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

A multi-modal, asymmetric, weighted, and signed description of anatomical connectivity

The macroscale connectome is the network of physical, white-matter tracts between brain areas. The connections are generally weighted and their values interpreted as measures of communication efficacy. In most applications, weights are either assigned based on imaging features-e.g. diffusion parameters-or inferred using statistical models. In reality, the ground-truth weights are unknown, motivating the exploration of alternative edge weighting schemes. Here, we explore a multi-modal, regression-based model that endows reconstructed fiber tracts with directed and signed weights. We find that the model fits observed data well, outperforming a suite of null models. The estimated weights are subject-specific and highly reliable, even when fit using relatively few training samples, and the networks maintain a number of desirable features. In summary, we offer a simple framework for weighting connectome data, demonstrating both its ease of implementation while benchmarking its utility for typical connectome analyses, including graph theoretic modeling and brain-behavior associations.

Global topological synchronization of weighted simplicial complexes

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so on. Topological signals can undergo collective phenomena such as synchronization, however, only some higher-order network topologies can sustain global synchronization of topological signals. Here we consider global topological synchronization of topological signals on weighted simplicial complexes. We demonstrate that topological signals can globally synchronize on weighted simplicial complexes, even if they are odd-dimensional, e.g., edge signals, thus overcoming a limitation of the unweighted case. These results thus demonstrate that weighted simplicial complexes are more advantageous for observing these collective phenomena than their unweighted counterpart. In particular, we present two weighted simplicial complexes: the weighted triangulated torus and the weighted waffle. We completely characterize their higher-order spectral properties and demonstrate that, under suitable conditions on their weights, they can sustain global synchronization of edge signals. Our results are interpreted geometrically by showing, among the other results, that in some cases edge weights can be associated with the lengths of the sides of curved simplices.

Functional and structural reorganization in brain tumors: a machine learning approach using desynchronized functional oscillations

Neuroimaging studies have allowed for non-invasive mapping of brain networks in brain tumors. Although tumor core and edema are easily identifiable using standard MRI acquisitions, imaging studies often neglect signals, structures, and functions within their presence. Therefore, both functional and diffusion signals, as well as their relationship with global patterns of connectivity reorganization, are poorly understood. Here, we explore the functional activity and the structure of white matter fibers considering the contribution of the whole tumor in a surgical context. First, we find intertwined alterations in the frequency domain of local and spatially distributed resting-state functional signals, potentially arising within the tumor. Second, we propose a fiber tracking pipeline capable of using anatomical information while still reconstructing bundles in tumoral and peritumoral tissue. Finally, using machine learning and healthy anatomical information, we predict structural rearrangement after surgery given the preoperative brain network. The generative model also disentangles complex patterns of connectivity reorganization for different types of tumors. Overall, we show the importance of carefully designing studies including MR signals within damaged brain tissues, as they exhibit and relate to non-trivial patterns of both structural and functional (dis-)connections or activity.

Brain connectivity analysis based classification of obstructive sleep apnea using electroencephalogram signals

Obstructive sleep apnea (OSA) is a disorder which blocks the upper airway during sleep. The severity of OSA will lead heart attack, stroke and end of life. This proposed study explored the classification of OSA and healthy subjects using brain connectivity analysis from electroencephalogram (EEG) signals. Institute of System and Robotics-University of Coimbra (ISRUC) database were used for acquiring 50 EEG signals using 4 channels and noise removal has been accomplished by 50 Hz notch filter. The Institute of System and Robotics-University of Coimbra (ISRUC) database contained 50 EEG signals, with four channels, and a 50 Hz notch filter was applied to remove noise. Wavelet packet decomposition method was performing the segregation of EEG signals into five bands; Gamma (γ), beta (β), alpha (α), theta (θ) and delta (δ). A total of 4 electrode positions were used for the brain connectivity analysis for each EEG band. Pearson correlation method was effectively used for measuring the correlation between healthy and OSA subjects. The nodes and edges were highlighted the connection between brain and subjects. The highest correlation was achieved in delta band of OSA subjects which starts from 0.7331 to 0.9172 respectively. For healthy subjects, the positive correlation achieved was 0.6995. The delta band has been correlated well with brain when compared other bands. It has been noted that the positive correlation well associated with brain in OSA subjects, which classifies OSA from healthy subjects.

