Tracking the time-varying cortical connectivity patterns by adaptive multivariate estimators

Electroencephalography Neurofeedback Training with Focus on the State of Attention: An Investigation Using Source Localization and Effective Connectivity

Identifying brain activity and flow direction can help in monitoring the effectiveness of neurofeedback tasks that aim to treat cognitive deficits. The goal of this study was to compare the neuronal electrical activity of the cortex between individuals from two groups-low and high difficulty-based on a spatial analysis of electroencephalography (EEG) acquired through neurofeedback sessions. These sessions require the subjects to maintain their state of attention when executing a task. EEG data were collected during three neurofeedback sessions for each person, including theta and beta frequencies, followed by a comprehensive preprocessing. The inverse solution based on cortical current density was applied to identify brain regions related to the state of attention. Thereafter, effective connectivity between those regions was estimated using the Directed Transfer Function. The average cortical current density of the high-difficulty group demonstrated that the medial prefrontal, dorsolateral prefrontal, and temporal regions are related to the attentional state. In contrast, the low-difficulty group presented higher current density values in the central regions. Furthermore, for both theta and beta frequencies, for the high-difficulty group, flows left and entered several regions, unlike the low-difficulty group, which presented flows leaving a single region. In this study, we identified which brain regions are related to the state of attention in individuals who perform more demanding tasks (high-difficulty group).

An evaluation of inter-brain EEG coupling methods in hyperscanning studies

EEG-based hyperscanning technology has been increasingly applied to analyze interpersonal interactions in social neuroscience in recent years. However, different methods are employed in various of studies without a complete investigation of the suitability of these methods. Our study aimed to systematically compare typical inter-brain EEG coupling methods, with simulated EEG data generated by real EEG data. In particular, two critical metrics of noise level and time delay were manipulated, and three different coupling models were tested. The results revealed that: (1) under certain conditions, various methods were leveraged by noise level and time delay, leading to different performances; (2) most algorithms achieved better experimental results and performance under high coupling degree; (3) with our simulation process, temporal and spectral models showed relatively good results, while data simulated with phase coupling model performed worse. This is the first systematic comparison of typical inter-brain EEG coupling methods, with simulated EEG data generated by real EEG data from different subjects. Existing methods mainly focused on intra-brain coupling. To our knowledge, there was only one previous study that compared five inter-brain EEG coupling methods (Burgess in Front Human Neurosci 7:881, 2013). However, the simulated data used in this study were generated time series with varied degrees of phase coupling without considering any EEG characteristics. For future research, appropriate methods need to be selected based on possible underlying mechanisms (temporal, spectral and phase coupling model hypothesis) of a specific study, as well as the expected coupling degree and conditions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09911-1.

Time-varying information measures: an adaptive estimation of information storage with application to brain-heart interactions

Network Physiology is a rapidly growing field of study that aims to understand how physiological systems interact to maintain health. Within the information theory framework the information storage (IS) allows to measure the regularity and predictability of a dynamic process under stationarity assumption. However, this assumption does not allow to track over time the transient pathways occurring in the dynamical activity of a physiological system. To address this limitation, we propose a time-varying approach based on the recursive least squares algorithm (RLS) for estimating IS at each time instant, in non-stationary conditions. We tested this approach in simulated time-varying dynamics and in the analysis of electroencephalographic (EEG) signals recorded from healthy volunteers and timed with the heartbeat to investigate brain-heart interactions. In simulations, we show that the proposed approach allows to track both abrupt and slow changes in the information stored in a physiological system. These changes are reflected in its evolution and variability over time. The analysis of brain-heart interactions reveals marked differences across the cardiac cycle phases of the variability of the time-varying IS. On the other hand, the average IS values exhibit a weak modulation over parieto-occiptal areas of the scalp. Our study highlights the importance of developing more advanced methods for measuring IS that account for non-stationarity in physiological systems. The proposed time-varying approach based on RLS represents a useful tool for identifying spatio-temporal dynamics within the neurocardiac system and can contribute to the understanding of brain-heart interactions.

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks.

Exploring the Temporal Patterns of Dynamic Information Flow during Attention Network Test (ANT)

The attentional processes are conceptualized as a system of anatomical brain areas involving three specialized networks of alerting, orienting and executive control, each of which has been proven to have a relation with specified time-frequency oscillations through electrophysiological techniques. Nevertheless, at present, it is still unclear how the idea of these three independent attention networks is reflected in the specific short-time topology propagation of the brain, assembled with complexity and precision. In this study, we investigated the temporal patterns of dynamic information flow in each attention network via electroencephalograph (EEG)-based analysis. A modified version of the attention network test (ANT) with an EEG recording was adopted to probe the dynamic topology propagation in the three attention networks. First, the event-related potentials (ERP) analysis was used to extract sub-stage networks corresponding to the role of each attention network. Then, the dynamic network model of each attention network was constructed by post hoc test between conditions followed by the short-time-windows fitting model and brain network construction. We found that the alerting involved long-range interaction among the prefrontal cortex and posterior cortex of brain. The orienting elicited more sparse information flow after the target onset in the frequency band 1-30 Hz, and the executive control contained complex top-down control originating from the frontal cortex of the brain. Moreover, the switch of the activated regions in the associated time courses was elicited in attention networks contributing to diverse processing stages, which further extends our knowledge of the mechanism of attention networks.

Interictal Functional Connectivity in Focal Refractory Epilepsies Investigated by Intracranial EEG

Introduction: Focal epilepsies are diseases of neuronal excitability affecting macroscopic networks of cortical and subcortical neural structures. These networks ("epileptogenic networks") can generate pathological electrophysiological activities during seizures, and also between seizures (interictal period). Many works attempt to describe these networks by using quantification methods, particularly based on the estimation of statistical relationships between signals produced by brain regions, namely functional connectivity (FC). Results: FC has been shown to be greatly altered during seizures and in the immediate peri-ictal period. An increasing number of studies have shown that FC is also altered during the interictal period depending on the degree of epileptogenicity of the structures. Furthermore, connectivity values could be correlated with other clinical variables including surgical outcome. Significance: This leads to a conceptual change and to consider epileptic areas as both hyperexcitable and abnormally connected. These data open the door to the use of interictal FC as a marker of epileptogenicity and as a complementary tool for predicting the effect of surgery. Aim: In this article, we review the available data concerning interictal FC estimated from intracranial electroencephalograhy (EEG) in focal epilepsies and discuss it in the light of data obtained from other modalities (EEG imaging) and modeling studies.

