A spectrum of routing strategies for brain networks

Synaptic signaling modeled by functional connectivity predicts metabolic demands of the human brain

PURPOSE

The human brain is characterized by interacting large-scale functional networks fueled by glucose metabolism. Since former studies could not sufficiently clarify how these functional connections shape glucose metabolism, we aimed to provide a neurophysiologically-based approach.

METHODS

51 healthy volunteers underwent simultaneous PET/MRI to obtain BOLD functional connectivity and [18F]FDG glucose metabolism. These multimodal imaging proxies of fMRI and PET were combined in a whole-brain extension of metabolic connectivity mapping. Specifically, functional connectivity of all brain regions were used as input to explain glucose metabolism of a given target region. This enabled the modeling of postsynaptic energy demands by incoming signals from distinct brain regions.

RESULTS

Functional connectivity input explained a substantial part of metabolic demands but with pronounced regional variations (34 - 76%). During cognitive task performance this multimodal association revealed a shift to higher network integration compared to resting state. In healthy aging, a dedifferentiation (decreased segregated/modular structure of the brain) of brain networks during rest was observed. Furthermore, by including data from mRNA maps, [11C]UCB-J synaptic density and aerobic glycolysis (oxygen-to-glucose index from PET data), we show that whole-brain functional input reflects non-oxidative, on-demand metabolism of synaptic signaling. The metabolically-derived directionality of functional inputs further marked them as top-down predictions. In addition, the approach uncovered formerly hidden networks with superior efficiency through metabolically informed network partitioning.

CONCLUSIONS

Applying multimodal imaging, we decipher a crucial part of the metabolic and neurophysiological basis of functional connections in the brain as interregional on-demand synaptic signaling fueled by anaerobic metabolism. The observed task- and age-related effects indicate promising future applications to characterize human brain function and clinical alterations.

Optimal navigability of weighted human brain connectomes in physical space

Communication protocols in the brain connectome describe how to transfer information from one region to another. Typically, these protocols hinge on either the spatial distances between brain regions or the intensity of their connections. Yet, none of them combine both factors to achieve optimal efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that integrates link weights and the spatial embedding of connectomes to route signal transmission. We implemented the protocols on connectomes from individuals in two cohorts and on group-representative connectomes designed to capture weighted connectivity properties. We identified an intermediate domain of routing strategies, a sweet spot, where navigation achieves maximum communication efficiency at low transmission cost. This phenomenon is robust and independent of the particular configuration of weights. Our findings suggest an interplay between the intensity of neural connections and their topology and geometry that amplifies communicability, where weights play the role of noise in a stochastic resonance phenomenon. Such enhancement may support more effective responses to external and internal stimuli, underscoring the intricate diversity of brain functions.

Spatial and temporal pattern of structure-function coupling of human brain connectome with development

Brain structural circuitry shapes a richly patterned functional synchronization, supporting for complex cognitive and behavioural abilities. However, how coupling of structural connectome (SC) and functional connectome (FC) develops and its relationships with cognitive functions and transcriptomic architecture remain unclear. We used multimodal magnetic resonance imaging data from 439 participants aged 5.7-21.9 years to predict functional connectivity by incorporating intracortical and extracortical structural connectivity, characterizing SC-FC coupling. Our findings revealed that SC-FC coupling was strongest in the visual and somatomotor networks, consistent with evolutionary expansion, myelin content, and functional principal gradient. As development progressed, SC-FC coupling exhibited heterogeneous alterations dominated by an increase in cortical regions, broadly distributed across the somatomotor, frontoparietal, dorsal attention, and default mode networks. Moreover, we discovered that SC-FC coupling significantly predicted individual variability in general intelligence, mainly influencing frontoparietal and default mode networks. Finally, our results demonstrated that the heterogeneous development of SC-FC coupling is positively associated with genes in oligodendrocyte-related pathways and negatively associated with astrocyte-related genes. This study offers insight into the maturational principles of SC-FC coupling in typical development.

A Hybrid Routing Pattern in Human Brain Structural Network Revealed By Evolutionary Computation

The human brain functional connectivity network (FCN) is constrained and shaped by the communication processes in the structural connectivity network (SCN). The underlying communication mechanism thus becomes a critical issue for understanding the formation and organization of the FCN. A number of communication models supported by different routing strategies have been proposed, with shortest path (SP), random diffusion (DIF), and spatial navigation (NAV) as the most typical, respectively requiring network global knowledge, local knowledge, and both for path seeking. Yet these models all assumed every brain region to use one routing strategy uniformly, ignoring convergent evidence that supports the regional heterogeneity in both terms of biological substrates and functional roles. In this regard, the current study developed a hybrid communication model that allowed each brain region to choose a routing strategy from SP, DIF, and NAV independently. A genetic algorithm was designed to uncover the underlying region-wise hybrid routing strategy (namely HYB). The HYB was found to outperform the three typical routing strategies in predicting FCN and facilitating robust communication. Analyses on HYB further revealed that brain regions in lower-order functional modules inclined to route signals using global knowledge, while those in higher-order functional modules preferred DIF that requires only local knowledge. Compared to regions that used global knowledge for routing, regions using DIF had denser structural connections, participated in more functional modules, but played a less dominant role within modules. Together, our findings further evidenced that hybrid routing underpins efficient SCN communication and locally heterogeneous structure-function coupling.

Structural-functional brain network coupling predicts human cognitive ability

Individual differences in general cognitive ability (GCA) have a biological basis within the structure and function of the human brain. Network neuroscience investigations revealed neural correlates of GCA in structural as well as in functional brain networks. However, whether the relationship between structural and functional networks, the structural-functional brain network coupling (SC-FC coupling), is related to individual differences in GCA remains an open question. We used data from 1030 adults of the Human Connectome Project, derived structural connectivity from diffusion weighted imaging, functional connectivity from resting-state fMRI, and assessed GCA as a latent g-factor from 12 cognitive tasks. Two similarity measures and six communication measures were used to model possible functional interactions arising from structural brain networks. SC-FC coupling was estimated as the degree to which these measures align with the actual functional connectivity, providing insights into different neural communication strategies. At the whole-brain level, higher GCA was associated with higher SC-FC coupling, but only when considering path transitivity as neural communication strategy. Taking region-specific variations in the SC-FC coupling strategy into account and differentiating between positive and negative associations with GCA, allows for prediction of individual cognitive ability scores in a cross-validated prediction framework (correlation between predicted and observed scores: r = 0.25, p < .001). The same model also predicts GCA scores in a completely independent sample (N = 567, r = 0.19, p < .001). Our results propose structural-functional brain network coupling as a neurobiological correlate of GCA and suggest brain region-specific coupling strategies as neural basis of efficient information processing predictive of cognitive ability.

