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Identifying the driver nodes of a network has crucial implications in biological systems from unveiling causal interactions to informing effective intervention strategies. Despite recent advances in network control theory, results remain inaccurate as the number of drivers becomes too small compared to the network size, thus limiting the concrete usability in many real-life applications. To overcome this issue, we introduced a framework that integrates principles from spectral graph theory and output controllability to project the network state into a smaller topological space formed by the Laplacian network structure. Through extensive simulations on synthetic and real networks, we showed that a relatively low number of projected components can significantly improve the control accuracy. By introducing a new low-dimensional controllability metric we experimentally validated our method on N = 6134 human connectomes obtained from the UK-biobank cohort. Results revealed previously unappreciated influential brain regions, enabled to draw directed maps between differently specialized cerebral systems, and yielded new insights into hemispheric lateralization. Taken together, our results offered a theoretically grounded solution to deal with network controllability and provided insights into the causal interactions of the human brain., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2025 Ben Messaoud et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

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., (Copyright © 2020 The Authors. Published by Elsevier Inc. All rights reserved.)

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., (© 2018 The Author(s).)

Alzheimer's disease (AD) causes alterations of brain network structure and function. The latter consists of connectivity changes between oscillatory processes at different frequency channels. We proposed a multi-layer network approach to analyze multiple-frequency brain networks inferred from magnetoencephalographic recordings during resting-states in AD subjects and age-matched controls. Main results showed that brain networks tend to facilitate information propagation across different frequencies, as measured by the multi-participation coefficient (MPC). However, regional connectivity in AD subjects was abnormally distributed across frequency bands as compared to controls, causing significant decreases of MPC. This effect was mainly localized in association areas and in the cingulate cortex, which acted, in the healthy group, as a true inter-frequency hub. MPC values significantly correlated with memory impairment of AD subjects, as measured by the total recall score. Most predictive regions belonged to components of the default-mode network that are typically affected by atrophy, metabolism disruption and amyloid-β deposition. We evaluated the diagnostic power of the MPC and we showed that it led to increased classification accuracy (78.39%) and sensitivity (91.11%). These findings shed new light on the brain functional alterations underlying AD and provide analytical tools for identifying multi-frequency neural mechanisms of brain diseases.

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., (© 2017 The Author(s).)

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., Competing Interests: The authors have declared that no competing interests exist.

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., (© 2014 The Author(s) Published by the Royal Society. All rights reserved.)

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., (Copyright © 2013 Elsevier Inc. All rights reserved.)

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.

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.

In the present study, we propose a theoretical graph procedure to investigate multiple pathways in brain functional networks. By taking into account all the possible paths consisting of h links between the nodes pairs of the network, we measured the global network redundancy R(h) as the number of parallel paths and the global network permeability P(h) as the probability to get connected. We used this procedure to investigate the structural and dynamical changes in the cortical networks estimated from a dataset of high-resolution EEG signals in a group of spinal cord injured (SCI) patients during the attempt of foot movement. In the light of a statistical contrast with a healthy population, the permeability index P(h) of the SCI networks increased significantly (P < 0.01) in the Theta frequency band (3-6 Hz) for distances h ranging from 2 to 4. On the contrary, no significant differences were found between the two populations for the redundancy index R(h). The most significant changes in the brain functional network of SCI patients occurred mainly in the lower spectral contents. These changes were related to an improved propagation of communication between the closest cortical areas rather than to a different level of redundancy. This evidence strengthens the hypothesis of the need for a higher functional interaction among the closest ROIs as a mechanism to compensate the lack of feedback from the peripheral nerves to the sensomotor areas.

Brain Hyperscanning, i.e. the simultaneous recording of the cerebral activity of different human subjects involved in interaction tasks, is a very recent field of Neuroscience aiming at understanding the cerebral processes generating and generated by social interactions. This approach allows the observation and modeling of the neural signature specifically dependent on the interaction between subjects, and, even more interestingly, of the functional links existing between the activities in the brains of the subjects interacting together. In this EEG hyperscanning study we explored the functional hyperconnectivity between the activity in different scalp sites of couples of Civil Aviation Pilots during different phases of a flight reproduced in a flight simulator. Results shown a dense network of connections between the two brains in the takeoff and landing phases, when the cooperation between them is maximal, in contrast with phases during which the activity of the two pilots was independent, when no or quite few links were shown. These results confirms that the study of the brain connectivity between the activity simultaneously acquired in human brains during interaction tasks can provide important information about the neural basis of the "spirit of the group".

