in order to maximize each model's performance.

Predictive power of models

In agreement with H1, SC explained a significant amount of the variance of whole-session FC for all subjects, as did all generative models (permutation test, p <0.05 corrected) ( Figure 1 , panel A). Generative models predicted FC better than SC alone (paired permutation test, p <0.05 corrected). Predictive power obtained with the average subject ranged from 0.32 for SC alone to 0.43 for the SAR model ( Table 1 ). For a given model, predictive power was reproducible across subjects. Contrary to our hypothesis H2, generative models had similar performance, and complexity was not predictive of performance. The results remained unchanged when no global signal regression was applied ( Figure S1 ). Also, findings were found to be similar for SC alone and the SAR model at finer spatial scales ( N  = 461 and N  = 825 regions, Figure S2 ) and consistent with a replication dataset ( Figure S3 ). Most importantly, a large part of the variance ( R 2 ) in the empirical data (at least 82%) remained unexplained by this first round of simulations.

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(A) Predictive power for all connections and when restricted to intra/interhemispheric, direct/indirect connections. For each type of connections and each model, we represented the individual predictive powers (bar chart representing means and associated standard deviations), as well as the predictive power for the average subject computed using the original SC (diamonds), or after adding homotopic connections (circles). Of note, SC alone has no predictive power (zero) for the subset of indirect connections, by definition. (B) Patterns of SC, empirical FC and FC simulated from the SAR model for the average subject and associated scatter plot of simulated versus empirical FC (solid line represents perfect match). SARh stands for the SAR model with added homotopic connections. Matrices were rearranged such that network structure is highlighted. Homologous regions were arranged symmetrically with respect to the center of the matrix; for instance, the first and last regions are homologous. (C) Similarity of functional brain networks across subjects (bar chart with means and associated standard deviations), for the average subject (diamonds), and when adding homotopic connections (circles) (left). Network maps for the average subject and empirical FC, as well as for FC simulated using either the SAR model with original SC or the SARh.

https://doi.org/10.1371/journal.pcbi.1003530.g001

https://doi.org/10.1371/journal.pcbi.1003530.t001

Role of homotopic connections

We reasoned (see hypothesis H3) that part of the unexplained variance could reflect issues with the estimation of SC from DWI, which can be expected because of limitations in current fiber tracking algorithms and the problem of crossing fibers [38] . We know for instance that many fibers passing through the corpus callosum are poorly estimated in diffusion imaging, in particular those connecting more lateral parts of the cerebral cortex [39] . Yet, the corpus callosum is the main interhemispheric commissure of the mammal brain, see [40] . It systematically connects homologous sectors of the cerebral cortex across the two hemispheres in a topographically organized manner, with an antero-posterior gradient, through a system of myelinated homotopic fibers or ‘homotopic connections’. The hypothesis of an impact of SC estimation problems on FC unexplained variance was supported by the observation that, in our results, intrahemispheric connections yielded on average a much higher predictive power (e.g., 0.59 for the SAR model) than interhemispheric connections (0.16 for the SAR model).

In order to further test the role of white matter connections in driving FC, we artificially set all homotopic connections to a constant SC value (0.5) for the average subject and reran all simulations. As a result, the predictive power strongly increased for all models ( Figure 1 , panels A and B), ranging from 0.39 for SC alone to 0.61 for the SAR model ( Table 1 ). Thus the variance unexplained (1- R 2 ) was reduced to 63%. Moreover, predictive power for intra and interhemispheric connections became equivalent (0.60 and 0.62, respectively). Interestingly, adding homotopic connections also led to a substantial increase in predictive power for indirect connections, that is, pairs of regions for which SC is zero (increasing from 0.07 to 0.45). The effect of adding interhemispheric anatomical connections on increasing predictive power was highly specific to homotopic connections. When applying the SAR model to the SC matrix with added homotopic connections and randomly permuting (10 000 permutations) the 80 corresponding interhemispheric connections (one region in one hemisphere was connected to one and only one region in the other hemisphere), the predictive power strongly decreased, even compared to results with the original SC ( Figure 2 , panel A). Moreover, we further assessed the specificity of this result by systematically manipulating SC. In three different simulations, we randomly removed, added, and permuted structural connections (10 000 times). In all cases, the predictive power decreased as a function of the proportion of connections manipulated ( Figure 2 , panel B). Moreover, changes induced by these manipulations remained small (<0.05), far below the changes that we were able to induce by adding homotopic connections. All in all, these results suggest that homotopic connections play a key role in shaping the network dynamics, in a complex and non-trivial manner.

(A) Predictive power of the SAR model with original SC (green), when adding homotopic connections (‘SARh’, red), or with shuffled homotopic connections (black). (B) Predictive power of the SAR model with original SC (red) and when SC values were randomly permuted, removed or added (from left to right). For each graph, predictive power was quantified as a function of the percentage of connections manipulated.

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Predicting functional brain networks

Beyond predicting the overall pattern of FC, we also assessed whether models could predict the empirical organization of FC into a set of intrinsic networks. Connectivity matrices were clustered into groups of non-overlapping brain regions showing high within-group correlation and low between-group correlation, and the resulting partitions into functional brain networks were compared between empirical and simulated FC using the adjusted Rand index (see Methods ). Again, the SAR model tended to perform best among all computational models ( Figure 1 , panel C).

Without adding homotopic connections in the SC matrix, the simulated networks highly differed from the empirical networks. In particular, most networks were found to be lateralized. After adding homotopic connections, the resemblence between simulated and empirical networks greatly improved. Networks were more often bilateral and overall consistent with the topography of empirical functional networks, including somatosensory, motor, visual, and associative networks. High FC between the amygdala and ventral-lateral sectors of the prefrontal cortex was also correctly predicted by the simulations. There were nevertheless some notable differences. First, the clustering of empirical FC yielded a long-range fronto-parieto-temporal association network ( Figure 1 , panel C, cyan) that was not observed in simulated FC as such. Second, a parieto-temporal cluster ( Figure 1 , panel C, red), which was associated with thalamo-striatal networks, was predicted by simulations but was not present in the empirical data. Third, a cluster encompassing the entire cingulate gyrus and precuneus ( Figure 1 , panel C, green) was predicted by simulations but was broken down into more clusters in the empirical data.

Stationary FC, non-stationary FC, and non-stationarities

The results above show that SC plays a causal role in FC, but one can still wonder what aspects of the underlying dynamics are the most directly related to this influence. A hypothesis is that SC, in combination with stable physiological processes (e.g., overall gain in synaptic transmission), drives a stationary regime of the dynamics. This hypothesis is supported by the finding that all models tested in this study, which were used in a stationary regime (in the strong sense), could explain significantly more variance than SC alone. Furthermore, the fact that the SAR could predict FC significantly better than all other models is evidence that this stationary regime is associated with stationary FC (paired permutation test, p <0.05 corrected).

But, clearly, many variations in the dynamical patterns of brain activity, be it in the process of spontaneous cognition, physiological regulation, or context-dependent changes, cannot be expected to be associated with a purely stationary FC. Modeling how the brain dynamics deal with endogenous and environmental contexts should require more complex models, either stationary or non-stationary, that are able to generate non-stationary (i.e., time-varying) patterns of FC. Given that at best 37% of the variance could be explained by the model of a purely stationary FC (the SAR), we can wonder why the models of higher complexity used in our simulation testbed did not perform better in predicting FC. One possible hypothesis is that the SAR model was favored in the simulations, because we estimated FC over about 10 minutes of actual brain dynamics. In such configuration, we can imagine that the non-stationarities of FC cancel out, the estimation effectively keeping the stationary part of FC. We thus wondered whether the more complex models would better perform when non-stationary FC had the potential of being more strongly reflected in the data. We approached this question by computing predictive power on windowed FC as a function of the length of the time-window used [22] , for all possible time-windows over which FC could be estimated and for all models. We also investigated the effect of simulation duration (see Methods ). We found that the relative performance of more complex models was still lower than that of the SAR model ( Figures 3 and S4 ). The average predictive power was lower for shorter time-windows and increased towards a limit for longer time-windows. The SAR model behaved like an ‘upper-bound’ for predictive power. The performance of all other models, irrespective of the size of the time-window, was between that of SC alone and that of the SAR model.

Predictive power as a function of time-window length across subjects (left) and of duration of simulated runs on the average subject (right). For color code see Figure 1 .

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A straightforward explanation is that the non-stationary patterns of FC, as generated by the simulation models, did not match the non-stationary patterns of the empirical FC as they unfolded during the acquisition in the brain of the participants. Context-dependent and transient dynamics are likely to be missed by models of the dynamics that cannot be contextually constrained in the absence of further information. It is thus difficult to infer how much of the 63% of unexplained variance remaining in whole-session FC actually reflect physiologically meaningful non-stationary FC, and more broadly, non-stationary dynamics.

In the present study, we investigated the respective contributions of anatomical connections, stationary dynamics, and non-stationarities to the emergence of empirical functional connectivity. We compared the performance of computational models in modeling FC and manipulated SC in order to analyze the impact of SC on FC, with and without the filter of combined physiological models of the dynamics.

The importance of white matter fiber pathways in shaping functional brain networks is a known fact, for a review, see [15] , [17] , [21] , [23] . Previous modeling studies have supported the importance of the underlying anatomical connections, i.e., SC, in shaping functional relationships among brain systems [16] , [41] , [42] . In agreement with our hypothesis H1, we showed that functional connectivity could at least in part be explained by structural connectivity alone. Adding homotopic connections in the matrix of SC, we found a slight increase in explained variance when considering the prediction of whole-session FC from SC alone (+4% of explained variance). In agreement with H2, adding models of physiological interactions above and beyond SC alone increased the explained variance in whole-session FC, by 8% for the best performing model, the SAR model, when no homotopic connections were added, and by 22% when homotopic connections were added. This latter fact, which strongly supports H3, suggests a complex interplay between anatomy as reflected by SC and physiological mechanisms in generating FC. This impact of SC manipulations on predicted FC pertained not only to direct but also to indirect connections. For indirect connections, whole-session FC was much better predicted after adding homotopic connections to SC than before adding them (0.45 versus 0.07 in predictive power). The problem of limited predictive power for FC based on SC when considering indirect connections has puzzled the field [43] . For this reasons many studies only assess the performance of models on direct connections. Here, we showed that a major factor in driving FC for indirect anatomical connections (+20% in explained variance) is the interplay between a subset of anatomical connections, i.e., homotopic connections (which are typically underestimated by DWI), and physiological parameters that generate the dynamics underlying FC, themselves conditioned by the possible interactions defined by SC.

Contrary to our expectation (see hypothesis H2), all models tended to perform similarly, irrespective of model complexity. The best performing model in most cases was the SAR model, a model of stationary FC driven by SC, with 63% of the variance remaining unexplained. It is likely that, above and beyond problems with the estimation of SC from DWI, and other incompressible sources of irrelevant noise, much of the unexplained variance in FC relates to non-stationary patterns in FC, and more generally to non-stationarities in the strong-sense. Such non-stationarities are difficult to model in the experimentally unconstrained resting-state and in the absence of further information regarding the specific parameters shaping FC. Irrespective of their complexity, computational models are only capable of generating prototypical brain activities, and not the subject-dependent activity that took place in the brain of the participants during scanning. The scientific necessity of modeling brain dynamics is hindered by such uncertainty and it will be a challenge to find solutions to approach this problem [26] , [44] . Even though one objective for neuroscience is to propose generative models that are capable of generating detailed neuronal dynamics, generative models cannot be informed by this unknown context and, as a consequence, cannot generate context-dependent activity in a manner that would be predictive of empirical data, in the absence of additional measures and experimental controls. Nevertheless, and perhaps for that very reason, the study of non-stationarity in FC should become of central interest for the field, as such non-stationarities could explain much of FC (up to 63% according to our simulation results), and thus reflect critical mechanisms for neurocognitive processing.