Information decomposition and the informational architecture of the brain

To explain how the brain orchestrates information-processing for cognition, we must understand information itself. Importantly, information is not a monolithic entity. Information decomposition techniques provide a way to split information into its constituent elements: unique, redundant, and synergistic information. We review how disentangling synergistic and redundant interactions is redefining our understanding of integrative brain function and its neural organisation. To explain how the brain navigates the trade-offs between redundancy and synergy, we review converging evidence integrating the structural, molecular, and functional underpinnings of synergy and redundancy; their roles in cognition and computation; and how they might arise over evolution and development. Overall, disentangling synergistic and redundant information provides a guiding principle for understanding the informational architecture of the brain and cognition.

Spatial and temporal pattern of structure-function coupling of human brain connectome with development

Brain structural circuitry shapes a richly patterned functional synchronization, supporting for complex cognitive and behavioural abilities. However, how coupling of structural connectome (SC) and functional connectome (FC) develops and its relationships with cognitive functions and transcriptomic architecture remain unclear. We used multimodal magnetic resonance imaging data from 439 participants aged 5.7 to 21.9 years to predict functional connectivity by incorporating intracortical and extracortical structural connectivity, characterizing SC-FC coupling. Our findings revealed that SC-FC coupling was strongest in the visual and somatomotor networks, consistent with evolutionary expansion, myelin content, and functional principal gradient. As development progressed, SC-FC coupling exhibited heterogeneous alterations dominated by an increase in cortical regions, broadly distributed across the somatomotor, frontoparietal, dorsal attention, and default mode networks. Moreover, we discovered that SC-FC coupling significantly predicted individual variability in general intelligence, mainly influencing frontoparietal and default mode networks. Finally, our results demonstrated that the heterogeneous development of SC-FC coupling is positively associated with genes in oligodendrocyte-related pathways and negatively associated with astrocyte-related genes. This study offers insight into the maturational principles of SC-FC coupling in typical development.

Whole-brain structural connectome asymmetry in autism

Autism spectrum disorder is a common neurodevelopmental condition that manifests as a disruption in sensory and social skills. Although it has been shown that the brain morphology of individuals with autism is asymmetric, how this differentially affects the structural connectome organization of each hemisphere remains under-investigated. We studied whole-brain structural connectivity-based brain asymmetry in individuals with autism using diffusion magnetic resonance imaging obtained from the Autism Brain Imaging Data Exchange initiative. By leveraging dimensionality reduction techniques, we constructed low-dimensional representations of structural connectivity and calculated their asymmetry index. Comparing the asymmetry index between individuals with autism and neurotypical controls, we found atypical structural connectome asymmetry in the sensory and default-mode regions, particularly showing weaker asymmetry towards the right hemisphere in autism. Network communication provided topological underpinnings by demonstrating that the inferior temporal cortex and limbic and frontoparietal regions showed reduced global network communication efficiency and decreased send-receive network navigation in the inferior temporal and lateral visual cortices in individuals with autism. Finally, supervised machine learning revealed that structural connectome asymmetry could be used as a measure for predicting communication-related autistic symptoms and nonverbal intelligence. Our findings provide insights into macroscale structural connectome alterations in autism and their topological underpinnings.

Connectome-wide structure-function coupling models implicate polysynaptic alterations in autism

Autism spectrum disorder (ASD) is one of the most common neurodevelopmental diagnoses. Although incompletely understood, structural and functional network alterations are increasingly recognized to be at the core of the condition. We utilized multimodal imaging and connectivity modeling to study structure-function coupling in ASD and probed mono- and polysynaptic mechanisms on structurally-governed network function. We examined multimodal magnetic resonance imaging data in 80 ASD and 61 neurotypical controls from the Autism Brain Imaging Data Exchange (ABIDE) II initiative. We predicted intrinsic functional connectivity from structural connectivity data in each participant using a Riemannian optimization procedure that varies the times that simulated signals can unfold along tractography-derived personalized connectomes. In both ASD and neurotypical controls, we observed improved structure-function prediction at longer diffusion time scales, indicating better modeling of brain function when polysynaptic mechanisms are accounted for. Prediction accuracy differences (∆prediction accuracy) were marked in transmodal association systems, such as the default mode network, in both neurotypical controls and ASD. Differences were, however, lower in ASD in a polysynaptic regime at higher simulated diffusion times. We compared regional differences in ∆prediction accuracy between both groups to assess the impact of polysynaptic communication on structure-function coupling. This analysis revealed that between-group differences in ∆prediction accuracy followed a sensory-to-transmodal cortical hierarchy, with an increased gap between controls and ASD in transmodal compared to sensory/motor systems. Multivariate associative techniques revealed that structure-function differences reflected inter-individual differences in autistic symptoms and verbal as well as non-verbal intelligence. Our network modeling approach sheds light on atypical structure-function coupling in autism, and suggests that polysynaptic network mechanisms are implicated in the condition and that these can help explain its wide range of associated symptoms.

Brain network communication: concepts, models and applications

Understanding communication and information processing in nervous systems is a central goal of neuroscience. Over the past two decades, advances in connectomics and network neuroscience have opened new avenues for investigating polysynaptic communication in complex brain networks. Recent work has brought into question the mainstay assumption that connectome signalling occurs exclusively via shortest paths, resulting in a sprawling constellation of alternative network communication models. This Review surveys the latest developments in models of brain network communication. We begin by drawing a conceptual link between the mathematics of graph theory and biological aspects of neural signalling such as transmission delays and metabolic cost. We organize key network communication models and measures into a taxonomy, aimed at helping researchers navigate the growing number of concepts and methods in the literature. The taxonomy highlights the pros, cons and interpretations of different conceptualizations of connectome signalling. We showcase the utility of network communication models as a flexible, interpretable and tractable framework to study brain function by reviewing prominent applications in basic, cognitive and clinical neurosciences. Finally, we provide recommendations to guide the future development, application and validation of network communication models.