Partial Directed Coherence (PDC) is a powerful tool to estimate a frequency domain description of Granger causality between multivariate time series. One of the main limitation of this estimator, however, has been so far the criteria used to assess the statistical significance, which have been obtained through surrogate data approach or arbitrarily imposed thresholds. The aim of this work is to test the performances of a validation approach based on the rigorous asymptotic distributions of PDC, recently proposed in literature. The performances of this method, defined in terms of percentages of false positives and false negatives, were evaluated by means of a simulation study taking into account factors like the Signal to Noise Ratio (SNR) and the amount of data available for the estimation and the use of different methods for the statistical corrections for multiple comparisons. Results of the Analysis Of Variance (ANOVA) performed on false positives and false negatives revealed a strong dependency of the performances from all the factors investigated. In particular, results indicate an amount of Type I errors below 7% for all conditions, while Type II errors are below 10% when the SNR is at least 1, the data length of at least 50 seconds and the appropriate correction for multiple comparisons is applied.

The evaluation of the topological properties of brain networks is an emergent research topic, since the estimated cerebral connectivity patterns often have relatively large size and complex structure. Since a graph is a mathematical representation of a network, the use of a theoretical graph approach would describe concisely the topological features of the functional brain connectivity network estimated using neuroimaging techniques. In the present study, we analyze the changes in brain synchronization networks using high-resolution EEG signals obtained during performance of a complex goal-directed visuomotor task. Our results show that the cortical network is more stable when subjects reach the goal than when they fail by hitting an obstacle. These findings suggest the presence of a possible cerebral "marker" for motor actions that result in successful reaching of a target.

In this study we measured simultaneously by EEG hyperscannings the neuroelectric activity in 6 couples of subjects during the performance of the "Chicken's game", derived from game theory. The simultaneous recording of the EEG in couples of interacting subjects allows to observe and model directly the neural signature of human interactions in order to understand the cerebral processes generating and generated by social cooperation or competition. Results suggested that the one of the most consistently activated structure in this particular social interaction paradigm is the left orbitofrontal cortex. Connectivity results also showed a significant involvement of the orbitofrontal regions of both hemispheres across the observed population. Taken together, results confirms that the study of the brain activities in humans during social interactions can take benefit from the simultaneous acquisition of brain activity during such interaction.

Synchronous brain activity in motor cortex in perception or in complex cognitive processing has been the subject of several studies. The advanced analysis of cerebral electro-physiological activity during the course of planning (PRE) or execution of movement (EXE) in a high temporal resolution could reveal interesting information about the brain functional organization in patients following stroke damage. High-power (128 channels) electroencephalography registration was carried out on 8 healthy subjects and on a patient with stroke with capsular lacuna in the right hemisphere. For activation of motor cortex, the finger tapping paradigm was used. In this preliminary study, we tested a theoretical graph approach to characterize the task-related spectral coherence. All of the obtained brain functional networks were analyzed by the connectivity degree, the degree distribution, and efficiency parameters in the Theta, Alpha, Beta, and Gamma bands during the PRE and EXE intervals. All the brain networks were found to hold a regular and ordered topology. However, significant differences (P < 0.01) emerged between the patient with stroke and the control subjects, independently of the neural processes related to the PRE or EXE periods. In the Beta (13-29 Hz) and Gamma (30-40 Hz) bands, the significant (P < 0.01) decrease in global- and local-efficiency in the patient's networks, reflected a lower capacity to integrate communication between distant brain regions and a lower tendency to be modular. This weak organization is principally due to the significant (P < 0.01 Bonferroni corrected) increase in disconnected nodes together with the significant increase in the links in some other crucial vertices., ((c) 2009 Wiley-Liss, Inc.)

In this paper, different linear and nonlinear methodologies for the estimation of cortical connectivity from neuroelectric and hemodynamic measurements are reviewed and applied on common data set in order to highlight similarities and differences in the results. Different effective and functional connectivity methods were applied to motor and cognitive data sets, including structural equation modeling (SEM), directed transfer function (DTF), partial directed coherence (PDC), and direct directed transfer function (dDTF). Comparisons were made between the results in order to understand if, for a same dataset, effective and functional connectivity estimators can return the same cortical connectivity patterns. An application of a nonlinear method [phase synchronization index (PSI)] to similar executed and imagined movements was also reviewed. Connectivity patterns estimated with the use of the neuroelectric information and of the information from the multimodal integration of neuroelectric and hemodynamic data were also compared. Results suggests that the estimation of the cortical connectivity patterns performed with the linear methods (SEM, DTF, PDC, dDTF) or with the nonlinear method (PSI) on movement related potentials returned similar cortical networks. Differences in cortical connectivity were noted between the patterns estimated with the use of multimodal integration and those estimated by using only the neuroelectric data.