In the absence of adequate modeling principles, determining the precise contribution of non-stationarities to the unexplained variance in FC is impossible, as other confounding sources of unexplained variance are expected. As we showed, even naive manipulations aimed at estimating the impact of the known errors in DWI-based reconstruction of homotopic connections showed that such errors could cause 20% of the unexplained variance in predicting empirical FC. How DWI and fiber tracking should be used for an optimal estimation of structural connectivity is still a topic of intense debates [45] – [48] . It is likely that part of the unexplained variance in predicting FC will be reduced as better estimates of SC become available.

The model showing the best results, the SAR model, explicitly modeled a stationary process with a stationary FC. In line with our hypothesis H4, empirical FC is likely to incorporate stationary components driven by SC. Further knowledge about this stationary process might be gained by analyzing FC computed over much longer periods of time than is commonly performed (e.g., hours versus minutes). This stationary process is itself likely to be only locally stationary, as it might be expected that slow physiological cycles, from nycthemeral cycles to hormonal cycles, development, learning and aging, will modify the parameters controlling it.

In the present study, we did not take into account the statistical fluctuations induced by the fact that the time series were of finite length. Such a finiteness entails that even a model that is stationary in the strong sense could generate sample moments that fluctuate over time. For instance, the sample sum of square of a multivariate normal model with covariance matrix Σ computed from time series of size N is not equal to N Σ but is Wishart distributed with N -1 degrees of freedom and scale matrix Σ. This phenomenon will artificially increase the part of variance that cannot be accounted for by stationary models and, hence, play against stationary models. Since it is conversely very unlikely for a non-stationary model to generate sample moments that are constant over time, statistical fluctuations cannot at the same time artificially increase the part of variance that can be accounted for by stationary models. As a consequence, not considering these statistical fluctuations made us underestimate the part of variance that can be accounted for by models that are stationary in the strong sense. In other words, our estimate of the part of variance accounted for by a stationary model is a lower bound for the true value. We can therefore be confident that taking statistical fluctuations into account will only strengthen H4.

Our goal here was to investigate how current generative models of brain acticity fare in predicting the relationship between structure and function. The complexity of some of these models was such that the simulations included here were only possible thanks to a computer cluster. The behavior of all these models depends on the values of some parameters and, in the present study, we set these parameters in agreement with the literature. In what measure this choice affects how well models predict FC is unclear. Yet a full investigation of this issue remains beyond the scope of this study, since parameter optimization through extensive exploration of the parameter space for all models is at this stage unrealistic. Nevertheless, in order to get a sense of the sensitivity of our results to parameter values in a way that is compatible with the computational power available, we explored the behavior of the Fitzhugh-Nagumo, Wilson and Kuramoto models over a subset of the parameter space (see Figures S5 and S6 ). We found that parameter values had little influence on predictive power, which, in all cases, remained below that of the SAR, the simplest model tested.

We formulated H2 to test for the existence of a relationship between complexity and realism in the models that we used. Indeed, there should exist a very tight connection between the two, since the more complex generative models in our study have been designed to take biophysical mechanisms into account, with parameters that are physiologically relevant and values often chosen based on prior experimental results. Now, realism usually comes at the cost of complexity. As a consequence, it is often (implicitely) assumed that, among the models we selected, the more complex a model is, the more realistic it will also be and the better it will fit the data. This is the reason why we stated H2, based on such rationale inspired from the literature, in order to put such hypothesis to the test. The results show that for the models we used, with their sets of parameters, an increase in complexity was not associated with an increase in performance. This suggests that, for these models, complexity and realism are not quite as tightly connected as expected.

Given that the SAR model is the only model that does not include a step of hemodynamic modeling (Balloon-Windkessel), it cannot be ruled out that the superiority of the SAR reflects issues with this step. In order to check that this is not the case, we computed predictive power for all models without the hemodynamic model. The predictive power was largely insensitive to the presence of the hemodynamic model (see Figure S7 ). In particular, the SAR model remained overall an upper bound in terms of predictive power.

Finally, we should note that we relied on a definition of SC restricted to the white matter compartment. Although this is standard in the field, in reality, local intrinsic SC exists in the gray matter. However, current models generally make prior assumptions about such SC. Moreover, intrinsic SC currently remains impossible to measure reliably for the entire brain.

In spite of the complexity of the problems and the limitations of current modeling approaches, computational modeling of large-scale brain dynamics remains an essential scientific endeavor. It is key to better understand generative mechanisms and make progress in brain physiology, physiopathology and, more generally, theoretical neuroscience. It is also central to the endeavor of searching for accurate and meaningful biomarkers in aging and disease [49] . Moreover, computational modeling of FC opens the possibility of making inference on specific biophysical parameters, including inference about the underlying anatomical connectivity itself. In spite of their limited predictive powers, simpler models can be useful in this context. The SAR model, introduced in [36] , may appear well-suited to model essential stationary aspects of the generative mechanisms of FC. One interest of such a simple and analytically tractable model is that, beyond its very low computational burden, it could be the basis for straightforward estimation of the model parameters that can be used to compare clinical populations, and could constitute a potentially important biomarker of disease.

Ethics statement

All participants gave written informed consent and the protocol was approved by the local Ethics Committee of the Pitié-Salpêtrière Hospital (number: 44-08; Paris, France).

Twenty-one right-handed healthy volunteers were recruited within local community (11 males, mean age 22±2.4 years). Data were acquired using a 3 T Siemens Trio TIM MRI scanner (CENIR, Paris, France). For acquisition and preprocessing details, see Text S1 . For each subject, the preprocessing yielded three matrices: one of SC, one with the average fiber lengths, and one of empirical FC. These matrices were also averaged across subjects (‘average subject’).

Simulations

We used eight generative models with various levels of complexity: the SAR model, a purely spatial model with no dynamics that expresses BOLD fluctuations within one region as a linear combination of the fluctuations in other regions; the Wilson-Cowan system, a model expressing excitatory and inhibitory neuronal populations activity; the two rate models (with or without conduction delays), simplified versions of the Wilson-Cowan system obtained by considering exclusively the excitatory population; the Kuramoto model, which simulates neuronal activity using oscillators; the Fitzhugh-Nagumo model, which aims at reproducing complex behaviors such as those observed in conductance-based models; the neural-mass model, also based on conductance and with strong biophysiological constraints; and finally, the model of spiking neurons, the most constrained model in the current study which models neuron populations as attractors. For more details, see Text S2 .

All models took an SC matrix as input, and all but the SAR were taken as models of neuronal (rather than BOLD) activity. Simulated fMRI BOLD signal was obtained from simulated neuronal activity by means of the Balloon-Windkessel hemodynamic model [50] , [51] . Global mean signal was then regressed out from each region's time series. Finally, simulated FC was computed as Pearson correlation between simulated time series. For the SAR model, we directly computed simulated FC from the analytical expression of the covariance, see Equation (2) in Text S2 . All models had a parameter that represents the coupling strength between regions. This parameter was optimized separately for each model on the average subject to limit computational burden ( Text S2 ). After optimization, we generated three runs of 8 min BOLD activity and averaged the corresponding FCs to obtain the simulated FC for each dynamical model and each subject. For the average subject, simulated FC was obtained by feeding the average SC matrix to the different models.

Performance

Modeling performance was assessed using predictive power and similarity of spatial patterns. Predictive power was quantified for each subject and for the average subject by means of Pearson correlation between simulated and empirical FC [29] . Regarding the similarity of functional brain networks, SC, empirical FC and simulated FC were decomposed into 10 networks using agglomerative hierarchical clustering and generalized Ward criterion [52] . The resulting networks from SC and simulated FC were compared to the ones resulting from empirical FC using the adjusted Rand index [53] , [54] . The Rand index quantifies the similarity between two partitions of the brain into networks by computing the proportion of pairs of regions for which the two partitions are consistent (i.e., they are either in the same network for both partitions, or in a different network for both partitions). The adjustment accounts for the level of similarity that would be expected by chance only.

Analysis of dynamics

Empirical and simulated windowed FC were computed on individual subjects using sliding time-windows (increment of 20 s) of varying length (from 20 to 420 s by step of 20 s). Predictive power was computed as the correlation between any pair of time-windows of equal length corresponding to simulated and empirical windowed FC, respectively. This approach was only applied to the dynamical models; for SC alone and the SAR model, simulated FC remained, by definition, constant through time and, as a consequence, windowed FC was equaled to whole-session FC. The influence of simulated run duration on predictive power was also investigated. For each model, three runs of one hour were simulated on the average subject. Predictive power was then computed as a function of simulated run duration. For the same reason as above, SC alone and the SAR model did not depend on simulation duration.

Supporting Information

Performance of computational models when no global signal regression was performed. (A) Predictive power for all connections and when restricted to intra/interhemispheric, direct/indirect connections. For each type of connections and each model, we represented the individual predictive powers (bar chart representing means and associated standard deviations), as well as the predictive power for the average subject computed using the original SC (diamonds), or after adding homotopic connections (circles). Of note, SC alone has no predictive power (zero) for the subset of indirect connections, by definition. (B) Patterns of SC, empirical FC and FC simulated from the SAR model for the average subject and associated scatter plot of simulated versus empirical FC (solid line represents perfect match). SARh stands for the SAR model with added homotopic connections. Matrices were rearranged such that network structure is highlighted. Homologous regions were arranged symmetrically with respect to the center of the matrix; for instance, the first and last regions are homologous. (C) Similarity of functional brain networks across subjects (bar chart with means and associated standard deviations), for the average subject (diamonds), and when adding homotopic connections (circles) (left). Network maps for the average subject and empirical FC, as well as for FC simulated using either the SAR model with original SC or the SARh.

https://doi.org/10.1371/journal.pcbi.1003530.s001

Performance of SC alone and the SAR model at finer spatial scales. Predictive power for all connections and when restricted to intra/interhemispheric, direct/indirect connections. For each type of connections and each model, we represented the individual predictive powers (bar chart representing mean and associated standard deviation), as well as the predictive power of the average subject computed using the original SC (diamonds), or after adding homotopic connections (circles).

https://doi.org/10.1371/journal.pcbi.1003530.s002

Performance of computational models on the replication dataset. The replication dataset was from the study of Hagmann and colleagues [55] . Brain network was defined at low anatomical granularity (N = 66 regions), and connectivity measures were averaged over five healthy volunteer subjects. (A) Predictive power for all connections and when restricted to intra/interhemispheric, direct/indirect connections. For each type of connections and each model, we represented the individual predictive powers (bar chart representing means and associated standard deviations), as well as the predictive power for the average subject computed using the original SC (diamonds), or after adding homotopic connections (circles). Of note, SC alone has no predictive power (zero) for the subset of indirect connections, by definition. (B) Patterns of SC, empirical FC and FC simulated from the SAR model for the average subject and associated scatter plot of simulated versus empirical FC (solid line represents perfect match). SARh stands for the SAR model with added homotopic connections. Matrices were rearranged such that network structure is highlighted. Homologous regions were arranged symmetrically with respect to the center of the matrix; for instance, the first and last regions are homologous. (C) Similarity of functional brain networks across subjects (bar chart with means and associated standard deviations), for the average subject (diamonds), and when adding homotopic connections (circles) (left). Network maps for the average subject and empirical FC, as well as for FC simulated using either the SAR model with original SC or the SARh.

https://doi.org/10.1371/journal.pcbi.1003530.s003

Effect of time on performance. Predictive power of computational models as a function of the time-window length for each subject (graphs) and model (color).

