A framework for quantifying the coupling between brain connectivity and heartbeat dynamics: Insights into the disrupted network physiology in Parkinson's disease

Parkinson's disease (PD) often shows disrupted brain connectivity and autonomic dysfunctions, progressing alongside with motor and cognitive decline. Recently, PD has been linked to a reduced sensitivity to cardiac inputs, that is, cardiac interoception. Altogether, those signs suggest that PD causes an altered brain-heart connection whose mechanisms remain unclear. Our study aimed to explore the large-scale network disruptions and the neurophysiology of disrupted interoceptive mechanisms in PD. We focused on examining the alterations in brain-heart coupling in PD and their potential connection to motor symptoms. We developed a proof-of-concept method to quantify relationships between the co-fluctuations of brain connectivity and cardiac sympathetic and parasympathetic activities. We quantified the brain-heart couplings from electroencephalogram and electrocardiogram recordings from PD patients on and off dopaminergic medication, as well as in healthy individuals at rest. Our results show that the couplings of fluctuating alpha and gamma connectivity with cardiac sympathetic dynamics are reduced in PD patients, as compared to healthy individuals. Furthermore, we show that PD patients under dopamine medication recover part of the brain-heart coupling, in proportion with the reduced motor symptoms. Our proposal offers a promising approach to unveil the physiopathology of PD and promoting the development of new evaluation methods for the early stages of the disease.

Exploration-Exploitation Paradigm for Networked Biological Systems

The stochastic exploration of the configuration space and the exploitation of functional states underlie many biological processes. The evolutionary dynamics stands out as a remarkable example. Here, we introduce a novel formalism that mimics evolution and encodes a general exploration-exploitation dynamics for biological networks. We apply it to the brain wiring problem, focusing on the maturation of that of the nematode Caenorhabditis elegans. We demonstrate that a parsimonious maxent description of the adult brain combined with our framework is able to track down the entire developmental trajectory.

Measuring neuronal avalanches to inform brain-computer interfaces

Large-scale interactions among multiple brain regions manifest as bursts of activations called neuronal avalanches, which reconfigure according to the task at hand and, hence, might constitute natural candidates to design brain-computer interfaces (BCIs). To test this hypothesis, we used source-reconstructed magneto/electroencephalography during resting state and a motor imagery task performed within a BCI protocol. To track the probability that an avalanche would spread across any two regions, we built an avalanche transition matrix (ATM) and demonstrated that the edges whose transition probabilities significantly differed between conditions hinged selectively on premotor regions in all subjects. Furthermore, we showed that the topology of the ATMs allows task-decoding above the current gold standard. Hence, our results suggest that neuronal avalanches might capture interpretable differences between tasks that can be used to inform brain-computer interfaces.

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.

Vizaj-A free online interactive software for visualizing spatial networks

In many fields of science and technology we are confronted with complex networks. Making sense of these networks often require the ability to visualize and explore their intermingled structure consisting of nodes and links. To facilitate the identification of significant connectivity patterns, many methods have been developed based on the rearrangement of the nodes so as to avoid link criss-cross. However, real networks are often embedded in a geometrical space and the nodes code for an intrinsic physical feature of the system that one might want to preserve. For these spatial networks, it is therefore crucial to find alternative strategies operating on the links and not on the nodes. Here, we introduce Vizaj a javascript web application to render spatial networks based on optimized geometrical criteria that reshape the link profiles. While optimized for 3D networks, Vizaj can also be used for 2D networks and offers the possibility to interactively customize the visualization via several controlling parameters, including network filtering and the effect of internode distance on the link trajectories. Vizaj is further equipped with additional options allowing to improve the final aesthetics, such as the color/size of both nodes and links, zooming/rotating/translating, and superimposing external objects. Vizaj is an open-source software which can be freely downloaded and updated via a github repository. Here, we provide a detailed description of its main features and algorithms together with a guide on how to use it. Finally, we validate its potential on several synthetic and real spatial networks from infrastructural to biological systems. We hope that Vizaj will help scientists and practitioners to make sense of complex networks and provide aesthetic while informative visualizations.

Decreased brain network global efficiency after attachment memories retrieval in individuals with unresolved/disorganized attachment-related state of mind

The main aim of the study was to examine how brain network metrics change after retrieval of attachment memories in individuals with unresolved/disorganized (U/D) attachment-related state of mind and those with organized/resolved (O/R) state of mind. We focused on three main network metrics associated with integration and segregation: global (E_glob) efficiency for the first function, local (E_loc) efficiency and modularity for the second. We also examined assortativity and centrality metrics. Electroencephalography (EEG) recordings were performed before and after the Adult Attachment Interview (AAI) in a sample of 50 individuals previously assessed for parenting quality. Functional connectivity matrices were constructed by means of the exact Low-Resolution Electromagnetic Tomography (eLORETA) software and then imported into MATLAB to compute brain network metrics. Compared to individuals with O/R attachment-related state of mind, those with U/D show a significant decrease in beta E_glob after AAI. No statistically significant difference among groups emerged in E_loc and modularity metrics after AAI, neither in assortativity nor in betweenness centrality. These results may help to better understand the neurophysiological patterns underlying the disintegrative effects of retrieving traumatic attachment memories in individuals with disorganized state of mind in relation to attachment.