Objective: This work intends to evaluate the functional characteristics of the cerebral network during the successful memory encoding of TV commercials., Methods: We estimated the functional networks in the frequency domain from a set of high-resolution EEG data in a group of healthy subjects during the showing of commercial spots within a neutral documentary. We evaluated the differences in the cortical network associated with later remembered and not-remembered commercials by calculating the global-E(g) and local-efficiency E(l) indexes., Results: Successful encoding of TV spots significantly affects the functional communication among cortical areas irrespectively of the frequency band. During the visualization of the video-clips that will be forgotten (FRG), the cortical network exhibited high values of global- and local-efficiency, reflecting a small-world configuration. During the visualization of the video-clips that will be remembered (RMB), the same indexes appeared significantly lower. This difference was especially evident for E(l) in the alpha band and for E(g) in the beta and gamma bands., Conclusions: The presence of attentional and semantic processes during the RMB condition leads to a significant reduction of the network communication efficiency., Significance: Such a reduction could represent a predictive measure of accurate recalls of TV spots.

The extraction of the salient characteristics from brain connectivity patterns is an open challenging topic since often the estimated cerebral networks have a relative large size and complex structure. Since a graph is a mathematical representation of a network, which is essentially reduced to nodes and connections between them, the use of a theoretical graph approach would extract significant information from the functional brain networks estimated through different neuroimaging techniques. The present work intends to support the development of the "brain network analysis:" a mathematical tool consisting in a body of indexes based on the graph theory able to improve the comprehension of the complex interactions within the brain. In the present work, we applied for demonstrative purpose some graph indexes to the time-varying networks estimated from a set of high-resolution EEG data in a group of healthy subjects during the performance of a motor task. The comparison with a random benchmark allowed extracting the significant properties of the estimated networks in the representative Alpha (7-12 Hz) band. Altogether, our findings aim at proving how the brain network analysis could reveal important information about the time-frequency dynamics of the functional cortical networks.

The present work intends to evaluate the dynamics of the cerebral networks during the preparation and the execution of the foot movement. In order to achieve this objective, we have used mathematical tools capable of estimating the cortical activity via high-resolution EEG techniques. Afterwards we estimated, the instantaneous relationships occurring among the time-series of sixteen regions of interest (ROIs) in the Alpha (7-12 Hz) and Beta (13-29 Hz) band through the adaptive multivariate autoregressive models. Eventually, we evaluated the weighted-topology of the cerebral networks by calculating some theoretical graph indexes. The results show that the main structural changes are encoded in the highest spectral contents (Beta band). In particular, during the execution of the foot movement the cingulate motor areas (CM) work as network "hubs" presenting a large amount of outgoing links to the other ROIs. Moreover, the connectivity pattern changes its structure according to the different temporal stages of the task. In particular, the communication between the ROIs reaches its highest level of efficiency during the preparation of the foot movement, as revealed by the "small-world" property of the network, which is characterized by the presence of abundant clustering connections combined with short average distances between the cortical areas.

In the present study, we estimated the cortical networks were from high-resolution EEG recordings in a group of spinal cord injured patients and in a group of healthy subjects, during the preparation of a limb movement. Then, we use the Markov Clustering method to analyse the division of the network into community structures. The results indicate large differences between the injured patients and the healthy subjects. In particular, the networks of spinal cord injured patient exhibited a higher density of clusters. In the Alpha (7-12 Hz) frequency band, the two observed largest communities were mainly composed by the cingulate motor areas with the supplementary motor areas, and by the pre-motor areas with the right primary motor area of the foot. This functional separation could reflect the partial alteration in the primary motor areas because of the effects of the spinal cord injury.

