Navigation of brain networks

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.

Can structure predict function at individual level in the human connectome?

Several studies predicting Functional Connectivity (FC) from Structural Connectivity (SC) at individual level have been published in recent years, each promising increased performance and utility. We investigated three of these studies, analyzing whether the results truly represent a meaningful individual-level mapping from SC to FC. Using data from the Human Connectome Project shared accross the three studies, we constructed a predictor by averaging FC of training data and analyzed its performance in the same way. In each case, we found that group average FC is an equivalent or better predictor of individual FC than the predictive models in terms of raw prediction performance. Furthermore, we showed that additional analyses performed by the authors of the three studies, in which they attempt to show that their predicted FC has value beyond raw prediction performance, could also be reproduced using the group average FC predictor. This makes it unclear whether any of the three methods represent a meaningful individual-level predictive model. We conclude that either the methods are not appropriate for the data, that the sample size is too small, or that the data does not contain sufficient information to learn a mapping from SC to FC. We advise future individual-level studies to explicitly report results in comparison to the performance of the group average, and carefully demonstrate that their predictions contain meaningful individual-level information. Finally, we believe that investigating alternatives for the construction of SC and FC may improve the chances of developing a meaningful individual-level mapping from SC to FC.

Quantifying synergy and redundancy between networks

Understanding how different networks relate to each other is key for understanding complex systems. We introduce an intuitive yet powerful framework to disentangle different ways in which networks can be (dis)similar and complementary to each other. We decompose the shortest paths between nodes as uniquely contributed by one source network, or redundantly by either, or synergistically by both together. Our approach considers the networks' full topology, providing insights at multiple levels of resolution: from global statistics to individual paths. Our framework is widely applicable across scientific domains, from public transport to brain networks. In humans and 124 other species, we demonstrate the prevalence of unique contributions by long-range white-matter fibers in structural brain networks. Across species, efficient communication also relies on significantly greater synergy between long-range and short-range fibers than expected by chance. Our framework could find applications for designing network systems or evaluating existing ones.

Release the Krakencoder: A unified brain connectome translation and fusion tool

Brain connectivity can be estimated in many ways, depending on modality and processing strategy. Here we present the Krakencoder, a joint connectome mapping tool that simultaneously, bidirectionally translates between structural (SC) and functional connectivity (FC), and across different atlases and processing choices via a common latent representation. These mappings demonstrate unprecedented accuracy and individual-level identifiability; the mapping between SC and FC has identifiability 42-54% higher than existing models. The Krakencoder combines all connectome flavors via a shared low-dimensional latent space. This "fusion" representation i) better reflects familial relatedness, ii) preserves age- and sex-relevant information and iii) enhances cognition-relevant information. The Krakencoder can be applied without retraining to new, out-of-age-distribution data while still preserving inter-individual differences in the connectome predictions and familial relationships in the latent representations. The Krakencoder is a significant leap forward in capturing the relationship between multi-modal brain connectomes in an individualized, behaviorally- and demographically-relevant way.

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.

Brain tissue segmentation in neurosurgery: a systematic analysis for quantitative tractography approaches

Diffusion magnetic resonance imaging (dMRI) is a cutting-edge imaging method that provides a macro-scale in vivo map of the white matter pathways in the brain. The measurement of brain microstructure and the enhancement of tractography rely heavily on dMRI tissue segmentation. Anatomical MRI technique (e.g., T1- and T2-weighted imaging) is the most widely used method for segmentation in dMRI. In comparison to anatomical MRI, dMRI suffers from higher image distortions, lower image quality, and making inter-modality registration more difficult. The dMRI tractography study of brain connectivity has become a major part of the neuroimaging landscape in recent years. In this research, we provide a high-level overview of the methods used to segment several brain tissues types, including grey and white matter and cerebrospinal fluid, to enable quantitative studies of structural connectivity in the brain in health and illness. In the first part of our review, we discuss the three main phases in the quantitative analysis of tractography, which are correction, segmentation, and quantification. Methodological possibilities are described for each phase, along with their popularity and potential benefits and drawbacks. After that, we will look at research that used quantitative tractography approaches to examine the white and grey matter of the brain, with an emphasis on neurodevelopment, ageing, neurological illnesses, mental disorders, and neurosurgery as possible applications. Even though there have been substantial advancements in methodological technology and the spectrum of applications, there is still no consensus regarding the "optimal" approach in the quantitative analysis of tractography. As a result, researchers should tread carefully when interpreting the findings of quantitative analysis of tractography.