Temporal exponential random graph models of longitudinal brain networks after stroke

Plasticity after stroke is a complex phenomenon. Functional reorganization occurs not only in the perilesional tissue but throughout the brain. However, the local connection mechanisms generating such global network changes remain largely unknown. To address this question, time must be considered as a formal variable of the problem rather than a simple repeated observation. Here, we hypothesized that the presence of temporal connection motifs, such as the formation of temporal triangles (T) and edges (E) over time, would explain large-scale brain reorganization after stroke. To test our hypothesis, we adopted a statistical framework based on temporal exponential random graph models (tERGMs), where the aforementioned temporal motifs were implemented as parameters and adapted to capture global network changes after stroke. We first validated the performance on synthetic time-varying networks as compared to standard static approaches. Then, using real functional brain networks, we showed that estimates of tERGM parameters were sufficient to reproduce brain network changes from 2 weeks to 1 year after stroke. These temporal connection signatures, reflecting within-hemisphere segregation (T) and between hemisphere integration (E), were associated with patients' future behaviour. In particular, interhemispheric temporal edges significantly correlated with the chronic language and visual outcome in subcortical and cortical stroke, respectively. Our results indicate the importance of time-varying connection properties when modelling dynamic complex systems and provide fresh insights into modelling of brain network mechanisms after stroke.

Functional connectivity ensemble method to enhance BCI performance (FUCONE)

OBJECTIVE

Relying on the idea that functional connectivity provides important insights on the underlying dynamic of neuronal interactions, we propose a novel framework that combines functional connectivity estimators and covariance-based pipelines to improve the classification of mental states, such as motor imagery.

METHODS

A Riemannian classifier is trained for each estimator and an ensemble classifier combines the decisions in each feature space. A thorough assessment of the functional connectivity estimators is provided and the best performing pipeline among those tested, called FUCONE, is evaluated on different conditions and datasets.

RESULTS

Using a meta-analysis to aggregate results across datasets, FUCONE performed significantly better than all state-of-the-art methods.

CONCLUSION

The performance gain is mostly imputable to the improved diversity of the feature spaces, increasing the robustness of the ensemble classifier with respect to the inter- and intra-subject variability.

SIGNIFICANCE

Our results offer new insights into the need to consider functional connectivity-based methods to improve the BCI performance.

Phase/Amplitude Synchronization of Brain Signals During Motor Imagery BCI Tasks

In the last decade, functional connectivity (FC) has been increasingly adopted based on its ability to capture statistical dependencies between multivariate brain signals. However, the role of FC in the context of brain-computer interface applications is still poorly understood. To address this gap in knowledge, we considered a group of 20 healthy subjects during an EEG-based hand motor imagery (MI) task. We studied two well-established FC estimators, i.e. spectral- and imaginary-coherence, and we investigated how they were modulated by the MI task. We characterized the resulting FC networks by extracting the strength of connectivity of each EEG sensor and we compared the discriminant power with respect to standard power spectrum features. At the group level, results showed that while spectral-coherence based network features were increasing in the sensorimotor areas, those based on imaginary-coherence were significantly decreasing. We demonstrated that this opposite, but complementary, behavior was respectively determined by the increase in amplitude and phase synchronization between the brain signals. At the individual level, we eventually assessed the potential of these network connectivity features in a simple off-line classification scenario. Taken together, our results provide fresh insights into the oscillatory mechanisms subserving brain network changes during MI and offer new perspectives to improve BCI performance.

Stepwise target controllability identifies dysregulations of macrophage networks in multiple sclerosis

Identifying the nodes able to drive the state of a network is crucial to understand, and eventually control, biological systems. Despite recent advances, such identification remains difficult because of the huge number of equivalent controllable configurations, even in relatively simple networks. Based on the evidence that in many applications it is essential to test the ability of individual nodes to control a specific target subset, we develop a fast and principled method to identify controllable driver-target configurations in sparse and directed networks. We demonstrate our approach on simulated networks and experimental gene networks to characterize macrophage dysregulation in human subjects with multiple sclerosis.

BCI learning induces core-periphery reorganization in M/EEG multiplex brain networks

Brain-computer interfaces (BCIs) constitute a promising tool for communication and control. However, mastering non-invasive closed-loop systems remains a learned skill that is difficult to develop for a non-negligible proportion of users. The involved learning process induces neural changes associated with a brain network reorganization that remains poorly understood. To address this inter-subject variability, we adopted a multilayer approach to integrate brain network properties from electroencephalographic (EEG) and magnetoencephalographic (MEG) data resulting from a four-session BCI training program followed by a group of healthy subjects. Our method gives access to the contribution of each layer to multilayer network that tends to be equal with time. We show that regardless the chosen modality, a progressive increase in the integration of somatosensory areas in the α band was paralleled by a decrease of the integration of visual processing and working memory areas in the β band. Notably, only brain network properties in multilayer network correlated with future BCI scores in the α2 band: positively in somatosensory and decision-making related areas and negatively in associative areas. Our findings cast new light on neural processes underlying BCI training. Integrating multimodal brain network properties provides new information that correlates with behavioral performance and could be considered as a potential marker of BCI learning.

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.