https://doi.org/10.1371/journal.pcbi.1003530.s004

Exploration of the parameter space for the Fitzhugh-Nagumo model. (Left) Phase diagrams (i.e., x - y plane) for an uncoupled model ( k  = 0) over various parameter values of α and β . The model operate mostly in an oscillatory regime for the range of parameter values investigated. (Right) Predictive power as a function of α and β . The black dot represents the parameter set used in our simulations, while the black square corresponds to the values from [28] . The values used in our simulations gave rise to higher predictive power than the parameters values from [28] . In any case, for the range of parameters considered, the predictive power always remained lower than that obtained with a SAR model.

https://doi.org/10.1371/journal.pcbi.1003530.s005

Effect of velocity on predictive power. Predictive power as a function of the coupling strength and velocity values in generative models. Black dots represent values used for subsequent simulations. These simulations show that the predictive power is little influenced by velocity. In any case, for the range of parameters considered, the predictive power also always remained lower than that obtained with a SAR model.

https://doi.org/10.1371/journal.pcbi.1003530.s006

Effect of the hemodynamic model. Predictive power for all connections and when restricted to intra/interhemispheric, direct/indirect connections. For each type of connections and each model, we represented the predictive power for the average subject computed using the BOLD signal (diamonds, solid line) or using the neuronal activity (circles, dashed line). Of note, the prediction differs slightly from that of the Figure 1 due to the stochastic component of most models at each run.

https://doi.org/10.1371/journal.pcbi.1003530.s007

Data and preprocessing.

https://doi.org/10.1371/journal.pcbi.1003530.s008

Computational models.

https://doi.org/10.1371/journal.pcbi.1003530.s009

Acknowledgments

The authors are thankful to Olaf Sporns (Department of Psychology, Princeton University, Princeton, USA) and Christopher J. Honey (Department of Psychological and Brain Sciences, Indiana University, Bloomington, USA) for providing the neural-mass model; to Gustavo Deco, Étienne Hugues and Joanna Cabral (Computational Neuroscience Group, Department of Technology, Universitat pompeu Fabra, Barcelona, Spain) for providing the Kuramoto and rate models as well as the spike model; and to Olaf Sporns and Patric Hagmann (Department of Radiology, University Hospital Center and University of Lausanne, Lausanne, Switzerland) for sharing their data for replication. We would also like to thank them for fruitful discussions. The authors are grateful to Stéphane Lehéricy and his team (Center for Neuroimaging Research, Paris, France) for providing them with the data, and especially to Romain Valabrègue for his help in handling coarse-grained distributed parallelization of computational tasks.

Author Contributions

Conceived and designed the experiments: AM DR HB GM. Performed the experiments: AM DR GM. Analyzed the data: AM. Wrote the paper: AM DR HB GM.

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JSmol Viewer

Brain structure and function: insights from chemical neuroanatomy.

1. General Premises

2. from the contributions of golgi and cajal to modern chemical neuroanatomy: a brief survey.

• Private channel: physically delimited pathway between two nodes of the network
• Diffuse channel: the whole available space between the network nodes is potentially used to exchange signals
• Reserved signal: Signal needing a specific “decoder” in order to be decrypted. Neurotransmitters and, more generally, signals using specific receptor systems are of this type
• Broadcast signal: “Public” signal, i.e., interpreted by all the elements that it can reach. Physical processes (e.g., pressure waves) or membrane permeable molecules (e.g., oxygen) are of this type
• Electrical signals from the pre-synaptic side can affect the post-synaptic side by means of induction;
• Electrical signals can be conducted by the extracellular fluid (electrotonic currents);
• A chemical mediator (neurotransmitter) can cross the synaptic cleft;
• Transient connection can take place between the pre-synaptic and post-synaptic neuron and also via the extracellular matrix surrounding the synaptic contact; the matrix is part of the extracellular molecular network, and affects pre- and post-synaptic morpho-functional aspects of some synaptic contacts [ 94 ].

3. Experimental Contributions to Investigations of the Morpho-Functional Organization of Brain Networks at Different Levels of Miniaturization

3.1. the “mismatch” in several histochemical images between the nerve terminals, and hence the neurotransmitter stores, and their respective decoding receptors: a basic datum in the proposal of non-synaptic transmission, i.e., volume transmission, 3.1.1. types of vt signals, 3.1.2. pathways of vt-signal migration, 3.1.3. energy gradients for vt-signal migration.

• Concentration Gradients (ref. [ 104 ] and References Therein)
• Gradients of Electrical Potentials (for Charged Signals) (ref. [ 104 ] and References Therein)
• Pressure Gradients (ref. [ 104 ] and References Therein)
• Temperature Gradients (ref. [ 104 ]; See also [ 107 ])

3.1.4. Decoding Systems for VT-Signals

3.2. evidence of the existence of horizontal molecular networks at cell membrane levels and of the integrative role of gpcr aggregates.

• The possible appearance of new binding sites or binding characteristics in each monomer (refs. [ 121 , 123 , 126 , 127 ]; see also [ 140 ]);
• Different localization of the RM at plasma membrane levels, in comparison with the isolated monomers (e.g., preferential localization in the lipid rafts) [ 141 , 142 ];
• Different turnover rate and desensitization of the monomers in the RM in comparison with the isolated GPCRs [ 143 , 144 , 145 ];
• The possible existence of a “Hub Receptor” in an RM that is made up of three or more GPCRs. The Hub Receptor has been defined as the GPCR that can interact with multiple molecules, including receptors of the RM or membrane-associated proteins [ 18 , 144 , 145 , 146 , 147 , 148 , 149 ].

4. Future Investigations on Integrative Functions of the Brain

5. final comment: epistemological considerations.

•    The Brain—is wider than the Sky—
•    For—put them side by side—
•    The one the other will contain
•    With ease—and You—beside—.

Author Contributions

Institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest, list of abbreviations.

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Agnati, L.F.; Guidolin, D.; Cervetto, C.; Maura, G.; Marcoli, M. Brain Structure and Function: Insights from Chemical Neuroanatomy. Life 2023 , 13 , 940. https://doi.org/10.3390/life13040940

Agnati LF, Guidolin D, Cervetto C, Maura G, Marcoli M. Brain Structure and Function: Insights from Chemical Neuroanatomy. Life . 2023; 13(4):940. https://doi.org/10.3390/life13040940

Agnati, Luigi F., Diego Guidolin, Chiara Cervetto, Guido Maura, and Manuela Marcoli. 2023. "Brain Structure and Function: Insights from Chemical Neuroanatomy" Life 13, no. 4: 940. https://doi.org/10.3390/life13040940

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• Perspective
• Published: 08 November 2021

Anatomical structures, cell types and biomarkers of the Human Reference Atlas

• Katy Börner   ORCID: orcid.org/0000-0002-3321-6137 1 ,
• Sarah A. Teichmann   ORCID: orcid.org/0000-0002-6294-6366 2 ,
• Ellen M. Quardokus 1 ,
• James C. Gee 3 ,
• Kristen Browne 4 ,
• David Osumi-Sutherland 5 ,
• Bruce W. Herr II   ORCID: orcid.org/0000-0002-6703-7647 1 ,
• Andreas Bueckle   ORCID: orcid.org/0000-0002-8977-498X 1 ,
• Hrishikesh Paul 1 ,
• Muzlifah Haniffa   ORCID: orcid.org/0000-0002-3927-2084 6 ,
• Laura Jardine 6 ,
• Amy Bernard   ORCID: orcid.org/0000-0003-2540-1153 7 ,
• Song-Lin Ding 8 ,
• Jeremy A. Miller 8 ,
• Shin Lin 9 ,
• Marc K. Halushka 10 ,
• Avinash Boppana 11 ,
• Teri A. Longacre 12 ,
• John Hickey 12 ,
• Yiing Lin 13 ,
• M. Todd Valerius   ORCID: orcid.org/0000-0001-8143-9231 14 ,
• Yongqun He   ORCID: orcid.org/0000-0001-9189-9661 15 ,
• Gloria Pryhuber 16 ,
• Xin Sun 17 ,
• Marda Jorgensen 18 ,
• Andrea J. Radtke   ORCID: orcid.org/0000-0003-4379-8967 19 ,
• Clive Wasserfall 18 ,
• Fiona Ginty 20 ,
• Jonhan Ho 21 ,
• Joel Sunshine 22 ,
• Rebecca T. Beuschel 19 ,
• Maigan Brusko 18 ,
• Sujin Lee 23 ,
• Rajeev Malhotra   ORCID: orcid.org/0000-0003-0120-4630 14 , 23 ,
• Sanjay Jain 24 , 25 &
• Griffin Weber 26  

Nature Cell Biology volume  23 ,  pages 1117–1128 ( 2021 ) Cite this article

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• Cellular imaging
• Computational biology and bioinformatics
• Molecular biology

The Human Reference Atlas (HRA) aims to map all of the cells of the human body to advance biomedical research and clinical practice. This Perspective presents collaborative work by members of 16 international consortia on two essential and interlinked parts of the HRA: (1) three-dimensional representations of anatomy that are linked to (2) tables that name and interlink major anatomical structures, cell types, plus biomarkers (ASCT+B). We discuss four examples that demonstrate the practical utility of the HRA.

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Advances and prospects for the Human BioMolecular Atlas Program (HuBMAP)

Specimen, biological structure, and spatial ontologies in support of a Human Reference Atlas

Tissue registration and exploration user interfaces in support of a human reference atlas

With developments in massively parallel sequencing in bulk and at the single-cell level, researchers can now detect genomic features and genome expression with great precision 1 . Profiling single cells within tissues and organs enables researchers to map the distribution of cells and their developmental trajectories across organs and gives indications as to their functions. In 2021, there are several ongoing, ambitious efforts to map all of the cells in the human body and to create a digital reference atlas of the human body. The final atlas will encompass the three-dimensional (3D) organization of whole organs and thousands of anatomical structures, the interdependencies between trillions of cells, and the biomarkers that characterize and distinguish cell types. It will make the human body computable, supporting spatial and semantic queries run over 3D structures linked to their scientific terminology and existing ontologies. It will establish a benchmark reference that helps us to understand how the healthy human body works and what changes during ageing or disease.

A network of 16 consortia is contributing to the construction of the HRA based on studies of 30 organs (Fig. 1a ) with funding by the National Institutes of Health (NIH, blue) and strong support by the international Human Cell Atlas (HCA, red) 2 , 3 as well as expert input by reviewers from many different countries. The 16 consortia include the Allen Brain Atlas 4 , the Brain Research through Advancing Innovative Neurotechnologies Initiative—Cell Census Network Initiative 5 , the Chan Zuckerberg Initiative Seed Networks for HCA 2 , 3 , 6 , HCA awards by the EU’s Horizon 2020 program, the Genotype-Tissue Expression project 7 , the GenitoUrinary Developmental Molecular Anatomy Project 8 , Helmsley Charitable Trust: Gut Cell Atlas 2 , 3 , 6 , 9 , the Human Tumor Atlas Network 10 , the Human Biomolecular Atlas Program (HuBMAP) 11 , the Kidney Precision Medicine Project (KPMP) 12 , 13 , LungMAP 14 , HCA grants from the United Kingdom Research and Innovation Medical Research Council ( https://mrc.ukri.org ), (Re)building the Kidney 15 , Stimulating Peripheral Activity to Relieve Conditions 16 , The Cancer Genome Atlas 17 , 18 , 19 and Wellcome funding for HCA pilot projects 2 , 3 , 6 . In total, more than 2,000 experts from around the globe are working together to construct an open-source and free-to-use digital HRA using a wide variety of single or multimodal spatially resolved and bulk tissue assays. Imaging methods for anatomical structure segmentation include computed tomography, magnetic resonance imaging or optical coherence tomography (OCT) 20 . Spatially resolved single-cell methods detect metabolites or lipids using high-resolution nanospray desorption electrospray ionization mass spectrometry imaging 21 , proteins using co-detection by indexing 22 or tissue microarray-based immunohistochemistry 23 , simultaneous mRNA and chromatin accessibility using assay for transposase-accessible chromatin with high-throughput sequencing 24 , simultaneous protein and mRNA using cellular indexing of transcriptomes and epitopes by sequencing 25 , and mRNA using multiplexed error robust fluorescent hybridization (MERFISH) 26 , 27 , Slide-seq 28 , 29 , Nanostring’s GeoMX 30 or 10x Genomics Visium 31 .

a , Alphabetical listing of 16 HRA construction efforts (left) linked to the 30 human organs that they study (right). The lungs are studied by ten consortia (orange links). This review focuses on ten organs (bold) plus vasculature. BICCN, Brain Research through Advancing Innovative Neurotechnologies Initiative—Cell Census Network Initiative; CZI, Chan Zuckerberg Initiative; H2020, Horizon 2020; GTEx, Genotype-Tissue Expression project; GUDMAP, GenitoUrinary Developmental Molecular Anatomy Project; HTAN, Human Tumor Atlas Network; MRC, Medical Research Council; RBK, (Re)building the Kidney; SPARC, Stimulating Peripheral Activity to Relieve Conditions; TCGA, The Cancer Genome Atlas. b , The 3D reference objects for major anatomical structures were jointly developed for 11 organs. c , An exemplary ASCT+B table showing anatomical structures (AS) and cell types (CT) and some biomarkers (B) for the glomerulus in the kidneys, annotated with the names of the three entity types (anatomical structures, cell types and biomarkers) and four relationship types (part_of, is_a, located_in and characterize). Note that the is_a relationship exists for cell types and biomarkers.