Constructing Time-varying Directed EEG network by Multivariate Nonparametric Dynamical Granger Causality

Time-varying directed electroencephalography (EEG) network is the potential tool for studying the dynamical causality among brain areas at a millisecond level; which conduces to understanding how our brain effectively adapts to information processing, giving inspiration to causality- and brain-inspired machine learning. Currently, its construction still mainly relies on the parametric approach such as multivariate adaptive autoregressive (MVAAR), represented by the most widely used adaptive directed transfer function (ADTF). Restricted by the model assumption, the corresponding performance largely depends on the MVAAR modeling which usually encounters difficulty in fitting complex spectral features. In this study, we proposed to construct EEG directed network with multivariate nonparametric dynamical Granger causality (mndGC) method that infers the causality of a network, instead, in a data-driven way directly and therefore avoids the trap in the model-dependent parametric approach. Comparisons between mndGC and ADTF were conducted both with simulation and real data application. Simulation study demonstrated the superiority of mndGC both in noise resistance and capturing the instantaneous directed network changes. When applying to the real motor imagery (MI) data set, distinguishable network characters between left- and right-hand MI during different MI stages were better revealed by mndGC. Our study extends the nonparametric causality exploration and provides practical suggestions for the time-varying directed EEG network analysis.

Effective connectivity in cortical networks during deception: A lie detection study using EEG

Previous studies have identified activated regions associated with deceptive tasks and most of them utilized time, frequency, or temporal features to identify deceptive responses. However, when deception behaviors occur, the functional connectivity pattern and the communication between different brain areas remain largely unclear. In this study, we explored the most important information flows between different brain cortices during deception. First, we employed the guilty knowledge test protocol and recorded on 64 electrodes electroencephalogram (EEG) signals from 30 subjects (15 guilty and 15 innocent). EEG source estimation was then performed to compute the cortical activities on the 24 regions of interest (ROIs). Next, effective connectivity was calculated by partial directed coherence (PDC) analysis applied to the cortical signals. Furthermore, based on the graph-theoretical analysis, the network parameters with significant differences were extracted as features to identify two groups of subjects. In addition, the ROIs frequently involved in the above network parameters were selected, and based on the difference in the group mean of PDC values of all the edges connected with the selected ROIs, we presented the strongest information flows (MIIF) in the guilty group relative to the innocent group. Experimental results first show that the optimal classification features are mainly in-degree and out-degree measures of the ROI and the high classification accuracy for four bands demonstrated that the proposed method is suitable for lie detection. In addition, the frontoparietal network was found to be most prominent among all the MIIFs in four bands. Finally, combining the neurophysiology signification of four frequency bands, respectively, we analyzed the roles of all the important information flows to uncover the underlying cognitive processes and mechanisms used in deception.

Dynamic corticomuscular multi-regional modulations during finger movement revealed by time-varying network analysis

OBJECTIVE

A body movement involves the complicated information exchange between the central and peripheral systems, which is characterized by the dynamical coupling patterns between the multiple brain areas and multiple muscle units. How the central and peripheral nerves coordinate multiple internal brain regions and muscle groups is very important when accomplishing the action.

APPROACH

In this study, we extend the adaptive directed transfer function to construct the time-varying networks between multiple corticomuscular regions and divide the movement duration into different stages by the time-varying corticomuscular network patterns.

MAIN RESULTS

The inter dynamical corticomuscular network demonstrated the different interaction patterns between the central and peripheral systems during the different hand movement stages. The muscles transmit bottom-up movement information in the preparation stage, but the brain issues top-down control commands and dominates in the execution stage, and finally, the brain's dominant advantage gradually weakens in the relaxation stage. When classifying the different movement stages based on time-varying corticomuscular network indicators, an average accuracy above 74% could be reliably achieved.

SIGNIFICANCE

The findings of this study help deepen our knowledge of central-peripheral nerve pathways and coordination mechanisms, and also provide opportunities for monitoring and regulating movement disorders.

Detecting changes in dynamical structures in synchronous neural oscillations using probabilistic inference

Recent neuroscience studies have suggested that cognitive functions and learning capacity are reflected in the time-evolving dynamics of brain networks. However, an efficient method to detect changes in dynamical brain structures using neural data has yet to be established. To address this issue, we developed a new model-based approach to detect change points in dynamical network structures by combining the model-based network estimation with a phase-coupled oscillator model and sequential Bayesian inference. By giving the model parameter as the prior distribution, applying Bayesian inference allows the extent of temporal changes in dynamic brain networks to be quantified by comparing the prior distribution with the posterior distribution using information theoretical criteria. For this, we used the Kullback-Leibler divergence as an index of such changes. To validate our method, we applied it to numerical data and electroencephalography data. As a result, we confirmed that the Kullback-Leibler divergence only increased when changes in dynamical network structures occurred. Our proposed method successfully estimated both directed network couplings and change points of dynamical structures in the numerical and electroencephalography data. These results suggest that our proposed method can reveal the neural basis of dynamic brain networks.

Deep Transfer Learning for Parkinson’s Disease Monitoring by Image-Based Representation of Resting-State EEG Using Directional Connectivity

Parkinson’s disease (PD) is characterized by abnormal brain oscillations that can change rapidly. Tracking neural alternations with high temporal resolution electrophysiological monitoring methods such as EEG can lead to valuable information about alterations observed in PD. Concomitantly, there have been advances in the high-accuracy performance of deep neural networks (DNNs) using few-patient data. In this study, we propose a method to transform resting-state EEG data into a deep latent space to classify PD subjects from healthy cases. We first used a general orthogonalized directed coherence (gOPDC) method to compute directional connectivity (DC) between all pairwise EEG channels in four frequency bands (Theta, Alpha, Beta, and Gamma) and then converted the DC maps into 2D images. We then used the VGG-16 architecture (trained on the ImageNet dataset) as our pre-trained model, enlisted weights of convolutional layers as initial weights, and fine-tuned all layer weights with our data. After training, the classification achieved 99.62% accuracy, 100% precision, 99.17% recall, 0.9958 F1 score, and 0.9958 AUC averaged for 10 random repetitions of training/evaluating on the proposed deep transfer learning (DTL) network. Using the latent features learned by the network and employing LASSO regression, we found that latent features (as opposed to the raw DC values) were significantly correlated with five clinical indices routinely measured: left and right finger tapping, left and right tremor, and body bradykinesia. Our results demonstrate the power of transfer learning and latent space derivation for the development of oscillatory biomarkers in PD.

Selective attention involves a feature-specific sequential release from inhibitory gating

Selective attention is a fundamental cognitive mechanism that allows our brain to preferentially process relevant sensory information, while filtering out distracting information. Attention is thought to flexibly gate the communication of irrelevant information through top-down alpha-rhythmic (8-12 Hz) functional connections, which influence early visual processing. However, the dynamic effects of top-down influence on downstream visual processing remain unknown. Here, we used electroencephalography to investigate local and network effects of selective attention while subjects attended to distinct features of identical stimuli. We found that attention-related changes in the functional brain network organization emerge shortly after stimulus onset, accompanied by an overall decrease of functional connectivity. Signatures of attentional selection were evident from a sequential release from alpha-band parietal gating in feature-selective areas. The directed connectivity paths and temporal evolution of this release from gating were consistent with the sensory effect of each feature, providing a neural basis for how visual processing quickly prioritizes relevant information in functionally specialized areas.

