Weighted Stochastic Block Models of the Human Connectome across the Life Span

Hierarchical communities in the larval Drosophila connectome: Links to cellular annotations and network topology

One of the longstanding aims of network neuroscience is to link a connectome's topological properties-i.e., features defined from connectivity alone-with an organism's neurobiology. One approach for doing so is to compare connectome properties with annotational maps. This type of analysis is popular at the meso-/macroscale, but is less common at the nano-scale, owing to a paucity of neuron-level connectome data. However, recent methodological advances have made possible the reconstruction of whole-brain connectomes at single-neuron resolution for a select set of organisms. These include the fruit fly, Drosophila melanogaster, and its developing larvae. In addition to fine-scale descriptions of connectivity, these datasets are accompanied by rich annotations. Here, we use a variant of the stochastic blockmodel to detect multilevel communities in the larval Drosophila connectome. We find that communities partition neurons based on function and cell type and that most interact assortatively, reflecting the principle of functional segregation. However, a small number of communities interact nonassortatively, forming form a "rich-club" of interneurons that receive sensory/ascending inputs and deliver outputs along descending pathways. Next, we investigate the role of community structure in shaping communication patterns. We find that polysynaptic signaling follows specific trajectories across modular hierarchies, with interneurons playing a key role in mediating communication routes between modules and hierarchical scales. Our work suggests a relationship between system-level architecture and the biological function and classification of individual neurons. We envision our study as an important step toward bridging the gap between complex systems and neurobiological lines of investigation in brain sciences.

Functional network modules overlap and are linked to interindividual connectome differences during human brain development

The modular structure of functional connectomes in the human brain undergoes substantial reorganization during development. However, previous studies have implicitly assumed that each region participates in one single module, ignoring the potential spatial overlap between modules. How the overlapping functional modules develop and whether this development is related to gray and white matter features remain unknown. Using longitudinal multimodal structural, functional, and diffusion MRI data from 305 children (aged 6 to 14 years), we investigated the maturation of overlapping modules of functional networks and further revealed their structural associations. An edge-centric network model was used to identify the overlapping modules, and the nodal overlap in module affiliations was quantified using the entropy measure. We showed a regionally heterogeneous spatial topography of the overlapping extent of brain nodes in module affiliations in children, with higher entropy (i.e., more module involvement) in the ventral attention, somatomotor, and subcortical regions and lower entropy (i.e., less module involvement) in the visual and default-mode regions. The overlapping modules developed in a linear, spatially dissociable manner, with decreased entropy (i.e., decreased module involvement) in the dorsomedial prefrontal cortex, ventral prefrontal cortex, and putamen and increased entropy (i.e., increased module involvement) in the parietal lobules and lateral prefrontal cortex. The overlapping modular patterns captured individual brain maturity as characterized by chronological age and were predicted by integrating gray matter morphology and white matter microstructural properties. Our findings highlight the maturation of overlapping functional modules and their structural substrates, thereby advancing our understanding of the principles of connectome development.

Evolving brain network dynamics in early childhood: Insights from modular graph metrics

Modular dynamic graph theory metrics effectively capture the patterns of dynamic information interaction during human brain development. While existing research has employed modular algorithms to examine the overall impact of dynamic changes in community structure throughout development, there is a notable gap in understanding the cross-community dynamic changes within different functional networks during early childhood and their potential contributions to the efficiency of brain information transmission. This study seeks to address this gap by tracing the trajectories of cross-community structural changes within early childhood functional networks and modeling their contributions to information transmission efficiency. We analyzed 194 functional imaging scans from 83 children aged 2 to 8 years, who participated in passive viewing functional magnetic resonance imaging sessions. Utilizing sliding windows and modular algorithms, we evaluated three spatiotemporal metrics-temporal flexibility, spatiotemporal diversity, and within-community spatiotemporal diversity-and four centrality metrics: within-community degree centrality, eigenvector centrality, between-community degree centrality, and between-community eigenvector centrality. Mixed-effects linear models revealed significant age-related increases in the temporal flexibility of the default mode network (DMN), executive control network (ECN), and salience network (SN), indicating frequent adjustments in community structure within these networks during early childhood. Additionally, the spatiotemporal diversity of the SN also displayed significant age-related increases, highlighting its broad pattern of cross-community dynamic interactions. Conversely, within-community spatiotemporal diversity in the language network exhibited significant age-related decreases, reflecting the network's gradual functional specialization. Furthermore, our findings indicated significant age-related increases in between-community degree centrality across the DMN, ECN, SN, language network, and dorsal attention network, while between-community eigenvector centrality also increased significantly for the DMN, ECN, and SN. However, within-community eigenvector centrality remained stable across all functional networks during early childhood. These results suggest that while centrality of cross-community interactions in early childhood functional networks increases, centrality within communities remains stable. Finally, mediation analysis was conducted to explore the relationships between age, brain dynamic graph metrics, and both global and local efficiency based on community structure. The results indicated that the dynamic graph metrics of the SN primarily mediated the relationship between age and the decrease in global efficiency, while those of the DMN, language network, ECN, dorsal attention network, and SN primarily mediated the relationship between age and the increase in local efficiency. This pattern suggests a developmental trajectory in early childhood from global information integration to local information segregation, with the SN playing a pivotal role in this transformation. This study provides novel insights into the mechanisms by which early childhood brain functional development impacts information transmission efficiency through cross-community adjustments in functional networks.