A major challenge in constructing the HRA is combining data generated by the different consortia without a common ‘language’ shared across them for describing and indexing the data in a spatially explicit and semantically consistent way. Rapid progress in single-cell technologies has led to an explosion of cell-type definitions. When researchers profile the expression of genes, proteins or other biomarkers, they can and do assign different cell types making it difficult, if not impossible, to compare results across studies—particularly across organ systems. Indeed, except for the brain 32 , no standards exist for the naming of anatomical structures, cell types and biomarkers. Furthermore, information on what cell types are commonly found in which anatomical structures and what biomarkers best characterize certain cell types is scattered across many ontologies (such as Uberon multi-species anatomy ontology 33 , the Foundational Model of Anatomy Ontology 34 , 35 , Cell Ontology (CL) 36 or the Human Gene Ontology Nomenclature Committee ( https://www.genenames.org/ )) and hundreds of publications about cells identified during development, disease and across multiple species (for example, the atlas efforts for brain 37 , heart 38 , lungs 14 and kidneys 13 ). Some critically important details (such as the morphology and distribution of microanatomical structures or the spatial layout of functionally interdependent cell types) are captured through hand-drawn figures—not digitally—without a shared 3D spatial reference system. The lack of a central, unified benchmark reference framework and language impedes progress in biomedical science as it is challenging or impossible to manage, compare, harmonize or use published data.

Towards a unified reference framework for mapping the human body

To address these issues, an NIH–HCA-organized meeting in March 2020 brought together leading experts to agree on major ontologies and associated 3D anatomical reference objects and to expand them as needed to capture the healthy human adult body. On the basis of ensuing discussions, more than 50 experts—including physicians, surgeons, anatomists, pathologists, experimentalists and representatives from the various consortia—have agreed on a reference framework to digitally represent relevant knowledge. The framework includes data structures, standard operating procedures and visual user interfaces that can be used by anatomists, pathologists, surgeons and other domain experts to digitize, integrate and analyse massive amounts of heterogeneous data. Experts also agreed on the major ontologies that will be used to create a ‘Rosetta Stone’ across existing anatomy, cell and biomarker ontologies. As a proof of concept, experts compiled inventories for 11 major organs (Fig. 1a,b ): bone marrow and blood plus pelvis reference organ 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , brain 4 , 32 , 37 , 53 , 54 , heart 55 , 56 , large intestine 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , kidneys 13 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , lungs (refs. 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 and Sun, X. & Morrisey, E., manuscript in preparation), lymph nodes 87 , 88 , 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , skin 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , spleen 89 , 111 , 112 , 113 , 114 , 115 , 116 , 117 , 118 , 119 , 120 , 121 , 122 , thymus 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 , 132 , 133 , 134 and vasculature 78 , 135 , 136 , 137 , 138 , 139 , 140 , 141 . For each organ, the experts listed known anatomical structures, the cell types located in these structures and the biomarkers that are commonly used to characterize each cell type (such as gene and protein markers). The results are captured in ASCT+B tables (Fig. 1c ) that list and anatomical structures, cell types and biomarker entities, their relationships as well as references to supporting publications. As spatial position and context matter for cell function, the experts collaborated with medical designers to compile 3D, semantically annotated reference objects that cover the anatomically correct size and shape of major anatomical structures in a systematic and computable manner (see the final set for the initial 11 ASCT+B tables in Fig. 1b ). Together, the ASCT+B tables and associated 3D reference objects constitute the HRA.

An initial set of the ASCT+B tables and reference objects have been published ( Supplementary Information ). They capture data and knowledge that are mandatory for compiling a comprehensive HRA, and they are critically important for facilitating data exchange and collaboration among the 16 consortia and other efforts. They demonstrate how existing knowledge can be captured digitally and reorganized in support of a HRA. The tables and associated 3D reference objects provide an agreed-on framework for experimental data annotation across organs and scales (that is, from whole body to organs, tissues, cell types and biomarkers); they make it possible to compare and integrate data from different assay types (such as single-cell RNA-sequencing (scRNA-seq) 142 and MERFISH 143 data) for spatially equivalent tissue samples; they are a semantically and spatially explicit reference for healthy tissue and cell identity data that can then be compared against disease settings. Finally, the tables and associated reference organs can be used to evaluate progress on the semantic naming and definition of cell types and their anatomically accurate spatial characterization.

The ultimate goal is an HRA that correctly matches human diversity across populations. However, like the Human Genome Project 144 , 145 , the initial HRA covers a limited set of donors. For example, the Allen Human Reference Atlas—which is included in the HRA—was derived from one donor. It describes one half of a human brain that is intended to be mirrored to characterize a whole human brain. Most of the other reference organs in the current HRA are constructed from the Visible Human Project (VHP) male and female dataset made available by the National Library of Medicine 146 .

The presented ASCT+B tables and 3D reference objects are designed to be representative of organs and general enough to encompass all donors regardless of variation. All of the listed anatomical structures are expected to be present in a donor, except for sex-specific organs. There exists scientific evidence that the listed cell types are known to be located in the given anatomical structure, and that listed biomarkers are commonly used to identify a cell type. Future versions of the tables are in development and will make it possible to capture and compare data about variations in the size, location, shape and frequency of anatomical structures and cell types across donors. We next describe the data format, design and use of ASCT+B tables and the associated 3D reference objects. The initial HRA presents ten ASCT+B tables interlinked through a vasculature table together with a reference library of major anatomical structures. We discuss four examples that showcase the usage of the initial eleven-organ HRA for tissue registration and exploration, data integration, disease studies and measuring progress towards a more complete HRA. We conclude with a discussion of the next steps and an invitation to collaborate on the construction and usage of a reference atlas for healthy human adults.

ASCT+B tables

In 2019, the KPMP project published a first version of the ASCT+B tables to serve as a guide to annotate structures and cell types across multiple technologies in the kidneys 13 . The table data format was expanded and the process for constructing, reviewing and approving the ASCT+B tables was formalized (the key steps are described in Box 1 and the terminology is explained in Tables 1 and 2 ). Note that the HRA framework is in line with reproducibility best-practices and principles that make data findable, accessible, interoperable and reusable 147 , which are essential for the development of disease atlases, biomedical discovery and, ultimately, health improvements.

In September 2021, there exist 11 ASCT+B tables, version 1.0. These master tables are available for free online 148 . They capture 1,424 anatomical structures, 591 cell types and 1,867 biomarkers. The anatomical structures are linked by 2,543 ‘part_of’ relationships, 4,611 ‘located_in’ relationships between cell types and anatomical structures and 3,708 ‘characterize’ links between biomarkers and cells, supported by 293 unique scholarly publications and 506 web links ( Supplementary Information ). Like the first maps of our world, the first ASCT+B tables are imperfect and incomplete (see the ‘Limitations’ section). However, they digitize and standardize existing data and knowledge by clinicians, pathologists, anatomists and surgeons at the gross anatomical level; biologists, computer scientists and others at the single-cell level; and chemists, engineers and others at the biomarker level.

Box 1 Constructing the ASCT+B tables

At their core, the ASCT+B tables represent three entity types (anatomical structures, cell types and biomarkers; Fig. 1c ) and five relationship types (Fig. 1c and Table 2 ). Anatomical structures are connected through part_of relationships, creating a partonomy tree. In other words, the connections define whether anatomical structures may be shared parts within an organ or greater anatomical structure. Cell types are linked to other cell types through is_a relationships (for example, T cell is an immune cell, a cardiac cell is a muscle cell), defining the nature of the cell within a cellular lineage. Biomarkers can be of different types indicated by is_a (for example, they can be of type gene, protein, lipid, or metabolite); they are therefore defined in terms of their molecular nature. A bimodal network links cell types and anatomical structures on the basis of located_in relationships. Note that the same cell type might be located_in multiple anatomical structures, whereas a single anatomical structure might comprise multiple cell types. Biomarkers are linked to the cell types that they characterize through a second bimodal network. Note that one biomarker might be used to characterize multiple cell types, and multiple biomarkers might be required to uniquely characterize one cell type.

The ASCT+B v.1.0 table format makes it possible for human experts to represent the three entity types and five relationship types in a table. The initial set of 11 tables was authored using templated Google sheets. Experts filled in organ-specific tables by entering critical metadata (for example, authors, data and version number) in the top ten rows. Row 11 contains the header of the ASCT+B table, listing the anatomical structures, cell types, biomarkers and publication references from left to right. The table columns can be adjusted as needed (for example, anatomical structures partonomies might have only a few levels (5 for kidney), whereas others have many (19 for vasculature)). The v.1.0 format captures two biomarker types: gene markers (BG) and protein markers (BP); proteoforms, lipids and metabolites will be added in v1.1. Publication references document scientific evidence for the existence of the three entity types and their five interrelationships. The remaining rows, starting at row 12, contain the ASCT+B data—as many rows as there are unique cell types in the organ. Each unique anatomical structure, cell type and biomarker is represented by three columns. The first column lists the domain expert preferred name; whenever possible, this name should match the ontology name in the second column. The third column lists the unique, universally resolvable ontology ID, if available.

To ease table construction and ensure compliance with existing ontologies, a table of organ-specific, non-developmental human data captured in existing formalized ontologies was compiled by ontology experts and provided to the ASCT+B table authors. The ontologies used initially were Uberon 33 and Foundational Model of Anatomy for anatomical structures 34 , 35 , CL 36 for cell types and Human Gene Ontology Nomenclature Committee (HGNC) ( https://www.genenames.org/ ) for biomarkers. Data validation was performed by human experts and computationally by testing expert-curated relationships for validity in Uberon using Ubergraph 170 , a knowledge graph combining mutually referential Open Biological and Biomedical Ontology ontologies, including Cell Ontology and Uberon, and featuring precomputed classifications and relationships.

Box 2 Designing the 3D reference object library

To create male and female reference objects for the 11 initial organs, experts collaborated closely with medical designers to develop anatomically correct, vector-based objects that correctly represent human anatomy and are labelled using the ontology terms captured in the ASCT+B tables.

