Comparing multilayer brain networks between groups: Introducing graph metrics and recommendations

From bench to bedside: Overview of magnetoencephalography in basic principle, signal processing, source localization and clinical applications

Magnetoencephalography (MEG) is a non-invasive technique that can precisely capture the dynamic spatiotemporal patterns of the brain by measuring the magnetic fields arising from neuronal activity along the order of milliseconds. Observations of brain dynamics have been used in cognitive neuroscience, the diagnosis of neurological diseases, and the brain-computer interface (BCI). In this study, we outline the basic principle, signal processing, and source localization of MEG, and describe its clinical applications for cognitive assessment, the diagnoses of neurological diseases and mental disorders, preoperative evaluation, and the BCI. This review not only provides an overall perspective of MEG, ranging from practical techniques to clinical applications, but also enhances the prevalent understanding of neural mechanisms. The use of MEG is expected to lead to significant breakthroughs in neuroscience.

Multiplex dynamic networks in the newborn brain disclose latent links with neurobehavioral phenotypes

The higher brain functions arise from coordinated neural activity between distinct brain regions, but the spatial, temporal, and spectral complexity of these functional connectivity networks (FCNs) has challenged the identification of correlates with neurobehavioral phenotypes. Characterizing behavioral correlates of early life FCNs is important to understand the activity dependent emergence of neurodevelopmental performance and for improving health outcomes. Here, we develop an analysis pipeline for identifying multiplex dynamic FCNs that combine spectral and spatiotemporal characteristics of the newborn cortical activity. This data-driven approach automatically uncovers latent networks that show robust neurobehavioral correlations and consistent effects by in utero drug exposure. Altogether, the proposed pipeline provides a robust end-to-end solution for an objective assessment and quantitation of neurobehaviorally meaningful network constellations in the highly dynamic cortical functions.

Reconstruction of multiplex networks via graph embeddings

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations of a large variety of real systems whose elements interact in multiple fashions or flavors. However, multiplex networks are not always simple to observe in the real world; often, only partial information on the layer structure of the networks is available, whereas the remaining information is in the form of aggregated, single-layer networks. Recent works have proposed solutions to the problem of reconstructing the hidden multiplexity of single-layer networks using tools proper for network science. Here, we develop a machine-learning framework that takes advantage of graph embeddings, i.e., representations of networks in geometric space. We validate the framework in systematic experiments aimed at the reconstruction of synthetic and real-world multiplex networks, providing evidence that our proposed framework not only accomplishes its intended task, but often outperforms existing reconstruction techniques.

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.

The longitudinal relation between executive functioning and multilayer network topology in glioma patients

Many patients with glioma, primary brain tumors, suffer from poorly understood executive functioning deficits before and/or after tumor resection. We aimed to test whether frontoparietal network centrality of multilayer networks, allowing for integration across multiple frequencies, relates to and predicts executive functioning in glioma. Patients with glioma (n = 37) underwent resting-state magnetoencephalography and neuropsychological tests assessing word fluency, inhibition, and set shifting before (T1) and one year after tumor resection (T2). We constructed binary multilayer networks comprising six layers, with each layer representing frequency-specific functional connectivity between source-localized time series of 78 cortical regions. Average frontoparietal network multilayer eigenvector centrality, a measure for network integration, was calculated at both time points. Regression analyses were used to investigate associations with executive functioning. At T1, lower multilayer integration (p = 0.017) and epilepsy (p = 0.006) associated with poorer set shifting (adj. R2 = 0.269). Decreasing multilayer integration (p = 0.022) and not undergoing chemotherapy at T2 (p = 0.004) related to deteriorating set shifting over time (adj. R2 = 0.283). No significant associations were found for word fluency or inhibition, nor did T1 multilayer integration predict changes in executive functioning. As expected, our results establish multilayer integration of the frontoparietal network as a cross-sectional and longitudinal correlate of executive functioning in glioma patients. However, multilayer integration did not predict postoperative changes in executive functioning, which together with the fact that this correlate is also found in health and other diseases, limits its specific clinical relevance in glioma.