Spatially heterogeneous structure-function coupling in haemodynamic and electromagnetic brain networks

The relationship between structural and functional connectivity in the brain is a key question in connectomics. Here we quantify patterns of structure-function coupling across the neocortex, by comparing structural connectivity estimated using diffusion MRI with functional connectivity estimated using both neurophysiological (MEG-based) and haemodynamic (fMRI-based) recordings. We find that structure-function coupling is heterogeneous across brain regions and frequency bands. The link between structural and functional connectivity is generally stronger in multiple MEG frequency bands compared to resting state fMRI. Structure-function coupling is greater in slower and intermediate frequency bands compared to faster frequency bands. We also find that structure-function coupling systematically follows the archetypal sensorimotor-association hierarchy, as well as patterns of laminar differentiation, peaking in granular layer IV. Finally, structure-function coupling is better explained using structure-informed inter-regional communication metrics than using structural connectivity alone. Collectively, these results place neurophysiological and haemodynamic structure-function relationships in a common frame of reference and provide a starting point for a multi-modal understanding of structure-function coupling in the brain.

Co-evolving dynamics and topology in a coupled oscillator model of resting brain function

Dynamic models of ongoing BOLD fMRI brain dynamics and models of communication strategies have been two important approaches to understanding how brain network structure constrains function. However, dynamic models have yet to widely incorporate one of the most important insights from communication models: the brain may not use all of its connections in the same way or at the same time. Here we present a variation of a phase delayed Kuramoto coupled oscillator model that dynamically limits communication between nodes on each time step. An active subgraph of the empirically derived anatomical brain network is chosen in accordance with the local dynamic state on every time step, thus coupling dynamics and network structure in a novel way. We analyze this model with respect to its fit to empirical time-averaged functional connectivity, finding that, with the addition of only one parameter, it significantly outperforms standard Kuramoto models with phase delays. We also perform analyses on the novel time series of active edges it produces, demonstrating a slowly evolving topology moving through intermittent episodes of integration and segregation. We hope to demonstrate that the exploration of novel modeling mechanisms and the investigation of dynamics of networks in addition to dynamics on networks may advance our understanding of the relationship between brain structure and function.

Toward computational neuroconstructivism: a framework for developmental systems neuroscience

Brain development is underpinned by complex interactions between neural assemblies, driving structural and functional change. This neuroconstructivism (the notion that neural functions are shaped by these interactions) is core to some developmental theories. However, due to their complexity, understanding underlying developmental mechanisms is challenging. Elsewhere in neurobiology, a computational revolution has shown that mathematical models of hidden biological mechanisms can bridge observations with theory building. Can we build a similar computational framework yielding mechanistic insights for brain development? Here, we outline the conceptual and technical challenges of addressing this theory gap, and demonstrate that there is great potential in specifying brain development as mathematically defined processes operating within physical constraints. We provide examples, alongside broader ingredients needed, as the field explores computational explanations of system-wide development.

EEG alpha band functional connectivity reveals distinct cortical dynamics for overt and covert emotional face processing

Current knowledge regarding how the focus of our attention during face processing influences neural responses largely comes from neuroimaging studies reporting on regional brain activations. The present study was designed to add novel insights to this research by studying how attention can differentially impact the way cortical regions interact during emotional face processing. High-density electroencephalogram was recorded in a sample of fifty-two healthy participants during an emotional face processing task. The task required participants to either attend to the expressions (i.e., overt processing) or attend to a perceptual distractor, which rendered the expressions task-irrelevant (i.e., covert processing). Functional connectivity in the alpha band was estimated in source space and modeled using graph theory to quantify whole-brain integration and segregation. Results revealed that overt processing of facial expressions is linked to reduced cortical segregation and increased cortical integration, this latter specifically for negative expressions of fear and sadness. Furthermore, we observed increased communication efficiency during overt processing of negative expressions between the core and the extended face processing systems. Overall, these findings reveal that attention makes the interaction among the nodes involved in face processing more efficient, also uncovering a connectivity signature of the prioritized processing mechanism of negative expressions, that is an increased cross-communication within the nodes of the face processing network.

Structural-functional connectivity bandwidth predicts processing speed in mild traumatic brain Injury: A multiplex network analysis

An emerging body of work has revealed alterations in structural (SC) and functional (FC) brain connectivity following mild TBI (mTBI), with mixed findings. However, these studies seldom integrate complimentary neuroimaging modalities within a unified framework. Multilayer network analysis is an emerging technique to uncover how white matter organization enables functional communication. Using our novel graph metric (SC-FC Bandwidth), we quantified the information capacity of synchronous brain regions in 53 mild TBI patients (46 females; age mean = 40.2 years (y), σ = 16.7 (y), range: 18-79 (y). Diffusion MRI and resting state fMRI were administered at the acute and chronic post-injury intervals. Moreover, participants completed a cognitive task to measure processing speed (30 Seconds and Counting Task; 30-SACT). Processing speed was significantly increased at the chronic, relative to the acute post-injury intervals (p = <0.001). Nonlinear principal components of direct (t = -1.84, p = 0.06) and indirect SC-FC Bandwidth (t = 3.86, p = <0.001) predicted processing speed with a moderate effect size (R2 = 0.43, p < 0.001), while controlling for age. A subnetwork of interhemispheric edges with increased SC-FC Bandwidth was identified at the chronic, relative to the acute mTBI post-injury interval (pFDR = 0.05). Increased interhemispheric SC-FC Bandwidth of this network corresponded with improved processing speed at the chronic post-injury interval (partial r = 0.32, p = 0.02). Our findings revealed that mild TBI results in complex reorganization of brain connectivity optimized for maximum information flow, supporting improved cognitive performance as a compensatory mechanism. Moving forward, this measurement may complement clinical assessment as an objective marker of mTBI recovery.