Prediction of cognitive outcome after mild traumatic brain injury from acute measures of communication within brain networks

A considerable but ill-defined proportion of patients with mild traumatic brain injury (mTBI) experience persistent cognitive sequelae; the ability to identify such individuals early can help their neurorehabilitation. Here we tested the hypothesis that acute measures of efficient communication within brain networks are associated with patients' risk for unfavorable cognitive outcome six months after mTBI. Diffusion and T1-weighted magnetic resonance imaging, alongside cognitive measures, were obtained to map connectomes both one week and six months post injury in 113 adult patients with mTBI (71 males). For task-related brain networks, communication measures (characteristic path length, global efficiency, navigation efficiency) were moderately correlated with changes in cognition. Taking into account the covariance of age and sex, more unfavorable communication within networks were associated with worse outcomes within cognitive domains frequently impacted by mTBI (episodic and working memory, verbal fluency, inductive reasoning, and processing speed). Individuals with more unfavorable outcomes had significantly longer and less efficient pathways within networks supporting verbal fluency (all t > 2.786, p < .006), highlighting the vulnerability of language to mTBI. Participants in whom a task-related network was relatively inefficient one week post injury were up to eight times more likely to have unfavorable cognitive outcome pertaining to that task. Our findings suggest that communication measures within task-related networks identify mTBI patients who are unlikely to develop persistent cognitive deficits after mTBI. Our approach and findings can help to stratify mTBI patients according to their expected need for follow-up and/or neurorehabilitation.

How brain structure-function decoupling supports individual cognition and its molecular mechanism

Functional signals emerge from the structural network, supporting multiple cognitive processes through underlying molecular mechanism. The link between human brain structure and function is region-specific and hierarchical across the neocortex. However, the relationship between hierarchical structure-function decoupling and the manifestation of individual behavior and cognition, along with the significance of the functional systems involved, and the specific molecular mechanism underlying structure-function decoupling remain incompletely characterized. Here, we used the structural-decoupling index (SDI) to quantify the dependency of functional signals on the structural connectome using a significantly larger cohort of healthy subjects. Canonical correlation analysis (CCA) was utilized to assess the general multivariate correlation pattern between region-specific SDIs across the whole brain and multiple cognitive traits. Then, we predicted five composite cognitive scores resulting from multivariate analysis using SDIs in primary networks, association networks, and all networks, respectively. Finally, we explored the molecular mechanism related to SDI by investigating its genetic factors and relationship with neurotransmitter receptors/transporters. We demonstrated that structure-function decoupling is hierarchical across the neocortex, spanning from primary networks to association networks. We revealed better performance in cognition prediction is achieved by using high-level hierarchical SDIs, with varying significance of different brain regions in predicting cognitive processes. We found that the SDIs were associated with the gene expression level of several receptor-related terms, and we also found the spatial distributions of four receptors/transporters significantly correlated with SDIs, namely D2, NET, MOR, and mGluR5, which play an important role in the flexibility of neuronal function. Collectively, our findings corroborate the association between hierarchical macroscale structure-function decoupling and individual cognition and provide implications for comprehending the molecular mechanism of structure-function decoupling. PRACTITIONER POINTS: Structure-function decoupling is hierarchical across the neocortex, spanning from primary networks to association networks. High-level hierarchical structure-function decoupling contributes much more than low-level decoupling to individual cognition. Structure-function decoupling could be regulated by genes associated with pivotal receptors that are crucial for neuronal function flexibility.

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.

Enhanced brain structure-function tethering in transmodal cortex revealed by high-frequency eigenmodes

While the link between brain structure and function remains an ongoing challenge, the prevailing hypothesis is that the structure-function relationship may itself be gradually decoupling from unimodal to transmodal cortex. However, this hypothesis is constrained by the underlying models which may neglect requisite information. Here we relate structural and functional connectivity derived from diffusion and functional MRI through orthogonal eigenmodes governing frequency-specific diffusion patterns. We find that low-frequency eigenmodes contribute little to functional interactions in transmodal cortex, resulting in divergent structure-function relationships. Conversely, high-frequency eigenmodes predominantly support neuronal coactivation patterns in these areas, inducing structure-function convergence along a unimodal-transmodal hierarchy. High-frequency information, although weak and scattered, could enhance the structure-function tethering, especially in transmodal association cortices. Our findings suggest that the structure-function decoupling may not be an intrinsic property of brain organization, but can be narrowed through multiplexed and regionally specialized spatiotemporal propagation regimes.

Resolving inter-regional communication capacity in the human connectome

Applications of graph theory to the connectome have inspired several models of how neural signaling unfolds atop its structure. Analytic measures derived from these communication models have mainly been used to extract global characteristics of brain networks, obscuring potentially informative inter-regional relationships. Here we develop a simple standardization method to investigate polysynaptic communication pathways between pairs of cortical regions. This procedure allows us to determine which pairs of nodes are topologically closer and which are further than expected on the basis of their degree. We find that communication pathways delineate canonical functional systems. Relating nodal communication capacity to meta-analytic probabilistic patterns of functional specialization, we also show that areas that are most closely integrated within the network are associated with higher order cognitive functions. We find that these regions' proclivity towards functional integration could naturally arise from the brain's anatomical configuration through evenly distributed connections among multiple specialized communities. Throughout, we consider two increasingly constrained null models to disentangle the effects of the network's topology from those passively endowed by spatial embedding. Altogether, the present findings uncover relationships between polysynaptic communication pathways and the brain's functional organization across multiple topological levels of analysis and demonstrate that network integration facilitates cognitive integration.