Neural substrates of verbal memory impairment in schizophrenia: A multimodal connectomics study

While verbal memory is among the most compromised cognitive domains in schizophrenia (SZ), its neural substrates remain elusive. Here, we explored the structural and functional brain network correlates of verbal memory impairment in SZ. We acquired diffusion and resting-state functional MRI data of 49 SZ patients, classified as having preserved (VMP, n = 22) or impaired (VMI, n = 26) verbal memory based on the List Learning task, and 55 healthy controls (HC). Structural and functional connectivity matrices were obtained and analyzed to assess associations with disease status (SZ vs. HC) and verbal memory impairment (VMI vs. VMP) using two complementary data-driven approaches: threshold-free network-based statistics (TFNBS) and hybrid connectivity independent component analysis (connICA). TFNBS showed altered connectivity in SZ patients compared with HC (p < .05, FWER-corrected), with distributed structural changes and functional reorganization centered around sensorimotor areas. Specifically, functional connectivity was reduced within the visual and somatomotor networks and increased between visual areas and associative and subcortical regions. Only a tiny cluster of increased functional connectivity between visual and bilateral parietal attention-related areas correlated with verbal memory dysfunction. Hybrid connICA identified four robust traits, representing fundamental patterns of joint structural-functional connectivity. One of these, mainly capturing the functional connectivity profile of the visual network, was significantly associated with SZ (HC vs. SZ: Cohen's d = .828, p < .0001) and verbal memory impairment (VMP vs. VMI: Cohen's d = -.805, p = .01). We suggest that aberrant connectivity of sensorimotor networks may be a key connectomic signature of SZ and a putative biomarker of SZ-related verbal memory impairment, in consistency with bottom-up models of cognitive disruption.

Assessing the Repeatability of Multi-Frequency Multi-Layer Brain Network Topologies Across Alternative Researcher's Choice Paths

There is a growing interest in the neuroscience community on the advantages of multilayer functional brain networks. Researchers usually treated different frequencies separately at distinct functional brain networks. However, there is strong evidence that these networks share complementary information while their interdependencies could reveal novel findings. For this purpose, neuroscientists adopt multilayer networks, which can be described mathematically as an extension of trivial single-layer networks. Multilayer networks have become popular in neuroscience due to their advantage to integrate different sources of information. Here, Ι will focus on the multi-frequency multilayer functional connectivity analysis on resting-state fMRI (rs-fMRI) recordings. However, constructing a multilayer network depends on selecting multiple pre-processing steps that can affect the final network topology. Here, I analyzed the rs-fMRI dataset from a single human performing scanning over a period of 18 months (84 scans in total), and the rs-fMRI dataset containing 25 subjects with 3 repeat scans. I focused on assessing the reproducibility of multi-frequency multilayer topologies exploring the effect of two filtering methods for extracting frequencies from BOLD activity, three connectivity estimators, with or without a topological filtering scheme, and two spatial scales. Finally, I untangled specific combinations of researchers' choices that yield consistently brain networks with repeatable topologies, giving me the chance to recommend best practices over consistent topologies.

Multimodal multilayer network centrality relates to executive functioning

Executive functioning (EF) is a higher order cognitive process that is thought to depend on a network organization facilitating integration across subnetworks, in the context of which the central role of the fronto-parietal network (FPN) has been described across imaging and neurophysiological modalities. However, the potentially complementary unimodal information on the relevance of the FPN for EF has not yet been integrated. We employ a multilayer framework to allow for integration of different modalities into one 'network of networks.' We used diffusion MRI, resting-state functional MRI, MEG, and neuropsychological data obtained from 33 healthy adults to construct modality-specific single-layer networks as well as a single multilayer network per participant. We computed single-layer and multilayer eigenvector centrality of the FPN as a measure of integration in this network and examined their associations with EF. We found that higher multilayer FPN centrality, but not single-layer FPN centrality, was related to better EF. We did not find a statistically significant change in explained variance in EF when using the multilayer approach as compared to the single-layer measures. Overall, our results show the importance of FPN integration for EF and underline the promise of the multilayer framework toward better understanding cognitive functioning.