A principled framework to assess the information-theoretic fitness of brain functional sub-circuits

In systems and network neuroscience, many common practices in brain connectomic analysis are often not properly scrutinized. One such practice is mapping a predetermined set of sub-circuits, like functional networks (FNs), onto subjects' functional connectomes (FCs) without adequately assessing the information-theoretic appropriateness of the partition. Another practice that goes unchallenged is thresholding weighted FCs to remove spurious connections without justifying the chosen threshold. This paper leverages recent theoretical advances in Stochastic Block Models (SBMs) to formally define and quantify the information-theoretic fitness (e.g., prominence) of a predetermined set of FNs when mapped to individual FCs under different fMRI task conditions. Our framework allows for evaluating any combination of FC granularity, FN partition, and thresholding strategy, thereby optimizing these choices to preserve important topological features of the human brain connectomes. By applying to the Human Connectome Project with Schaefer parcellations at multiple levels of granularity, the framework showed that the common thresholding value of 0.25 was indeed information-theoretically valid for group-average FCs despite its previous lack of justification. Our results pave the way for the proper use of FNs and thresholding methods and provide insights for future research in individualized parcellations.

A generative model of the connectome with dynamic axon growth

Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization - axonal growth. Emulating the chemoaffinity guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective.

Relation of connectome topology to brain volume across 103 mammalian species

The brain connectome is an embedded network of anatomically interconnected brain regions, and the study of its topological organization in mammals has become of paramount importance due to its role in scaffolding brain function and behavior. Unlike many other observable networks, brain connections incur material and energetic cost, and their length and density are volumetrically constrained by the skull. Thus, an open question is how differences in brain volume impact connectome topology. We address this issue using the MaMI database, a diverse set of mammalian connectomes reconstructed from 201 animals, covering 103 species and 12 taxonomy orders, whose brain size varies over more than 4 orders of magnitude. Our analyses focus on relationships between volume and modular organization. After having identified modules through a multiresolution approach, we observed how connectivity features relate to the modular structure and how these relations vary across brain volume. We found that as the brain volume increases, modules become more spatially compact and dense, comprising more costly connections. Furthermore, we investigated how spatial embedding shapes network communication, finding that as brain volume increases, nodes' distance progressively impacts communication efficiency. We identified modes of variation in network communication policies, as smaller and bigger brains show higher efficiency in routing- and diffusion-based signaling, respectively. Finally, bridging network modularity and communication, we found that in larger brains, modular structure imposes stronger constraints on network signaling. Altogether, our results show that brain volume is systematically related to mammalian connectome topology and that spatial embedding imposes tighter restrictions on larger brains.

Cortical timescales and the modular organization of structural and functional brain networks

Recent years have seen growing interest in characterizing the properties of regional brain dynamics and their relationship to other features of brain structure and function. In particular, multiple studies have observed regional differences in the "timescale" over which activity fluctuates during periods of quiet rest. In the cerebral cortex, these timescales have been associated with both local circuit properties as well as patterns of inter-regional connectivity, including the extent to which each region exhibits widespread connectivity to other brain areas. In the current study, we build on prior observations of an association between connectivity and dynamics in the cerebral cortex by investigating the relationship between BOLD fMRI timescales and the modular organization of structural and functional brain networks. We characterize network community structure across multiple scales and find that longer timescales are associated with greater within-community functional connectivity and diverse structural connectivity. We also replicate prior observations of a positive correlation between timescales and structural connectivity degree. Finally, we find evidence for preferential functional connectivity between cortical areas with similar timescales. We replicate these findings in an independent dataset. These results contribute to our understanding of functional brain organization and structure-function relationships in the human brain, and support the notion that regional differences in cortical dynamics may in part reflect the topological role of each region within macroscale brain networks.

Aberrant Functional Connectivity in Core-Periphery Structure Based on WSBM in ADHD

OBJECTIVE

Brain network studies have revealed that the community structure of ADHD is altered. However, these studies have only focused on modular community structure, ignoring the core-periphery community structure.

METHOD

This paper employed the weighted stochastic block model to divide the functional connectivity (FC) into 10 communities. And we adopted core score to define the core-periphery structure of FC. Finally, connectivity strength (CS) and disruption index (DI) were used to evaluate the changes of core-periphery structure in ADHD.

RESULTS

The core community of visual network showed reduced CS and a positive value of DI, while the CS of periphery community was enhanced. In addition, the interaction between core communities (involving the sensorimotor and visual network) and periphery community of attention network showed increased CS and a negative valve of DI.

CONCLUSION

Anomalies in core-periphery community structure provide a new perspective for understanding the community structure of ADHD.

Characterizing upper extremity fine motor function in the presence of white matter hyperintensities: A 7 T MRI cross-sectional study in older adults

BACKGROUND

White matter hyperintensities (WMH) are a prevalent radiographic finding in the aging brain studies. Research on WMH association with motor impairment is mostly focused on the lower-extremity function and further investigation on the upper-extremity is needed. How different degrees of WMH burden impact the network of activation recruited during upper limb motor performance could provide further insight on the complex mechanisms of WMH pathophysiology and its interaction with aging and neurological disease processes.