Learning in brain-computer interface control evidenced by joint decomposition of brain and behavior

OBJECTIVE

Motor imagery-based brain-computer interfaces (BCIs) use an individual's ability to volitionally modulate localized brain activity, often as a therapy for motor dysfunction or to probe causal relations between brain activity and behavior. However, many individuals cannot learn to successfully modulate their brain activity, greatly limiting the efficacy of BCI for therapy and for basic scientific inquiry. Formal experiments designed to probe the nature of BCI learning have offered initial evidence that coherent activity across spatially distributed and functionally diverse cognitive systems is a hallmark of individuals who can successfully learn to control the BCI. However, little is known about how these distributed networks interact through time to support learning.

APPROACH

Here, we address this gap in knowledge by constructing and applying a multimodal network approach to decipher brain-behavior relations in motor imagery-based brain-computer interface learning using magnetoencephalography. Specifically, we employ a minimally constrained matrix decomposition method - non-negative matrix factorization - to simultaneously identify regularized, covarying subgraphs of functional connectivity, to assess their similarity to task performance, and to detect their time-varying expression.

MAIN RESULTS

We find that learning is marked by diffuse brain-behavior relations: good learners displayed many subgraphs whose temporal expression tracked performance. Individuals also displayed marked variation in the spatial properties of subgraphs such as the connectivity between the frontal lobe and the rest of the brain, and in the temporal properties of subgraphs such as the stage of learning at which they reached maximum expression. From these observations, we posit a conceptual model in which certain subgraphs support learning by modulating brain activity in sensors near regions important for sustaining attention. To test this model, we use tools that stipulate regional dynamics on a networked system (network control theory), and find that good learners display a single subgraph whose temporal expression tracked performance and whose architecture supports easy modulation of sensors located near brain regions important for attention.

SIGNIFICANCE

The nature of our contribution to the neuroscience of BCI learning is therefore both computational and theoretical; we first use a minimally-constrained, individual specific method of identifying mesoscale structure in dynamic brain activity to show how global connectivity and interactions between distributed networks supports BCI learning, and then we use a formal network model of control to lend theoretical support to the hypothesis that these identified subgraphs are well suited to modulate attention.

Functional disconnection of associative cortical areas predicts performance during BCI training

Brain-computer interfaces (BCIs) have been largely developed to allow communication, control, and neurofeedback in human beings. Despite their great potential, BCIs perform inconsistently across individuals and the neural processes that enable humans to achieve good control remain poorly understood. To address this question, we performed simultaneous high-density electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings in a motor imagery-based BCI training involving a group of healthy subjects. After reconstructing the signals at the cortical level, we showed that the reinforcement of motor-related activity during the BCI skill acquisition is paralleled by a progressive disconnection of associative areas which were not directly targeted during the experiments. Notably, these network connectivity changes reflected growing automaticity associated with BCI performance and predicted future learning rate. Altogether, our findings provide new insights into the large-scale cortical organizational mechanisms underlying BCI learning, which have implications for the improvement of this technology in a broad range of real-life applications.

EEG evidence of compensatory mechanisms in preclinical Alzheimer’s disease

Early biomarkers are needed to identify individuals at high risk of preclinical Alzheimer’s disease and to better understand the pathophysiological processes of disease progression. Preclinical Alzheimer’s disease EEG changes would be non-invasive and cheap screening tools and could also help to predict future progression to clinical Alzheimer’s disease. However, the impact of amyloid-β deposition and neurodegeneration on EEG biomarkers needs to be elucidated. We included participants from the INSIGHT-preAD cohort, which is an ongoing single-centre multimodal observational study that was designed to identify risk factors and markers of progression to clinical Alzheimer’s disease in 318 cognitively normal individuals aged 70–85 years with a subjective memory complaint. We divided the subjects into four groups, according to their amyloid status (based on 18F-florbetapir PET) and neurodegeneration status (evidenced by 18F-fluorodeoxyglucose PET brain metabolism in Alzheimer’s disease signature regions). The first group was amyloid-positive and neurodegeneration-positive, which corresponds to stage 2 of preclinical Alzheimer’s disease. The second group was amyloid-positive and neurodegeneration-negative, which corresponds to stage 1 of preclinical Alzheimer’s disease. The third group was amyloid-negative and neurodegeneration-positive, which corresponds to ‘suspected non-Alzheimer’s pathophysiology’. The last group was the control group, defined by amyloid-negative and neurodegeneration-negative subjects. We analysed 314 baseline 256-channel high-density eyes closed 1-min resting state EEG recordings. EEG biomarkers included spectral measures, algorithmic complexity and functional connectivity assessed with a novel information-theoretic measure, weighted symbolic mutual information. The most prominent effects of neurodegeneration on EEG metrics were localized in frontocentral regions with an increase in high frequency oscillations (higher beta and gamma power) and a decrease in low frequency oscillations (lower delta power), higher spectral entropy, higher complexity and increased functional connectivity measured by weighted symbolic mutual information in theta band. Neurodegeneration was associated with a widespread increase of median spectral frequency. We found a non-linear relationship between amyloid burden and EEG metrics in neurodegeneration-positive subjects, either following a U-shape curve for delta power or an inverted U-shape curve for the other metrics, meaning that EEG patterns are modulated differently depending on the degree of amyloid burden. This finding suggests initial compensatory mechanisms that are overwhelmed for the highest amyloid load. Together, these results indicate that EEG metrics are useful biomarkers for the preclinical stage of Alzheimer’s disease.