Structure-function clustering in weighted brain networks

Functional networks, which typically describe patterns of activity taking place across the cerebral cortex, are widely studied in neuroscience. The dynamical features of these networks, and in particular their deviation from the relatively static structural network, are thought to be key to higher brain function. The interactions between such structural networks and emergent function, and the multimodal neuroimaging approaches and common analysis according to frequency band motivate a multilayer network approach. However, many such investigations rely on arbitrary threshold choices that convert dense, weighted networks to sparse, binary structures. Here, we generalise a measure of multiplex clustering to describe weighted multiplexes with arbitrarily-many layers. Moreover, we extend a recently-developed measure of structure-function clustering (that describes the disparity between anatomical connectivity and functional networks) to the weighted case. To demonstrate its utility we combine human connectome data with simulated neural activity and bifurcation analysis. Our results indicate that this new measure can extract neurologically relevant features not readily apparent in analogous single-layer analyses. In particular, we are able to deduce dynamical regimes under which multistable patterns of neural activity emerge. Importantly, these findings suggest a role for brain operation just beyond criticality to promote cognitive flexibility.

Applying multilayer analysis to morphological, structural, and functional brain networks to identify relevant dysfunction patterns

In recent years, research on network analysis applied to MRI data has advanced significantly. However, the majority of the studies are limited to single networks obtained from resting-state fMRI, diffusion MRI, or gray matter probability maps derived from T1 images. Although a limited number of previous studies have combined two of these networks, none have introduced a framework to combine morphological, structural, and functional brain connectivity networks. The aim of this study was to combine the morphological, structural, and functional information, thus defining a new multilayer network perspective. This has proved advantageous when jointly analyzing multiple types of relational data from the same objects simultaneously using graph- mining techniques. The main contribution of this research is the design, development, and validation of a framework that merges these three layers of information into one multilayer network that links and relates the integrity of white matter connections with gray matter probability maps and resting-state fMRI. To validate our framework, several metrics from graph theory are expanded and adapted to our specific domain characteristics. This proof of concept was applied to a cohort of people with multiple sclerosis, and results show that several brain regions with a synchronized connectivity deterioration could be identified.

Altered Brain Volume, Microstructure Metrics and Functional Connectivity Features in Multiple System Atrophy

In order to deeply understand the specific patterns of volume, microstructure, and functional changes in Multiple System Atrophy patients with cerebellar ataxia syndrome (MSA-c), we perform the current study by simultaneously applying structural (T1-weighted imaging), Diffusion tensor imaging (DTI), functional (BOLD fMRI) and extended Network-Based Statistics (extended-NBS) analysis. Twenty-nine MSA-c type patients and twenty-seven healthy controls (HCs) were involved in this study. First, we analyzed the whole brain changes of volume, microstructure, and functional connectivity (FC) in MSA-c patients. Then, we explored the correlations between significant multimodal MRI features and the total Unified Multiple System Atrophy Rating Scale (UMSARS) scores. Finally, we searched for sensitive imaging biomarkers for the diagnosis of MSA-c using support vector machine (SVM) classifier. Results showed significant grey matter atrophy in cerebellum and white matter microstructural abnormalities in cerebellum, left fusiform gyrus, right precentral gyrus and lingual gyrus. Extended-NBS analysis found two significant different connected components, featuring altered functional connectivity related to left and right cerebellar sub-regions, respectively. Moreover, the reduced fiber bundle counts at right Cerebellum_3 (Cbe3) and decreased fractional anisotropy (FA) values at bilateral Cbe9 were negatively associated with total UMSARS scores. Finally, the significant features at left Cbe9, Cbe1, and Cbe7b were found to be useful as sensitive biomarkers to differentiate MSA-c from HCs according to the SVM analysis. These findings advanced our understanding of the neural pathophysiological mechanisms of MSA from the perspective of multimodal neuroimaging.

Graph theory approach for the structural-functional brain connectome of depression

To decipher the organizational styles of neural underpinning in major depressive disorder (MDD), the current article reviewed recent neuroimaging studies (published during 2015-2020) that applied graph theory approach to the diffusion tensor imaging data or functional brain activation data acquired during task-free resting state. The global network organization of resting-state functional connectivity network in MDD were diverse according to the onset age and medication status. Intra-modular functional connections were weaker in MDD compared to healthy controls (HC) for default mode and limbic networks. Weaker local graph metrics of default mode, frontoparietal, and salience network components in MDD compared to HC were also found. On the contrary, brain regions comprising the limbic, sensorimotor, and subcortical networks showed higher local graph metrics in MDD compared to HC. For the brain white matter-based structural connectivity network, the global network organization was comparable to HC in adult MDD but was attenuated in late-life depression. Local graph metrics of limbic, salience, default-mode, subcortical, insular, and frontoparietal network components in structural connectome were affected from the severity of depressive symptoms, burden of perceived stress, and treatment effects. Collectively, the current review illustrated changed global network organization of structural and functional brain connectomes in MDD compared to HC and were varied according to the onset age and medication status. Intra-modular functional connectivity within the default mode and limbic networks were weaker in MDD compared to HC. Local graph metrics of structural connectome for MDD reflected severity of depressive symptom and perceived stress, and were also changed after treatments. Further studies that explore the graph metrics-based neural correlates of clinical features, cognitive styles, treatment response and prognosis in MDD are required.