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.

Network bypasses sustain complexity

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.

Tissues as networks of cells: towards generative rules of complex organ development

Network analysis is a well-known and powerful tool in molecular biology. More recently, it has been introduced in developmental biology. Tissues can be readily translated into spatial networks such that cells are represented by nodes and intercellular connections by edges. This discretization of cellular organization enables mathematical approaches rooted in network science to be applied towards the understanding of tissue structure and function. Here, we describe how such tissue abstractions can enable the principles that underpin tissue formation and function to be uncovered. We provide an introduction into biologically relevant network measures, then present an overview of different areas of developmental biology where these approaches have been applied. We then summarize the general developmental rules underpinning tissue topology generation. Finally, we discuss how generative models can help to link the developmental rule back to the tissue topologies. Our collection of results points at general mechanisms as to how local developmental rules can give rise to observed topological properties in multicellular systems.

Atypical structural connectome asymmetry and associations with network communication in autism spectrum disorder

Autism spectrum disorder is a common neurodevelopmental condition showing connectome disorganization in sensory and transmodal cortices. However, alterations in the inter-hemispheric asymmetry of structural connectome are remained to be investigated. Here, we studied structural connectome asymmetry in individuals with autism using dimensionality reduction techniques and assessed its topological underpinnings by associating with network communication measures. We found that the sensory and heteromodal association regions showed significant between-group differences in inter-hemispheric asymmetry between individuals with autism and neurotypical controls. In addition, the network communication ability was particularly altered between visual and limbic areas. Our findings provide insights for understanding structural connectome alteration in autism and its topological underpinnings.Clinical Relevance- This study provides insights into the understanding of atypical macroscale structural connectome organization in individuals with autism.

Noise improves the association between effects of local stimulation and structural degree of brain networks

Stimulation to local areas remarkably affects brain activity patterns, which can be exploited to investigate neural bases of cognitive function and modify pathological brain statuses. There has been growing interest in exploring the fundamental action mechanisms of local stimulation. Nevertheless, how noise amplitude, an essential element in neural dynamics, influences stimulation-induced brain states remains unknown. Here, we systematically examine the effects of local stimulation by using a large-scale biophysical model under different combinations of noise amplitudes and stimulation sites. We demonstrate that noise amplitude nonlinearly and heterogeneously tunes the stimulation effects from both regional and network perspectives. Furthermore, by incorporating the role of the anatomical network, we show that the peak frequencies of unstimulated areas at different stimulation sites averaged across noise amplitudes are highly positively related to structural connectivity. Crucially, the association between the overall changes in functional connectivity as well as the alterations in the constraints imposed by structural connectivity with the structural degree of stimulation sites is nonmonotonically influenced by the noise amplitude, with the association increasing in specific noise amplitude ranges. Moreover, the impacts of local stimulation of cognitive systems depend on the complex interplay between the noise amplitude and average structural degree. Overall, this work provides theoretical insights into how noise amplitude and network structure jointly modulate brain dynamics during stimulation and introduces possibilities for better predicting and controlling stimulation outcomes.

Graph Neural Networks in Network Neuroscience

Noninvasive medical neuroimaging has yielded many discoveries about the brain connectivity. Several substantial techniques mapping morphological, structural and functional brain connectivities were developed to create a comprehensive road map of neuronal activities in the human brain -namely brain graph. Relying on its non-euclidean data type, graph neural network (GNN) provides a clever way of learning the deep graph structure and it is rapidly becoming the state-of-the-art leading to enhanced performance in various network neuroscience tasks. Here we review current GNN-based methods, highlighting the ways that they have been used in several applications related to brain graphs such as missing brain graph synthesis and disease classification. We conclude by charting a path toward a better application of GNN models in network neuroscience field for neurological disorder diagnosis and population graph integration. The list of papers cited in our work is available at https://github.com/basiralab/GNNs-in-Network-Neuroscience.

Parameter estimation for connectome generative models: Accuracy, reliability, and a fast parameter fitting method

Generative models of the human connectome enable in silico generation of brain networks based on probabilistic wiring rules. These wiring rules are governed by a small number of parameters that are typically fitted to individual connectomes and quantify the extent to which geometry and topology shape the generative process. A significant shortcoming of generative modeling in large cohort studies is that parameter estimation is computationally burdensome, and the accuracy and reliability of current estimation methods remain untested. Here, we propose a fast, reliable, and accurate parameter estimation method for connectome generative models that is scalable to large sample sizes. Our method achieves improved estimation accuracy and reliability and reduces computational cost by orders of magnitude, compared to established methods. We demonstrate an inherent tradeoff between accuracy, reliability, and computational expense in parameter estimation and provide recommendations for leveraging this tradeoff. To enable power analyses in future studies, we empirically approximate the minimum sample size required to detect between-group differences in generative model parameters. While we focus on the classic two-parameter generative model based on connection length and the topological matching index, our method can be generalized to other growth-based generative models. Our work provides a statistical and practical guide to parameter estimation for connectome generative models.