The present work aims at analyzing the structure of cortical connectivity during the attempt to move a paralyzed limb by a group of spinal cord injured (SCI) patients. Connectivity patterns were obtained by means of the Directed Transfer Function applied to the cortical signals estimated from high resolution EEG recordings. Electrical activity were estimated in normals (Healthy) and SCI patients on twelve regions of interest (ROIs) coincident with Brodmann areas. Degree distributions showed the presence of few cortical regions with a lot of outgoing connections in all the cortical networks estimated irrespectively of the frequency band investigated. For both of the groups (SCI and Healthy), bilateral cingulate motor area (CMA) acts as hub transmitting information flows. The efficiency index, allowed to assert the ordered properties of such estimated cortical networks in both populations. The comparison of such estimated networks with those obtained from random networks, elicited significant differences (P < 0.05, Bonferroni-corrected for multiple comparisons). A statistical comparison (ANOVA) between SCI patients and healthy subjects showed a significant difference (P < 0.05) between the local efficiency of their respective networks. For three frequency bands (theta 4-7 Hz, alpha 8-12 Hz, and beta 13-29 Hz) the higher value observed in the spinal cord injured population entails a larger level of internal organization and fault tolerance. This fact suggests a sort of compensative mechanism as local response to the alteration in their MIF areas, which is probably due to the indirect effects of the spinal injury., ((copyright) 2007 Wiley-Liss, Inc.)

In this work, a novel approach is proposed in order to capture relevant features related to the structure and organization of the functional brain networks estimated in the time-frequency domain. To achieve this, we used a cascade of computational tools able to estimate first the electrical activity of the cortical surface by using high resolution EEG techniques. Then, on the cortical signals from different regions of interests we estimated the time-varying functional connectivity patterns by means of the adaptive Partial Directed Coherence. Such time-varying connectivity estimation returns a series of causality patterns evolving during the examined task which can be summarized and interpreted with the aid of mathematical indexes based on the graph theory. The combination of all these methods is demonstrated on a set of high resolution EEG data recorded from a healthy subject performing a simple foot movement.

In this paper we propose the use of an adaptive multivariate approach to define time-varying multivariate estimators based on the Directed Transfer Function (DTF) and the Partial Directed Coherence (PDC). DTF and PDC are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. Time-varying DTF and PDC were obtained by the adaptive recursive fit of an MVAR model with time-dependent parameters, by means of a generalized recursive least-square (RLS) algorithm, taking into consideration a set of EEG epochs. Such estimators are able to follow rapid changes in the connectivity between cortical areas during an experimental task. We provide an application to the cortical estimations obtained from high resolution EEG data, recorded from a group of healthy subject during a combined foot-lips movement, and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected, one constant across the task and the other evolving during the preparation of the joint movement.

The aim of this paper is to test a technique called partial directed coherence (PDC) and its modification (squared PDC; sPDC) for the estimation of human cortical connectivity by means of simulation study, in which both PDC and sPDC were studied by analysis of variance. The statistical analysis performed returned that both PDC and sPDC are able to estimate correctly the imposed connectivity patterns when data exhibit a signal-to-noise ratio of at least 3 and a length of at least 27 s of nonconsecutive recordings at 250 Hz of sampling rate, equivalent, more generally, to 6750 data samples.

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.

The Directed Transfer Function (DTF) and the Partial Directed Coherence (PDC) are frequency-domain estimators, based on the multivariate autoregressive modelling (MVAR) of time series, that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods requires the stationary of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR). This approach will allow the observation of transient influences between the cortical areas during the execution of a task. Time-varying DTF and PDC were obtained by the adaptive recursive fit of an MVAR model with time-dependent parameters, by means of a generalized recursive least-square (RLS) algorithm, taking into consideration a set of EEG epochs. Simulations were performed under different levels of Signal to Noise Ratio (SNR), number of trials (TRIALS) and frequency bands (BAND), and of different values of the RLS adaptation factor adopted (factor C). The results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of SNR ad number of trials. Moreover, the capability of follow the rapid changes in connectivity is highly increased by the number of trials at disposal, and by the right choice of the value adopted for the adaptation factor C. The results of the simulation study indicate that DTF and PDC computed on adaptive MVAR can be effectively used to estimate time-varying patterns of functional connectivity between cortical activations, under general conditions met in practical EEG recordings.

The problem of the definition and evaluation of brain connectivity has become a central one in neuroscience during the latest years, as a way to understand the organization and interaction of cortical areas during the execution of cognitive or motor tasks. In this paper we propose the use of the DTF method on cortical signals estimated from high resolution EEG recordings. An application of the proposed technique to the estimation of cortical connectivity pattern in normal subjects and in one spinal cord injured patient is also provided.