Multilayer Network Approach in EEG Motor Imagery with an Adaptive Threshold

The brain has been understood as an interconnected neural network generally modeled as a graph to outline the functional topology and dynamics of brain processes. Classic graph modeling is based on single-layer models that constrain the traits conveyed to trace brain topologies. Multilayer modeling, in contrast, makes it possible to build whole-brain models by integrating features of various kinds. The aim of this work was to analyze EEG dynamics studies while gathering motor imagery data through single-layer and multilayer network modeling. The motor imagery database used consists of 18 EEG recordings of four motor imagery tasks: left hand, right hand, feet, and tongue. Brain connectivity was estimated by calculating the coherence adjacency matrices from each electrophysiological band (δ, θ, α and β) from brain areas and then embedding them by considering each band as a single-layer graph and a layer of the multilayer brain models. Constructing a reliable multilayer network topology requires a threshold that distinguishes effective connections from spurious ones. For this reason, two thresholds were implemented, the classic fixed (average) one and Otsu’s version. The latter is a new proposal for an adaptive threshold that offers reliable insight into brain topology and dynamics. Findings from the brain network models suggest that frontal and parietal brain regions are involved in motor imagery tasks.

Cross-Frequency Coupling in Childhood Absence Epilepsy

Objective: Absence seizures are the prototypic primarily generalized seizures, but there is incomplete understanding regarding their generation and maintenance. A core network for absence seizures has been defined, including focal cortical and thalamic regions that have frequency-dependent interactions. The purpose of this study was to investigate within-frequency coupling and cross-frequency coupling (CFC) during human absence seizures, to identify key regions (hubs) within the absence network that contribute to propagation and maintenance. Methods: Thirteen children with new-onset and untreated childhood absence epilepsy had over 60 typical absence seizures during both electroencephalography-functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) recordings. The spatial map of the ictal network was defined using fMRI and used as prior information for MEG connectivity. A multilayer network approach was used to investigate within-frequency coupling and CFC for canonical frequency bands. A rigorous null-modeling approach was used to determine connections outside the noise floor. Results: Strong coupling between beta and gamma frequencies, within the left frontal cortex, and between the left frontal and right parietal regions was observed. There was also strong connectivity between left frontal and right parietal nodes within the gamma band. Multilayer versatility analysis identified a cluster of network hubs in the left frontal region. Interpretation: Cortical regions commonly identified as being critical for absence seizure generation (frontal cortex, precuneus) have strong CFC and within-frequency coupling between beta and gamma bands. As nonpharmacologic treatments, such as neuromodulation, become available for generalized epilepsies, detailed mechanistic understanding of how "diffuse" seizures are generated and maintained will be necessary to provide optimal outcomes.

The functional brain favours segregated modular connectivity at old age unless affected by neurodegeneration

Brain's modular connectivity gives this organ resilience and adaptability. The ageing process alters the organised modularity of the brain and these changes are further accentuated by neurodegeneration, leading to disorganisation. To understand this further, we analysed modular variability-heterogeneity of modules-and modular dissociation-detachment from segregated connectivity-in two ageing cohorts and a mixed cohort of neurodegenerative diseases. Our results revealed that the brain follows a universal pattern of high modular variability in metacognitive brain regions: the association cortices. The brain in ageing moves towards a segregated modular structure despite presenting with increased modular heterogeneity-modules in older adults are not only segregated, but their shape and size are more variable than in young adults. In the presence of neurodegeneration, the brain maintains its segregated connectivity globally but not locally, and this is particularly visible in dementia with Lewy bodies and Parkinson's disease dementia; overall, the modular brain shows patterns of differentiated pathology.