Abnormal Structural Network Communication Reflects Cognitive Deficits in Schizophrenia

Schizophrenia has long been thought to be a disconnection syndrome and several previous studies have reported widespread abnormalities in white matter tracts in individuals with schizophrenia. Furthermore, reductions in structural connectivity may also impair communication between anatomically unconnected pairs of brain regions, potentially impacting global signal traffic in the brain. Therefore, we used different communication models to examine direct and indirect structural connections (polysynaptic) communication in large-scale brain networks in schizophrenia. Diffusion-weighted magnetic resonance imaging scans were acquired from 62 patients diagnosed with schizophrenia and 35 controls. In this study, we used five network communication models including, shortest paths, navigation, diffusion, search information and communicability to examine polysynaptic communication in large-scale brain networks in schizophrenia. We showed less efficient communication between spatially widespread brain regions particulary encompassing cortico-subcortical basal ganglia network in schizophrenia group relative to controls. Then, we also examined whether reduced communication efficiency was related to clinical symptoms in schizophrenia group. Among different measures of communication efficiency, only navigation efficiency was associated with global cognitive impairment across multiple cognitive domains including verbal learning, processing speed, executive functions and working memory, in individuals with schizophrenia. We did not find any association between communication efficiency measures and positive or negative symptoms within the schizophrenia group. Our findings are important for improving our mechanistic understanding of neurobiological process underlying cognitive symptoms in schizophrenia.

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.

Altered vigilant maintenance and reorganization of rich-clubs in functional brain networks after total sleep deprivation

BACKGROUND

Sleep deprivation strongly deteriorates the stability of vigilant maintenance. In previous neuroimaging studies of large-scale networks, neural variations in the resting state after sleep deprivation have been well documented, highlighting that large-scale networks implement efficient cognitive functions and attention regulation in a spatially hierarchical organization. However, alterations of neural networks during cognitive tasks have rarely been investigated.

METHODS AND PURPOSES

The present study used a within-participant design of 35 healthy right-handed adults and used task-based functional magnetic resonance imaging to examine the neural mechanism of attentional decline after sleep deprivation from the perspective of rich-club architecture during a psychomotor vigilance task.

RESULTS

We found that a significant decline in the hub disruption index was related to impaired vigilance due to sleep loss. The hierarchical rich-club architectures were reconstructed after sleep deprivation, especially in the default mode network and sensorimotor network. Notably, the relatively fast alert response compensation was correlated with the feeder organizational hierarchy that connects core (rich-club) and peripheral nodes.

SIGNIFICANCES

Our findings provide novel insights into understanding the relationship of alterations in vigilance and the hierarchical architectures of the human brain after sleep deprivation, emphasizing the significance of optimal collaboration between different functional hierarchies for regular attention maintenance.

Classification of Brain Disorders in rs-fMRI via Local-to-Global Graph Neural Networks

Recently, functional brain network has been used for the classification of brain disorders, such as Autism Spectrum Disorder (ASD) and Alzheimer's disease (AD). Existing methods either ignore the non-imaging information associated with the subjects and the relationship between the subjects, or cannot identify and analyze disease-related local brain regions and biomarkers, leading to inaccurate classification results. This paper proposes a local-to-global graph neural network (LG-GNN) to address this issue. A local ROI-GNN is designed to learn feature embeddings of local brain regions and identify biomarkers, and a global Subject-GNN is then established to learn the relationship between the subjects with the embeddings generated by the local ROI-GNN and the non-imaging information. The local ROI-GNN contains a self-attention based pooling module to preserve the embeddings most important for the classification. The global Subject-GNN contains an adaptive weight aggregation block to generate the multi-scale feature embedding corresponding to each subject. The proposed LG-GNN is thoroughly validated using two public datasets for ASD and AD classification. The experimental results demonstrated that it achieves the state-of-the-art performance in terms of various evaluation metrics.

Nine insights from internet engineering that help us understand brain network communication

Philosophers have long recognized the value of metaphor as a tool that opens new avenues of investigation. By seeing brains as having the goal of representation, the computer metaphor in its various guises has helped systems neuroscience approach a wide array of neuronal behaviors at small and large scales. Here I advocate a complementary metaphor, the internet. Adopting this metaphor shifts our focus from computing to communication, and from seeing neuronal signals as localized representational elements to seeing neuronal signals as traveling messages. In doing so, we can take advantage of a comparison with the internet's robust and efficient routing strategies to understand how the brain might meet the challenges of network communication. I lay out nine engineering strategies that help the internet solve routing challenges similar to those faced by brain networks. The internet metaphor helps us by reframing neuronal activity across the brain as, in part, a manifestation of routing, which may, in different parts of the system, resemble the internet more, less, or not at all. I describe suggestive evidence consistent with the brain's use of internet-like routing strategies and conclude that, even if empirical data do not directly implicate internet-like routing, the metaphor is valuable as a reference point for those investigating the difficult problem of network communication in the brain and in particular the problem of routing.