Laminar dynamics of high amplitude beta bursts in human motor cortex

Motor cortical activity in the beta frequency range is one of the strongest and most studied movement-related neural signals. At the single trial level, beta band activity is often characterized by transient, high amplitude, bursting events rather than slowly modulating oscillations. The timing of these bursting events is tightly linked to behavior, suggesting a more dynamic functional role for beta activity than previously believed. However, the neural mechanisms underlying beta bursts in sensorimotor circuits are poorly understood. To address this, we here leverage and extend recent developments in high precision MEG for temporally resolved laminar analysis of burst activity, combined with a neocortical circuit model that simulates the biophysical generators of the electrical currents which drive beta bursts. This approach pinpoints the generation of beta bursts in human motor cortex to distinct excitatory synaptic inputs to deep and superficial cortical layers, which drive current flow in opposite directions. These laminar dynamics of beta bursts in motor cortex align with prior invasive animal recordings within the somatosensory cortex, and suggest a conserved mechanism for somatosensory and motor cortical beta bursts. More generally, we demonstrate the ability for uncovering the laminar dynamics of event-related neural signals in human non-invasive recordings. This provides important constraints to theories about the functional role of burst activity for movement control in health and disease, and crucial links between macro-scale phenomena measured in humans and micro-circuit activity recorded from animal models.

Stimulus evoked causality estimation in stereo-EEG

Objective.Stereo-electroencephalography (SEEG) has recently gained importance in analyzing brain functions. Its high temporal resolution and spatial specificity make it a powerful tool to investigate the strength, direction, and spectral content of brain networks interactions, especially when these connections are stimulus-evoked. However, choosing the best approach to evaluate the flow of information is not trivial, due to the lack of validated methods explicitly designed for SEEG.Approach.We propose a novel non-parametric statistical test for event-related causality (ERC) assessment on SEEG recordings. Here, we refer to the ERC as the causality evoked by a particular part of the stimulus (a response window (RW)). We also present a data surrogation method to evaluate the performance of a causality estimation algorithm. We finally validated our pipeline using surrogate SEEG data derived from an experimentally collected dataset, and compared the most used and successful measures to estimate effective connectivity, belonging to the Geweke-Granger causality framework.Main results.Here we show that our workflow correctly identified all the directed connections in the RW of the surrogate data and prove the robustness of the procedure against synthetic noise with amplitude exceeding physiological-plausible values. Among the causality measures tested, partial directed coherence performed best.Significance.This is the first non-parametric statistical test for ERC estimation explicitly designed for SEEG datasets. The pipeline, in principle, can also be applied to the analysis of any type of time-varying estimator, if there exists a clearly defined RW.

Dyconnmap: Dynamic connectome mapping-A neuroimaging python module

Despite recent progress in the analysis of neuroimaging data sets, our comprehension of the main mechanisms and principles which govern human brain cognition and function remains incomplete. Network neuroscience makes substantial efforts to manipulate these challenges and provide real answers. For the last decade, researchers have been modelling brain structure and function via a graph or network that comprises brain regions that are either anatomically connected via tracts or functionally via a more extensive repertoire of functional associations. Network neuroscience is a relatively new multidisciplinary scientific avenue of the study of complex systems by pursuing novel ways to analyze, map, store and model the essential elements and their interactions in complex neurobiological systems, particularly the human brain, the most complex system in nature. Due to a rapid expansion of neuroimaging data sets' size and complexity, it is essential to propose and adopt new empirical tools to track dynamic patterns between neurons and brain areas and create comprehensive maps. In recent years, there is a rapid growth of scientific interest in moving functional neuroimaging analysis beyond simplified group or time‐averaged approaches and sophisticated algorithms that can capture the time‐varying properties of functional connectivity. We describe algorithms and network metrics that can capture the dynamic evolution of functional connectivity under this perspective. We adopt the word ‘chronnectome’ (integration of the Greek word ‘Chronos’, which means time, and connectome) to describe this specific branch of network neuroscience that explores how mutually informed brain activity correlates across time and brain space in a functional way. We also describe how good temporal mining of temporally evolved dynamic functional networks could give rise to the detection of specific brain states over which our brain evolved. This characteristic supports our complex human mind. The temporal evolution of these brain states and well‐known network metrics could give rise to new analytic trends. Functional brain networks could also increase the multi‐faced nature of the dynamic networks revealing complementary information. Finally, we describe a python module (https://github.com/makism/dyconnmap) which accompanies this article and contains a collection of dynamic complex network analytics and measures and demonstrates its great promise for the study of a healthy subject's repeated fMRI scans.

Partial directed coherence: twenty years on some history and an appraisal

Here while we reminisce about how partial directed coherence was proposed, its motivation and evolution, we take the opportunity to relate it to some of its kin quantities and some of its offspring. Emphasis is placed on our development of asymptotic criteria to place it as a reliable investigation tool, where the connectivity detection problem is completely solved as opposed to what we call the characterization problem. We end by musing over some points now on our wishlist.

SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms

EEG signals are widely used to estimate brain circuits associated with specific tasks and cognitive processes. The testing of connectivity estimators is still an open issue because of the lack of a ground-truth in real data. Existing solutions such as the generation of simulated data based on a manually imposed connectivity pattern or mass oscillators can model only a few real cases with limited number of signals and spectral properties that do not reflect those of real brain activity. Furthermore, the generation of time series reproducing non-ideal and non-stationary ground-truth models is still missing. In this work, we present the SEED-G toolbox for the generation of pseudo-EEG data with imposed connectivity patterns, overcoming the existing limitations and enabling control of several parameters for data simulation according to the user's needs. We first described the toolbox including guidelines for its correct use and then we tested its performances showing how, in a wide range of conditions, datasets composed by up to 60 time series were successfully generated in less than 5 s and with spectral features similar to real data. Then, SEED-G is employed for studying the effect of inter-trial variability Partial Directed Coherence (PDC) estimates, confirming its robustness.

Roles of Very Fast Ripple (500-1000 Hz) in the Hippocampal Network During Status Epilepticus

Very fast ripples (VFRs, 500-1000 Hz) are considered more specific than high-frequency oscillations (80-500 Hz) as biomarkers of epileptogenic zones. Although VFRs are frequent abnormal phenomena in epileptic seizures, their functional roles remain unclear. Here, we detected the VFRs in the hippocampal network and tracked their roles during status epilepticus (SE) in rats with pilocarpine-induced temporal lobe epilepsy (TLE). All regions in the hippocampal network exhibited VFRs in the baseline, preictal, ictal and postictal states, with the ictal state containing the most VFRs. Moreover, strong phase-locking couplings existed between VFRs and slow oscillations (1-12 Hz) in the ictal and postictal states for all regions. Further investigation indicated that during VFRs, the build-up of slow oscillations in the ictal state began from the temporal lobe and then spread through the whole hippocampal network via two different pathways, which might be associated with the underlying propagation of epileptiform discharges in the hippocampal network. Overall, we provide a functional description of the emergence of VFRs in the hippocampal network during SE, and we also establish that VFRs may be the physiological representation of the pathological alterations in hippocampal network activity during SE in TLE.