METHODS

40 healthy elderly subjects without a neurological/psychiatric diagnosis were included in the study (16F, mean age 69.3 years). All subjects underwent ultra-high field 7 T MRI including structural and finger tapping task-fMRI. First, we quantified the WMH lesion load and its spatial distribution. Secondly, we performed a data-driven stratification of the subjects according to their periventricular and deep WMH burdens. Thirdly, we investigated the distribution of neural recruitment and the corresponding activity assessed through BOLD signal changes among different brain regions for groups of subjects. We clustered the degree of WMH based on location, numbers, and volume into three categories; ranging from mild, moderate, and severe. Finally, we explored how the spatial distribution of WMH, and activity elicited during task-fMRI relate to motor function, measured with the 9-Hole Peg Test.

RESULTS

Within our population, we found three subgroups of subjects, partitioned according to their periventricular and deep WMH lesion load. We found decreased activity in several frontal and cingulate cortex areas in subjects with a severe WMH burden. No statistically significant associations were found when performing the brain-behavior statistical analysis for structural or functional data.

CONCLUSION

WMH burden has an effect on brain activity during fine motor control and the activity changes are associated with varying degrees of the total burden and distributions of WMH lesions. Collectively, our results shed new light on the potential impact of WMH on motor function in the context of aging and neurodegeneration.

Brain tumour genetic network signatures of survival

Tumour heterogeneity is increasingly recognized as a major obstacle to therapeutic success across neuro-oncology. Gliomas are characterized by distinct combinations of genetic and epigenetic alterations, resulting in complex interactions across multiple molecular pathways. Predicting disease evolution and prescribing individually optimal treatment requires statistical models complex enough to capture the intricate (epi)genetic structure underpinning oncogenesis. Here, we formalize this task as the inference of distinct patterns of connectivity within hierarchical latent representations of genetic networks. Evaluating multi-institutional clinical, genetic and outcome data from 4023 glioma patients over 14 years, across 12 countries, we employ Bayesian generative stochastic block modelling to reveal a hierarchical network structure of tumour genetics spanning molecularly confirmed glioblastoma, IDH-wildtype; oligodendroglioma, IDH-mutant and 1p/19q codeleted; and astrocytoma, IDH-mutant. Our findings illuminate the complex dependence between features across the genetic landscape of brain tumours and show that generative network models reveal distinct signatures of survival with better prognostic fidelity than current gold standard diagnostic categories.

Statistical models of complex brain networks: a maximum entropy approach

The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying network structure is crucial to understand the brain functioning under both healthy and pathological conditions. Yet, analyzing brain networks is challenging, in part because their structure represents only one possible realization of a generative stochastic process which is in general unknown. Having a formal way to cope with such intrinsic variability is therefore central for the characterization of brain network properties. Addressing this issue entails the development of appropriate tools mostly adapted from network science and statistics. Here, we focus on a particular class of maximum entropy models for networks, i.e. exponential random graph models, as a parsimonious approach to identify the local connection mechanisms behind observed global network structure. Efforts are reviewed on the quest for basic organizational properties of human brain networks, as well as on the identification of predictive biomarkers of neurological diseases such as stroke. We conclude with a discussion on how emerging results and tools from statistical graph modeling, associated with forthcoming improvements in experimental data acquisition, could lead to a finer probabilistic description of complex systems in network neuroscience.

Cortical timescales and the modular organization of structural and functional brain networks

Recent years have seen growing interest in characterizing the properties of regional brain dynamics and their relationship to other features of brain structure and function. In particular, multiple studies have observed regional differences in the "timescale" over which activity fluctuates during periods of quiet rest. In the cerebral cortex, these timescales have been associated with both local circuit properties as well as patterns of inter-regional connectivity, including the extent to which each region exhibits widespread connectivity to other brain areas. In the current study, we build on prior observations of an association between connectivity and dynamics in the cerebral cortex by investigating the relationship between BOLD fMRI timescales and the modular organization of structural and functional brain networks. We characterize network community structure across multiple scales and find that longer timescales are associated with greater within-community functional connectivity and diverse structural connectivity. We also replicate prior observations of a positive correlation between timescales and structural connectivity degree. Finally, we find evidence for preferential functional connectivity between cortical areas with similar timescales. We replicate these findings in an independent dataset. These results contribute to our understanding of functional brain organization and structure-function relationships in the human brain, and support the notion that regional differences in cortical dynamics may in part reflect the topological role of each region within macroscale brain networks.

Dynamic rewiring of electrophysiological brain networks during learning

Human learning is an active and complex process. However, the brain mechanisms underlying human skill learning and the effect of learning on the communication between brain regions, at different frequency bands, are still largely unknown. Here, we tracked changes in large-scale electrophysiological networks over a 6-week training period during which participants practiced a series of motor sequences during 30 home training sessions. Our findings showed that brain networks become more flexible with learning in all the frequency bands from theta to gamma ranges. We found consistent increase of flexibility in the prefrontal and limbic areas in the theta and alpha band, and over somatomotor and visual areas in the alpha band. Specific to the beta rhythm, we revealed that higher flexibility of prefrontal regions during the early stage of learning strongly correlated with better performance measured during home training sessions. Our findings provide novel evidence that prolonged motor skill practice results in higher, frequency-specific, temporal variability in brain network structure.