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.

Exploring personalized structural connectomics for moderate to severe traumatic brain injury

Graph theoretical analysis of the structural connectome has been employed successfully to characterize brain network alterations in patients with traumatic brain injury (TBI). However, heterogeneity in neuropathology is a well-known issue in the TBI population, such that group comparisons of patients against controls are confounded by within-group variability. Recently, novel single-subject profiling approaches have been developed to capture inter-patient heterogeneity. We present a personalized connectomics approach that examines structural brain alterations in five chronic patients with moderate to severe TBI who underwent anatomical and diffusion magnetic resonance imaging. We generated individualized profiles of lesion characteristics and network measures (including personalized graph metric GraphMe plots, and nodal and edge-based brain network alterations) and compared them against healthy reference cases (N = 12) to assess brain damage qualitatively and quantitatively at the individual level. Our findings revealed alterations of brain networks with high variability between patients. With validation and comparison to stratified, normative healthy control comparison cohorts, this approach could be used by clinicians to formulate a neuroscience-guided integrative rehabilitation program for TBI patients, and for designing personalized rehabilitation protocols based on their unique lesion load and connectome.

Geometrical congruence, greedy navigability and myopic transfer in complex networks and brain connectomes

We introduce in network geometry a measure of geometrical congruence (GC) to evaluate the extent a network topology follows an underlying geometry. This requires finding all topological shortest-paths for each nonadjacent node pair in the network: a nontrivial computational task. Hence, we propose an optimized algorithm that reduces 26 years of worst scenario computation to one week parallel computing. Analysing artificial networks with patent geometry we discover that, different from current belief, hyperbolic networks do not show in general high GC and efficient greedy navigability (GN) with respect to the geodesics. The myopic transfer which rules GN works best only when degree-distribution power-law exponent is strictly close to two. Analysing real networks-whose geometry is often latent-GC overcomes GN as marker to differentiate phenotypical states in macroscale structural-MRI brain connectomes, suggesting connectomes might have a latent neurobiological geometry accounting for more information than the visible tridimensional Euclidean.

Aberrant resting-state functional connectivity and topological properties of the subcortical network in functional dyspepsia patients

Functional dyspepsia (FD) is a disorder of gut-brain interaction. Previous studies have demonstrated a wide range of abnormalities in functional brain activity and connectivity patterns in FD. However, the connectivity pattern of the subcortical network (SCN), which is a hub of visceral information transmission and processing, remains unclear in FD patients. The study compared the resting-state functional connectivity (rsFC) and the global and nodal topological properties of SCN between 109 FD patients and 98 healthy controls, and then explored the correlations between the connectivity metrics and clinical symptoms in FD patients. The results demonstrated that FD patients manifested the increased rsFC in seventeen edges among the SCN, decreased small-worldness and local efficiency in SCN, as well as increased nodal efficiency and nodal degree centrality in the anterior thalamus than healthy controls (p &lt; 0.05, false discovery rate corrected). Moreover, the rsFC of the right anterior thalamus-left nucleus accumbens edge was significantly correlated with the NDSI scores (r = 0.255, p = 0.008, uncorrected) and NDLQI scores (r = −0.241, p = 0.013, uncorrected), the nodal efficiency of right anterior thalamus was significantly correlated with NDLQI scores (r = 0.204, p = 0.036, uncorrected) in FD patients. This study indicated the abnormal rsFC pattern, as well as global and nodal topological properties of the SCN, especially the bilateral anterior thalamus in FD patients, which enhanced our understanding of the central pathophysiology of FD and will lay the foundation for the objective diagnosis of FD and the development of new therapies.

Functional orderly topography of brain networks associated with gene expression heterogeneity

The human cerebral cortex is vastly expanded relative to nonhuman primates and rodents, leading to a functional orderly topography of brain networks. Here, we show that functional topography may be associated with gene expression heterogeneity. The neocortex exhibits greater heterogeneity in gene expression, with a lower expression of housekeeping genes, a longer mean path length, fewer clusters, and a lower degree of ordering in networks than archicortical and subcortical areas in human, rhesus macaque, and mouse brains. In particular, the cerebellar cortex displays greater heterogeneity in gene expression than cerebellar deep nuclei in the human brain, but not in the mouse brain, corresponding to the emergence of novel functions in the human cerebellar cortex. Moreover, the cortical areas with greater heterogeneity, primarily located in the multimodal association cortex, tend to express genes with higher evolutionary rates and exhibit a higher degree of functional connectivity measured by resting-state fMRI, implying that such a spatial distribution of gene expression may be shaped by evolution and is favourable for the specialization of higher cognitive functions. Together, the cross-species imaging and genetic findings may provide convergent evidence to support the association between the orderly topography of brain function networks and gene expression.