Data from the VHP male and female dataset, which was made available by the National Library of Medicine 146 , were used to model all of the 3D reference organs except for the brain, large intestine and lymph node. The brain uses the 141 anatomical structures of the ‘Allen Human Reference Atlas—3D, 2020’ representing one half of the human brain 4 ; these structures were mirrored to arrive at a whole human brain (as intended by the brain model authors) and resized to fit the visible human male and female bodies. A 3D model of the male large intestine was provided by A. Kaufman (Stony Brook University) modified to fit into the VHP male body, and used to guide the design of the female large intestine. The lymph node was created using mouse data and the clearing-enhanced 3D method developed by W. Li at the Laboratory of Immune System Biology, National Institute of Allergy and Infectious Diseases, NIH 171 . Although the size and cellular composition of mouse and human lymph nodes vary, the overall anatomy is well conserved between species.

All models were created using the medical image processing tool 3D Slicer 172 , 173 and modelling tools such as ZBrush 174 and Maya 175 . Files are provided in the Graphics Language Transmission Format (GLB) format 150 , which is a widely used standard file format for 3D scenes and models. GLB formats can be viewed in the free Babylon.js Sandbox ( https://sandbox.babylonjs.com/ ), making it possible for anyone to explore the 3D reference objects using a web browser, without downloading or installing new software.

Three-dimensional reference object library

The spatial location of cell types within anatomical structures matters, as do the number and types of cells within the same anatomical structure. A 3D reference object library was compiled (key steps are described in Box 2) to capture the size, shape, position and rotation of major anatomical structures in the organ-specific ASCT+B tables (Box 1 , Tables 1 and 2 , and Supplementary Information ).

In September 2021, there exist 26 organ objects that complement the 11 ASCT+B tables discussed above. Male and female versions exist for all organs, and left and right versions exist for kidneys and lymph nodes. All organs are properly positioned in the male and female bodies and are freely available online 149 . The resulting 3D reference object library captures a total of 1,185 unique 3D structures (for example, the left female kidney has 11 renal papillae; see the complete listing in the HuBMAP Consortium 3D Reference Object Library 149 ) with 557 unique Uberon terms, including the name of the organ. Files are provided in the GLB format 150 and are used in several user interfaces (see the ‘Tissue registration and exploration’ section).

A ‘crosswalk’ mapping file links the anatomical structure names listed in the ASCT+B tables and the terminology used in the 3D reference object library GLB files (see the ‘CCF 3D reference object library & crosswalk’ section in the Supplementary Information ). This interlinkage of ontology terms (for example, kidney or cortex of kidney; Fig. 1c ), and the 3D references objects with well-defined polygon meshes (Table 1 ) that describe the size and shape of these anatomical structures in 3D (Fig. 1b ) is critical for using 3D collision-detection algorithms for tissue registration and spatial search (see the ‘Tissue registration and exploration’ section).

How to use the HRA

The ASCT+B tables and associated 3D reference organ objects provide a starting point for the systematic construction of a HRA. They provide common nomenclature for major entities and relationships along with cross-references to existing ontologies and supporting literature. In the following sections, we provide four examples illustrating the value of the tables and associated 3D reference organs: (1) to support experimental tissue data registration and annotation across organs and scales (see the next section); (2) to compare and integrate data from different assay types (see the ‘Comparing cell states across different tissues and in disease’ section); (3) to compare healthy and disease data (see the ‘Understanding disease’ section); (4) and to evaluate progress toward the compilation of a comprehensive HRA (see the ‘Measuring progress’ section).

Tissue registration and exploration

Like any atlas, a HRA is a collection of maps that capture a multiscale 3D reality. Like other digital maps, it supports panning and zoom, from the whole body (macro scale; metres), to the organ level (meso scale; centimetres), to the level of functional tissue units (such as alveoli in the lungs, crypts in the colon and glomeruli in the kidneys; millimetres), down to the single-cell level (micro scale; micrometres). To be usable, the maps in an HRA must use the same index terms and a unifying topological coordinate system such that cells and anatomical structures in adjacent overlapping maps or at different zoom levels can be uniquely named and properly aligned.

The ASCT+B tables and 3D reference organs provide a framework for experimental data annotation and exploration across organs and scales—that is, from the entire body down to organs, tissues, cell types and biomarkers. For example, they are used to support the registration of new tissue data as well as spatial and semantic search, browsing and exploration of human tissue data. The HuBMAP CCF Registration User Interface 151 (RUI; Fig. 2a ) and CCF Exploration User Interface (EUI) 152 (Fig. 2b ) are available at the HuBMAP portal 153 . The code for both user interfaces is freely available at GitHub HuBMAP Consortium CCF User Interfaces 154 ( https://github.com/hubmapconsortium/ccf-ui ). Several consortia and single investigators have used the stand-alone version of the CCF RUI 151 to register human tissue samples. Resulting data have been added to the CCF EUI making it possible for data providers and others to explore these tissue datasets in the context of human anatomy, to search and filter for datasets that match certain criteria (such as a specific age, sex and assay type) and to access and download raw data.

a , Registration and anatomical structure annotation of tissue data (blue block) in 3D through collision detection in the RUI. A user sizes, positions and rotates tissue blocks, and saves the results in the JavaScript Object Notation (JSON) format. b , Tissue data can be queried, filtered and explored through the EUI. RUI-registered tissue data (white blocks in the spleen and kidneys) can be explored semantically using the anatomical structure partonomy on the left and spatially using the anatomy browser in the middle; a filter at the top right supports subsetting by sex, age, tissue provider and so on. Clicking on a tissue sample on the right links to the Vitessce image viewer 169 .

To make it easy for anyone to explore or contribute HRA data, we developed diverse learning modules as part of the free Visible Human Massive Open Online Course ( https://expand.iu.edu/browse/sice/cns/courses/hubmap-visible-human-mooc ). This course describes the compilation and coverage of HRA data, demonstrates new single-cell analysis and mapping techniques, and introduces the diverse HRA user interfaces. Delivered entirely online, all coursework can be completed asynchronously to fit busy schedules.

Comparing cell states across different tissues and in disease

The ASCT+B framework provides a ‘look-up table’ from the 3D reference models to the unique ontology name and ID for anatomical structures and their cell-type composition across organs that are present in the ASCT+B tables. Researchers can use the tables to determine in what anatomical structure a cell type is commonly located. Specifically, the ASCT+B tables capture information on cells formed within and resident in a specific tissue (such as epithelia and stroma) as well as cells that migrate across tissues (such as immune cells) 155 . For example, immune cells originate primarily in the bone marrow in postnatal life. Adaptive lymphocytes subsequently differentiate and mature in lymphoid tissues such as the thymus and spleen before circulating to non-lymphoid tissues and lymph nodes (Fig. 3a ). Thus, these cells recur across the ASCT+B tables in both the lymphoid (bone marrow, thymus, spleen, lymph node) and non-lymphoid (brain, heart, kidney, lung, skin) tissue tables. Existing data support a more nuanced and tissue-specific, ontology-based assignment of blood and immune cells. For example, scRNA-seq enables deep phenotyping of haematopoietic stem cells (HSCs) and haematopoietic stem and progenitor cells (HSPCs) and their differentiated progenies across various tissues. When comparing fetal liver versus thymic cell states (Fig. 3a (right)), a small region of the HSPCs highlighted as lymphoid progenitors is shared across the two organs, indicating cells that have migrated from the liver to the thymus 52 , 125 . Data integration defines molecules (such as chemokine receptors) that determine tissue residency versus migratory properties. These biomarkers in turn define tissue-resident versus migratory cell states, which can be added to the ASCT+B tables to refine cellular ontology.

a , HSCs (CL:0000037) migrate from the liver (UBERON:0002107) to the thymus (UBERON:0002370) during embryonic and fetal development. The transcriptomic identity of these HSCs changes throughout pregnancy. The differences in these anatomical structures are shown by the maroon versus blue shading of the HSCs on the left (embryo) and right (fetal) parts of the figure. The scRNA-seq data in the uniform manifold approximation and projection plots are from a published single-cell transcriptomic profile of the thymus across the human lifetime 125 . The top plot shows liver cells (blue) and thymus cells (orange) overlapping, which are labelled lymphoid progenitors in the bottom plot. The other cell populations shown include HSCs; double negative T cells (DNT); megakaryocytes (MKs); megakaryocyte/erythrocyte/mast cell progenitors (MEMPs); pro-B cells; neutrophil–myeloid progenitors (NMPs); mast cells; and erythrocytes (Ery). b , The nature of HSC subsets in the adult blood shifts in health versus COVID-19. HSCs in the blood of patients with COVID-19 (top left) show a megakaryocyte priming bias compared with healthy cells (top right). This is quantified in the histogram from the human thymus single-cell atlas of relative HSPC contributions for different donor/patient cohorts 156 .

A well-annotated healthy HRA can then be used to understand the molecular and cellular alterations in response to perturbations such as infection. For example, data from several single-cell multi-omics studies of patients’ blood can be combined to compute the cellular response during COVID-19 pathogenesis, including HSC progenitor states that emerge during disease 156 (Fig. 3b ).

Understanding disease

As a reference for healthy tissue, the ASCT+B tables can be used to identify changes in molecular states in normal ageing or disease. For example, the kidney master table links relevant anatomical structures, cell types and biomarkers to disease and other ontologies for increasing our understanding of disease states. The top significant and specific biomarkers in each reference cell/state cluster might differ during disease or in a cell undergoing repair, regeneration, or in a state of failed or maladaptive repair. Loss of expression or alteration in the cellular distribution of a specific biomarker may provide clues to the underlying disease. The Kidney Precision Medicine Project is working towards ASCT+B tables that characterize disease. Researchers aim to include biomarkers with important physiological roles in maintaining the cellular architecture or function and biomarkers that reveal shifts in cell types that are associated with acute and chronic diseases 157 . Changes in biomarkers in healthy and injured cells provide information about the underlying biological pathways that drive these shifts and therefore provide critical insights into pathogenic mechanisms. For example, the gene NPHS1 , which encodes nephrin, is one of the top markers of healthy podocytes and is essential for glomerular function. Mutations in NPHS1 may be found in patients with proteinuria 158 . The kidney ASCT+B table records that the gene biomarker NPHS1 (Fig. 1c (bottom right)) is expressed in the podocytes of the kidney. Ontology suggests injury to podocytes and glomerular function may cause proteinuria (Fig. 4 ). Ontology IDs provided for anatomical structures, cell types and biomarkers facilitate linkages to clinicopathological knowledge and help to provide broader insights into disease 159 . For example, the ASCT+B kidney master table and single-nucleus RNA-seq atlas data 70 have been used to characterize diabetic nephropathy disease states by distinguishing the healthy interstitium from a diabetic one 160 . Note that some of the existing data are not at the single-cell level; in these cases, regional data (such as data bounded by tissue blocks registered within reference organs with known anatomical structures, cell types and biomarkers (see the RUI and EUI discussion above)) can be compared to the kidney master table. In summary, ASCT+B tables interlinked with existing ontologies provide a foundation for new data analysis and the functional study of diseases.

Processes, anatomical structures, cell types, biomarkers and disease relevant for understanding proteinuria, in kidney. The example shows how the ASCT+B tables help link clinicopathology information and ontology data.

Measuring progress

The ASCT+B tables provide objective measures for tracking progress towards an accurate and complete HRA. In particular, if a scholarly publication includes a new ASCT+B table, that table can be compared with existing master tables and the number and type of identical (confirmatory) and different (new) anatomical structures, cell types and biomarkers, as well as their relationships, can be determined. The value of a new data release for reference atlas design can be evaluated in terms of the number and type of new anatomical structures, cell types, biomarkers and their relationships that it contributes. The ASCT+B Reporter 161 supports the visual exploration and comparison of ASCT+B tables. Table authors and reviewers can use this online tool to upload new tables, examine them visually and compare them with existing master tables. Power analysis methods can be run to assess the coverage and completeness of cell states and/or types and decide what tissues and cells should be sampled next 139 in support of a data-driven experimental design.