Communication dynamics in the human connectome shape the cortex-wide propagation of direct electrical stimulation

Communication between gray matter regions underpins all facets of brain function. We study inter-areal communication in the human brain using intracranial EEG recordings, acquired following 29,055 single-pulse direct electrical stimulations in a total of 550 individuals across 20 medical centers (average of 87 ± 37 electrode contacts per subject). We found that network communication models-computed on structural connectivity inferred from diffusion MRI-can explain the causal propagation of focal stimuli, measured at millisecond timescales. Building on this finding, we show that a parsimonious statistical model comprising structural, functional, and spatial factors can accurately and robustly predict cortex-wide effects of brain stimulation (R²=46% in data from held-out medical centers). Our work contributes toward the biological validation of concepts in network neuroscience and provides insight into how connectome topology shapes polysynaptic inter-areal signaling. We anticipate that our findings will have implications for research on neural communication and the design of brain stimulation paradigms.

Investigating cognitive neuroscience theories of human intelligence: A connectome-based predictive modeling approach

Central to modern neuroscientific theories of human intelligence is the notion that general intelligence depends on a primary brain region or network, engaging spatially localized (rather than global) neural representations. Recent findings in network neuroscience, however, challenge this assumption, providing evidence that general intelligence may depend on system-wide network mechanisms, suggesting that local representations are necessary but not sufficient to account for the neural architecture of human intelligence. Despite the importance of this key theoretical distinction, prior research has not systematically investigated the role of local versus global neural representations in predicting general intelligence. We conducted a large-scale connectome-based predictive modeling study (N = 297), administering resting-state fMRI and a comprehensive cognitive battery to evaluate the efficacy of modern neuroscientific theories of human intelligence, including spatially localized theories (Lateral Prefrontal Cortex Theory, Parieto-Frontal Integration Theory, and Multiple Demand Theory) and recent global accounts (Process Overlap Theory and Network Neuroscience Theory). The results of our study demonstrate that general intelligence can be predicted by local functional connectivity profiles but is most robustly explained by global profiles of whole-brain connectivity. Our findings further suggest that the improved efficacy of global theories is not reducible to a greater strength or number of connections, but instead results from considering both strong and weak connections that provide the basis for intelligence (as predicted by the Network Neuroscience Theory). Our results highlight the importance of considering local neural representations in the context of a global information-processing architecture, suggesting future directions for theory-driven research on system-wide network mechanisms underlying general intelligence.

Comparing models of information transfer in the structural brain network and their relationship to functional connectivity: diffusion versus shortest path routing

The relationship between structural and functional connectivity in the human brain is a core question in network neuroscience, and a topic of paramount importance to our ability to meaningfully describe and predict functional outcomes. Graph theory has been used to produce measures based on the structural connectivity network that are related to functional connectivity. These measures are commonly based on either the shortest path routing model or the diffusion model, which carry distinct assumptions about how information is transferred through the network. Unlike shortest path routing, which assumes the most efficient path is always known, the diffusion model makes no such assumption, and lets information diffuse in parallel based on the number of connections to other regions. Past research has also developed hybrid measures that use concepts from both models, which have better predicted functional connectivity from structural connectivity than the shortest path length alone. We examined the extent to which each of these models can account for the structure-function relationship of interest using graph theory measures that are exclusively based on each model. This analysis was performed on multiple parcellations of the Human Connectome Project using multiple approaches, which all converged on the same finding. We found that the diffusion model accounts for much more variance in functional connectivity than the shortest path routing model, suggesting that the diffusion model is better suited to describing the structure-function relationship in the human brain at the macroscale.

Asymmetric signaling across the hierarchy of cytoarchitecture within the human connectome

Cortical variations in cytoarchitecture form a sensory-fugal axis that shapes regional profiles of extrinsic connectivity and is thought to guide signal propagation and integration across the cortical hierarchy. While neuroimaging work has shown that this axis constrains local properties of the human connectome, it remains unclear whether it also shapes the asymmetric signaling that arises from higher-order topology. Here, we used network control theory to examine the amount of energy required to propagate dynamics across the sensory-fugal axis. Our results revealed an asymmetry in this energy, indicating that bottom-up transitions were easier to complete compared to top-down. Supporting analyses demonstrated that asymmetries were underpinned by a connectome topology that is wired to support efficient bottom-up signaling. Lastly, we found that asymmetries correlated with differences in communicability and intrinsic neuronal time scales and lessened throughout youth. Our results show that cortical variation in cytoarchitecture may guide the formation of macroscopic connectome topology.

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

A Riemannian approach to predicting brain function from the structural connectome

Ongoing brain function is largely determined by the underlying wiring of the brain, but the specific rules governing this relationship remain unknown. Emerging literature has suggested that functional interactions between brain regions emerge from the structural connections through mono- as well as polysynaptic mechanisms. Here, we propose a novel approach based on diffusion maps and Riemannian optimization to emulate this dynamic mechanism in the form of random walks on the structural connectome and predict functional interactions as a weighted combination of these random walks. Our proposed approach was evaluated in two different cohorts of healthy adults (Human Connectome Project, HCP; Microstructure-Informed Connectomics, MICs). Our approach outperformed existing approaches and showed that performance plateaus approximately around the third random walk. At macroscale, we found that the largest number of walks was required in nodes of the default mode and frontoparietal networks, underscoring an increasing relevance of polysynaptic communication mechanisms in transmodal cortical networks compared to primary and unimodal systems.

Network communication models narrow the gap between the modular organization of structural and functional brain networks

Structural and functional brain networks are modular. Canonical functional systems, such as the default mode network, are well-known modules of the human brain and have been implicated in a large number of cognitive, behavioral and clinical processes. However, modules delineated in structural brain networks inferred from tractography generally do not recapitulate canonical functional systems. Neuroimaging evidence suggests that functional connectivity between regions in the same systems is not always underpinned by anatomical connections. As such, direct structural connectivity alone would be insufficient to characterize the functional modular organization of the brain. Here, we demonstrate that augmenting structural brain networks with models of indirect (polysynaptic) communication unveils a modular network architecture that more closely resembles the brain's established functional systems. We find that diffusion models of polysynaptic connectivity, particularly communicability, narrow the gap between the modular organization of structural and functional brain networks by 20-60%, whereas routing models based on single efficient paths do not improve mesoscopic structure-function correspondence. This suggests that functional modules emerge from the constraints imposed by local network structure that facilitates diffusive neural communication. Our work establishes the importance of modeling polysynaptic communication to understand the structural basis of functional systems.