Connecting brain and behavior in clinical neuroscience: A network approach

In recent years, there has been an increase in applications of network science in many different fields. In clinical neuroscience and psychopathology, the developments and applications of network science have occurred mostly simultaneously, but without much collaboration between the two fields. The promise of integrating these network applications lies in a united framework to tackle one of the fundamental questions of our time: how to understand the link between brain and behavior. In the current overview, we bridge this gap by introducing conventions in both fields, highlighting similarities, and creating a common language that enables the exploitation of synergies. We provide research examples in autism research, as it accurately represents research lines in both network neuroscience and psychological networks. We integrate brain and behavior not only semantically, but also practically, by showcasing three methodological avenues that allow to combine networks of brain and behavioral data. As such, the current paper offers a stepping stone to further develop multi-modal networks and to integrate brain and behavior.

Visual Effect on Brain Connectome That Scales Feedforward and Feedback Processes of Aged Postural System During Unstable Stance

Older adults with degenerative declines in sensory systems depend strongly on visual input for postural control. By connecting advanced neural imaging and a postural control model, this study investigated the visual effect on the brain functional network that regulates feedback and feedforward processes of the postural system in older adults under somatosensory perturbations. Thirty-six older adults conducted bilateral stance on a foam surface in the eyes-open (EO) and eyes-closed (EC) conditions while their center of pressure (COP) and scalp EEG were recorded. The stochastic COP trajectory was modeled with non-linear stabilogram diffusion analysis (SDA) to characterize shifts in postural control in a continuum of feedback and feedforward processes. The EEG network was analyzed with the phase-lag index (PLI) and minimum spanning tree (MST). The results indicated that visual input rebalanced feedforward and feedback processes for postural sway, resulting in a greater critical point of displacement (CD), short-term effective diffusion coefficients (D_s) and short-term exponent (H_s), but the smaller critical point of time (CT) and long-term exponent (H_l) for the EC state. The EC network demonstrated stronger frontoparietal-occipital connectivity but weaker fronto-tempo-motor connectivity of the theta (4–7 Hz), alpha (8–12 Hz), and beta (13–35 Hz) bands than did the EO network. MST analysis revealed generally greater leaf fraction and maximal betweenness centrality (BC_max) and kappa of the EC network, as compared with those of the EO network. In contrast, the EC network exhibited a smaller diameter and average eccentricity than those of the EO network. The modulation of long-term negative feedback gain of the aged postural system with visual occlusion was positively correlated with leaf fraction, BC_max, and kappa, but negatively correlated with the diameter and average eccentricity for all EEG sub-bands. In conclusion, the aged brain functional network in older adults is tuned to visual information for modulating long-term negative feedback of the postural system under somatosensory perturbations.

Structural and Functional Connectivity Substrates of Cognitive Impairment in Multiple Sclerosis

Cognitive impairment (CI) occurs in 43 to 70% of multiple sclerosis (MS) patients at both early and later disease stages. Cognitive domains typically involved in MS include attention, information processing speed, memory, and executive control. The growing use of advanced magnetic resonance imaging (MRI) techniques is furthering our understanding on the altered structural connectivity (SC) and functional connectivity (FC) substrates of CI in MS. Regarding SC, different diffusion tensor imaging (DTI) measures (e.g., fractional anisotropy, diffusivities) along tractography-derived white matter (WM) tracts showed relevance toward CI. Novel diffusion MRI techniques, including diffusion kurtosis imaging, diffusion spectrum imaging, high angular resolution diffusion imaging, and neurite orientation dispersion and density imaging, showed more pathological specificity compared to the traditional DTI but require longer scan time and mathematical complexities for their interpretation. As for FC, task-based functional MRI (fMRI) has been traditionally used in MS to brain mapping the neural activity during various cognitive tasks. Analysis methods of resting fMRI (seed-based, independent component analysis, graph analysis) have been applied to uncover the functional substrates of CI in MS by revealing adaptive or maladaptive mechanisms of functional reorganization. The relevance for CI in MS of SC–FC relationships, reflecting common pathogenic mechanisms in WM and gray matter, has been recently explored by novel MRI analysis methods. This review summarizes recent advances on MRI techniques of SC and FC and their potential to provide a deeper understanding of the pathological substrates of CI in MS.