Comparative analysis of human, macaque and mouse function and genetic heterogeneity in the brain reveals links between gene expression and orderly topography of functional networks.

Benchmarking functional connectivity by the structure and geometry of the human brain

The brain's structural connectivity supports the propagation of electrical impulses, manifesting as patterns of coactivation, termed functional connectivity. Functional connectivity emerges from the underlying sparse structural connections, particularly through polysynaptic communication. As a result, functional connections between brain regions without direct structural links are numerous, but their organization is not completely understood. Here we investigate the organization of functional connections without direct structural links. We develop a simple, data-driven method to benchmark functional connections with respect to their underlying structural and geometric embedding. We then use this method to reweigh and reexpress functional connectivity. We find evidence of unexpectedly strong functional connectivity among distal brain regions and within the default mode network. We also find unexpectedly strong functional connectivity at the apex of the unimodal-transmodal hierarchy. Our results suggest that both phenomena-functional modules and functional hierarchies-emerge from functional interactions that transcend the underlying structure and geometry. These findings also potentially explain recent reports that structural and functional connectivity gradually diverge in transmodal cortex. Collectively, we show how structural connectivity and geometry can be used as a natural frame of reference with which to study functional connectivity patterns in the brain.

Structural-Functional Connectivity Bandwidth of the Human Brain

BACKGROUND

The human brain is a complex network that seamlessly manifests behaviour and cognition. This network comprises neurons that directly, or indirectly mediate communication between brain regions. Here, we show how multilayer/multiplex network analysis provides a suitable framework to uncover the throughput of structural connectivity (SC) to mediate information transfer-giving rise to functional connectivity (FC).

METHOD

We implemented a novel method to reconcile SC and FC using diffusion and resting-state functional MRI connectivity data from 484 subjects (272 females, 212 males; age = 29.15 ± 3.47) from the Human Connectome Project. First, we counted the number of direct and indirect structural paths that mediate FC. FC nodes with indirect SC paths were then weighted according to their least restrictive SC path. We refer to this as SC-FC Bandwidth. We then mapped paths with the highest SC-FC Bandwidth across 7 canonical resting-state networks.

FINDINGS

We found that most pairs of FC nodes were connected by SC paths of length two and three (SC paths of length >5 were virtually non-existent). Direct SC-FC connections accounted for only 10% of all SC-FC connections. The majority of FC nodes without a direct SC path were mediated by a proportion of two (44%) or three SC path lengths (39%). Only a small proportion of FC nodes were mediated by SC path lengths of four (5%). We found high-bandwidth direct SC-FC connections show dense intra- and sparse inter-network connectivity, with a bilateral, anteroposterior distribution. High bandwidth SC-FC triangles have a right superomedial distribution within the somatomotor network. High-bandwidth SC-FC quads have a superoposterior distribution within the default mode network.

CONCLUSION

Our method allows the measurement of indirect SC-FC using undirected, weighted graphs derived from multimodal MRI data in order to map the location and throughput of SC to mediate FC. An extension of this work may be to explore how SC-FC Bandwidth changes over time, relates to cognition/behavior, and if this measure reflects a marker of neurological injury or psychiatric disorders.

Percolation may explain efficiency, robustness, and economy of the brain

The brain consists of billions of neurons connected by ultra-dense synapses, showing remarkable efficiency, robust flexibility, and economy in information processing. It is generally believed that these advantageous properties are rooted in brain connectivity; however, direct evidence remains absent owing to technical limitations or theoretical vacancy. This research explores the origins of these properties in the largest yet brain connectome of the fruit fly. We reveal that functional connectivity formation in the brain can be explained by a percolation process controlled by synaptic excitation-inhibition (E/I) balance. By increasing the E/I balance gradually, we discover the emergence of these properties as byproducts of percolation transition when the E/I balance arrives at 3:7. As the E/I balance keeps increase, an optimal E/I balance 1:1 is unveiled to ensure these three properties simultaneously, consistent with previous in vitro experimental predictions. Once the E/I balance reaches over 3:2, an intrinsic limitation of these properties determined by static (anatomical) brain connectivity can be observed. Our work demonstrates that percolation, a universal characterization of critical phenomena and phase transitions, may serve as a window toward understanding the emergence of various brain properties.

Time-resolved structure-function coupling in brain networks

The relationship between structural and functional connectivity in the brain is a key question in systems neuroscience. Modern accounts assume a single global structure-function relationship that persists over time. Here we study structure-function coupling from a dynamic perspective, and show that it is regionally heterogeneous. We use a temporal unwrapping procedure to identify moment-to-moment co-fluctuations in neural activity, and reconstruct time-resolved structure-function coupling patterns. We find that patterns of dynamic structure-function coupling are region-specific. We observe stable coupling in unimodal and transmodal cortex, and dynamic coupling in intermediate regions, particularly in insular cortex (salience network) and frontal eye fields (dorsal attention network). Finally, we show that the variability of a region’s structure-function coupling is related to the distribution of its connection lengths. Collectively, our findings provide a way to study structure-function relationships from a dynamic perspective.