Local structure-function relationships in human brain networks across the lifespan

A growing number of studies have used stylized network models of communication to predict brain function from structure. Most have focused on a small set of models applied globally. Here, we compare a large number of models at both global and regional levels. We find that globally most predictors perform poorly. At the regional level, performance improves but heterogeneously, both in terms of variance explained and the optimal model. Next, we expose synergies among predictors by using pairs to jointly predict FC. Finally, we assess age-related differences in global and regional coupling across the human lifespan. We find global decreases in the magnitude of structure-function coupling with age. We find that these decreases are driven by reduced coupling in sensorimotor regions, while higher-order cognitive systems preserve local coupling with age. Our results describe patterns of structure-function coupling across the cortex and how this may change with age.

Quantitative mapping of the brain's structural connectivity using diffusion MRI tractography: A review

Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo reconstruction of the brain's white matter connections at macro scale. It provides an important tool for quantitative mapping of the brain's structural connectivity using measures of connectivity or tissue microstructure. Over the last two decades, the study of brain connectivity using dMRI tractography has played a prominent role in the neuroimaging research landscape. In this paper, we provide a high-level overview of how tractography is used to enable quantitative analysis of the brain's structural connectivity in health and disease. We focus on two types of quantitative analyses of tractography, including: 1) tract-specific analysis that refers to research that is typically hypothesis-driven and studies particular anatomical fiber tracts, and 2) connectome-based analysis that refers to research that is more data-driven and generally studies the structural connectivity of the entire brain. We first provide a review of methodology involved in three main processing steps that are common across most approaches for quantitative analysis of tractography, including methods for tractography correction, segmentation and quantification. For each step, we aim to describe methodological choices, their popularity, and potential pros and cons. We then review studies that have used quantitative tractography approaches to study the brain's white matter, focusing on applications in neurodevelopment, aging, neurological disorders, mental disorders, and neurosurgery. We conclude that, while there have been considerable advancements in methodological technologies and breadth of applications, there nevertheless remains no consensus about the "best" methodology in quantitative analysis of tractography, and researchers should remain cautious when interpreting results in research and clinical applications.

The hidden community architecture of human brain networks

The organizational principles of the community architecture of human brain networks are still mostly unknown. Here, we found that brain networks have a moderate degree of community segregation but are specifically organized to achieve high community overlap while maintaining their segregated community structures. These properties are distinct from other real-world complex networks. Additionally, we found that human subjects with a higher degree of community overlap in their brain networks show greater dynamic reconfiguration and cognitive flexibility.

Efficient coding in the economics of human brain connectomics

In systems neuroscience, most models posit that brain regions communicate information under constraints of efficiency. Yet, evidence for efficient communication in structural brain networks characterized by hierarchical organization and highly connected hubs remains sparse. The principle of efficient coding proposes that the brain transmits maximal information in a metabolically economical or compressed form to improve future behavior. To determine how structural connectivity supports efficient coding, we develop a theory specifying minimum rates of message transmission between brain regions to achieve an expected fidelity, and we test five predictions from the theory based on random walk communication dynamics. In doing so, we introduce the metric of compression efficiency, which quantifies the trade-off between lossy compression and transmission fidelity in structural networks. In a large sample of youth (n = 1,042; age 8-23 years), we analyze structural networks derived from diffusion-weighted imaging and metabolic expenditure operationalized using cerebral blood flow. We show that structural networks strike compression efficiency trade-offs consistent with theoretical predictions. We find that compression efficiency prioritizes fidelity with development, heightens when metabolic resources and myelination guide communication, explains advantages of hierarchical organization, links higher input fidelity to disproportionate areal expansion, and shows that hubs integrate information by lossy compression. Lastly, compression efficiency is predictive of behavior-beyond the conventional network efficiency metric-for cognitive domains including executive function, memory, complex reasoning, and social cognition. Our findings elucidate how macroscale connectivity supports efficient coding and serve to foreground communication processes that utilize random walk dynamics constrained by network connectivity.

On the asymptotic behavior of the average geodesic distance L and the compactness CB of simple connected undirected graphs whose order approaches infinity

The average geodesic distance L Newman (2003) and the compactness CB Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple connected undirected graphs G of order n, we study the behavior of L(G) and CB(G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and CB(G) lies within the interval [0;1/3] and [2/3;1], respectively. Moreover, for any not necessarily rational number β ∈ [0;1/3] (α ∈ [2/3;1]) we show how to construct the sequence of graphs {G}, |V(G)| = n → ∞, for which the limit of L(G)/n (CB(G)) is exactly β (α) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.

Potential-driven random walks on interconnected systems

Interconnected systems have to route information to function properly: At the lowest scale neural cells exchange electrochemical signals to communicate, while at larger scales animals and humans move between distinct spatial patches and machines exchange information via the Internet through communication protocols. Nontrivial patterns emerge from the analysis of information flows, which are not captured either by broadcasting, such as in random walks, or by geodesic routing, such as shortest paths. In fact, alternative models between those extreme protocols are still eluding us. Here we propose a class of stochastic processes, based on biased random walks, where agents are driven by a physical potential pervading the underlying network topology. By considering a generalized Coulomb dependence on the distance on destination(s), we show that it is possible to interpolate between random walk and geodesic routing in a simple and effective way. We demonstrate that it is not possible to find a one-size-fit-all solution to efficient navigation and that network heterogeneity or modularity has measurable effects. We illustrate how our framework can describe the movements of animals and humans, capturing with a stylized model some measurable features of the latter. From a methodological perspective, our potential-driven random walks open the doors to a broad spectrum of analytical tools, ranging from random-walk centralities to geometry induced by potential-driven network processes.

Network Controllability in Transmodal Cortex Predicts Positive Psychosis Spectrum Symptoms

BACKGROUND

The psychosis spectrum (PS) is associated with structural dysconnectivity concentrated in transmodal cortex. However, understanding of this pathophysiology has been limited by an overreliance on examining direct interregional connectivity. Using network control theory, we measured variation in both direct and indirect connectivity to a region to gain new insights into the pathophysiology of the PS.

METHODS

We used psychosis symptom data and structural connectivity in 1068 individuals from the Philadelphia Neurodevelopmental Cohort. Applying a network control theory metric called average controllability, we estimated each brain region's capacity to leverage its direct and indirect structural connections to control linear brain dynamics. Using nonlinear regression, we determined the accuracy with which average controllability could predict PS symptoms in out-of-sample testing. We also examined the predictive performance of regional strength, which indexes only direct connections to a region, as well as several graph-theoretic measures of centrality that index indirect connectivity. Finally, we assessed how the prediction performance for PS symptoms varied over the functional hierarchy spanning unimodal to transmodal cortex.