GENERATIVE MODELS FOR LARGE-SCALE SIMULATIONS OF CONNECTOME DEVELOPMENT

Functional interactions and anatomic connections between brain regions form the connectome. Its mathematical representation in terms of a graph reflects the inherent neuroanatomical organization into structures and regions (nodes) that are interconnected through neural fiber tracts and/or interact functionally (edges). Without knowledge of the ground truth topology of the connectome, functional (directional or nondirectional) graphs represent estimates of signal correlations, from which underlying mechanisms and processes, such as development and aging, or neuropathologies, are difficult to unravel. Biologically meaningful simulations using synthetic graphs with controllable parameters can complement real data analyses and provide critical insights into mechanisms underlying the organization of the connectome. Generative models can be highly valuable tools for creating large datasets of synthetic graphs with known topological characteristics. However, for these graphs to be meaningful, the variation of model parameters needs to be driven by real data. This paper presents a novel, data-driven approach for tuning the parameters of the generative Lancichinetti-Fortunato-Radicchi (LFR) model, using a large dataset of connectomes (n = 5566) estimated from resting-state fMRI from early adolescents in the historically large Adolescent Brain Cognitive Development Study (ABCD). It also presents an application, i.e., simulations using the LFR, to generate large datasets of synthetic graphs representing brains at different stages of neural maturation, and gain insights into developmental changes in their topological organization.

Connectome topology of mammalian brains and its relationship to taxonomy and phylogeny

Network models of anatomical connections allow for the extraction of quantitative features describing brain organization, and their comparison across brains from different species. Such comparisons can inform our understanding of between-species differences in brain architecture and can be compared to existing taxonomies and phylogenies. Here we performed a quantitative comparative analysis using the MaMI database (Tel Aviv University), a collection of brain networks reconstructed from ex vivo diffusion MRI spanning 125 species and 12 taxonomic orders or superorders. We used a broad range of metrics to measure between-mammal distances and compare these estimates to the separation of species as derived from taxonomy and phylogeny. We found that within-taxonomy order network distances are significantly closer than between-taxonomy network distances, and this relation holds for several measures of network distance. Furthermore, to estimate the evolutionary divergence between species, we obtained phylogenetic distances across 10,000 plausible phylogenetic trees. The anatomical network distances were rank-correlated with phylogenetic distances 10,000 times, creating a distribution of coefficients that demonstrate significantly positive correlations between network and phylogenetic distances. Collectively, these analyses demonstrate species-level organization across scales and informational sources: we relate brain networks distances, derived from MRI, with evolutionary distances, derived from genotyping data.

Graph lesion-deficit mapping of fluid intelligence

Fluid intelligence is arguably the defining feature of human cognition. Yet the nature of its relationship with the brain remains a contentious topic. Influential proposals drawing primarily on functional imaging data have implicated 'multiple demand' frontoparietal and more widely distributed cortical networks, but extant lesion-deficit studies with greater causal power are almost all small, methodologically constrained, and inconclusive. The task demands large samples of patients, comprehensive investigation of performance, fine-grained anatomical mapping, and robust lesion-deficit inference, yet to be brought to bear on it. We assessed 165 healthy controls and 227 frontal or non-frontal patients with unilateral brain lesions on the best-established test of fluid intelligence, Raven's Advanced Progressive Matrices, employing an array of lesion-deficit inferential models responsive to the potentially distributed nature of fluid intelligence. Non-parametric Bayesian stochastic block models were used to reveal the community structure of lesion deficit networks, disentangling functional from confounding pathological distributed effects. Impaired performance was confined to patients with frontal lesions [F(2,387) = 18.491; P < 0.001; frontal worse than non-frontal and healthy participants P < 0.01, P <0.001], more marked on the right than left [F(4,385) = 12.237; P < 0.001; right worse than left and healthy participants P < 0.01, P < 0.001]. Patients with non-frontal lesions were indistinguishable from controls and showed no modulation by laterality. Neither the presence nor the extent of multiple demand network involvement affected performance. Both conventional network-based statistics and non-parametric Bayesian stochastic block modelling heavily implicated the right frontal lobe. Crucially, this localization was confirmed on explicitly disentangling functional from pathology-driven effects within a layered stochastic block model, prominently highlighting a right frontal network involving middle and inferior frontal gyrus, pre- and post-central gyri, with a weak contribution from right superior parietal lobule. Similar results were obtained with standard lesion-deficit analyses. Our study represents the first large-scale investigation of the distributed neural substrates of fluid intelligence in the focally injured brain. Combining novel graph-based lesion-deficit mapping with detailed investigation of cognitive performance in a large sample of patients provides crucial information about the neural basis of intelligence. Our findings indicate that a set of predominantly right frontal regions, rather than a more widely distributed network, is critical to the high-level functions involved in fluid intelligence. Further they suggest that Raven's Advanced Progressive Matrices is a useful clinical index of fluid intelligence and a sensitive marker of right frontal lobe dysfunction.

Multi-modal and multi-subject modular organization of human brain networks

The human brain is a complex network of anatomically interconnected brain areas. Spontaneous neural activity is constrained by this architecture, giving rise to patterns of statistical dependencies between the activity of remote neural elements. The non-trivial relationship between structural and functional connectivity poses many unsolved challenges about cognition, disease, development, learning and aging. While numerous studies have focused on statistical relationships between edge weights in anatomical and functional networks, less is known about dependencies between their modules and communities. In this work, we investigate and characterize the relationship between anatomical and functional modular organization of the human brain, developing a novel multi-layer framework that expands the classical concept of multi-layer modularity. By simultaneously mapping anatomical and functional networks estimated from different subjects into communities, this approach allows us to carry out a multi-subject and multi-modal analysis of the brain's modular organization. Here, we investigate the relationship between anatomical and functional modules during resting state, finding unique and shared structures. The proposed framework constitutes a methodological advance in the context of multi-layer network analysis and paves the way to further investigate the relationship between structural and functional network organization in clinical cohorts, during cognitively demanding tasks, and in developmental or lifespan studies.