Multilayer Connector Hub Mapping Reveals Key Brain Regions Supporting Expressive Language

Introduction: How components of the distributed brain networks that support cognition participate in typical functioning remains a largely unanswered question. An important subgroup of regions in the larger network are connector hubs, which are areas that are highly connected to several other functionally specialized sets of regions, and are likely important for sensorimotor integration. The present study attempts to characterize connector hubs involved in typical expressive language functioning using a data-driven, multimodal, full multilayer magnetoencephalography (MEG) connectivity-based pipeline. Methods: Twelve adolescents, 16-18 years of age (five males), participated in this study. Participants underwent MEG scanning during a verb generation task. MEG and structural connectivity were calculated at the whole-brain level. Amplitude/amplitude coupling (AAC) was used to compute functional connections both within and between discrete frequency bins. AAC values were then multiplied by a binary structural connectivity matrix, and then entered into full multilayer network analysis. Initially, hubs were defined based on multilayer versatility and subsequently reranked by a novel measure called delta centrality on interconnectedness (DCI). DCI is defined as the percent change in interfrequency interconnectedness after removal of a hub. Results: We resolved regions that are important for between-frequency communication among other areas during expressive language, with several potential theoretical and clinical applications that can be generalized to other cognitive domains. Conclusion: Our multilayer, data-driven framework captures nonlinear connections that span across scales that are often missed in conventional analyses. The present study suggests that crucial hubs may be conduits for interfrequency communication between action and perception systems that are crucial for typical functioning.

The Multilayer Network Approach in the Study of Personality Neuroscience

It has long been understood that a multitude of biological systems, from genetics, to brain networks, to psychological factors, all play a role in personality. Understanding how these systems interact with each other to form both relatively stable patterns of behaviour, cognition and emotion, but also vast individual differences and psychiatric disorders, however, requires new methodological insight. This article explores a way in which to integrate multiple levels of personality simultaneously, with particular focus on its neural and psychological constituents. It does so first by reviewing the current methodology of studies used to relate the two levels, where psychological traits, often defined with a latent variable model are used as higher-level concepts to identify the neural correlates of personality (NCPs). This is known as a top-down approach, which though useful in revealing correlations, is not able to include the fine-grained interactions that occur at both levels. As an alternative, we discuss the use of a novel complex system approach known as a multilayer network, a technique that has recently proved successful in revealing veracious interactions between networks at more than one level. The benefits of the multilayer approach to the study of personality neuroscience follow from its well-founded theoretical basis in network science. Its predictive and descriptive power may surpass that of statistical top-down and latent variable models alone, potentially allowing the discernment of more complete descriptions of individual differences, and psychiatric and neurological changes that accompany disease. Though in its infancy, and subject to a number of methodological unknowns, we argue that the multilayer network approach may contribute to an understanding of personality as a complex system comprised of interrelated psychological and neural features.

A Path-Based Distribution Measure for Network Comparison

As network data increases, it is more common than ever for researchers to analyze a set of networks rather than a single network and measure the difference between networks by developing a number of network comparison methods. Network comparison is able to quantify dissimilarity between networks by comparing the structural topological difference of networks. Here, we propose a kind of measures for network comparison based on the shortest path distribution combined with node centrality, capturing the global topological difference with local features. Based on the characterized path distributions, we define and compare network distance between networks to measure how dissimilar the two networks are, and the network entropy to characterize a typical network system. We find that the network distance is able to discriminate networks generated by different models. Combining more information on end nodes along a path can further amplify the dissimilarity of networks. The network entropy is able to detect tipping points in the evolution of synthetic networks. Extensive numerical simulations reveal the effectivity of the proposed measure in network reduction of multilayer networks, and identification of typical system states in temporal networks as well.