RESULTS

Average controllability outperformed all other connectivity features at predicting positive PS symptoms and was the only feature to yield above-chance predictive performance. Improved prediction for average controllability was concentrated in transmodal cortex, whereas prediction performance for strength was uniform across the cortex, suggesting that indexing indirect connections through average controllability is crucial in association cortex.

CONCLUSIONS

Examining interindividual variation in direct and indirect structural connections to transmodal cortex is crucial for accurate prediction of positive PS symptoms.

Multiscale communication in cortico-cortical networks

Signaling in brain networks unfolds over multiple topological scales. Areas may exchange information over local circuits, encompassing direct neighbours and areas with similar functions, or over global circuits, encompassing distant neighbours with dissimilar functions. Here we study how the organization of cortico-cortical networks mediate localized and global communication by parametrically tuning the range at which signals are transmitted on the white matter connectome. We show that brain regions vary in their preferred communication scale. By investigating the propensity for brain areas to communicate with their neighbors across multiple scales, we naturally reveal their functional diversity: unimodal regions show preference for local communication and multimodal regions show preferences for global communication. We show that these preferences manifest as region- and scale-specific structure-function coupling. Namely, the functional connectivity of unimodal regions emerges from monosynaptic communication in small-scale circuits, while the functional connectivity of transmodal regions emerges from polysynaptic communication in large-scale circuits. Altogether, the present findings reveal that communication preferences are highly heterogeneous across the cortex, shaping regional differences in structure-function coupling.

A generative network model of neurodevelopmental diversity in structural brain organization

The formation of large-scale brain networks, and their continual refinement, represent crucial developmental processes that can drive individual differences in cognition and which are associated with multiple neurodevelopmental conditions. But how does this organization arise, and what mechanisms drive diversity in organization? We use generative network modeling to provide a computational framework for understanding neurodevelopmental diversity. Within this framework macroscopic brain organization, complete with spatial embedding of its organization, is an emergent property of a generative wiring equation that optimizes its connectivity by renegotiating its biological costs and topological values continuously over time. The rules that govern these iterative wiring properties are controlled by a set of tightly framed parameters, with subtle differences in these parameters steering network growth towards different neurodiverse outcomes. Regional expression of genes associated with the simulations converge on biological processes and cellular components predominantly involved in synaptic signaling, neuronal projection, catabolic intracellular processes and protein transport. Together, this provides a unifying computational framework for conceptualizing the mechanisms and diversity in neurodevelopment, capable of integrating different levels of analysis-from genes to cognition.

Structure-informed functional connectivity driven by identifiable and state-specific control regions

Describing how the brain anatomical wiring contributes to the emergence of coordinated neural activity underlying complex behavior remains challenging. Indeed, patterns of remote coactivations that adjust with the ongoing task-demand do not systematically match direct, static anatomical links. Here, we propose that observed coactivation patterns, known as functional connectivity (FC), can be explained by a controllable linear diffusion dynamics defined on the brain architecture. Our model, termed structure-informed FC, is based on the hypothesis that different sets of brain regions controlling the information flow on the anatomical wiring produce state-specific functional patterns. We thus introduce a principled framework for the identification of potential control centers in the brain. We find that well-defined, sparse, and robust sets of control regions, partially overlapping across several tasks and resting state, produce FC patterns comparable to empirical ones. Our findings suggest that controllability is a fundamental feature allowing the brain to reach different states.

Understanding how brain anatomy promotes particular patterns of coactivations among neural regions is a key challenge in neuroscience. This challenge can be addressed using network science and systems theory. Here, we propose that coactivations result from the diffusion of information through the network of anatomical links connecting brain regions, with certain regions controlling the dynamics. We translate this hypothesis into a model called structure-informed functional connectivity, and we introduce a framework for identifying control regions based on empirical data. We find that our model produces coactivation patterns comparable to empirical ones, and that distinct sets of control regions are associated with different functional states. These findings suggest that controllability is an important feature allowing the brain to reach different states.

Inter-individual body mass variations relate to fractionated functional brain hierarchies

Variations in body mass index (BMI) have been suggested to relate to atypical brain organization, yet connectome-level substrates of BMI and their neurobiological underpinnings remain unclear. Studying 325 healthy young adults, we examined associations between functional connectivity and inter-individual BMI variations. We utilized non-linear connectome manifold learning techniques to represent macroscale functional organization along continuous hierarchical axes that dissociate low level and higher order brain systems. We observed an increased differentiation between unimodal and heteromodal association networks in individuals with higher BMI, indicative of a disrupted modular architecture and hierarchy of the brain. Transcriptomic decoding and gene enrichment analyses identified genes previously implicated in genome-wide associations to BMI and specific cortical, striatal, and cerebellar cell types. These findings illustrate functional connectome substrates of BMI variations in healthy young adults and point to potential molecular associations.

Cost-efficiency trade-offs of the human brain network revealed by a multiobjective evolutionary algorithm

It is widely believed that the formation of brain network architecture is under the pressure of optimal trade-off between reducing wiring cost and promoting communication efficiency. However, the questions of whether this trade-off exists in empirical human brain structural networks and, if so, how it takes effect are still not well understood. Here, we employed a multiobjective evolutionary algorithm to directly and quantitatively explore the cost-efficiency trade-off in human brain structural networks. Using this algorithm, we generated a population of synthetic networks with optimal but diverse cost-efficiency trade-offs. It was found that these synthetic networks could not only reproduce a large portion of connections in the empirical brain structural networks but also embed a resembling small-world organization. Moreover, the synthetic and empirical brain networks were found similar in terms of the spatial arrangement of hub regions and the modular structure, which are two important topological features widely assumed to be outcomes of cost-efficiency trade-offs. The synthetic networks had high robustness against random attacks as the empirical brain networks did. Additionally, we also revealed some differences between the synthetic networks and the empirical brain networks, including lower segregated processing capacity and weaker robustness against targeted attacks in the synthetic networks. These findings provide direct and quantitative evidence that the structure of human brain networks is indeed largely influenced by optimal cost-efficiency trade-offs. We also suggest that some additional factors (e.g., segregated processing capacity) might jointly determine the network organization with cost and efficiency.