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.

Hyperbolic disc embedding of functional human brain connectomes using resting-state fMRI

The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging, we constructed a scale-free binary graph for each subject, using internodal time series correlation of regions of interest as a proximity measure. The resulting network could be embedded onto manifolds of various curvatures and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using the 𝕊¹/ℍ² model, we reduced the dimension of the network into two-dimensional hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the hyperbolic discs. Each individual disc revealed relevance with its anatomic counterpart and absence of center-spaced node. Using the hyperbolic distance on the 𝕊¹/ℍ² model, we could detect the anomaly of network in autism spectrum disorder subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale.

Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block–connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer’s patients.

Edge-centric analysis of stroke patients: An alternative approach for biomarkers of lesion recovery

Most neuroimaging studies of post-stroke recovery rely on analyses derived from standard node-centric functional connectivity to map the distributed effects in stroke patients. Here, given the importance of nonlocal and diffuse damage, we use an edge-centric approach to functional connectivity in order to provide an alternative description of the effects of this disorder. These techniques allow for the rendering of metrics such as normalized entropy, which describes the diversity of edge communities at each node. Moreover, the approach enables the identification of high amplitude co-fluctuations in fMRI time series. We found that normalized entropy is associated with stroke lesion severity and continually increases across the time of patients' recovery. Furthermore, high amplitude co-fluctuations not only relate to the lesion severity but are also associated with patients' level of recovery. The current study is the first edge-centric application for a clinical population in a longitudinal dataset and demonstrates how a different perspective for functional data analysis can further characterize topographic modulations of brain dynamics.

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.

Different Approximation Methods for Calculation of Integrated Information Coefficient in the Brain during Instrumental Learning

The amount of integrated information, Φ, proposed in an integrated information theory (IIT) is useful to describe the degree of brain adaptation to the environment. However, its computation cannot be precisely performed for a reasonable time for time-series spike data collected from a large count of neurons.. Therefore, Φ was only used to describe averaged activity of a big group of neurons, and the behavior of small non-brain systems. In this study, we reported on ways for fast and precise Φ calculation using different approximation methods for Φ calculation in neural spike data, and checked the capability of Φ to describe a degree of adaptation in brain neural networks. We show that during instrumental learning sessions, all applied approximation methods reflect temporal trends of Φ in the rat hippocampus. The value of Φ is positively correlated with the number of successful acts performed by a rat. We also show that only one subgroup of neurons modulates their Φ during learning. The obtained results pave the way for application of Φ to investigate plasticity in the brain during the acquisition of new tasks.

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.

Brain Functional Connectivity Asymmetry: Left Hemisphere Is More Modular

Graph-theoretical approaches are increasingly used to study the brain and may enhance our understanding of its asymmetries. In this paper, we hypothesize that the structure of the left hemisphere is, on average, more modular. To this end, we analyzed resting-state functional magnetic resonance imaging data of 90 healthy subjects. We computed functional connectivity by Pearson’s correlation coefficient, turned the matrix into an unweighted graph by keeping a certain percentage of the strongest connections, and quantified modularity separately for the subgraph formed by each hemisphere. Our results show that the left hemisphere is more modular. The result is consistent across a range of binarization thresholds, regardless of whether the two hemispheres are thresholded together or separately. This illustrates that graph-theoretical analysis can provide a robust characterization of lateralization of brain functional connectivity.

The brainstem connectome database

Connectivity data of the nervous system and subdivisions, such as the brainstem, cerebral cortex and subcortical nuclei, are necessary to understand connectional structures, predict effects of connectional disorders and simulate network dynamics. For that purpose, a database was built and analyzed which comprises all known directed and weighted connections within the rat brainstem. A longterm metastudy of original research publications describing tract tracing results form the foundation of the brainstem connectome (BC) database which can be analyzed directly in the framework neuroVIISAS. The BC database can be accessed directly by connectivity tables, a web-based tool and the framework. Analysis of global and local network properties, a motif analysis, and a community analysis of the brainstem connectome provides insight into its network organization. For example, we found that BC is a scale-free network with a small-world connectivity. The Louvain modularity and weighted stochastic block matching resulted in partially matching of functions and connectivity. BC modeling was performed to demonstrate signal propagation through the somatosensory pathway which is affected in Multiple sclerosis.