BCI Training Effects on Chronic Stroke Correlate with Functional Reorganization in Motor-Related Regions: A Concurrent EEG and fMRI Study

Brain–computer interface (BCI)-guided robot-assisted training strategy has been increasingly applied to stroke rehabilitation, while few studies have investigated the neuroplasticity change and functional reorganization after intervention from multimodality neuroimaging perspective. The present study aims to investigate the hemodynamic and electrophysical changes induced by BCI training using functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) respectively, as well as the relationship between the neurological changes and motor function improvement. Fourteen chronic stroke subjects received 20 sessions of BCI-guided robot hand training. Simultaneous EEG and fMRI data were acquired before and immediately after the intervention. Seed-based functional connectivity for resting-state fMRI data and effective connectivity analysis for EEG were processed to reveal the neuroplasticity changes and interaction between different brain regions. Moreover, the relationship among motor function improvement, hemodynamic changes, and electrophysical changes derived from the two neuroimaging modalities was also investigated. This work suggested that (a) significant motor function improvement could be obtained after BCI training therapy, (b) training effect significantly correlated with functional connectivity change between ipsilesional M1 (iM1) and contralesional Brodmann area 6 (including premotor area (cPMA) and supplementary motor area (SMA)) derived from fMRI, (c) training effect significantly correlated with information flow change from cPMA to iM1 and strongly correlated with information flow change from SMA to iM1 derived from EEG, and (d) consistency of fMRI and EEG results illustrated by the correlation between functional connectivity change and information flow change. Our study showed changes in the brain after the BCI training therapy from chronic stroke survivors and provided a better understanding of neural mechanisms, especially the interaction among motor-related brain regions during stroke recovery. Besides, our finding demonstrated the feasibility and consistency of combining multiple neuroimaging modalities to investigate the neuroplasticity change.

Delta-gamma phase-amplitude coupling as a biomarker of postictal generalized EEG suppression

Postictal generalized EEG suppression is the state of suppression of electrical activity at the end of a seizure. Prolongation of this state has been associated with increased risk of sudden unexpected death in epilepsy, making characterization of underlying electrical rhythmic activity during postictal suppression an important step in improving epilepsy treatment. Phase-amplitude coupling in EEG reflects cognitive coding within brain networks and some of those codes highlight epileptic activity; therefore, we hypothesized that there are distinct phase-amplitude coupling features in the postictal suppression state that can provide an improved estimate of this state in the context of patient risk for sudden unexpected death in epilepsy. We used both intracranial and scalp EEG data from eleven patients (six male, five female; age range 21–41 years) containing 25 seizures, to identify frequency dynamics, both in the ictal and postictal EEG suppression states. Cross-frequency coupling analysis identified that during seizures there was a gradual decrease of phase frequency in the coupling between delta (0.5–4 Hz) and gamma (30+ Hz), which was followed by an increased coupling between the phase of 0.5–1.5 Hz signal and amplitude of 30–50 Hz signal in the postictal state as compared to the pre-seizure baseline. This marker was consistent across patients. Then, using these postictal-specific features, an unsupervised state classifier—a hidden Markov model—was able to reliably classify four distinct states of seizure episodes, including a postictal suppression state. Furthermore, a connectome analysis of the postictal suppression states showed increased information flow within the network during postictal suppression states as compared to the pre-seizure baseline, suggesting enhanced network communication. When the same tools were applied to the EEG of an epilepsy patient who died unexpectedly, ictal coupling dynamics disappeared and postictal phase-amplitude coupling remained constant throughout. Overall, our findings suggest that there are active postictal networks, as defined through coupling dynamics that can be used to objectively classify the postictal suppression state; furthermore, in a case study of sudden unexpected death in epilepsy, the network does not show ictal-like phase-amplitude coupling features despite the presence of convulsive seizures, and instead demonstrates activity similar to postictal. The postictal suppression state is a period of elevated network activity as compared to the baseline activity which can provide key insights into the epileptic pathology.

Nested oscillations and brain connectivity during sequential stages of feature-based attention

Brain mechanisms of visual selective attention involve both local and network-level activity changes at specific oscillatory rhythms, but their interplay remains poorly explored. Here, we investigate anticipatory and reactive effects of feature-based attention using separate fMRI and EEG recordings, while participants attended to one of two spatially overlapping visual features (motion and orientation). We focused on EEG source analysis of local neuronal rhythms and nested oscillations and on graph analysis of connectivity changes in a network of fMRI-defined regions of interest, and characterized a cascade of attentional effects at multiple spatial scales. We discuss how the results may reconcile several theories of selective attention, by showing how β rhythms support anticipatory information routing through increased network efficiency, while reactive α-band desynchronization patterns and increased α-γ coupling in task-specific sensory areas mediate stimulus-evoked processing of task-relevant signals.

Model-based design for seizure control by stimulation

OBJECTIVE

Current brain stimulation paradigms are largely empirical rather than theoretical. An opportunity exists to improve upon their modest effectiveness in closed-loop control strategies with the development of theoretically grounded, model-based designs.

APPROACH

Inspired by this need, here we couple experimental data and mathematical modeling with a control-theoretic strategy for seizure termination. We begin by exercising a dynamical systems approach to model seizures (n = 94) recorded using intracranial EEG (iEEG) from 21 patients with medication-resistant, localization-related epilepsy.

MAIN RESULTS

Although each patient's seizures displayed unique spatial and temporal patterns, their evolution can be parsimoniously characterized by the same model form. Idiosyncracies of the model can inform individualized intervention strategies, specifically in iEEG samples with well-localized seizure onset zones. Temporal fluctuations in the spatial profiles of the oscillatory modes show that seizure onset marks a transition into a regime in which the underlying system supports prolonged rhythmic and focal activity. Based on these observations, we propose a control-theoretic strategy that aims to stabilize ictal activity using static output feedback for linear time-invariant switching systems. Finally, we demonstrate in silico that our proposed strategy allows us to dampen the emerging focal oscillatory sources using only a small set of electrodes.

SIGNIFICANCE

Our integrative study informs the development of modulation and control algorithms for neurostimulation that could improve the effectiveness of implantable, closed-loop anti-epileptic devices.

A regularized and smoothed General Linear Kalman Filter for more accurate estimation of time-varying directed connectivity

Adaptive algorithms based on the Kalman filter are valuable tools to model the dynamic and directed Granger causal interactions between neurophysiological signals simultaneously recorded from multiple cortical regions. Among these algorithms, the General Linear Kalman Filter (GLKF) has proven to be the most accurate and reliable. Here we propose a regularized and smoothed GLKF (spsm-GLKF) with ℓ1 norm penalties based on lasso or group lasso and a fixedinterval smoother. We show that the group lasso penalty promotes sparse solutions by shrinking spurious connections to zero, while the smoothing increases the robustness of the estimates. Overall, our results demonstrate that spsm-GLKF outperforms the original GLKF, and represents a more accurate tool for the characterization of dynamical and sparse functional brain networks.