Navigating the link between processing speed and network communication in the human brain

Processing speed on cognitive tasks relies upon efficient communication between widespread regions of the brain. Recently, novel methods of quantifying network communication like 'navigation efficiency' have emerged, which aim to be more biologically plausible compared to traditional shortest path length-based measures. However, it is still unclear whether there is a direct link between these communication measures and processing speed. We tested this relationship in forty-five healthy adults (27 females), where processing speed was defined as decision-making time and measured using drift rate from the hierarchical drift diffusion model. Communication measures were calculated from a graph theoretical analysis of the whole-brain structural connectome and of a task-relevant fronto-parietal structural subnetwork, using the large-scale Desikan-Killiany atlas. We found that faster processing speed on trials that require greater cognitive control are correlated with higher navigation efficiency (of both the whole-brain and the task-relevant subnetwork). In contrast, faster processing speed on trials that require more automatic processing are correlated with shorter path length within the task-relevant subnetwork. Our findings reveal that differences in the way communication is modelled between shortest path length and navigation may be sensitive to processing of automatic and controlled responses, respectively. Further, our findings suggest that there is a relationship between the speed of cognitive processing and the structural constraints of the human brain network.

Accrual of functional redundancy along the lifespan and its effects on cognition

Despite the necessity to understand how the brain endures the initial stages of age-associated cognitive decline, no brain mechanism has been quantitatively specified to date. The brain may withstand the effects of cognitive aging through redundancy, a design feature in engineered and biological systems, which entails the presence of substitute elements to protect it against failure. Here, we investigated the relationship between functional network redundancy and age over the human lifespan and their interaction with cognition, analyzing resting-state functional MRI images and cognitive measures from 579 subjects. Network-wide redundancy was significantly associated with age, showing a stronger link with age than other major topological measures, presenting a pattern of accumulation followed by old-age decline. Critically, redundancy significantly mediated the association between age and executive function, with lower anti-correlation between age and cognition in subjects with high redundancy. The results suggest that functional redundancy accrues throughout the lifespan, mitigating the effects of age on cognition.

Random walk with memory on complex networks

We study random walks on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs of nodes, for a random walk with a memory of one step. We have analyzed one particular model of random walk, where the transition probabilities depend on the number of paths to the second neighbors. The numerical experiments on paradigmatic complex networks verify the validity of the theoretical expressions, and also indicate that the flattening of the stationary occupation probability accompanies a nearly optimal random search.

Network communication models improve the behavioral and functional predictive utility of the human structural connectome

The connectome provides the structural substrate facilitating communication between brain regions. We aimed to establish whether accounting for polysynaptic communication in structural connectomes would improve prediction of interindividual variation in behavior as well as increase structure-function coupling strength. Connectomes were mapped for 889 healthy adults participating in the Human Connectome Project. To account for polysynaptic signaling, connectomes were transformed into communication matrices for each of 15 different network communication models. Communication matrices were (a) used to perform predictions of five data-driven behavioral dimensions and (b) correlated to resting-state functional connectivity (FC). While FC was the most accurate predictor of behavior, communication models, in particular communicability and navigation, improved the performance of structural connectomes. Communication also strengthened structure-function coupling, with the navigation and shortest paths models leading to 35-65% increases in association strength with FC. We combined behavioral and functional results into a single ranking that provides insight into which communication models may more faithfully recapitulate underlying neural signaling patterns. Comparing results across multiple connectome mapping pipelines suggested that modeling polysynaptic communication is particularly beneficial in sparse high-resolution connectomes. We conclude that network communication models can augment the functional and behavioral predictive utility of the human structural connectome.

Creative destruction: Sparse activity emerges on the mammal connectome under a simulated communication strategy with collisions and redundancy

Signal interactions in brain network communication have been little studied. We describe how nonlinear collision rules on simulated mammal brain networks can result in sparse activity dynamics characteristic of mammalian neural systems. We tested the effects of collisions in "information spreading" (IS) routing models and in standard random walk (RW) routing models. Simulations employed synchronous agents on tracer-based mesoscale mammal connectomes at a range of signal loads. We find that RW models have high average activity that increases with load. Activity in RW models is also densely distributed over nodes: a substantial fraction is highly active in a given time window, and this fraction increases with load. Surprisingly, while IS models make many more attempts to pass signals, they show lower net activity due to collisions compared to RW, and activity in IS increases little as function of load. Activity in IS also shows greater sparseness than RW, and sparseness decreases slowly with load. Results hold on two networks of the monkey cortex and one of the mouse whole-brain. We also find evidence that activity is lower and more sparse for empirical networks compared to degree-matched randomized networks under IS, suggesting that brain network topology supports IS-like routing strategies.

Models of communication and control for brain networks: distinctions, convergence, and future outlook

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

Signal propagation via cortical hierarchies

The wiring of the brain is organized around a putative unimodal-transmodal hierarchy. Here we investigate how this intrinsic hierarchical organization of the brain shapes the transmission of information among regions. The hierarchical positioning of individual regions was quantified by applying diffusion map embedding to resting-state functional MRI networks. Structural networks were reconstructed from diffusion spectrum imaging and topological shortest paths among all brain regions were computed. Sequences of nodes encountered along a path were then labeled by their hierarchical position, tracing out path motifs. We find that the cortical hierarchy guides communication in the network. Specifically, nodes are more likely to forward signals to nodes closer in the hierarchy and cover a range of unimodal and transmodal regions, potentially enriching or diversifying signals en route. We also find evidence of systematic detours, particularly in attention networks, where communication is rerouted. Altogether, the present work highlights how the cortical hierarchy shapes signal exchange and imparts behaviorally relevant communication patterns in brain networks.

In the present report we asked how signals travel on brain networks and what types of nodes they potentially visit en route. We traced individual path motifs to investigate the propensity of communication paths to explore the putative unimodal-transmodal cortical hierarchy. We find that the architecture of the network promotes signaling via the hierarchy, suggesting a link between the structure and function of the network. Importantly, we also find instances where detours are promoted, particularly as paths traverse attention-related networks. Finally, information about hierarchical position aids navigation in some parts of the network, over and above spatial location. Altogether, the present results touch on several emerging themes in network neuroscience, including the nature of structure-function relationships, network communication and the role of cortical hierarchies.