Measurement(s)	brainstem
Technology Type(s)	tract tracing metastudy
Factor Type(s)	brain region
Sample Characteristic - Organism	Rattus rattus
Sample Characteristic - Environment	Experimental setup
Sample Characteristic - Location	Germany

Structural brain network topological alterations in stuttering adults

Persistent developmental stuttering is a speech disorder that primarily affects normal speech fluency but encompasses a complex set of symptoms ranging from reduced sensorimotor integration to socioemotional challenges. Here, we investigated the whole brain structural connectome and its topological alterations in adults who stutter. Diffusion weighted imaging data of 33 subjects (13 adults who stutter and 20 fluent speakers) was obtained along with a stuttering severity evaluation. The structural brain network properties were analyzed using Network-based statistics and graph theoretical measures particularly focusing on community structure, network hubs and controllability. Bayesian power estimation was used to assess the reliability of the structural connectivity differences by examining the effect size. The analysis revealed reliable and wide-spread decreases in connectivity for adults who stutter in regions associated with sensorimotor, cognitive, emotional, and memory-related functions. The community detection algorithms revealed different subnetworks for fluent speakers and adults who stutter, indicating considerable network adaptation in adults who stutter. Average and modal controllability differed between groups in a subnetwork encompassing frontal brain regions and parts of the basal ganglia.

The results revealed extensive structural network alterations and substantial adaptation in neural architecture in adults who stutter well beyond the sensorimotor network. These findings highlight the impact of the neurodevelopmental effects of persistent stuttering on neural organization and the importance of examining the full structural connectome and the network alterations that underscore the behavioral phenotype.

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.

Modularity maximization as a flexible and generic framework for brain network exploratory analysis

The modular structure of brain networks supports specialized information processing, complex dynamics, and cost-efficient spatial embedding. Inter-individual variation in modular structure has been linked to differences in performance, disease, and development. There exist many data-driven methods for detecting and comparing modular structure, the most popular of which is modularity maximization. Although modularity maximization is a general framework that can be modified and reparamaterized to address domain-specific research questions, its application to neuroscientific datasets has, thus far, been narrow. Here, we highlight several strategies in which the "out-of-the-box" version of modularity maximization can be extended to address questions specific to neuroscience. First, we present approaches for detecting "space-independent" modules and for applying modularity maximization to signed matrices. Next, we show that the modularity maximization frame is well-suited for detecting task- and condition-specific modules. Finally, we highlight the role of multi-layer models in detecting and tracking modules across time, tasks, subjects, and modalities. In summary, modularity maximization is a flexible and general framework that can be adapted to detect modular structure resulting from a wide range of hypotheses. This article highlights multiple frontiers for future research and applications.

Identification of community structure-based brain states and transitions using functional MRI

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Community-based detection of discrete brain states using stochastic latent block model.

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Bayesian change-point detection and model selection via posterior predictive discrepancy.

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Markov chain Monte Carlo methods for estimation of community memberships.

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Distinctive brain states for varying task demands in working memory task fMRI.

Brain function relies on a precisely coordinated and dynamic balance between the functional integration and segregation of distinct networks. Characterizing the way in which brain regions reconfigure their interactions to give rise to distinct but hidden brain states remains an open challenge. In this paper, we propose a Bayesian method for characterizing community structure-based latent brain states and showcase a novel strategy based on posterior predictive discrepancy using the latent block model to detect transitions between community structures in blood oxygen level-dependent (BOLD) time series. The set of estimated parameters in the model includes a latent label vector that assigns network nodes to communities, and also block model parameters that reflect the weighted connectivity within and between communities. Besides extensive in-silico model evaluation, we also provide empirical validation (and replication) using the Human Connectome Project (HCP) dataset of 100 healthy adults. Our results obtained through an analysis of task-fMRI data during working memory performance show appropriate lags between external task demands and change-points between brain states, with distinctive community patterns distinguishing fixation, low-demand and high-demand task conditions.

The diversity and multiplexity of edge communities within and between brain systems

The human brain is composed of functionally specialized systems that support cognition. Recently, we proposed an edge-centric model for detecting overlapping communities. It remains unclear how these communities and brain systems are related. Here, we address this question using data from the Midnight Scan Club and show that all brain systems are linked via at least two edge communities. We then examine the diversity of edge communities within each system, finding that heteromodal systems are more diverse than sensory systems. Next, we cluster the entire cortex to reveal it according to the regions' edge-community profiles. We find that regions in heteromodal systems are more likely to form their own clusters. Finally, we show that edge communities are personalized. Our work reveals the pervasive overlap of edge communities across the cortex and their relationship with brain systems. Our work provides pathways for future research using edge-centric brain networks.

Investigating the spectral features of the brain meso-scale structure at rest

Recent studies provide novel insights into the meso-scale organization of the brain, highlighting the co-occurrence of different structures: classic assortative (modular), disassortative, and core-periphery. However, the spectral properties of the brain meso-scale remain mostly unexplored. To fill this knowledge gap, we investigated how the meso-scale structure is organized across the frequency domain. We analyzed the resting state activity of healthy participants with source-localized high-density electroencephalography signals. Then, we inferred the community structure using weighted stochastic block-model (WSBM) to capture the landscape of meso-scale structures across the frequency domain. We found that different meso-scale modalities co-exist and are diversely organized over the frequency spectrum. Specifically, we found a core-periphery structure dominance, but we also highlighted a selective increase of disassortativity in the low frequency bands (<8 Hz), and of assortativity in the high frequency band (30-50 Hz). We further described other features of the meso-scale organization by identifying those brain regions which, at the same time, (a) exhibited the highest degree of assortativity, disassortativity, and core-peripheriness (i.e., participation) and (b) were consistently assigned to the same community, irrespective from the granularity imposed by WSBM (i.e., granularity-invariance). In conclusion, we observed that the brain spontaneous activity shows frequency-specific meso-scale organization, which may support spatially distributed and local information processing.