Personalized functional network mapping for autism spectrum disorder and attention-deficit/hyperactivity disorder

Autism spectrum disorder (ASD) and Attention-deficit/hyperactivity disorder (ADHD) are two typical neurodevelopmental disorders that have a long-term impact on physical and mental health. ASD is usually comorbid with ADHD and thus shares highly overlapping clinical symptoms. Delineating the shared and distinct neurophysiological profiles is important to uncover the neurobiological mechanisms to guide better therapy. In this study, we aimed to establish the behaviors, functional connectome, and network properties differences between ASD, ADHD-Combined, and ADHD-Inattentive using resting-state functional magnetic resonance imaging. We used the non-negative matrix fraction method to define personalized large-scale functional networks for each participant. The individual large-scale functional network connectivity (FNC) and graph-theory-based complex network analyses were executed and identified shared and disorder-specific differences in FNCs and network attributes. In addition, edge-wise functional connectivity analysis revealed abnormal edge co-fluctuation amplitude and number of transitions among different groups. Taken together, our study revealed disorder-specific and -shared regional and edge-wise functional connectivity and network differences for ASD and ADHD using an individual-level functional network mapping approach, which provides new evidence for the brain functional abnormalities in ASD and ADHD and facilitates understanding the neurobiological basis for both disorders.

Phase chimera states on nonlocal hyperrings

Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data, that complex systems are composed of multiple units experiencing many-body interactions that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a topology solely involving many-body, nonlocal, and nonregular interactions, hereby named nonlocal d-hyperring, (d+1) being the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and we show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are "flattened" to pairwise ones, the chimera behavior is weaker and more elusive.

Edge time series components of functional connectivity and cognitive function in Alzheimer's disease

Understanding the interrelationships of brain function as measured by resting-state magnetic resonance imaging and neuropsychological/behavioral measures in Alzheimer's disease is key for advancement of neuroimaging analysis methods in clinical research. The edge time-series framework recently developed in the field of network neuroscience, in combination with other network science methods, allows for investigations of brain-behavior relationships that are not possible with conventional functional connectivity methods. Data from the Indiana Alzheimer's Disease Research Center sample (53 cognitively normal control, 47 subjective cognitive decline, 32 mild cognitive impairment, and 20 Alzheimer's disease participants) were used to investigate relationships between functional connectivity components, each derived from a subset of time points based on co-fluctuation of regional signals, and measures of domain-specific neuropsychological functions. Multiple relationships were identified with the component approach that were not found with conventional functional connectivity. These involved attentional, limbic, frontoparietal, and default mode systems and their interactions, which were shown to couple with cognitive, executive, language, and attention neuropsychological domains. Additionally, overlapping results were obtained with two different statistical strategies (network contingency correlation analysis and network-based statistics correlation). Results demonstrate that connectivity components derived from edge time-series based on co-fluctuation reveal disease-relevant relationships not observed with conventional static functional connectivity.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Confounding Effects on the Performance of Machine Learning Analysis of Static Functional Connectivity Computed from rs-fMRI Multi-site Data

Resting-state functional magnetic resonance imaging (rs-fMRI) is a non-invasive imaging technique widely used in neuroscience to understand the functional connectivity of the human brain. While rs-fMRI multi-site data can help to understand the inner working of the brain, the data acquisition and processing of this data has many challenges. One of the challenges is the variability of the data associated with different acquisitions sites, and different MRI machines vendors. Other factors such as population heterogeneity among different sites, with variables such as age and gender of the subjects, must also be considered. Given that most of the machine-learning models are developed using these rs-fMRI multi-site data sets, the intrinsic confounding effects can adversely affect the generalizability and reliability of these computational methods, as well as the imposition of upper limits on the classification scores. This work aims to identify the phenotypic and imaging variables producing the confounding effects, as well as to control these effects. Our goal is to maximize the classification scores obtained from the machine learning analysis of the Autism Brain Imaging Data Exchange (ABIDE) rs-fMRI multi-site data. To achieve this goal, we propose novel methods of stratification to produce homogeneous sub-samples of the 17 ABIDE sites, as well as the generation of new features from the static functional connectivity values, using multiple linear regression models, ComBat harmonization models, and normalization methods. The main results obtained with our statistical models and methods are an accuracy of 76.4%, sensitivity of 82.9%, and specificity of 77.0%, which are 8.8%, 20.5%, and 7.5% above the baseline classification scores obtained from the machine learning analysis of the static functional connectivity computed from the ABIDE rs-fMRI multi-site data.