As the number of published ASCT+B tables grows, estimates can be run to determine the likely accuracy of anatomical structures, cell types, biomarkers and relationships. Entities and relationships based on high-quality data or multiple types of scholarly evidence are more likely to be correct compared with those with limited or no evidence. Incomplete data can be easily identified and flagged (for example, anatomical structures with no linkages to cell types and cell types with no biomarkers indicate missing data). Given that the tables disclose who contributes the data and who authors relevant publications, experts on anatomical structures, cell types, biomarkers and their relationships can be identified and invited to further improve the tables.

Limitations

The current format of the ASCT+B tables and 3D reference organs makes them easy to author, review, validate and use across organs and domains of expertise. The ASCT+B Reporter tool 161 supports the authoring and review of ASCT+B tables but also the comparison of these data with new datasets. 3D reference objects can be freely explored in the Babylon.js sandbox in a web browser ( https://sandbox.babylonjs.com/ ). However, the simplicity of the current tables and organs makes it impossible to fully capture the complexity of the human body. Thus, for each organ-specific table, experts recorded the process that they used to construct the table, which often included simplifying the anatomy to fit within a strict partonomy, making decisions about which cell types and biomarkers had sufficient evidence to be included in the table, or ignoring normal dynamic changes that occur in the organ over time. For several organs, such as the brain, the biomarkers are preliminary and are expected to improve in coverage and robustness in the future.

Biases in sampling with respect to donor demographics (for example, from convenience samples as opposed to using sampling strategies that reflect global demographics), organs (for example, as based on availability of funding) or cell types (for example, due to differential viability or capture efficiency) can be determined and need to be proactively addressed to arrive at an atlas that truly captures healthy human adults. The definition of ‘healthy’ is expected to evolve; HRA metadata for datasets that were used in the construction of the atlas include information on sex, age and ethnicity, but also comorbidities, making it possible to include or exclude datasets when inclusion criteria change and to recompute the HRA as needed.

Diversity, inclusion, and global scientific equity are major goals for all of the consortia involved in this effort 162 . Authors for the initial set of tables are from the United States and United Kingdom, but many have roots, training and collaborative connections in other parts of the world. Reviewers do not solely come from the United States and United Kingdom. Aiming to overcome the impact of COVID-19 related travel restrictions on collaboration across disciplinary, institutional and cultural boundaries, we organized the HRA panel at the virtual Spatial Biology Europe meeting in April 2021. The panel featured presentations by experts from Asia, Australia and North America. Slides and recordings are available online 163 . In the future, we hope to engage experts from many more countries as well as students from diverse backgrounds.

ASCT+B tables in combination with the 3D reference object library provide a rigorous cross-organ framework for experimental data annotation and exploration from the levels of organs and tissues to the levels of cell types and biomarkers. The construction and validation of the tables are iterative. Initially, ontology and publication data, along with knowledge from organ experts, are codified and unified. Later, experimental datasets are compared with existing master tables to confirm the tables or add to them as needed to capture healthy human tissue data. In the near future, the cell type typology will be expanded from one level to multiple levels, also using data from the evolving set of Azimuth references 164 , 165 and in close collaboration with the Cell Ontology curation effort (see ref. 166 in this issue). This will make it possible to compare anatomical structure partonomy and cell-type typology datasets at different levels of resolution. New organs will be added to the 3D reference library and microanatomical structures, such as glomeruli in the kidneys, crypts in the large intestine and alveoli in the lungs will be included.

Efforts are underway to integrate cell-specific protein biomarkers in the ASCT+B tables with well-characterized antibodies for multiplexed antibody-based imaging; the ASCT+B reporter has already contributed to detect protein biomarkers in situ 167 , 168 . The goal of these efforts is to generate expertly curated, tissue-specific antibody panels that can be used across consortia in support of a HRA.

The number of anatomical structures, cell types and robust biomarkers will probably increase as new single-cell technologies and computational workflows are developed. Thus, the tables and associated reference objects are a living ‘snapshot’ of the status of the collective work towards an open, authoritative, computable HRA, against which experimentalists can calibrate their data and to which they can contribute. Future uses of the HRA might include cross-species comparisons or cross-species annotations, cross-tissue/organ comparisons, comparisons of healthy versus common or rare genetic variations, and usage in teaching—expanding widely used anatomy books 78 , 135 to the single-cell level.

It will take extensive effort and expertise to arrive at a consensus HRA and to develop methods and user interfaces that use it to advance research and improve human health. Experts interested in contributing to this international and interdisciplinary effort are invited to register at https://iu.co1.qualtrics.com/jfe/form/SV_bpaBhIr8XfdiNRH to receive regular updates and invites to meetings that aim to advance the construction of the HRA.

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Acknowledgements

We thank B. B. Lake from University of California, San Diego, for assistance with annotations and analysing the single-nucleus RNA-seq HUBMAP data for several of the markers in the kidney ASCT+B tables; B. Steck and R. Dull from the University of Michigan for assistance with the nomenclature and curation of kidney partonomy; S. Winfree, IUPUI, for discussions regarding the kidney ASCT+B table; and staff at the KPMP, especially the Tissue Interrogation Sites and the Controlled Cell Vocabulary working group, for guidance and development of the initial sets of ASCT+B kidney tables. We acknowledge L. Yao for segmenting and optimizing the mouse popliteal lymph node model from high-resolution microscopy data. The work was funded, in part, by NIH Awards OT2OD026671, U54DK120058, 1UH3CA246594, 1U54AI142766, 1UG3CA256960, 1UG3HL145609, U54HL145608, U54HL145611, UH3DK114933, DK110814 and DK107350; National Institute of Allergy and Infectious Diseases (NIAID), Department of Health and Human Services under BCBB Support Services Contract HHSN316201300006W/HHSN27200002; the Intramural Research Program of the NIH at NIAID; and Helmsley Charitable Trust 2018PG-T1D071.

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Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, USA

Katy Börner, Ellen M. Quardokus, Bruce W. Herr II, Andreas Bueckle & Hrishikesh Paul

Wellcome Sanger Institute, Wellcome Genome Campus, Hinxton, Cambridge, UK

Sarah A. Teichmann

Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA

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Department of Health and Human Services, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD, USA

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European Bioinformatics Institute (EMBL-EBI), Wellcome Trust Genome Campus, Cambridge, UK

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Song-Lin Ding & Jeremy A. Miller

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Department of Pathology, Johns Hopkins University School of Medicine, Baltimore, MD, USA

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Avinash Boppana

Department of Microbiology and Immunology, Stanford University School of Medicine, Stanford, CA, USA

Teri A. Longacre & John Hickey

Department of Surgery, Washington University in St Louis, St Louis, MO, USA

Harvard Institute of Medicine, Harvard Medical School, Boston, MA, USA

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Department of Microbiology and Immunology, and Center for Computational Medicine and Bioinformatics, University of Michigan Medical School, Ann Arbor, MI, USA

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Center for Advanced Tissue Imaging, Laboratory of Immune System Biology, NIAID, NIH, Bethesda, MD, USA

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Börner, K., Teichmann, S.A., Quardokus, E.M. et al. Anatomical structures, cell types and biomarkers of the Human Reference Atlas. Nat Cell Biol 23 , 1117–1128 (2021). https://doi.org/10.1038/s41556-021-00788-6

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The nervous system is divided into the central nervous system (CNS) and the peripheral nervous system. The CNS includes the brain and spinal cord, while the peripheral nervous system consists of everything else. The CNS's responsibilities include receiving, processing, and responding to sensory information (see Image. Peripheral and Central Nervous Systems).

The brain is an organ of nervous tissue responsible for responses, sensation, movement, emotions, communication, thought processing, and memory. The skull, meninges, and cerebrospinal fluids protect the human brain. The nervous tissue is extremely delicate and can be damaged by the smallest amount of force. In addition, the brain has a blood-brain barrier that prevents the brain from any harmful substance floating in the blood.

The spinal cord is a vital aspect of the CNS found within the vertebral column. Its purpose is to send motor commands from the brain to the peripheral body and relay sensory information from the sensory organs to the brain. Bone, meninges, and cerebrospinal fluids provide spinal cord protection.

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Inside the brain of a neuron

Kyriaki sidiropoulou.

1 Institute of Molecular Biology and Biotechnology (IMBB), Foundation for Research and Technology–Hellas (FORTH), Vassilika Vouton PO Box 1583, Heraklion GR71110, Crete, Greece

Eleftheria Kyriaki Pissadaki

2 Department of Biology, University of Crete, Vassilika Vouton, Heraklion GR71409, Crete, Greece

Panayiota Poirazi

For many decades, neurons were considered to be the elementary computational units of the brain and were assumed to summate incoming signals and elicit action potentials only in response to suprathreshold stimuli. Although modelling studies predicted that single neurons constitute a much more powerful computational entity, able to perform an array of nonlinear calculations, this possibility was not explored experimentally until the discovery of active mechanisms in the dendrites of most neuron types. Here, we review several modelling studies that have addressed information processing in single neurons, starting with those characterizing the arithmetic of different dendritic components, to those tackling neuronal integration at the cell body and, finally, those analysing the computational abilities of the axon. We present modelling predictions along with supporting experimental data in an effort to highlight the significant contribution of modelling work to enhancing our understanding of single-neuron arithmetic.

Introduction

Understanding how the brain works remains one of the most exciting and intricate challenges of modern biology. Despite the wealth of information that has accumulated during the past years about the molecular and biophysical mechanisms that underlie neuronal activity, similar advances have yet to be made in understanding the rules that govern information processing and the relationship between the structure and function of a neuron.

Computational models provide a theoretical framework together with a technological platform for enhancing our understanding of nervous system functions. Certain tools are suitable for efficiently analysing and interpreting complex data sets, such as multi-channel recordings from hundreds of neurons, whereas others are used to simulate the activity of single cells, neural networks or systems of networks at various levels of abstraction. The development and application of such modelling tools enable researchers to quantitatively investigate several hypotheses by using interactive models of the systems under study. When used in conjunction with experimental techniques, these models facilitate hypothesis testing and help to identify key follow-up experiments.

In this review, we discuss several computational studies in which realistic biophysical models have been used to elucidate the computational tasks performed by a neuron. We focus on single-neuron models that incorporate a significant level of detail and compare modelling predictions with experimental findings. Although a great amount of work has also been devoted to modelling neural components as well as neuronal assemblies at a more abstract level, reviewing these studies is not the purpose of this article.

Single-neuron computations

Whether incredibly simple as bipolar cells in the retina or immensely complex as Purkinje cells in the cerebellum ( Ramon y Cajal, 1933 ), most neurons are composed of three main structural units: the dendrites, the soma (cell body) and the axon. For the past few decades, axons and dendrites have been considered to be simple transmitting devices that communicate signals to and from the soma in which thresholded computations take place. As a result, neuronal cells were initially represented as spherical point neurons—consisting only of a cell body—and information transfer was thought to lie entirely in their average firing rates ( McCulloch & Pitts, 1943 ). However, primarily computational, and more recently physiological, studies have shown that variations in the morphology and ionic conductance composition of different neurons provide the cell with enhanced computational abilities far outreaching those captured by a point neuron.

Computing with dendrites: new roles for old structures

The old view that dendrites are merely passive cables that relay incoming signals to the cell body no longer holds true. In the light of accumulating evidence highlighting the active role of dendrites in signal integration, these structures seem able to perform a variety of computational tasks, including temporal integration, signal amplification and attenuation, and detection of coincident incoming inputs (for a recent review, see London & Hausser, 2005 ). In this section, we further elucidate the role of dendrites in the information processing capacity of the neuron by focusing on insights gained primarily from modelling studies and by using a bottom-up approach: starting from the smallest dendritic subunit—the spine—up to the effect of network activity on dendritic and, subsequently, neuronal function.