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.

Quality Assessment of Single-Channel EEG for Wearable Devices

The recent embedding of electroencephalographic (EEG) electrodes in wearable devices raises the problem of the quality of the data recorded in such uncontrolled environments. These recordings are often obtained with dry single-channel EEG devices, and may be contaminated by many sources of noise which can compromise the detection and characterization of the brain state studied. In this paper, we propose a classification-based approach to effectively quantify artefact contamination in EEG segments, and discriminate muscular artefacts. The performance of our method were assessed on different databases containing either artificially contaminated or real artefacts recorded with different type of sensors, including wet and dry EEG electrodes. Furthermore, the quality of unlabelled databases was evaluated. For all the studied databases, the proposed method is able to rapidly assess the quality of the EEG signals with an accuracy higher than 90%. The obtained performance suggests that our approach provide an efficient, fast and automated quality assessment of EEG signals from low-cost wearable devices typically composed of a dry single EEG channel.

Integrating EEG and MEG Signals to Improve Motor Imagery Classification in Brain–Computer Interface

We adopted a fusion approach that combines features from simultaneously recorded electroencephalogram (EEG) and magnetoencephalogram (MEG) signals to improve classification performances in motor imagery-based brain–computer interfaces (BCIs). We applied our approach to a group of 15 healthy subjects and found a significant classification performance enhancement as compared to standard single-modality approaches in the alpha and beta bands. Taken together, our findings demonstrate the advantage of considering multimodal approaches as complementary tools for improving the impact of noninvasive BCIs.

Network neuroscience for optimizing brain-computer interfaces

Human-machine interactions are being increasingly explored to create alternative ways of communication and to improve our daily life. Based on a classification of the user's intention from the user's underlying neural activity, brain-computer interfaces (BCIs) allow direct interactions with the external environment while bypassing the traditional effector of the musculoskeletal system. Despite the enormous potential of BCIs, there are still a number of challenges that limit their societal impact, ranging from the correct decoding of a human's thoughts, to the application of effective learning strategies. Despite several important engineering advances, the basic neuroscience behind these challenges remains poorly explored. Indeed, BCIs involve complex dynamic changes related to neural plasticity at a diverse range of spatiotemporal scales. One promising antidote to this complexity lies in network science, which provides a natural language in which to model the organizational principles of brain architecture and function as manifest in its interconnectivity. Here, we briefly review the main limitations currently affecting BCIs, and we offer our perspective on how they can be addressed by means of network theoretic approaches. We posit that the emerging field of network neuroscience will prove to be an effective tool to unlock human-machine interactions.

Multiplex core-periphery organization of the human connectome

What is the core of the human brain is a fundamental question that has been mainly addressed by studying the anatomical connections between differently specialized areas, thus neglecting the possible contributions from their functional interactions. While many methods are available to identify the core of a network when connections between nodes are all of the same type, a principled approach to define the core when multiple types of connectivity are allowed is still lacking. Here, we introduce a general framework to define and extract the core-periphery structure of multi-layer networks by explicitly taking into account the connectivity patterns at each layer. We first validate our algorithm on synthetic networks of different size and density, and with tunable overlap between the cores at different layers. We then use our method to merge information from structural and functional brain networks, obtaining in this way an integrated description of the core of the human connectome. Results confirm the role of the main known cortical and subcortical hubs, but also suggest the presence of new areas in the sensori-motor cortex that are crucial for intrinsic brain functioning. Taken together these findings provide fresh evidence on a fundamental question in modern neuroscience and offer new opportunities to explore the mesoscale properties of multimodal brain networks.

Editorial: Bridging Scales and Levels

Network neuroscience strives to understand the networks of the brain on all spatiotemporal scales and levels of observation. Current experimental and theoretical capabilities are beginning to facilitate a more holistic perspective, uniting these networks. This focus feature, "Bridging Scales and Levels," aims to document current research and looks to future progress towards this vision.

Green Compressive Sampling Reconstruction in IoT Networks

In this paper, we address the problem of green Compressed Sensing (CS) reconstruction within Internet of Things (IoT) networks, both in terms of computing architecture and reconstruction algorithms. The approach is novel since, unlike most of the literature dealing with energy efficient gathering of the CS measurements, we focus on the energy efficiency of the signal reconstruction stage given the CS measurements. As a first novel contribution, we present an analysis of the energy consumption within the IoT network under two computing architectures. In the first one, reconstruction takes place within the IoT network and the reconstructed data are encoded and transmitted out of the IoT network; in the second one, all the CS measurements are forwarded to off-network devices for reconstruction and storage, i.e., reconstruction is off-loaded. Our analysis shows that the two architectures significantly differ in terms of consumed energy, and it outlines a theoretically motivated criterion to select a green CS reconstruction computing architecture. Specifically, we present a suitable decision function to determine which architecture outperforms the other in terms of energy efficiency. The presented decision function depends on a few IoT network features, such as the network size, the sink connectivity, and other systems’ parameters. As a second novel contribution, we show how to overcome classical performance comparison of different CS reconstruction algorithms usually carried out w.r.t. the achieved accuracy. Specifically, we consider the consumed energy and analyze the energy vs. accuracy trade-off. The herein presented approach, jointly considering signal processing and IoT network issues, is a relevant contribution for designing green compressive sampling architectures in IoT networks.