Temporal unwrapping analysis of diffusion weighted MRI connectivity and functional MRI scans reveals that the coupling between structure and function in the human brain is regionally heterogeneous and provides a framework to evaluate these relationships from a dynamic perspective.

Null models in network neuroscience

Recent advances in imaging and tracing technology provide increasingly detailed reconstructions of brain connectomes. Concomitant analytic advances enable rigorous identification and quantification of functionally important features of brain network architecture. Null models are a flexible tool to statistically benchmark the presence or magnitude of features of interest, by selectively preserving specific architectural properties of brain networks while systematically randomizing others. Here we describe the logic, implementation and interpretation of null models of connectomes. We introduce randomization and generative approaches to constructing null networks, and outline a taxonomy of network methods for statistical inference. We highlight the spectrum of null models - from liberal models that control few network properties, to conservative models that recapitulate multiple properties of empirical networks - that allow us to operationalize and test detailed hypotheses about the structure and function of brain networks. We review emerging scenarios for the application of null models in network neuroscience, including for spatially embedded networks, annotated networks and correlation-derived networks. Finally, we consider the limits of null models, as well as outstanding questions for the field.

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.

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.

A dynamic graph convolutional neural network framework reveals new insights into connectome dysfunctions in ADHD

The pathological mechanism of attention deficit hyperactivity disorder (ADHD) is incompletely specified, which leads to difficulty in precise diagnosis. Functional magnetic resonance imaging (fMRI) has emerged as a common neuroimaging technique for studying the brain functional connectome. Most existing methods that have either ignored or simply utilized graph structure, do not fully leverage the potentially important topological information which may be useful in characterizing brain disorders. There is a crucial need for designing novel and efficient approaches which can capture such information. To this end, we propose a new dynamic graph convolutional network (dGCN), which is trained with sparse brain regional connections from dynamically calculated graph features. We also develop a novel convolutional readout layer to improve graph representation. Our extensive experimental analysis demonstrates significantly improved performance of dGCN for ADHD diagnosis compared with existing machine learning and deep learning methods. Visualizations of the salient regions of interest (ROIs) and connectivity based on informative features learned by our model show that the identified functional abnormalities mainly involve brain regions in temporal pole, gyrus rectus, and cerebellar gyri from temporal lobe, frontal lobe, and cerebellum, respectively. A positive correlation was further observed between the identified connectomic abnormalities and ADHD symptom severity. The proposed dGCN model shows great promise in providing a functional network-based precision diagnosis of ADHD and is also broadly applicable to brain connectome-based study of mental disorders.

Edges in brain networks: Contributions to models of structure and function

Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized functional contributions of network nodes. Importantly, these functional contributions are determined and expressed by the web of their interrelationships, formed by network edges. Here, we underscore the important contributions made by brain network edges for understanding distributed brain organization. Different types of edges represent different types of relationships, including connectivity and similarity among nodes. Adopting a specific definition of edges can fundamentally alter how we analyze and interpret a brain network. Furthermore, edges can associate into collectives and higher order arrangements, describe time series, and form edge communities that provide insights into brain network topology complementary to the traditional node-centric perspective. Focusing on the edges, and the higher order or dynamic information they can provide, discloses previously underappreciated aspects of structural and functional network organization.

Functional Complex Networks Based on Operational Architectonics: Application on Electroencephalography-Brain-computer Interface for Imagined Speech

A new method for analyzing brain complex dynamics and states is presented. This method constructs functional brain graphs and is comprised of two pylons: (a) Operational architectonics (OA) concept of brain and mind functioning. (b) Network neuroscience. In particular, the algorithm utilizes OA framework for a non-parametric segmentation of EEGs, which leads to the identification of change points, namely abrupt jumps in EEG amplitude, called Rapid Transition Processes (RTPs). Subsequently, the time coordinates of RTPs are used for the generation of undirected weighted complex networks fulfilling a scale-free topology criterion, from which various network metrics of brain connectivity are estimated. These metrics form feature vectors, which can be used in machine learning algorithms for classification and/or prediction. The method is tested in classification problems on an EEG-based BCI data set, acquired from individuals during imagery pronunciation tasks of various words/vowels. The classification results, based on a Naïve Bayes classifier, show that the overall accuracies were found to be above chance level in all tested cases. This method was also compared with other state-of-the-art computational approaches commonly used for functional network generation, exhibiting competitive performance. The method can be useful to neuroscientists wishing to enhance their repository of brain research algorithms.

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.