Computations carried out by excitable spines

Dendritic spines were anatomically identified by Ramon y Cajal in 1911, who referred to them as espinas due to their resemblance to thorns on flower stems (for a review, see Segal, 2002 ). Theoretical findings first indicated that the anatomical characteristics of spines, as well as the possible presence of voltage-gated ion channels, allow for compartmentalized gain modulation of synaptic inputs in spine heads—that is, information can be combined nonlinearly from two or more sources ( Segev & Rall, 1998 ). Models predicted that strong inputs are able to initiate local dendritic spikes ( Baer & Rinzel, 1991 ), which in turn could activate additional nearby spines ( Shepherd et al , 1985 ) and therefore locally amplify incoming inputs. As schematically depicted in Fig 1 , individual spines can perform nonlinear integration of incoming coincident signals, and their interaction results in a spatially restricted enhancement of dendritic events. By contrast, if synaptic stimulation is sparse, the added resistance and capacitance load provided by the spine membrane coupled with the narrow spine neck would act as a local filter, promoting linear integration ( Yuste & Urban, 2004 ). In a recent compartmental modelling study, spine geometry together with a high density of sodium ion (Na + ) channels on spines might explain the efficacy of somatic action potentials for invading apical dendrites in CA1 pyramids ( Tsay & Yuste, 2002 , 2004 ). This implies a role for these structures in controlling back-propagating signals and perhaps in coincidence detection ( Tsay & Yuste, 2002 , 2004 ). Taken together, these studies reveal the exciting possibility that dendritic sections containing small clusters of spines act as individual computational units. Interestingly, in a recent experimental study, short (around 40 μm) basal dendritic compartments in layer V pyramidal neurons were shown to summate local signals as individually thresholded sigmoidal units ( Polsky et al , 2004 ), which supports this hypothesis.

The multiplicative neuron. Sigmoidal functions indicate nonlinear computations performed by various parts of the cell: gain modulation in spine heads, thresholded computations in small dendritic branchlets, and supralinearities at the main apical trunk and the cell body. The response of the cell is tuned by the overall effect of the network.

Dendritic computations

If sparse and clustered synaptic inputs can be differentially sensed by a dendritic section, is it possible that different spatial arrangements of synaptic inputs are differentially perceived by the cell? Early neuron models incorporating passive dendritic properties and applying the cable theory—that is, how voltage changes are propagated along dendritic segments—indicated a possible linear summation of inputs arriving at separate parts of the dendritic tree ( Rall, 1959 ). This implied that location is not important. By contrast, inputs that are close together were thought to combine sublinearly due to the activation of a shunting current ( Rall et al , 1967 ). Despite the simplicity of the early models and the presence of various active membrane mechanisms that could in principle support supralinear dendritic integration, experimental evidence in various neuron types has mostly reinforced the linear or sublinear summation rule ( Cash & Yuste, 1999 ; Magee & Cook, 2000 ; Tamas et al , 2002 ). However, at least two studies have shown the presence of powerful thresholding events isolated in the thin dendrites of neocortical ( Schiller et al , 2000 ) and CA1 ( Wei et al , 2001 ) pyramidal cells.

This idea of spatial compartmentalization in the neuron and its role in information processing was explored further with the use of a detailed CA1 pyramidal neuron model ( Poirazi et al , 2003a , b ). According to the model, each apical oblique dendrite—or part of it—acts as an independent computational unit that summates inputs using a sigmoidal activation function. Different branch outputs are then linearly combined at the cell body. Both of these predictions were verified experimentally in a layer V pyramidal neuron ( Polsky et al , 2004 ), and a recent study confirmed that radial oblique dendrites of CA1 pyramidal neurons function as single integrative compartments ( Losonczy & Magee, 2006 ). As shown in Fig 2 , layer V neocortical neurons linearly summate between-branch excitatory postsynaptic potentials (EPSPs), but implement a sigmoidal activation function for within-branch EPSPs ( Fig 2B ), as predicted by models of CA1 neurons ( Fig 2A ). In other words, thin dendritic branches seem to be able to combine incoming signals according to a thresholding nonlinearity, in a similar way to a typical point neuron. Interestingly, when synaptic inputs vary in both their temporal and spatial distribution, the distal apical trunk of a CA1 pyramidal cell operates in two fundamentally distinct integration forms ( Gasparini & Magee, 2006 ). Asynchronous or spatially distributed synaptic inputs—similar to those occurring during theta oscillations—summate linearly. Synchronous and clustered inputs—similar to those occurring during sharp waves—summate according to a steep sigmoidal nonlinearity. This bimodal dendritic integration code allows a single cell to perform two different state-dependent computations: input strength encoding during theta states and feature detection during sharp waves ( Gasparini & Magee, 2006 ).

Nonlinear dendritic computations. ( A ) Summation of paired, single-pulse inputs in the apical dendrites of a CA1 pyramidal model cell. Simulations predict a sigmoidal modulation of combined excitatory postsynaptic potentials (EPSPs) within a branch (red symbols) and a linear summation of EPSPs between branches (green symbols). Red curves correspond to within-branch data for dendrites at 92 μm (short dashes), 232 μm (solid) and 301 μm (long dashes) from the soma. Due to differences in local compared with somatic responses, axis values for the red curves are scaled up by a factor of 10. ( B ) Experimental verification of predicted summation rules in basal dendrites of a layer V pyramidal neuron. Single-pulse stimulation of synapses in different branches results in linear summation at the cell body (green squares). When γ-aminobutyric acid (GABA)ergic inhibition is blocked, the summation of within-branch EPSPs is modulated by a sigmoidal nonlinearity (all other symbols). Reproduced with permission from Polsky et al (2004) . ( C ) Schematic representation of a pyramidal neuron as a two-layer neural network. Radial oblique dendrites provide the first layer of the network, each performing individually thresholded computations as shown in ( A ) and ( B ). The outputs of this layer feed into the cell body, which constitutes the second layer of the network model. Adapted from Poirazi et al (2003b) .

Computing with regenerative dendritic events

What would be the benefit of a cell consisting of dendrites that are able to isolate complex events? Early physiological studies identified the presence of active dendritic events in neurons ( Kandel & Spencer, 1961 ); however, they were not further investigated experimentally at that time. Modelling studies predicted a role for Na + -mediated dendritic spikes—initially modelled with H-H conductances—in allowing the back-propagation of action potentials into the dendritic tree ( Rall & Shepherd, 1968 ), as well as enabling coincidence detection between proximal and distal inputs ( Softky & Koch, 1993 ).

A closer evaluation of dendritic events revealed that these spikes can be mediated by Na + ( Golding & Spruston, 1998 ) or calcium ion (Ca 2+ ; Yuste et al , 1994 ) channels in the distal dendrites, as well as by N-methyl D-aspartate (NMDA) channels ( Schiller et al , 2000 ) or a combination of Na + and NMDA channels ( Ariav et al , 2003 ) in the basal dendrites of pyramidal neurons. The quest is now to reveal their role in neuronal function. Although these spikes can be confined to their dendritic site of origin ( Wei et al , 2001 ; Schiller et al , 2000 ; Zhu, 2000 ), physiologically relevant situations such as large, suprathreshold synaptic stimuli in the distal dendrites or the activation of several branches together allow these spikes to act globally and modulate neuronal output ( Zhu, 2000 ; Larkum et al , 2001 ). In a compartmental CA1 neuron model, dendritic spike initiation in response to perforant path (PP) stimulation, which is confined in the distal tuft, could be transferred to the soma by activation of the Schaffer collateral (SC) pathway ( Jarsky et al , 2005 ). Similarly, dendritic Ca 2+ conductances in the distal tuft of a layer V cortical neuron model, which are unable to initiate an action potential at the soma, could be amplified by coincident back-propagating action potentials ( Larkum et al , 2004 ); in addition, dendritic Ca 2+ spikes have been suggested to convert single spikes into bursts in CA3 pyramidal neuron models ( Traub et al , 1991 ), leading to an enhanced neuronal response.

Although the above studies indicate that dendritic events might amplify neuronal gain and facilitate coincident detection of inputs, simulated experiments in a detailed CA1 pyramidal neuron model indicate that distal dendritic activation could bidirectionally gate suprathreshold SC input (E.K.P. and P.P., unpublished data). In particular, PP theta-burst stimulation coincident with or slightly preceding regular SC input, initiates Ca 2+ spikes in the distal dendrites and transforms a previously regular firing response into bursting ( Fig 3A,B ). By contrast, when subthreshold PP stimulation precedes the SC input by a few hundreds of milliseconds, the distal dendrites are hyperpolarized due to enhanced γ-aminobutyric acid (GABA) transmission. This results in a reduced gain of neuronal output, as seen by the blocking of the spikes induced by SC input only ( Fig 3A,C ). This PP-induced ‘spike blocking' was previously reported experimentally ( Dvorak-Carbone & Schuman, 1999 ). Collectively, dendritic regenerative events provide a means by which several localized events are combined to modulate neuronal output, thus expanding the response flexibility of single neurons.

Top-down gain modulation in a CA1 pyramidal neuron model. In a CA1 pyramidal neuron, afferents from the entorhinal cortex (EC) synapse onto distal dendrites, whereas axons from CA3 neurons project to proximal dendrites. ( A ) Synaptic activation (1 Hz) of proximal dendrites induces a regular firing response at the cell body of the model cell. ( B ) Strong (theta-burst) stimulation of EC inputs coinciding with CA3 stimulation evokes calcium spikes in the distal dendrites, the occurrence of which initiates bursts of action potentials (APs), and facilitates the somatic response. ( C ) Temporally distant activation of EC with subthreshold bursts (400 ms after the CA3 input) prevents the initiation of somatic action potentials for several seconds, thus weakening the somatic response. Green dots, excitatory inputs; red dots, inhibitory inputs.

Normalizing effects on synaptic integration

Whereas dendritic regenerative events allow gain modulation of neuronal output, passive properties and K + conductances in the dendrites act to spatially normalize and temporally integrate inputs, which provides the neuron with a different mode of information processing.

These passive properties (such as membrane time constant, input resistance and dendritic length) allow for differential integration of synaptic inputs that arrive at distal or proximal parts of the dendritic tree owing to the ‘large voltage attenuation and significant temporal delay' of propagated signals ( Koch & Segev, 2000 ). At the same time, incorporation of a hyperpolarization-activated, potassium ion (K + ) conductance ( I h ) in a CA1 compartmental model was shown to account for the experimentally observed normalization of EPSPs that originate from different parts of the dendritic tree so that all inputs induce similar depolarizations at the cell body ( Golding et al , 2005 ; Magee & Cook, 2000 ). Additional modelling experiments indicated that I h might be involved in setting the temporal window for input summation around subthreshold levels, thus enabling coincidence detection and minimizing the effectiveness of non-synchronized inputs ( Migliore et al , 2004 ; Migliore, 2003 ). Other dendritic K + conductances could either support or counteract the effect of I h on temporal summation ( Day et al , 2005 ).

Finally, the long-standing but quite neglected effect of background noise due to network activity on neuronal information processing should be considered. According to the work of Bernander and colleagues (1991) , background activity in a passive neuron model dampens the effectiveness of asynchronous—but not synchronous—inputs in generating a somatic action potential. This in turn facilitates the distinction between ‘unimportant' and ‘meaningful' signals, respectively. In a more detailed cortical neuron model that incorporates active dendritic conductances, intense synaptic network activity was shown to increase the membrane conductance, promote the location-independent effect of inputs arriving onto different dendritic regions (but see London & Segev, 2001 ) and increase the probability for dendritic spike initiation and its forward propagation to the axon ( Rudolph & Destexhe, 2003 ). Thus, incoming background noise from network activity could greatly influence the integrative properties of a neuron—for example, by modulating the spatiotemporal window for dendritic nonlinearities ( Azouz, 2005 ).

In conclusion, the neuron does not behave as a point neuron, but it might consist of many different point neurons in the form of a cluster of spines or a stretch of dendrite, each of which has its own integration rules according to its spatial location and temporal architecture of incoming inputs. When locally induced signals manage to escape their subunit, they are affected by global cellular parameters and are set by the overall network activity the cell receives, promoting a quasi-linear interaction mode.