A statistical model for brain networks inferred from large-scale electrophysiological signals

Network science has been extensively developed to characterize the structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally obtained biological data represent one instance of a larger number of realizations with similar intrinsic topology. A modelling approach is therefore needed to support statistical inference on the bottom-up local connectivity mechanisms influencing the formation of the estimated brain networks. Here, we adopted a statistical model based on exponential random graph models (ERGMs) to reproduce brain networks, or connectomes, estimated by spectral coherence between high-density electroencephalographic (EEG) signals. ERGMs are made up by different local graph metrics, whereas the parameters weight the respective contribution in explaining the observed network. We validated this approach in a dataset of N = 108 healthy subjects during eyes-open (EO) and eyes-closed (EC) resting-state conditions. Results showed that the tendency to form triangles and stars, reflecting clustering and node centrality, better explained the global properties of the EEG connectomes than other combinations of graph metrics. In particular, the synthetic networks generated by this model configuration replicated the characteristic differences found in real brain networks, with EO eliciting significantly higher segregation in the alpha frequency band (8-13 Hz) than EC. Furthermore, the fitted ERGM parameter values provided complementary information showing that clustering connections are significantly more represented from EC to EO in the alpha range, but also in the beta band (14-29 Hz), which is known to play a crucial role in cortical processing of visual input and externally oriented attention. Taken together, these findings support the current view of the functional segregation and integration of the brain in terms of modules and hubs, and provide a statistical approach to extract new information on the (re)organizational mechanisms in healthy and diseased brains.

A Topological Criterion for Filtering Information in Complex Brain Networks

In many biological systems, the network of interactions between the elements can only be inferred from experimental measurements. In neuroscience, non-invasive imaging tools are extensively used to derive either structural or functional brain networks in-vivo. As a result of the inference process, we obtain a matrix of values corresponding to a fully connected and weighted network. To turn this into a useful sparse network, thresholding is typically adopted to cancel a percentage of the weakest connections. The structural properties of the resulting network depend on how much of the inferred connectivity is eventually retained. However, how to objectively fix this threshold is still an open issue. We introduce a criterion, the efficiency cost optimization (ECO), to select a threshold based on the optimization of the trade-off between the efficiency of a network and its wiring cost. We prove analytically and we confirm through numerical simulations that the connection density maximizing this trade-off emphasizes the intrinsic properties of a given network, while preserving its sparsity. Moreover, this density threshold can be determined a-priori, since the number of connections to filter only depends on the network size according to a power-law. We validate this result on several brain networks, from micro- to macro-scales, obtained with different imaging modalities. Finally, we test the potential of ECO in discriminating brain states with respect to alternative filtering methods. ECO advances our ability to analyze and compare biological networks, inferred from experimental data, in a fast and principled way.

Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles

Fiber bundles stemming from tractography algorithms contain many streamlines. They require therefore a great amount of computer memory and computational resources to be stored, visualised and processed. We propose an approximation scheme for fiber bundles which results in a parsimonious representation of weighted prototypes. Prototypes are chosen among the streamlines and they represent groups of similar streamlines. Their weight is related to the number of approximated streamlines. Both streamlines and prototypes are modelled as weighted currents. This computational model does not need point-to-point correspondences and two streamlines are considered similar if their endpoints are close to each other and if their pathways follow similar trajectories. Moreover, the space of weighted currents is a vector space with a closed-form metric. This permits easy computation of the approximation error and the selection of the prototypes is based on the minimisation of this error. We propose an iterative algorithm which approximates independently and simultaneously all the fascicles of the bundle in a fast and accurate way. We show that the resulting representation preserves the shape of the bundle and it can be used to accurately reconstruct the original structural connectivity. We evaluate our algorithm on bundles obtained from both deterministic and probabilistic tractography algorithms. The resulting approximations use on average only 2% of the original streamlines as prototypes. This drastically reduces the computational burden of the processes where the geometry of the streamlines is considered. We demonstrate its effectiveness using as example the registration between two fiber bundles.

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

Hierarchy of neural organization in the embryonic spinal cord: Granger-causality graph analysis of in vivo calcium imaging data

The recent development of genetically encoded calcium indicators enables monitoring in vivo the activity of neuronal populations. Most analysis of these calcium transients relies on linear regression analysis based on the sensory stimulus applied or the behavior observed. To estimate the basic properties of the functional neural circuitry, we propose a network approach to calcium imaging recorded at single cell resolution. Differently from previous analysis based on cross-correlation, we used Granger-causality estimates to infer information propagation between the activities of different neurons. The resulting functional network was then modeled as a directed graph and characterized in terms of connectivity and node centralities. We applied our approach to calcium transients recorded at low frequency (4 Hz) in ventral neurons of the zebrafish spinal cord at the embryonic stage when spontaneous coiling of the tail occurs. Our analysis on population calcium imaging data revealed a strong ipsilateral connectivity and a characteristic hierarchical organization of the network hubs that supported established propagation of activity from rostral to caudal spinal cord. Our method could be used for detecting functional defects in neuronal circuitry during development and pathological conditions.