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.

Neuronal classification from network connectivity via adjacency spectral embedding

This work presents a novel strategy for classifying neurons, represented by nodes of a directed graph, based on their circuitry (edge connectivity). We assume a stochastic block model (SBM) in which neurons belong together if they connect to neurons of other groups according to the same probability distributions. Following adjacency spectral embedding of the SBM graph, we derive the number of classes and assign each neuron to a class with a Gaussian mixture model-based expectation maximization (EM) clustering algorithm. To improve accuracy, we introduce a simple variation using random hierarchical agglomerative clustering to initialize the EM algorithm and picking the best solution over multiple EM restarts. We test this procedure on a large (≈212-215 neurons), sparse, biologically inspired connectome with eight neuron classes. The simulation results demonstrate that the proposed approach is broadly stable to the choice of embedding dimension, and scales extremely well as the number of neurons in the network increases. Clustering accuracy is robust to variations in model parameters and highly tolerant to simulated experimental noise, achieving perfect classifications with up to 40% of swapped edges. Thus, this approach may be useful to analyze and interpret large-scale brain connectomics data in terms of underlying cellular components.

Connectomes across development reveal principles of brain maturation

An animal's nervous system changes as its body grows from birth to adulthood and its behaviours mature^1-8. The form and extent of circuit remodelling across the connectome is unknown^3,9-15. Here we used serial-section electron microscopy to reconstruct the full brain of eight isogenic Caenorhabditis elegans individuals across postnatal stages to investigate how it changes with age. The overall geometry of the brain is preserved from birth to adulthood, but substantial changes in chemical synaptic connectivity emerge on this consistent scaffold. Comparing connectomes between individuals reveals substantial differences in connectivity that make each brain partly unique. Comparing connectomes across maturation reveals consistent wiring changes between different neurons. These changes alter the strength of existing connections and create new connections. Collective changes in the network alter information processing. During development, the central decision-making circuitry is maintained, whereas sensory and motor pathways substantially remodel. With age, the brain becomes progressively more feedforward and discernibly modular. Thus developmental connectomics reveals principles that underlie brain maturation.

Network-based brain computer interfaces: principles and applications

Brain-computer interfaces (BCIs) make possible to interact with the external environment by decoding the mental intention of individuals. BCIs can therefore be used to address basic neuroscience questions but also to unlock a variety of applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In general, BCI usability critically depends on the ability to comprehensively characterize brain functioning and correctly identify the user's mental state. To this end, much of the efforts have focused on improving the classification algorithms taking into account localized brain activities as input features. Despite considerable improvement BCI performance is still unstable and, as a matter of fact, current features represent oversimplified descriptors of brain functioning. In the last decade, growing evidence has shown that the brain works as a networked system composed of multiple specialized and spatially distributed areas that dynamically integrate information. While more complex, looking at how remote brain regions functionally interact represents a grounded alternative to better describe brain functioning. Thanks to recent advances in network science, i.e. a modern field that draws on graph theory, statistical mechanics, data mining and inferential modelling, scientists have now powerful means to characterize complex brain networks derived from neuroimaging data. Notably, summary features can be extracted from these networks to quantitatively measure specific organizational properties across a variety of topological scales. In this topical review, we aim to provide the state-of-the-art supporting the development of a network theoretic approach as a promising tool for understanding BCIs and improve usability.

Path-dependent connectivity, not modularity, consistently predicts controllability of structural brain networks

The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the communication dynamics that can emerge therefrom is not well understood. In addition to offering insight into the structure-function relationship of networked systems, such an understanding is a critical step toward the ability to manipulate the brain's large-scale dynamical activity in a targeted manner. We investigate the role of community structure in the controllability of structural brain networks. At the region level, we find that certain network measures of community structure are sometimes statistically correlated with measures of linear controllability. However, we then demonstrate that this relationship depends on the distribution of network edge weights. We highlight the complexity of the relationship between community structure and controllability by performing numerical simulations using canonical graph models with varying mesoscale architectures and edge weight distributions. Finally, we demonstrate that weighted subgraph centrality, a measure rooted in the graph spectrum, and which captures higher order graph architecture, is a stronger and more consistent predictor of controllability. Our study contributes to an understanding of how the brain's diverse mesoscale structure supports transient communication dynamics.

Multimodal network dynamics underpinning working memory

Complex human cognition arises from the integrated processing of multiple brain systems. However, little is known about how brain systems and their interactions might relate to, or perhaps even explain, human cognitive capacities. Here, we address this gap in knowledge by proposing a mechanistic framework linking frontoparietal system activity, default mode system activity, and the interactions between them, with individual differences in working memory capacity. We show that working memory performance depends on the strength of functional interactions between the frontoparietal and default mode systems. We find that this strength is modulated by the activation of two newly described brain regions, and demonstrate that the functional role of these systems is underpinned by structural white matter. Broadly, our study presents a holistic account of how regional activity, functional connections, and structural linkages together support integrative processing across brain systems in order for the brain to execute a complex cognitive process.