Signal diffusion along connectome gradients and inter-hub routing differentially contribute to dynamic human brain function

Human cognition is dynamic, alternating over time between externally-focused states and more abstract, often self-generated, patterns of thought. Although cognitive neuroscience has documented how networks anchor particular modes of brain function, mechanisms that describe transitions between distinct functional states remain poorly understood. Here, we examined how time-varying changes in brain function emerge within the constraints imposed by macroscale structural network organization. Studying a large cohort of healthy adults (n = 326), we capitalized on manifold learning techniques that identify low dimensional representations of structural connectome organization and we decomposed neurophysiological activity into distinct functional states and their transition patterns using Hidden Markov Models. Structural connectome organization predicted dynamic transitions anchored in sensorimotor systems and those between sensorimotor and transmodal states. Connectome topology analyses revealed that transitions involving sensorimotor states traversed short and intermediary distances and adhered strongly to communication mechanisms of network diffusion. Conversely, transitions between transmodal states involved spatially distributed hubs and increasingly engaged long-range routing. These findings establish that the structure of the cortex is optimized to allow neural states the freedom to vary between distinct modes of processing, and so provides a key insight into the neural mechanisms that give rise to the flexibility of human cognition.

Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

Linking Structure and Function in Macroscale Brain Networks

Structure-function relationships are a fundamental principle of many naturally occurring systems. However, network neuroscience research suggests that there is an imperfect link between structural connectivity and functional connectivity in the brain. Here, we synthesize the current state of knowledge linking structure and function in macroscale brain networks and discuss the different types of models used to assess this relationship. We argue that current models do not include the requisite biological detail to completely predict function. Structural network reconstructions enriched with local molecular and cellular metadata, in concert with more nuanced representations of functions and properties, hold great potential for a truly multiscale understanding of the structure-function relationship.

Structural optimality and neurogenetic expression mediate functional dynamics in the human brain

The human brain exhibits a rich functional repertoire in terms of complex functional connectivity patterns during rest and tasks. However, how this is developed upon a fixed structural anatomy remains poorly understood. Here we investigated the hypothesis that resting state functional connectivity and the manner in which it changes during tasks related to a set of underlying structural connections that promote optimal communication in the brain. We used a game‐theoretic model to identify such optimal connections in the structural connectome of 50 healthy individuals and subsequently used the optimal structural connections to predict resting‐state functional connectivity with high accuracy. In contrast, we found that nonoptimal connections accurately predicted functional connectivity during a working memory task. We further found that this balance between optimal and nonoptimal connections between brain regions was associated with a specific gene expression linked to neurotransmission. This multimodal evidence shows for the first time that structure–function relationships in the human brain are related to how brain networks navigate information along different white matter connections as well as the brain's underlying genetic profile.

Navigable maps of structural brain networks across species

Connectomes are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Using a decentralized navigation protocol, we investigate the relationship between the structure of the connectomes of different species and their spatial layout. As a navigation strategy, we use greedy routing where nearest neighbors, in terms of geometric distance, are visited. We measure the fraction of successful greedy paths and their length as compared to shortest paths in the topology of connectomes. In Euclidean space, we find a striking difference between the navigability properties of mammalian and non-mammalian species, which implies the inability of Euclidean distances to fully explain the structural organization of their connectomes. In contrast, we find that hyperbolic space, the effective geometry of complex networks, provides almost perfectly navigable maps of connectomes for all species, meaning that hyperbolic distances are exceptionally congruent with the structure of connectomes. Hyperbolic maps therefore offer a quantitative meaningful representation of connectomes that suggests a new cartography of the brain based on the combination of its connectivity with its effective geometry rather than on its anatomy only. Hyperbolic maps also provide a universal framework to study decentralized communication processes in connectomes of different species and at different scales on an equal footing.

The role of detours in individual human navigation patterns of complex networks

Despite its importance for public transportation, communication within organizations or the general understanding of organized knowledge, our understanding of how human individuals navigate complex networked systems is still limited owing to the lack of datasets recording a sufficient amount of navigation paths of individual humans. Here, we analyse 10587 paths recorded from 259 human subjects when navigating between nodes of a complex word-morph network. We find a clear presence of systematic detours organized around individual hierarchical scaffolds guiding navigation. Our dataset is the first enabling the visualization and analysis of scaffold hierarchies whose presence and role in supporting human navigation is assumed in existing navigational models. By using an information-theoretic argumentation, we argue that taking short detours following the hierarchical scaffolds is a clear sign of human subjects simplifying the interpretation of the complex networked system by an order of magnitude. We also discuss the role of these scaffolds in the phases of learning to navigate a network from scratch.

Inferring neural signalling directionality from undirected structural connectomes

Neural information flow is inherently directional. To date, investigation of directional communication in the human structural connectome has been precluded by the inability of non-invasive neuroimaging methods to resolve axonal directionality. Here, we demonstrate that decentralized measures of network communication, applied to the undirected topology and geometry of brain networks, can infer putative directions of large-scale neural signalling. We propose the concept of send-receive communication asymmetry to characterize cortical regions as senders, receivers or neutral, based on differences between their incoming and outgoing communication efficiencies. Our results reveal a send-receive cortical hierarchy that recapitulates established organizational gradients differentiating sensory-motor and multimodal areas. We find that send-receive asymmetries are significantly associated with the directionality of effective connectivity derived from spectral dynamic causal modeling. Finally, using fruit fly, mouse and macaque connectomes, we provide further evidence suggesting that directionality of neural signalling is significantly encoded in the undirected architecture of nervous systems.

Columnar connectome: toward a mathematics of brain function

Understanding brain networks is important for many fields, including neuroscience, psychology, medicine, and artificial intelligence. To address this fundamental need, there are multiple ongoing connectome projects in the United States, Europe, and Asia producing brain connection maps with resolutions at macro- and microscales. However, still lacking is a mesoscale connectome. This viewpoint (1) explains the need for a mesoscale connectome in the primate brain (the columnar connectome), (2) presents a new method for acquiring such data rapidly on a large scale, and (3) proposes how one might use such data to achieve a mathematics of brain function.