Node accessibility in cortical networks during motor tasks

Recent findings suggest that the preparation and execution of voluntary self-paced movements are accompanied by the coordination of the oscillatory activities of distributed brain regions. Here, we use electroencephalographic source imaging methods to estimate the cortical movement-related oscillatory activity during finger extension movements. Then, we apply network theory to investigate changes (expressed as differences from the baseline) in the connectivity structure of cortical networks related to the preparation and execution of the movement. We compute the topological accessibility of different cortical areas, measuring how well an area can be reached by the rest of the network. Analysis of cortical networks reveals specific agglomerates of cortical sources that become less accessible during the preparation and the execution of the finger movements. The observed changes neither could be explained by other measures based on geodesics or on multiple paths, nor by power changes in the cortical oscillations.

Nonparametric resampling of random walks for spectral network clustering

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.

Multiscale topological properties of functional brain networks during motor imagery after stroke

In recent years, network analyses have been used to evaluate brain reorganization following stroke. However, many studies have often focused on single topological scales, leading to an incomplete model of how focal brain lesions affect multiple network properties simultaneously and how changes on smaller scales influence those on larger scales. In an EEG-based experiment on the performance of hand motor imagery (MI) in 20 patients with unilateral stroke, we observed that the anatomic lesion affects the functional brain network on multiple levels. In the beta (13-30 Hz) frequency band, the MI of the affected hand (Ahand) elicited a significantly lower smallworldness and local efficiency (Eloc) versus the unaffected hand (Uhand). Notably, the abnormal reduction in Eloc significantly depended on the increase in interhemispheric connectivity, which was in turn determined primarily by the rise of regional connectivity in the parieto-occipital sites of the affected hemisphere. Further, in contrast to the Uhand MI, in which significantly high connectivity was observed for the contralateral sensorimotor regions of the unaffected hemisphere, the regions with increased connectivity during the Ahand MI lay in the frontal and parietal regions of the contralaterally affected hemisphere. Finally, the overall sensorimotor function of our patients, as measured by Fugl-Meyer Assessment (FMA) index, was significantly predicted by the connectivity of their affected hemisphere. These results improve on our understanding of stroke-induced alterations in functional brain networks.

Resting state cortical EEG rhythms in Alzheimer's disease: toward EEG markers for clinical applications: a review

The human brain contains an intricate network of about 100 billion neurons. Aging of the brain is characterized by a combination of synaptic pruning, loss of cortico-cortical connections, and neuronal apoptosis that provoke an age-dependent decline of cognitive functions. Neural/synaptic redundancy and plastic remodeling of brain networking, also secondary to mental and physical training, promote maintenance of brain activity and cognitive status in healthy elderly subjects for everyday life. However, age is the main risk factor for neurodegenerative disorders such as Alzheimer's disease (AD) that impact on cognition. Growing evidence supports the idea that AD targets specific and functionally connected neuronal networks and that oscillatory electromagnetic brain activity might be a hallmark of the disease. In this line, digital electroencephalography (EEG) allows noninvasive analysis of cortical neuronal synchronization, as revealed by resting state brain rhythms. This review provides an overview of the studies on resting state eyes-closed EEG rhythms recorded in amnesic mild cognitive impairment (MCI) and AD subjects. Several studies support the idea that spectral markers of these EEG rhythms, such as power density, spectral coherence, and other quantitative features, differ among normal elderly, MCI, and AD subjects, at least at group level. Regarding the classification of these subjects at individual level, the most previous studies showed a moderate accuracy (70-80%) in the classification of EEG markers relative to normal and AD subjects. In conclusion, resting state EEG makers are promising for large-scale, low-cost, fully noninvasive screening of elderly subjects at risk of AD.

High-resolution EEG analysis of power spectral density maps and coherence networks in a proportional reasoning task

Proportional reasoning is very important logical skill required in mathematics and science problem solving as well as in everyday life decisions. However, there is a lack of studies on neurophysiological correlates of proportional reasoning. To explore the brain activity of healthy adults while performing a balance scale task, we used high-resolution EEG techniques and graph-theory based connectivity analysis. After unskilled subjects learned how to properly solve the task, their cortical power spectral density (PSD) maps revealed an increased parietal activity in the beta band. This indicated that subjects started to perform calculations. In addition, the number of inter-hemispheric connections decreased after learning, implying a rearrangement of the brain activity. Repeated performance of the task led to the PSD decrease in the beta and gamma bands among parietal and frontal regions along with a synchronization of lower frequencies. These findings suggest that repetition led to a more automatic task performance. Subjects were also divided in two groups according to their scores on the test of logical thinking (TOLT). Although no group differences in the accuracy and reaction times were found, EEG data showed higher activity in the beta and gamma bands for the group that scored better on TOLT. Learning and repetition induced changes in the pattern of functional connectivity were evident for all frequency bands. Overall, the results indicated that higher frequency oscillations in frontal and parietal regions are particularly important for proportional reasoning.