Static and dynamic functional connectome reveals reconfiguration profiles of whole-brain network across cognitive states

Assessment of functional connectivity (FC) has revealed a great deal of knowledge about the macroscale spatiotemporal organization of the brain network. Recent studies found task-versus-rest network reconfigurations were crucial for cognitive functioning. However, brain network reconfiguration remains unclear among different cognitive states, considering both aggregate and time-resolved FC profiles. The current study utilized static FC (sFC, i.e., long timescale aggregate FC) and sliding window-based dynamic FC (dFC, i.e., short timescale time-varying FC) approaches to investigate the similarity and alterations of edge weights and network topology at different cognitive loads, particularly their relationships with specific cognitive process. Both dFC/sFC networks showed subtle but significant reconfigurations that correlated with task performance. At higher cognitive load, brain network reconfiguration displayed increased functional integration in the sFC-based aggregate network, but faster and larger variability of modular reorganization in the dFC-based time-varying network, suggesting difficult tasks require more integrated and flexible network reconfigurations. Moreover, sFC-based network reconfigurations mainly linked with the sensorimotor and low-order cognitive processes, but dFC-based network reconfigurations mainly linked with the high-order cognitive process. Our findings suggest that reconfiguration profiles of sFC/dFC networks provide specific information about cognitive functioning, which could potentially be used to study brain function and disorders.

Dynamic structure of motor cortical neuron coactivity carries behaviorally relevant information

Skillful, voluntary movements are underpinned by computations performed by networks of interconnected neurons in the primary motor cortex (M1). Computations are reflected by patterns of coactivity between neurons. Using pairwise spike time statistics, coactivity can be summarized as a functional network (FN). Here, we show that the structure of FNs constructed from an instructed-delay reach task in nonhuman primates is behaviorally specific: Low-dimensional embedding and graph alignment scores show that FNs constructed from closer target reach directions are also closer in network space. Using short intervals across a trial, we constructed temporal FNs and found that temporal FNs traverse a low-dimensional subspace in a reach-specific trajectory. Alignment scores show that FNs become separable and correspondingly decodable shortly after the Instruction cue. Finally, we observe that reciprocal connections in FNs transiently decrease following the Instruction cue, consistent with the hypothesis that information external to the recorded population temporarily alters the structure of the network at this moment.

Neuroscience needs Network Science

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions.

Global Topological Synchronization on Simplicial and Cell Complexes

Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However, the investigation of their collective phenomena is only at its infancy. Here we combine topology and nonlinear dynamics to determine the conditions for global synchronization of topological signals defined on simplicial or cell complexes. On simplicial complexes we show that topological obstruction impedes odd dimensional signals to globally synchronize. On the other hand, we show that cell complexes can overcome topological obstruction and in some structures signals of any dimension can achieve global synchronization.

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

BrainGB: A Benchmark for Brain Network Analysis With Graph Neural Networks

Mapping the connectome of the human brain using structural or functional connectivity has become one of the most pervasive paradigms for neuroimaging analysis. Recently, Graph Neural Networks (GNNs) motivated from geometric deep learning have attracted broad interest due to their established power for modeling complex networked data. Despite their superior performance in many fields, there has not yet been a systematic study of how to design effective GNNs for brain network analysis. To bridge this gap, we present BrainGB, a benchmark for brain network analysis with GNNs. BrainGB standardizes the process by (1) summarizing brain network construction pipelines for both functional and structural neuroimaging modalities and (2) modularizing the implementation of GNN designs. We conduct extensive experiments on datasets across cohorts and modalities and recommend a set of general recipes for effective GNN designs on brain networks. To support open and reproducible research on GNN-based brain network analysis, we host the BrainGB website at https://braingb.us with models, tutorials, examples, as well as an out-of-box Python package. We hope that this work will provide useful empirical evidence and offer insights for future research in this novel and promising direction.

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.

A connectomics-based taxonomy of mammals

Mammalian taxonomies are conventionally defined by morphological traits and genetics. How species differ in terms of neural circuits and whether inter-species differences in neural circuit organization conform to these taxonomies is unknown. The main obstacle to the comparison of neural architectures has been differences in network reconstruction techniques, yielding species-specific connectomes that are not directly comparable to one another. Here, we comprehensively chart connectome organization across the mammalian phylogenetic spectrum using a common reconstruction protocol. We analyse the mammalian MRI (MaMI) data set, a database that encompasses high-resolution ex vivo structural and diffusion MRI scans of 124 species across 12 taxonomic orders and 5 superorders, collected using a unified MRI protocol. We assess similarity between species connectomes using two methods: similarity of Laplacian eigenspectra and similarity of multiscale topological features. We find greater inter-species similarities among species within the same taxonomic order, suggesting that connectome organization reflects established taxonomic relationships defined by morphology and genetics. While all connectomes retain hallmark global features and relative proportions of connection classes, inter-species variation is driven by local regional connectivity profiles. By encoding connectomes into a common frame of reference, these findings establish a foundation for investigating how neural circuits change over phylogeny, forging a link from genes to circuits to behaviour.