Overlapping connectivity patterns during semantic processing of abstract and concrete words revealed with multivariate Granger Causality analysis

. Abstract, unlike concrete, nouns refer to notions beyond our perception. Even though there is no consensus among linguists as to what exactly constitutes a concrete or abstract word, neuroscientists found clear evidence of a "concreteness" effect. This can, for instance, be seen in patients with language impairments due to brain injury or developmental disorder who are capable of perceiving one category better than another. Even though the results are inconclusive, neuroimaging studies on healthy subjects also provide a spatial and temporal account of differences in the processing of abstract versus concrete words. A description of the neural pathways during abstract word reading, the manner in which the connectivity patterns develop over the different stages of lexical and semantic processing compared to that of concrete word processing are still debated. We conducted a high-density EEG study on 24 healthy young volunteers using an implicit categorization task. From this, we obtained high spatio-temporal resolution data and, by means of source reconstruction, reduced the effect of signal mixing observed on scalp level. A multivariate, time-varying and directional method of analyzing connectivity based on the concept of Granger Causality (Partial Directed Coherence) revealed a dynamic network that transfers information from the right superior occipital lobe along the ventral and dorsal streams towards the anterior temporal and orbitofrontal lobes of both hemispheres. Some regions along these pathways appear to be primarily involved in either receiving or sending information. A clear difference in information transfer of abstract and concrete words was observed during the time window of semantic processing, specifically for information transferred towards the left anterior temporal lobe. Further exploratory analysis confirmed a generally stronger connectivity pattern for processing concrete words. We believe our study could guide future research towards a more refined theory of abstract word processing in the brain.

Bypassing the volume conduction effect by multilayer neural network for effective connectivity estimation

Differentiation of real interactions between different brain regions from spurious ones has been a challenge in neuroimaging researches. While using electroencephalographic data, those spurious interactions are mostly caused by the volume conduction (VC) effect between the recording sites. In this study, we address the problem by jointly modeling the causal relationships among brain regions and the mixing effects of volume conduction. The VC effect is formulated with a time-invariant linear equation, and the causal relationships between the brain regions are modeled with a nonlinear multivariate autoregressive process. These two models are simultaneously implemented by a multilayer neural network. The internal hidden layers represent the interactions among the regions, while the external layers are devoted for the relationship between the source activities and observed EEG measurements at the scalp. The causal interactions are estimated by the causality coefficient measure, which is based on the information (weights and parameters) embedded in the network. The proposed method is verified using various simulated data. It is then applied to the real EEG signals collected from a memory retrieval test. The results showed that the method is able to eliminate the volume conduction interferences and consequently leads to higher accuracy in identification of true causal interactions. Graphical abstract The proposed network structure used to simultaneously model the volume conduction and source interactions. By this special structure, we first move from the sensor space to the source space at the first layer. Then, within internal hidden layers, the interactions between the sources are represented in the form of a general (nonlinear) multivariate autoregressive (nMVAR) model. Finally, we return from the source space to the sensor space at the last layer of the network. The proposed method bypasses the effect of volume conduction and causes more accurate connectivity estimation.

L-Dopa Modulation of Brain Connectivity in Parkinson's Disease Patients: A Pilot EEG-fMRI Study

Studies of functional neurosurgery and electroencephalography in Parkinson's disease have demonstrated abnormally synchronous activity between basal ganglia and motor cortex. Functional neuroimaging studies investigated brain dysfunction during motor task or resting state and primarily have shown altered patterns of activation and connectivity for motor areas. L-dopa administration relatively normalized these functional alterations. The aim of this pilot study was to examine the effects of L-dopa administration on functional connectivity in early-stage PD, as revealed by simultaneous recording of functional magnetic resonance imaging (fMRI) and electroencephalographic (EEG) data. Six patients with diagnosis of probable PD underwent EEG-fMRI acquisitions (1.5 T MR scanner and 64-channel cap) before and immediately after the intake of L-dopa. Regions of interest in the primary motor and sensorimotor regions were used for resting state fMRI analysis. From the EEG data, weighted partial directed coherence was computed in the inverse space after the removal of gradient and cardioballistic artifacts. fMRI results showed that the intake of L-dopa increased functional connectivity within the sensorimotor network, and between motor areas and both attention and default mode networks. EEG connectivity among regions of the motor network did not change significantly, while regions of the default mode network showed a strong tendency to increase their outflow toward the rest of the brain. This pilot study provided a first insight into the potentiality of simultaneous EEG-fMRI acquisitions in PD patients, showing for both techniques the analogous direction of increased connectivity after L-dopa intake, mainly involving motor, dorsal attention and default mode networks.

Interictal epileptogenic zone localization in patients with focal epilepsy using electric source imaging and directed functional connectivity from low-density EEG

OBJECTIVE

Electrical source imaging (ESI) is used increasingly to estimate the epileptogenic zone (EZ) in patients with epilepsy. Directed functional connectivity (DFC) coupled to ESI helps to better characterize epileptic networks, but studies on interictal activity have relied on high-density recordings. We investigated the accuracy of ESI and DFC for localizing the EZ, based on low-density clinical electroencephalography (EEG).

METHODS

We selected patients with the following: (a) focal epilepsy, (b) interictal spikes on standard EEG, (c) either a focal structural lesion concordant with the electroclinical semiology or good postoperative outcome. In 34 patients (20 temporal lobe epilepsy [TLE], 14 extra-TLE [ETLE]), we marked interictal spikes and estimated the cortical activity during each spike in 82 cortical regions using a patient-specific head model and distributed linear inverse solution. DFC between brain regions was computed using Granger-causal modeling followed by network topologic measures. The concordance with the presumed EZ at the sublobar level was computed using the epileptogenic lesion or the resected area in postoperative seizure-free patients.

RESULTS

ESI, summed outflow, and efficiency were concordant with the presumed EZ in 76% of the patients, whereas the clustering coefficient and betweenness centrality were concordant in 70% of patients. There was no significant difference between ESI and connectivity measures. In all measures, patients with TLE had a significantly higher (P < 0.05) concordance with the presumed EZ than patients with with ETLE. The brain volume accepted for concordance was significantly larger in TLE.

SIGNIFICANCE

ESI and DFC derived from low-density EEG can reliably estimate the EZ from interictal spikes. Connectivity measures were not superior to ESI for EZ localization during interictal spikes, but the current validation of the localization of connectivity measure is promising for other applications.

A Novel Framework for Estimating Time-Varying Multivariate Autoregressive Models and Application to Cardiovascular Responses to Acute Exercise

OBJECTIVE

We present a novel modeling framework for identifying time-varying (TV) couplings between time-series of biomedical relevance.

METHODS

The proposed methodology is based on multivariate autoregressive (MVAR) models, which have been extensively used to study couplings between biosignals. Contrary to the standard estimation methods that assume time-invariant relationships, we propose a modified recursive Kalman filter (KF) to track changes in the model parameters. We perform model order selection and hyperparameter optimization simultaneously using Genetic Algorithms, greatly improving accuracy and computation time. In addition, we address the effect of residual heteroscedasticity, possibly associated with event-related changes or phase transitions during a given experimental protocol, on the TV-MVAR coupling measures by using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to fit the TV-MVAR residuals.

RESULTS

Using simulated data, we show that the proposed framework yields more accurate parameter estimates compared to the conventional KF, particularly when the true system parameters exhibit different rate of variations over time. Furthermore, by accounting for heteroskedasticity, we obtain more accurate estimates of the strength and directionality of the underlying couplings. We also use our approach to investigate TV hemodynamic interactions during exercise in young and old healthy adults, as well as individuals with chronic stroke. We extract TV coupling patterns that reflect well known exercise-induced effects on the underlying regulatory mechanisms with excellent time resolution.