The overall picture emerging from this analysis is that a single neuron could be decomposed into a multi-layer neural network, able to perform all sorts of nonlinear computations ( London & Hausser, 2005 ). Interestingly, the average firing rate of a detailed CA1 model to hundreds of different input patterns was accurately predicted by a two-layer neural network abstraction ( Fig 2 ), in which individual oblique dendrites provided the first layer and the soma acted as the output layer ( Poirazi et al , 2003b ). This implies a much larger storage capacity than originally assumed for single neurons. According to another computational study, the pattern discrimination capacity of such a cell exceeds that of a point neuron by at least one order of magnitude ( Poirazi & Mel, 2001 ). An even more complex single-neuron unit proposed by Hausser & Mel (2003) entails a two-compartment model in which the distal tuft acts as one compartment and the thin branches of the perisoma act as the other. Both compartments act as two-layer networks whose outputs combine at the cell body, giving rise to an extra powerful, three-layer computing unit.

Information processing at the cell body

Dendrites contribute to nonlinear summation of inputs, whereas the soma might support a different kind of information processing—that of enabling a persistent firing mode in the absence of stimulation. Recent experimental and modelling studies have highlighted the importance of somatic intrinsic membrane mechanisms in generating and maintaining persistent activity, in addition to the traditional network mechanisms (for a review, see Major & Tank, 2004 ). In vitro work in the entorhinal cortex ( Egorov et al, 2002 ; Tahvildari & Alonso, 2005 ) showed that a single neuron is able to generate graded persistent activity under pharmacological stimulation of muscarinic acetylcholine receptors in response to somatic or synaptic stimulation, owing to activation of a slow Ca 2+ -dependent mixed ionic (CAN) conductance. Modelling work has emphasized a possible involvement of the slow temporal decay of the EPSP ( Lisman et al , 1998 ), the CAN conductance ( Tegner et al , 2002 ) or the Ca 2+ -induced Ca 2+ release mechanism ( Loewenstein & Sompolinsky, 2003 ) in the maintenance of a stable persistent state at low physiological frequencies (10–50 Hz).

Persistent activity in vivo has also been observed in the hippocampus ( Wirth et al , 2003 ), although the underlying mechanisms are unclear. Ongoing work in our laboratory shows that persistent activity in a detailed CA1 pyramidal neuron model can be induced in response to theta-burst synaptic stimulation as well as in response to somatic stimulation under the influence of cholinergic modulation. The model supports a role for a slow, Ca 2+ -dependent tail current in maintaining sustained activity in hippocampal neurons ( Poirazi, 2005 ). The ability of single cells to be persistently active further enhances their computational power by adding another mode to their repertoire of complex functions.

Computing with axons

Axons provide a medium through which information, in the form of action potentials, flows across neuronal assemblies. Several computational studies have provided insights into the ionic mechanism for action-potential generation, particularly the seminal work of Hodgkin and Huxley, as well as the action-potential initiation site (reviewed in Stuart et al , 1997 ). More recent studies focusing on the reliability and accuracy of action-potential generation and propagation indicate that these properties, which are crucial for normal information processing, could be modified by changes in axonal geometry and ionic conductance composition ( Segev & Schneidman, 1999 ; Debanne, 2004 ). The work of Goldstein & Rall (1974) in simulated axons with changing diameter and different branching patterns first implicated the above structural characteristics in modifying action-potential curve and propagation speed. After quantifying the effect of such morphological changes on action-potential propagation velocity, another computational study suggested that synaptic boutons in different terminals are activated asynchronously in a reconstructed axon of a layer V neuron in the somatosensory cortex ( Manor et al , 1991 ). The density and type of ionic channels along the axon and branching points has also been suggested to gate action-potential propagation. For example, activation of just a few clusters of A-type K + channels has been shown to gate axonal propagation of action potentials in CA3 neurons in both simulations and experiments ( Debanne et al , 1997 ; Kopysova & Debanne, 1998 ). When combined, these findings imply that axons are much more than simple conducting devices for action potentials. Enriched with a variety of computational abilities, axons seem to be complex transmitting devices whose role in neuronal information processing is worth investigating thoroughly.

Concluding remarks

For several years, neuroscientists believed that the brain's transistor or fundamental processing unit was the neuron itself, which collects and processes incoming signals from neighbouring cells. In this review, we suggest that the morphological and ionic properties of the dendrites, the soma and the axon provide these structures with an array of computational abilities that might enable them to contribute differentially to neuronal function.

Dendrites seem to be key players in functions such as binocular disparity ( Archie & Mel, 2000 ) and directional selectivity in the visual system of various species ( Single & Borst, 1998 ; Euler et al , 2002 ; Vaney & Taylor, 2002 ), as well as in improving sound localization ( Agmon-Snir et al , 1998 ) and in supporting the transition between encoding and retrieval modes of associative memory systems ( Hasselmo et al , 1996 ; Dvorak-Carbone & Schuman, 1999 ). Conversely, persistent activity maintained by somatic mechanisms has been suggested to represent a cellular correlate of working memory functions ( Goldman-Rakic, 1995 ). Finally, propagation delays of the action potential along the axon have been attributed a role in precise temporal coding in the auditory system of the barn owl ( Carr et al , 2001 ), whereas axonal Na + channels have been suggested to act as a memory reservoir for previous activity levels ( Segev & Schneidman, 1999 ).

Linking computational properties to behaviour is the ultimate challenge for both modelling and experimental studies of the future. Recent papers applying modelling, physiological, molecular, genetic and behavioural techniques in Drosophila and mice have shown the contribution of different voltage-dependent K + conductances in light processing by photoreceptors and in reversing age-induced impairments in learning and memory, respectively ( Vahasoyrinki et al , 2006 ; Murphy et al , 2004 ). Such multidisciplinary approaches—in which models are used to formulate experimentally testable predictions and experiments are used to verify the predictions and refine the models—will enable a more thorough investigation of how different neuronal components and the cell as a whole contribute to information processing capacity and behaviour.

The following open questions could provide fertile ground for collaborations among molecular biologists, geneticists, physiologists, modellers and behaviourists for further explorations of the mysteries of the brain. Do specific behaviours require certain neuronal computational tasks? Which parts of the neural circuit or the neuron itself are responsible for these tasks? What are the underlying molecular mechanisms for the distinct operating modes of neuronal integration? Such holistic approaches should lend support to the growing idea reinforced by this review: that something smaller than the cell lies at the heart of neural computation.

Eleftheria Kyriaki Pissadaki, Panayiota Poirazi (who is an EMBO Young Investigator) & Kyriaki Sidiropoulou

Acknowledgments

This work was supported by Alexander S. Onassis Public Benefit Foundation (K.S.), General Secretariat of Research and Technology, ΠENEΔ 01EΔ311 (E.K.P.) and the EMBO Young investigator Programme.

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This Is the Most Detailed Map of Brain Connections Ever Made

This image could be hung in a gallery, but it started life as a tiny chunk of a woman’s brain. In 2014, a woman undergoing surgery for epilepsy had a tiny chunk of her cerebral cortex removed. This cubic millimeter of tissue has allowed Harvard and Google researchers to produce the most detailed wiring diagram of the human brain that the world has ever seen.

Biologists and machine-learning experts spent 10 years building an interactive map of the brain tissue, which contains approximately 57,000 cells and 150 million synapses. It shows cells that wrap around themselves, pairs of cells that seem mirrored, and egg-shaped “objects” that, according to the research, defy categorization. This mind-blowingly complex diagram is expected to help drive forward scientific research, from understanding human neural circuits to potential treatments for disorders.

“If we map things at a very high resolution, see all the connections between different neurons, and analyze that at a large scale, we may be able to identify rules of wiring,” says Daniel Berger, one of the project’s lead researchers and a specialist in connectomics, which is the science of how individual neurons link to form functional networks. “From this, we may be able to make models that mechanistically explain how thinking works or memory is stored.”

Jeff Lichtman, a professor in molecular and cellular biology at Harvard, explains that researchers in his lab, led by Alex Shapson-Coe, created the brain map by taking subcellular pictures of the tissue using electron microscopy. The tissue from the 45-year-old woman’s brain was stained with heavy metals, which bind to lipid membranes in cells. This was done so that cells would be visible when viewed through an electron microscope, as heavy metals reflect electrons.

The tissue was then embedded in resin so that it could be cut into really thin slices, just 34 nanometers thick (in comparison, the thickness of a typical piece of paper is around 100,000 nanometers). This was done to make the mapping easier, says Berger—to transform a 3D problem into a 2D problem. After this, the team took electron microscope images of each 2D slice, which amounted to a mammoth 1.4 petabytes of data.

Once the Harvard researchers had these images, they did what many of us do when faced with a problem: They turned to Google. A team at the tech giant led by Viren Jain aligned the 2D images using machine-learning algorithms to produce 3D reconstructions with automatic segmentation, which is where components within an image—for example, different cell types—are automatically differentiated and categorized. Some of the segmentation required what Lichtman called “ground-truth data,” which involved Berger (who worked closely with Google’s team) manually redrawing some of the tissue by hand to further inform the algorithms.

Digital technology, Berger explains, enabled him to see all the cells in this tissue sample and color them differently depending on their size. Traditional methods of imaging neurons, such as coloring samples with a chemical known as the Golgi stain, which has been used for over a century, leave some elements of nervous tissue hidden.

In the example above, Berger made the smallest cells blue and the biggest cells red, with all other cells between falling on a color spectrum. This helped researchers to identify the brain’s six cortical layers and white matter.

While researchers have been able to identify structures from the data, one ongoing difficulty of the project is proofreading the automatic segmentation. This involves individuals manually sifting through every part of the 3D map to check for segmentation errors. “This is a huge challenge for human beings, because now we’re generating datasets that are larger than a single human can experience,” says Lichtman.

In parts of the data that have been proofread, Berger says that particular cells seem “really interested in contacting.” The researchers have found examples of over 50 synapses to one singular neuron, which, according to Berger, is a phenomenon previously overlooked that could be integral to cortical processing.

On top of identifying structures and connections, researchers have identified abnormal cells. Berger said he came across an unidentifiable egg-shaped “object” (much smaller than a cell body but part of a cell) when attempting to systematically categorize each cell in the dataset. Other ambiguous cells include those seemingly mirrored in shape and “tangled” cells that wrap around themselves; until further research is done, these cells remain mysteries. However, they may not remain so for long.

The brain map has been made open access, which means that these images have opened up boundless possibilities for progress in neuroscience, particularly as this is the first publicly available wiring diagram of the human brain at subcellular level. Both Berger and Lichtman emphasized that they did not go into the project with concrete aims of discovery but rather wanted to create the “possibility to observe,” and from this, they hope (and expect) that “further insights will come” from both the Lichtman lab and external researchers.

Berger anticipates that advancements could be made in understanding and treating mental conditions such as schizophrenia. Potential future discoveries could also expand beyond the mind, as Berger thinks the functions of the biological brain may be used to improve deep-learning AI systems and their structures.

In terms of future projects, the Harvard Lichtman lab plans to continue its collaboration with Google to “factor this rendering up another scale of a thousand” by studying a whole mouse brain. The research lab is also working on more human brain samples, to expand research into other regions of the brain. This will enhance the already invaluable resource and its ability to inform and expand future discoveries.

This article appears in the September/October 2024 issue of WIRED UK magazine.

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Computer Science > Computer Vision and Pattern Recognition

Title: imagen 3.

Abstract: We introduce Imagen 3, a latent diffusion model that generates high quality images from text prompts. We describe our quality and responsibility evaluations. Imagen 3 is preferred over other state-of-the-art (SOTA) models at the time of evaluation. In addition, we discuss issues around safety and representation, as well as methods we used to minimize the potential harm of our models.

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