Multilayer MEG functional connectivity as a potential marker for suicidal thoughts in major depressive disorder

Major depressive disorder (MDD) is highly heterogeneous in its clinical presentation. The present exploratory study used magnetoencephalography (MEG) to investigate electrophysiological intrinsic connectivity differences between healthy volunteers and unmedicated participants with treatment-resistant MDD. The study examined canonical frequency bands from delta through gamma. In addition to group comparisons, correlational studies were conducted to determine whether connectivity was related to five symptom factors: depressed mood, tension, negative cognition, suicidal thoughts, and amotivation. The MDD and healthy volunteer groups did not differ significantly at baseline when corrected across all frequencies and clusters, although evidence of generalized slowing in MDD was observed. Notably, however, electrophysiological connectivity was strongly related to suicidal thoughts, particularly as coupling of low frequency power fluctuations (delta and theta) with alpha and beta power. This analysis revealed hub areas underlying this symptom cluster, including left hippocampus, left anterior insula, and bilateral dorsolateral prefrontal cortex. No other symptom cluster demonstrated a relationship with neurophysiological connectivity, suggesting a specificity to these results as markers of suicidal ideation.

Dissociated neuronal phase- and amplitude-coupling patterns in the human brain

Coupling of neuronal oscillations may reflect and facilitate the communication between neuronal populations. Two primary neuronal coupling modes have been described: phase-coupling and amplitude-coupling. Theoretically, both coupling modes are independent, but so far, their neuronal relationship remains unclear. Here, we combined MEG, source-reconstruction and simulations to systematically compare cortical amplitude-coupling and phase-coupling patterns in the human brain. Importantly, we took into account a critical bias of amplitude-coupling measures due to phase-coupling. We found differences between both coupling modes across a broad frequency range and most of the cortex. Furthermore, by combining empirical measurements and simulations we ruled out that these results were caused by methodological biases, but instead reflected genuine neuronal amplitude coupling. Our results show that cortical phase- and amplitude-coupling patterns are non-redundant, which may reflect at least partly distinct neuronal mechanisms. Furthermore, our findings highlight and clarify the compound nature of amplitude coupling measures.

Disrupted core-periphery structure of multimodal brain networks in Alzheimer's disease

In Alzheimer's disease (AD), the progressive atrophy leads to aberrant network reconfigurations both at structural and functional levels. In such network reorganization, the core and peripheral nodes appear to be crucial for the prediction of clinical outcome because of their ability to influence large-scale functional integration. However, the role of the different types of brain connectivity in such prediction still remains unclear. Using a multiplex network approach we integrated information from DWI, fMRI, and MEG brain connectivity to extract an enriched description of the core-periphery structure in a group of AD patients and age-matched controls. Globally, the regional coreness-that is, the probability of a region to be in the multiplex core-significantly decreased in AD patients as result of a random disconnection process initiated by the neurodegeneration. Locally, the most impacted areas were in the core of the network-including temporal, parietal, and occipital areas-while we reported compensatory increments for the peripheral regions in the sensorimotor system. Furthermore, these network changes significantly predicted the cognitive and memory impairment of patients. Taken together these results indicate that a more accurate description of neurodegenerative diseases can be obtained from the multimodal integration of neuroimaging-derived network data.

Variational Bayesian inversion for hierarchical unsupervised generative embedding (HUGE)

A recently introduced hierarchical generative model unified the inference of effective connectivity in individual subjects and the unsupervised identification of subgroups defined by connectivity patterns. This hierarchical unsupervised generative embedding (HUGE) approach combined a hierarchical formulation of dynamic causal modelling (DCM) for fMRI with Gaussian mixture models and relied on Markov chain Monte Carlo (MCMC) sampling for inference. While well suited for the inversion of complex hierarchical models, MCMC-based sampling suffers from a computational burden that is prohibitive for many applications. To address this problem, this paper derives an efficient variational Bayesian (VB) inversion scheme for HUGE that simultaneously provides approximations to the posterior distribution over model parameters and to the log model evidence. The face validity of the VB scheme was tested using two synthetic fMRI datasets with known ground truth. Additionally, an empirical fMRI dataset of stroke patients and healthy controls was used to evaluate the practical utility of the method in application to real-world problems. Our analyses demonstrate good performance of our VB scheme, with a marked speed-up of model inversion by two orders of magnitude compared to MCMC, while maintaining a similar level of accuracy. Notably, additional acceleration would be possible if parallel computing techniques were applied. Generally, our VB implementation of HUGE is fast enough to support multi-start procedures for whole-group analyses, a useful strategy to ameliorate problems with local extrema. HUGE thus represents a potentially useful practical solution for an important problem in clinical neuromodeling and computational psychiatry, i.e., the unsupervised detection of subgroups in heterogeneous populations that are defined by effective connectivity.