A graph-theoretical approach in brain functional networks. Possible implications in EEG studies

BACKGROUND

Recently, it was realized that the functional connectivity networks estimated from actual brain-imaging technologies (MEG, fMRI and EEG) can be analyzed by means of the graph theory, that is a mathematical representation of a network, which is essentially reduced to nodes and connections between them.

METHODS

We used high-resolution EEG technology to enhance the poor spatial information of the EEG activity on the scalp and it gives a measure of the electrical activity on the cortical surface. Afterwards, we used the Directed Transfer Function (DTF) that is a multivariate spectral measure for the estimation of the directional influences between any given pair of channels in a multivariate dataset. Finally, a graph theoretical approach was used to model the brain networks as graphs. These methods were used to analyze the structure of cortical connectivity during the attempt to move a paralyzed limb in a group (N=5) of spinal cord injured patients and during the movement execution in a group (N=5) of healthy subjects.

RESULTS

Analysis performed on the cortical networks estimated from the group of normal and SCI patients revealed that both groups present few nodes with a high out-degree value (i.e. outgoing links). This property is valid in the networks estimated for all the frequency bands investigated. In particular, cingulate motor areas (CMAs) ROIs act as ''hubs'' for the out fl ow of information in both groups, SCI and healthy. Results also suggest that spinal cord injuries affect the functional architecture of the cortical network sub-serving the volition of motor acts mainly in its local feature property.In particular, a higher local efficiency El can be observed in the SCI patients for three frequency bands, theta (3-6 Hz), alpha (7-12 Hz) and beta (13-29 Hz).By taking into account all the possible pathways between different ROI couples, we were able to separate clearly the network properties of the SCI group from the CTRL group. In particular, we report a sort of compensatory mechanism in the SCI patients for the Theta (3-6 Hz) frequency band, indicating a higher level of "activation" Omega within the cortical network during the motor task. The activation index is directly related to diffusion, a type of dynamics that underlies several biological systems including possible spreading of neuronal activation across several cortical regions.

CONCLUSIONS

The present study aims at demonstrating the possible applications of graph theoretical approaches in the analyses of brain functional connectivity from EEG signals. In particular, the methodological aspects of the i) cortical activity from scalp EEG signals, ii) functional connectivity estimations iii) graph theoretical indexes are emphasized in the present paper to show their impact in a real application.

Patterns of cortical activity during the observation of Public Service Announcements and commercial advertisings

BACKGROUND

In the present research we were interested to study the cerebral activity of a group of healthy subjects during the observation a documentary intermingled by a series of TV advertisements. In particular, we desired to examine whether Public Service Announcements (PSAs) are able to elicit a different pattern of activity, when compared with a different class of commercials, and correlate it with the memorization of the showed stimuli, as resulted from a following subject's verbal interview.

METHODS

We recorded the EEG signals from a group of 15 healthy subjects and applied the High Resolution EEG techniques in order to estimate and map their Power Spectral Density (PSD) on a realistic cortical model. The single subjects' activities have been z-score transformed and then grouped to define four different datasets, related to subjects who remembered and forgotten the PSAs and to subjects who remembered and forgotten cars commercials (CAR) respectively, which we contrasted to investigate cortical areas involved in this encoding process.

RESULTS

The results we here present show that the cortical activity elicited during the observation of the TV commercials that were remembered (RMB) is higher and localized in the left frontal brain areas when compared to the activity elicited during the vision of the TV commercials that were forgotten (FRG) in theta and gamma bands for both categories of advertisements (PSAs and CAR). Moreover, the cortical maps associated with the PSAs also show an increase of activity in the alpha and beta band.

CONCLUSIONS

In conclusion, the TV advertisements that will be remembered by the experimental population have increased their cerebral activity, mainly in the left hemisphere. These results seem to be congruent with and well inserted in the already existing literature, on this topic, related to the HERA model. The different pattern of activity in different frequency bands elicited by the observation of PSAs may be justified by the existence of additional cortical networks processing these kind of audiovisual stimuli. Further research with an extended set of subjects will be necessary to further validate the observations reported in this paper.

The study of brain activity during the observation of commercial advertising by using high resolution EEG techniques

In this paper we illustrate the capability of tracking brain activity during the observation of commercial TV spots by using advanced high resolution EEG statistical techniques in time and frequency domains. In particular, we analyzed the statistically significant cortical spectral power activity in different frequency bands during the observation of a commercial video clip related to the use of a beer in a group of 13 normal subjects. In addition, a TV speech of the prime minister of Italy was analyzed in two groups of swing and "supporter" voters. Results suggested that the cortical activity during the observation of commercial spots could vary consistently across the spot. This fact suggest the possibility to remove the part of the spot that are not particularly attractive by using those cerebral indexes. The cortical activity during the observation of the political speech indicated a major cortical activity in the supporters group when compared to the swing voters. In this case, it is possible to conclude that the communication proposed has failed to raise attention or interest on swing voters. In conclusions, high resolution EEG have been proved able to generate useful insights about the particular fruition of TV messages, related to both commercial as well as political fields.