CONCLUSION AND SIGNIFICANCE

The proposed modeling framework can be used to efficiently quantify TV couplings between biosignals. It is fully automated and does not require prior knowledge of the system TV characteristics.

Large-Scale 3-5 Hz Oscillation Constrains the Expression of Neocortical Fast Ripples in a Mouse Model of Mesial Temporal Lobe Epilepsy

Large-scale slow oscillations allow the integration of neuronal activity across brain regions during sensory or cognitive processing. However, evidence that this form of coding also holds for pathological networks, such as for distributed networks in epileptic disorders, does not yet exist. Here, we show in a mouse model of unilateral hippocampal epilepsy that epileptic fast ripples generated in the neocortex distant from the primary focus occur during transient trains of interictal epileptic discharges. During these epileptic paroxysms, local phase-locking of neuronal firing and a phase-amplitude coupling of the epileptic discharges over a slow oscillation at 3-5 Hz are detected. Furthermore, the buildup of the slow oscillation begins in the bihippocampal network that includes the focus, which synchronizes and drives the activity across the large-scale epileptic network into the frontal cortex. This study provides the first functional description of the emergence of neocortical fast ripples in hippocampal epilepsy and shows that cross-frequency coupling might be a fundamental mechanism underlying the spreading of epileptic activity.

Layer 3 Dynamically Coordinates Columnar Activity According to Spatial Context

To reduce statistical redundancy of natural inputs and increase the sparseness of coding, neurons in primary visual cortex (V1) show tuning for stimulus size and surround suppression. This integration of spatial information is a fundamental, context-dependent neural operation involving extensive neural circuits that span across all cortical layers of a V1 column, and reflects both feedforward and feedback processing. However, how spatial integration is dynamically coordinated across cortical layers remains poorly understood. We recorded single- and multiunit activity and local field potentials across V1 layers of awake mice (both sexes) while they viewed stimuli of varying size and used dynamic Bayesian model comparisons to identify when laminar activity and interlaminar functional interactions showed surround suppression, the hallmark of spatial integration. We found that surround suppression is strongest in layer 3 (L3) and L4 activity, where suppression is established within ∼10 ms after response onset, and receptive fields dynamically sharpen while suppression strength increases. Importantly, we also found that specific directed functional connections were strongest for intermediate stimulus sizes and suppressed for larger ones, particularly for connections from L3 targeting L5 and L1. Together, the results shed light on the different functional roles of cortical layers in spatial integration and on how L3 dynamically coordinates activity across a cortical column depending on spatial context.SIGNIFICANCE STATEMENT Neurons in primary visual cortex (V1) show tuning for stimulus size, where responses to stimuli exceeding the receptive field can be suppressed (surround suppression). We demonstrate that functional connectivity between V1 layers can also have a surround-suppressed profile. A particularly prominent role seems to have layer 3, the functional connections to layers 5 and 1 of which are strongest for stimuli of optimal size and decreased for large stimuli. Our results therefore point toward a key role of layer 3 in coordinating activity across the cortical column according to spatial context.

Gating by induced Α-Γ asynchrony in selective attention

Visual selective attention operates through top-down mechanisms of signal enhancement and suppression, mediated by α-band oscillations. The effects of such top-down signals on local processing in primary visual cortex (V1) remain poorly understood. In this work, we characterize the interplay between large-scale interactions and local activity changes in V1 that orchestrates selective attention, using Granger-causality and phase-amplitude coupling (PAC) analysis of EEG source signals. The task required participants to either attend to or ignore oriented gratings. Results from time-varying, directed connectivity analysis revealed frequency-specific effects of attentional selection: bottom-up γ-band influences from visual areas increased rapidly in response to attended stimuli while distributed top-down α-band influences originated from parietal cortex in response to ignored stimuli. Importantly, the results revealed a critical interplay between top-down parietal signals and α-γ PAC in visual areas. Parietal α-band influences disrupted the α-γ coupling in visual cortex, which in turn reduced the amount of γ-band outflow from visual areas. Our results are a first demonstration of how directed interactions affect cross-frequency coupling in downstream areas depending on task demands. These findings suggest that parietal cortex realizes selective attention by disrupting cross-frequency coupling at target regions, which prevents them from propagating task-irrelevant information.

Influence of imputation strategies on the identification of brain functional connectivity networks

Whenever neurophysiological data, such as EEG data are recorded, occurring artifacts pose an essential problem. This study addresses this issue by using imputation methods whereby whole data sets of a trial, or distinct electrodes, are not removed from the analysis of the EEG data but are replaced. We present different imputation strategies but use only two which are optimal for this particular study; predictive mean matching and data augmentation. The study addresses the as of yet unresolved question if the quality of derived brain functional networks is improved by imputation methods compared to traditional exclusion techniques which drop data, and will finally assesses the differences between the two imputation methods themselves used here. In this study, EEG data from a study evaluating dyslexia-specific therapy on a neurophysiological level were used to investigate imputation strategies in research of cortical interaction. Several recorded values were artificially declared as 'missing'. This enables the comparison of networks based on the complete data set without any missing values (pseudo ground truth) and those derived from imputation approaches in a realistic situation of disturbed data. Functional connectivity was quantified by time-variant partial directed coherence, providing a directed, temporally varying and frequency-selective connectivity measure. Based on the comparison between pseudo ground truth and networks of data with excluded missing values and data with imputed values, we found that any imputation strategy is preferable to the entire exclusion of data. The study also showed that the choice of the applied imputation algorithm impacts the resulting networks only marginally.

Identification of Time-Varying Cortico-cortical and Cortico-Muscular Coherence during Motor Tasks with Multivariate Autoregressive Models

Neural populations coordinate at fast subsecond time-scales during rest and task execution. As a result, functional brain connectivity assessed with different neuroimaging modalities (EEG, MEG, fMRI) may also change over different time scales. In addition to the more commonly used sliding window techniques, the General Linear Kalman Filter (GLFK) approach has been proposed to estimate time-varying brain connectivity. In the present work, we propose a modification of the GLFK approach to model timevarying connectivity. We also propose a systematic method to select the hyper-parameters of the model. We evaluate the performance of the method using MEG and EMG data collected from 12 young subjects performing two motor tasks (unimanual and bimanual hand grips), by quantifying time-varying cortico-cortical and corticomuscular coherence (CCC and CMC). The CMC results revealed patterns in accordance with earlier findings, as well as an improvement in both time and frequency resolution compared to sliding window approaches. These results suggest that the proposed methodology is able to unveil accurate time-varying connectivity patterns with an excellent time resolution.