High-resolution spatiotemporal analysis of single serotonergic axons in an in vitro system

Vertebrate brains have a dual structure, composed of (i) axons that can be well-captured with graph-theoretical methods and (ii) axons that form a dense matrix in which neurons with precise connections operate. A core part of this matrix is formed by axons (fibers) that store and release 5-hydroxytryptamine (5-HT, serotonin), an ancient neurotransmitter that supports neuroplasticity and has profound implications for mental health. The self-organization of the serotonergic matrix is not well understood, despite recent advances in experimental and theoretical approaches. In particular, individual serotonergic axons produce highly stochastic trajectories, fundamental to the construction of regional fiber densities, but further advances in predictive computer simulations require more accurate experimental information. This study examined single serotonergic axons in culture systems (co-cultures and monolayers), by using a set of complementary high-resolution methods: confocal microscopy, holotomography (refractive index-based live imaging), and super-resolution (STED) microscopy. It shows that serotonergic axon walks in neural tissue may strongly reflect the stochastic geometry of this tissue and it also provides new insights into the morphology and branching properties of serotonergic axons. The proposed experimental platform can support next-generation analyses of the serotonergic matrix, including seamless integration with supercomputing approaches.

Structural Brain Network Abnormalities in Parkinson’s Disease With Freezing of Gait

Objective

Diffusion tensor imaging (DTI) studies have investigated white matter (WM) integrity abnormalities in Parkinson’s disease (PD). However, little is known about the topological changes in the brain network. This study aims to reveal these changes by comparing PD without freezing of gait (FOG) (PD FOG–), PD with FOG (PD FOG+), and healthy control (HC).

Methods

21 PD FOG+, 34 PD FOG-, and 23 HC were recruited, and DTI images were acquired. The graph theoretical analysis and network-based statistical method were used to calculate the topological parameters and assess connections.

Results

PD FOG+ showed a decreased normalized clustering coefficient, small-worldness, clustering coefficient, and increased local network efficiency compared with HCs. PD FOG+ showed decreased centrality, degree centrality, and nodal efficiency in the striatum, frontal gyrus, and supplementary motor area (SMA). PD FOG+ showed decreased connections in the frontal gyrus, cingulate gyrus, and caudate nucleus (CAU). The between centrality of the left SMA and left CAU was negatively correlated with FOG questionnaire scores.

Conclusion

This study demonstrates that PD FOG+ exhibits disruption of global and local topological organization in structural brain networks, and the disrupted topological organization can be potential biomarkers in PD FOG+. These new findings may provide increasing insight into the pathophysiological mechanism of PD FOG+.

Information evolution in complex networks

Many biological phenomena or social events critically depend on how information evolves in complex networks. However, a general theory to characterize information evolution is yet absent. Consequently, numerous unknowns remain about the mechanisms underlying information evolution. Among these unknowns, a fundamental problem, being a seeming paradox, lies in the coexistence of local randomness, manifested as the stochastic distortion of information content during individual-individual diffusion, and global regularity, illustrated by specific non-random patterns of information content on the network scale. Here, we attempt to formalize information evolution and explain the coexistence of randomness and regularity in complex networks. Applying network dynamics and information theory, we discover that a certain amount of information, determined by the selectivity of networks to the input information, frequently survives from random distortion. Other information will inevitably experience distortion or dissipation, whose speeds are shaped by the diversity of information selectivity in networks. The discovered laws exist irrespective of noise, but noise accounts for disturbing them. We further demonstrate the ubiquity of our discovered laws by analyzing the emergence of neural tuning properties in the primary visual and medial temporal cortices of animal brains and the emergence of extreme opinions in social networks.

Cortico-subcortical interactions in overlapping communities of edge functional connectivity

Both cortical and subcortical regions can be functionally organized into networks. Regions of the basal ganglia are extensively interconnected with the cortex via reciprocal connections that relay and modulate cortical function. Here we employ an edge-centric approach, which computes co-fluctuations among region pairs in a network to investigate the role and interaction of subcortical regions with cortical systems. By clustering edges into communities, we show that cortical systems and subcortical regions couple via multiple edge communities, with hippocampus and amygdala having a distinct pattern from striatum and thalamus. We show that the edge community structure of cortical networks is highly similar to one obtained from cortical nodes when the subcortex is present in the network. Additionally, we show that the edge community profile of both cortical and subcortical nodes can be estimates solely from cortico-subcortical interactions. Finally, we used a motif analysis focusing on edge community triads where a subcortical region coupled to two cortical regions and found that two community triads where one community couples the subcortex to the cortex were overrepresented. In summary, our results show organized coupling of the subcortex to the cortex that may play a role in cortical organization of primary sensorimotor/attention and heteromodal systems and puts forth the motif analysis of edge community triads as a promising method for investigation of communication patterns in networks.