Cortical network analysis in patients affected by schizophrenia

In the present study, we studied the structural changes of the brain functional network in a group of schizophrenic (SCHZ) patients during a 2-back working memory task. Cortical signals were obtained from scalp EEG signals through the high-resolution EEG technique, which relies on realistic head models and linear inverse solutions. Functional networks were estimated by computing the spectral coherence--i.e. a measure of synchronization in the frequency domain--between the time series of all the available cortical sources. To analyze those cortical networks we followed a theoretical graph approach by computing the network density as the total number of links and the node degree as the number of links of each cortical source. The major result suggest that in the Alpha2 frequency band (11-13 Hz) the cortical functional networks of the SCHZ patients present the largest differences when compared with those of a group of control (CTRL) subjects. In particular, the structure of the SCHZ network altered radically during the memory task, as the number of links that were different from the REST condition increased sensibly with respect to the CTRL network. In addition, a compensatory mechanism was found in the SCHZ patients during the correct performance of the memory task where the node degree showed a frontal asymmetry with higher activation of the left frontal lobe--i.e. higher number of connections--in the Alpha2 frequency band.

Cortical network analysis in patients affected by schizophrenia

In the present study, we studied the structural changes of the brain functional network in a group of schizophrenic (SCHZ) patients during a 2-back working memory task. Cortical signals were obtained from scalp EEG signals through the high-resolution EEG technique, which relies on realistic head models and linear inverse solutions. Functional networks were estimated by computing the spectral coherence--i.e. a measure of synchronization in the frequency domain--between the time series of all the available cortical sources. To analyze those cortical networks we followed a theoretical graph approach by computing the network density as the total number of links and the node degree as the number of links of each cortical source. The major result suggest that in the Alpha2 frequency band (11-13 Hz) the cortical functional networks of the SCHZ patients present the largest differences when compared with those of a group of control (CTRL) subjects. In particular, the structure of the SCHZ network altered radically during the memory task, as the number of links that were different from the REST condition increased sensibly with respect to the CTRL network. In addition, a compensatory mechanism was found in the SCHZ patients during the correct performance of the memory task where the node degree showed a frontal asymmetry with higher activation of the left frontal lobe--i.e. higher number of connections--in the Alpha2 frequency band.

Time-Varying Cortical Connectivity Estimation from Noninvasive, High-Resolution EEG Recordings

Objective: In this paper, we propose a body of techniques for the estimation of rapidly changing connectivity relationships between EEG signals estimated in cortical areas, based on the use of adaptive multivariate autoregressive modeling (AMVAR) for the estimation of a time-varying partial directed coherence (PDC). This approach allows the observation of rapidly changing influences between the cortical areas during the execution of a task, and does not require the stationarity of the signals. Methods: High resolution EEG data were recorded from a group of spinal cord injured (SCI) patients during the attempt to move a paralyzed limb. These data were compared with the time-varying connectivity patterns estimated in a control group during the real execution of the movement. Connectivity was estimated with the use of realistic head modeling and the linear inverse estimation of the cortical activity in a series of regions of interest by using time-varying PDC. Results: The SCI population involved a different cortical network than those generated by the healthy subjects during the task performance. Such a network differs for the involvement of the parietal cortices, which increases in strength near to the movement imagination onset for the SCI when compared to the normal population. Conclusions: The application of time-varying PDC allows tracking the evolution of the connectivity between cortical areas in the analyzed populations during the proposed tasks. Such details about the temporal evolution of the connectivity patterns estimated cannot be obtained with the application of the standard estimators of connectivity.

Brain activity during the memorization of visual scenes from TV commercials: an application of high resolution EEG and steady state somatosensory evoked potentials technologies

The aim of this study was to elucidate if the TV commercials that were remembered by the subjects after their observation within a documentary elicited particular brain activity when compared to the activity generated during the observation of TV commercials that were forgotten. High resolution EEG recordings were performed in a group of 10 healthy subjects with the steady state somatosensory evoked potentials (SSSEPs) technique, in which a series of light electrical stimulation at the left wrist were delivered at the frequency of 20Hz. The brain activity was indexed by the phase delay of the EEG spectral responses at 20Hz with respect to the stimulus delivering and evaluated at the scalp level as well as at the cortical surface using several regions of interest coincident with the Brodmann areas (BAs). Results suggest that the cerebral processes involved during the observation of TV commercials that were remembered by the population examined (RMB dataset) are generated by the posterior parietal cortices and the prefrontal areas, rather bilaterally. These results are compatible with previously results obtained in literature by using MEG and fMRI devices during similar experimental tasks. High resolution EEG is able to summarize, with the use of SSSEPs methodologies, the behavior of the estimated cortical networks subserving the proposed memory tasks. It is likely that such tool could play a role in the next future for the investigation of the neural substrates of the human behavior in decision-making and recognition tasks.

Brain connectivity structure in spinal cord injured: evaluation by graph analysis

The problem of the evaluation of brain connectivity has become a fundamental one in the neurosciences during the latest years, as a way to understand the organization and the interaction of several cortical areas during the execution of cognitive or motor tasks. Following an approach that derives from the graph theory, we analyzed the architectural properties of the networks obtained by the use of DTF measures on the cortical signals estimated from the high resolution EEG recordings. The present work aims at analyse the structure of cortical connectivity during the imagination of a limb movement in spinal cord injured patients, by the computation of the characteristic path length L and the cluster indices Cin and Cout.