Time-varying MVAR algorithms for directed connectivity analysis: Critical comparison in simulations and benchmark EEG data

Human brain function depends on directed interactions between multiple areas that evolve in the subsecond range. Time-varying multivariate autoregressive (tvMVAR) modeling has been proposed as a way to help quantify directed functional connectivity strengths with high temporal resolution. While several tvMVAR approaches are currently available, there is a lack of unbiased systematic comparative analyses of their performance and of their sensitivity to parameter choices. Here, we critically compare four recursive tvMVAR algorithms and assess their performance while systematically varying adaptation coefficients, model order, and signal sampling rate. We also compared two ways of exploiting repeated observations: single-trial modeling followed by averaging, and multi-trial modeling where one tvMVAR model is fitted across all trials. Results from numerical simulations and from benchmark EEG recordings showed that: i) across a broad range of model orders all algorithms correctly reproduced patterns of interactions; ii) signal downsampling degraded connectivity estimation accuracy for most algorithms, although in some cases downsampling was shown to reduce variability in the estimates by lowering the number of parameters in the model; iii) single-trial modeling followed by averaging showed optimal performance with larger adaptation coefficients than previously suggested, and showed slower adaptation speeds than multi-trial modeling. Overall, our findings identify strengths and weaknesses of existing tvMVAR approaches and provide practical recommendations for their application to modeling dynamic directed interactions from electrophysiological signals.

Electrophysiological Source Imaging: A Noninvasive Window to Brain Dynamics

Brain activity and connectivity are distributed in the three-dimensional space and evolve in time. It is important to image brain dynamics with high spatial and temporal resolution. Electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive measurements associated with complex neural activations and interactions that encode brain functions. Electrophysiological source imaging estimates the underlying brain electrical sources from EEG and MEG measurements. It offers increasingly improved spatial resolution and intrinsically high temporal resolution for imaging large-scale brain activity and connectivity on a wide range of timescales. Integration of electrophysiological source imaging and functional magnetic resonance imaging could further enhance spatiotemporal resolution and specificity to an extent that is not attainable with either technique alone. We review methodological developments in electrophysiological source imaging over the past three decades and envision its future advancement into a powerful functional neuroimaging technology for basic and clinical neuroscience applications.

Topographical assessment of neurocortical connectivity by using directed transfer function and partial directed coherence during meditation

Due to the presence of nonlinearity and volume conduction in electroencephalography (EEG), sometimes it's challenging to find out the actual brain network from neurodynamical alteration. In this paper, two well-known time-frequency brain connectivity measures, namely partial directed coherence (PDC) and directed transfer function (DTF), have been applied to evaluate the performance analysis of EEG signals obtained during meditation. These measures are implemented to the multichannel meditation EEG data to get the directed neural information flow. Mostly the assessment of PDC and DTF is entirely subjective and there are probabilities to have erroneous connectivity estimation. To avoid the subjective evaluation, the performance results are compared in terms of absolute energy, signal-to-noise ratio (SNR) and relative SNR (R-SNR) scale. In most of the cases, the PDC result is found to be more efficient than DTF. The limitation of DTF and PDC in terms of the time-varying multivariate autoregressive (MVAR) model is highlighted. The time-varying MVAR model can track the neurodynamical changes better than any other method. In the present study, we would like to show that the PDC-based connectivity gives a better understanding of the non-symmetric relation in EEG obtained during Kriya Yoga meditation in comparison to DTF. However, it needs to be investigated further to warrant this claim.

Influence of Time-Series Normalization, Number of Nodes, Connectivity and Graph Measure Selection on Seizure-Onset Zone Localization from Intracranial EEG

We investigated the influence of processing steps in the estimation of multivariate directed functional connectivity during seizures recorded with intracranial EEG (iEEG) on seizure-onset zone (SOZ) localization. We studied the effect of (i) the number of nodes, (ii) time-series normalization, (iii) the choice of multivariate time-varying connectivity measure: Adaptive Directed Transfer Function (ADTF) or Adaptive Partial Directed Coherence (APDC) and (iv) graph theory measure: outdegree or shortest path length. First, simulations were performed to quantify the influence of the various processing steps on the accuracy to localize the SOZ. Afterwards, the SOZ was estimated from a 113-electrodes iEEG seizure recording and compared with the resection that rendered the patient seizure-free. The simulations revealed that ADTF is preferred over APDC to localize the SOZ from ictal iEEG recordings. Normalizing the time series before analysis resulted in an increase of 25-35% of correctly localized SOZ, while adding more nodes to the connectivity analysis led to a moderate decrease of 10%, when comparing 128 with 32 input nodes. The real-seizure connectivity estimates localized the SOZ inside the resection area using the ADTF coupled to outdegree or shortest path length. Our study showed that normalizing the time-series is an important pre-processing step, while adding nodes to the analysis did only marginally affect the SOZ localization. The study shows that directed multivariate Granger-based connectivity analysis is feasible with many input nodes (> 100) and that normalization of the time-series before connectivity analysis is preferred.

Extracting neuronal functional network dynamics via adaptive Granger causality analysis

Quantifying the functional relations between the nodes in a network based on local observations is a key challenge in studying complex systems. Most existing time series analysis techniques for this purpose provide static estimates of the network properties, pertain to stationary Gaussian data, or do not take into account the ubiquitous sparsity in the underlying functional networks. When applied to spike recordings from neuronal ensembles undergoing rapid task-dependent dynamics, they thus hinder a precise statistical characterization of the dynamic neuronal functional networks underlying adaptive behavior. We develop a dynamic estimation and inference paradigm for extracting functional neuronal network dynamics in the sense of Granger, by integrating techniques from adaptive filtering, compressed sensing, point process theory, and high-dimensional statistics. We demonstrate the utility of our proposed paradigm through theoretical analysis, algorithm development, and application to synthetic and real data. Application of our techniques to two-photon Ca²⁺ imaging experiments from the mouse auditory cortex reveals unique features of the functional neuronal network structures underlying spontaneous activity at unprecedented spatiotemporal resolution. Our analysis of simultaneous recordings from the ferret auditory and prefrontal cortical areas suggests evidence for the role of rapid top-down and bottom-up functional dynamics across these areas involved in robust attentive behavior.

Time, frequency, and time-varying Granger-causality measures in neuroscience

This article proposes a systematic methodological review and an objective criticism of existing methods enabling the derivation of time, frequency, and time-varying Granger-causality statistics in neuroscience. The capacity to describe the causal links between signals recorded at different brain locations during a neuroscience experiment is indeed of primary interest for neuroscientists, who often have very precise prior hypotheses about the relationships between recorded brain signals. The increasing interest and the huge number of publications related to this topic calls for this systematic review, which describes the very complex methodological aspects underlying the derivation of these statistics. In this article, we first present a general framework that allows us to review and compare Granger-causality statistics in the time domain, and the link with transfer entropy. Then, the spectral and the time-varying extensions are exposed and discussed together with their estimation and distributional properties. Although not the focus of this article, partial and conditional Granger causality, dynamical causal modelling, directed transfer function, directed coherence, partial directed coherence, and their variant are also mentioned.