Sub-optimal modulation of gain by the cognitive control system in young adults with early psychosis

Executive dysfunctions in early psychosis (EP) are subtle but persistent, hindering recovery. We asked whether changes in the cognitive control system (CCS) disrupt the response to increased cognitive load in persons with EP. In all, 30 EP and 30 control participants undertook multimodal MRI. Computational models of structural and effective connectivity amongst regions in the CCS were informed by cortical responses to the multi-source interference task, a paradigm that selectively introduces stimulus conflict. EP participants showed greater activation of CCS regions, including the superior parietal cortex, and were disproportionately slower at resolving stimulus conflict in the task. Computational models of the effective connectivity underlying this behavioral response suggest that the normative (control) group resolved stimulus conflict through an efficient and direct modulation of gain between the visual cortex and the anterior insula (AI). In contrast, the EP group utilized an indirect path, with parallel and multi-region hops to resolve stimulus conflict at the AI. Individual differences in task performance were dependent on initial linear gain modulations in the EP group versus a single nonlinear modulation in the control group. Effective connectivity in the EP group was associated with reduced structural integration amongst those connections critical for task execution. CCS engagement during stimulus conflict is hampered in EP owing to inefficient use of higher-order network interactions, with high tonic gain impeding task-relevant (phasic) signal amplification.

Toward an information theoretical description of communication in brain networks

Modeling communication dynamics in the brain is a key challenge in network neuroscience. We present here a framework that combines two measurements for any system where different communication processes are taking place on top of a fixed structural topology: path processing score (PPS) estimates how much the brain signal has changed or has been transformed between any two brain regions (source and target); path broadcasting strength (PBS) estimates the propagation of the signal through edges adjacent to the path being assessed. We use PPS and PBS to explore communication dynamics in large-scale brain networks. We show that brain communication dynamics can be divided into three main "communication regimes" of information transfer: absent communication (no communication happening); relay communication (information is being transferred almost intact); and transducted communication (the information is being transformed). We use PBS to categorize brain regions based on the way they broadcast information. Subcortical regions are mainly direct broadcasters to multiple receivers; Temporal and frontal nodes mainly operate as broadcast relay brain stations; visual and somatomotor cortices act as multichannel transducted broadcasters. This work paves the way toward the field of brain network information theory by providing a principled methodology to explore communication dynamics in large-scale brain networks.

Persistence of information flow: A multiscale characterization of human brain

Information exchange in the human brain is crucial for vital tasks and to drive diseases. Neuroimaging techniques allow for the indirect measurement of information flows among brain areas and, consequently, for reconstructing connectomes analyzed through the lens of network science. However, standard analyses usually focus on a small set of network indicators and their joint probability distribution. Here, we propose an information-theoretic approach for the analysis of synthetic brain networks (based on generative models) and empirical brain networks, and to assess connectome's information capacity at different stages of dementia. Remarkably, our framework accounts for the whole network state, overcoming limitations due to limited sets of descriptors, and is used to probe human connectomes at different scales. We find that the spectral entropy of empirical data lies between two generative models, indicating an interpolation between modular and geometry-driven structural features. In fact, we show that the mesoscale is suitable for characterizing the differences between brain networks and their generative models. Finally, from the analysis of connectomes obtained from healthy and unhealthy subjects, we demonstrate that significant differences between healthy individuals and the ones affected by Alzheimer's disease arise at the microscale (max. posterior probability smaller than 1%) and at the mesoscale (max. posterior probability smaller than 10%).

Dissecting whole-brain conduction delays through MRI microstructural measures

Network models based on structural connectivity have been increasingly used as the blueprint for large-scale simulations of the human brain. As the nodes of this network are distributed through the cortex and interconnected by white matter pathways with different characteristics, modeling the associated conduction delays becomes important. The goal of this study is to estimate and characterize these delays directly from the brain structure. To achieve this, we leveraged microstructural measures from a combination of advanced magnetic resonance imaging acquisitions and computed the main determinants of conduction velocity, namely axonal diameter and myelin content. Using the model proposed by Rushton, we used these measures to calculate the conduction velocity and estimated the associated delays using tractography. We observed that both the axonal diameter and conduction velocity distributions presented a rather constant trend across different connection lengths, with resulting delays that scale linearly with the connection length. Relying on insights from graph theory and Kuramoto simulations, our results support the approximation of constant conduction velocity but also show path- and region-specific differences.

The structural connectome constrains fast brain dynamics

Brain activity during rest displays complex, rapidly evolving patterns in space and time. Structural connections comprising the human connectome are hypothesized to impose constraints on the dynamics of this activity. Here, we use magnetoencephalography (MEG) to quantify the extent to which fast neural dynamics in the human brain are constrained by structural connections inferred from diffusion MRI tractography. We characterize the spatio-temporal unfolding of whole-brain activity at the millisecond scale from source-reconstructed MEG data, estimating the probability that any two brain regions will significantly deviate from baseline activity in consecutive time epochs. We find that the structural connectome relates to, and likely affects, the rapid spreading of neuronal avalanches, evidenced by a significant association between these transition probabilities and structural connectivity strengths (r = 0.37, p<0.0001). This finding opens new avenues to study the relationship between brain structure and neural dynamics.