Temporal fluctuations in the brain's modular architecture during movie-watching

Brain networks are flexible and reconfigure over time to support ongoing cognitive processes. However, tracking statistically meaningful reconfigurations across time has proven difficult. This has to do largely with issues related to sampling variability, making instantaneous estimation of network organization difficult, along with increased reliance on task-free (cognitively unconstrained) experimental paradigms, limiting the ability to interpret the origin of changes in network structure over time. Here, we address these challenges using time-varying network analysis in conjunction with a naturalistic viewing paradigm. Specifically, we developed a measure of inter-subject network similarity and used this measure as a coincidence filter to identify synchronous fluctuations in network organization across individuals. Applied to movie-watching data, we found that periods of high inter-subject similarity coincided with reductions in network modularity and increased connectivity between cognitive systems. In contrast, low inter-subject similarity was associated with increased system segregation and more rest-like architectures. We then used a data-driven approach to uncover clusters of functional connections that follow similar trajectories over time and are more strongly correlated during movie-watching than at rest. Finally, we show that synchronous fluctuations in network architecture over time can be linked to a subset of features in the movie. Our findings link dynamic fluctuations in network integration and segregation to patterns of inter-subject similarity, and suggest that moment-to-moment fluctuations in functional connectivity reflect shared cognitive processing across individuals.

Mapping the community structure of the rat cerebral cortex with weighted stochastic block modeling

The anatomical architecture of the mammalian brain can be modeled as the connectivity between functionally distinct areas of cortex and sub-cortex, which we refer to as the connectome. The community structure of the connectome describes how the network can be parsed into meaningful groups of nodes. This process, called community detection, is commonly carried out to find internally densely connected communities-a modular topology. However, other community structure patterns are possible. Here we employ the weighted stochastic block model (WSBM), which can identify a wide range of topologies, to the rat cerebral cortex connectome, to probe the network for evidence of modular, core, periphery, and disassortative organization. Despite its algorithmic flexibility, the WSBM identifies substantial modular and assortative topology throughout the rat cerebral cortex connectome, significantly aligning to the modular approach in some parts of the network. Significant deviations from modular partitions include the identification of communities that are highly enriched in core (rich club) areas. A comparison of the WSBM and modular models demonstrates that the former, when applied as a generative model, more closely captures several nodal network attributes. An analysis of variation across an ensemble of partitions reveals that certain parts of the network participate in multiple topological regimes. Overall, our findings demonstrate the potential benefits of adopting the WSBM, which can be applied to a single weighted and directed matrix such as the rat cerebral cortex connectome, to identify community structure with a broad definition that transcends the common modular approach.

Co-existence of Network Architectures Supporting the Human Gut Microbiome

Microbial organisms of the human gut microbiome do not exist in isolation but form complex and diverse interactions to maintain health and reduce risk of disease development. The organization of the gut microbiome is assumed to be a singular assortative network, where interactions between operational taxonomic units (OTUs) can readily be clustered into segregated and distinct communities. Here, we leverage recent methodological advances in network modeling to assess whether communities in the human microbiome exhibit a single network structure or whether co-existing mesoscale network architectures are present. We found evidence for core-periphery structures in the microbiome, supported by strong, assortative community interactions. This complex architecture, coupled with previously reported functional roles of OTUs, provides a nuanced understanding of how the microbiome simultaneously promotes high microbial diversity and maintains functional redundancy.

Charting shared developmental trajectories of cortical thickness and structural connectivity in childhood and adolescence

The cortex is organised into broadly hierarchical functional systems with distinct neuroanatomical characteristics reflected by macroscopic measures of cortical morphology. Diffusion-weighted magnetic resonance imaging allows the delineation of areal connectivity, changes to which reflect the ongoing maturation of white matter tracts. These developmental processes are intrinsically linked with timing coincident with the development of cognitive function. In this study, we use a data-driven multivariate approach, nonnegative matrix factorisation, to define cortical regions that co-vary together across a large paediatric cohort (n = 456) and are associated with specific subnetworks of cortical connectivity. We find that age between 3 and 21 years is associated with accelerated cortical thinning in frontoparietal regions, whereas relative thinning of primary motor and sensory regions is slower. Together, the subject-specific weights of the derived set of cortical components can be combined to predict chronological age. Structural connectivity networks reveal a relative increase in strength in connection within, as opposed to between hemispheres that vary in line with cortical changes. We confirm our findings in an independent sample.

The reliability of the isotropic fractionator method for counting total cells and neurons

BACKGROUND

The Isotropic Fractionator (IF) is a method to determine the cellular composition of nervous tissue. It has been mostly applied to assess variation across species, where differences are expected to be large enough not to be masked by methodological error. However, understanding the sources of variation in the method is important if the goal is to detect smaller differences, for example, in same-species comparisons. Comparisons between different mice strains suggest that the IF is consistent enough to detect these differences. Nevertheless, the reliability of the method has not yet been examined directly.

METHOD

In this study, we evaluate the reliability of the method for the determination of cellular and neuronal numbers of Swiss mice. We performed repeated cell counts of the same material by different experimenters to quantify different sources of variation.

RESULTS

In total cell counts, we observed that for the cerebral cortex most of the variance was at the counter level. For the cerebellum, most of the variance is attributed to the sample itself. As for neurons, random error along with the immunostaining correspond to most of the variation, both in the cerebral cortex and in the cerebellum. Test-retest reliability coefficients were relatively high, especially for cell counts.

CONCLUSIONS

Although biases between counters and random variation in staining could be problematic when aggregating data from different sources, we offer practical suggestions to improve the reliability of the method. While small, this study is a most needed step towards more precise measurement of the brain's cellular composition.