Localization of Epileptogenic Zone With the Correction of Pathological Networks

Patients with focal drug-resistant epilepsy are potential candidates for surgery. Stereo-electroencephalograph (SEEG) is often considered as the “gold standard” to identify the epileptogenic zone (EZ) that accounts for the onset and propagation of epileptiform discharges. However, visual analysis of SEEG still prevails in clinical practice. In addition, epilepsy is increasingly understood to be the result of network disorder, but the specific organization of the epileptic network is still unclear. Therefore, it is necessary to quantitatively localize the EZ and investigate the nature of epileptogenic networks. In this study, intracranial recordings from 10 patients were analyzed through adaptive directed transfer function, and the out-degree of effective network was selected as the principal indicator to localize the epileptogenic area. Furthermore, a coupled neuronal population model was used to qualitatively simulate electrical activity in the brain. By removing individual populations, virtual surgery adjusting the network organization could be performed. Results suggested that the accuracy and detection rate of the EZ localization were 82.86 and 85.29%, respectively. In addition, the same stage shared a relatively stable connectivity pattern, while the patterns changed with transition to different processes. Meanwhile, eight cases of simulations indicated that networks in the ictal stage were more likely to generate rhythmic spikes. This indicated the existence of epileptogenic networks, which could enhance local excitability and facilitate synchronization. The removal of the EZ could correct these pathological networks and reduce the amount of spikes by at least 75%. This might be one reason why accurate resection could reduce or even suppress seizures. This study provides novel insights into epilepsy and surgical treatments from the network perspective.

A Time-Varying Connectivity Analysis from Distributed EEG Sources: A Simulation Study

Time-varying connectivity analysis based on sources reconstructed using inverse modeling of electroencephalographic (EEG) data is important to understand the dynamic behaviour of the brain. We simulated cortical data from a visual spatial attention network with a time-varying connectivity structure, and then simulated the propagation to the scalp to obtain EEG data. Distributed EEG source modeling using sLORETA was applied. We compared different dipole (representing a source) selection strategies based on their time series in a region of interest. Next, we estimated multivariate autoregressive (MVAR) parameters using classical Kalman filter and general linear Kalman filter approaches followed by the calculation of partial directed coherence (PDC). MVAR parameters and PDC values for the selected sources were compared with the ground-truth. We found that the best strategy to extract the time series of a region of interest was to select a dipole with time series showing the highest correlation with the average time series in the region of interest. Dipole selection based on power or based on the largest singular value offer comparable alternatives. Among the different Kalman filter approaches, the use of a general linear Kalman filter was preferred to estimate PDC based connectivity except when only a small number of trials are available. In the latter case, the classical Kalman filter can be an alternative.

Estimation of effective connectivity using multi-layer perceptron artificial neural network

Studies on interactions between brain regions estimate effective connectivity, (usually) based on the causality inferences made on the basis of temporal precedence. In this study, the causal relationship is modeled by a multi-layer perceptron feed-forward artificial neural network, because of the ANN's ability to generate appropriate input-output mapping and to learn from training examples without the need of detailed knowledge of the underlying system. At any time instant, the past samples of data are placed in the network input, and the subsequent values are predicted at its output. To estimate the strength of interactions, the measure of "Causality coefficient" is defined based on the network structure, the connecting weights and the parameters of hidden layer activation function. Simulation analysis demonstrates that the method, called "CREANN" (Causal Relationship Estimation by Artificial Neural Network), can estimate time-invariant and time-varying effective connectivity in terms of MVAR coefficients. The method shows robustness with respect to noise level of data. Furthermore, the estimations are not significantly influenced by the model order (considered time-lag), and the different initial conditions (initial random weights and parameters of the network). CREANN is also applied to EEG data collected during a memory recognition task. The results implicate that it can show changes in the information flow between brain regions, involving in the episodic memory retrieval process. These convincing results emphasize that CREANN can be used as an appropriate method to estimate the causal relationship among brain signals.

EEG source connectivity to localize the seizure onset zone in patients with drug resistant epilepsy

Electrical source imaging (ESI) from interictal scalp EEG is increasingly validated and used as a valuable tool in the presurgical evaluation of epilepsy as a reflection of the irritative zone. ESI of ictal scalp EEG to localize the seizure onset zone (SOZ) remains challenging. We investigated the value of an approach for ictal imaging using ESI and functional connectivity analysis (FC). Ictal scalp EEG from 111 seizures in 27 patients who had Engel class I outcome at least 1 year following resective surgery was analyzed. For every seizure, an artifact-free epoch close to the seizure onset was selected and ESI using LORETA was applied. In addition, the reconstructed sources underwent FC using the spectrum-weighted Adaptive Directed Transfer Function. This resulted in the estimation of the SOZ in two ways: (i) the source with maximal power after ESI, (ii) the source with the strongest outgoing connections after combined ESI and FC. Next, we calculated the distance between the estimated SOZ and the border of the resected zone (RZ) for both approaches and called this the localization error ((i) LE_pow and (ii) LE_conn respectively). By comparing LE_pow and LE_conn, we assessed the added value of FC. The source with maximal power after ESI was inside the RZ (LE_pow = 0 mm) in 31% of the seizures and estimated within 10 mm from the border of the RZ (LE_pow ≤ 10 mm) in 42%. Using ESI and FC, these numbers increased to 72% for LE_conn = 0 mm and 94% for LE_conn ≤ 10 mm. FC provided a significant added value to ESI alone (p < 0.001). ESI combined with subsequent FC is able to localize the SOZ in a non-invasive way with high accuracy. Therefore it could be a valuable tool in the presurgical evaluation of epilepsy.

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ESI + functional connectivity analysis allows localizing the SOZ with high accuracy.

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Functional connectivity analysis offered a significant added value to ESI.

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The method is robust for inter- and intra-patient variability.

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The method could be a useful tool in the presurgical evaluation of epilepsy.

Directional connectivity in the EEG is able to discriminate wakefulness from NREM sleep

A reliable measure of consciousness is of great interest for various clinical applications including sleep studies and the assessment of depth of anaesthesia. A number of measures of consciousness based on the EEG have been proposed in the literature and tested in studies of dreamless sleep, general anaesthesia and disorders of consciousness. However, reliability has remained a persistent challenge. Despite considerable theoretical and experimental effort, the neural mechanisms underlying consciousness remain unclear, but connectivity between brain regions is thought to be disrupted, impairing information flow.

OBJECTIVE

The objective of the current work was to assess directional connectivity between brain regions using directed coherence and propose and assess an index that robustly reflects changes associated with non-REM sleep.

APPROACH

We tested the performance on polysomnographic recordings from ten healthy subjects and compared directed coherence (and derived features) with more established measures calculated from EEG spectra. We compared the performance of the different indexes to discriminate the level of consciousness at group and individual level.

MAIN RESULTS

At a group level all EEG measures could significantly discriminate NREM sleep from waking, but there was considerable individual variation. Across all individuals, normalized power, the strength of long-range connections and the direction of functional links strongly correlate with NREM sleep stages over the experimental timeline. At an individual level, of the EEG measures considered, the direction of functional links constitutes the most reliable index of the level of consciousness, highly correlating with the individual experimental time-line of sleep in all subjects.

SIGNIFICANCE

Directed coherence provides a promising new means of assessing level of consciousness, firmly based on current physiological understanding of consciousness.