Measuring connectivity in linear multivariate processes: definitions, interpretation, and practical analysis

Measurable transitions during seizures in intracranial EEG: A stereoelectroencephalography and SPECT study

OBJECTIVE

Ictal Single Photon Emission Computed Tomography (SPECT) and stereo-electroencephalography (SEEG) are diagnostic techniques used for the management of patients with drug-resistant focal epilepsies. While hyperperfusion patterns in ictal SPECT studies reveal seizure onset and propagation pathways, the role of ictal hypoperfusion remains poorly understood. The goal of this study was to systematically characterize the spatio-temporal information flow dynamics between differently perfused brain regions using stereo-EEG recordings.

METHODS

We identified seizure-free patients after resective epilepsy surgery who had prior ictal SPECT and SEEG investigations. We estimated directional connectivity between the epileptogenic-zone (EZ), non-resected areas of hyperperfusion, hypoperfusion, and baseline perfusion during the interictal, preictal, ictal, and postictal periods.

RESULTS

Compared to the background, we noted significant information flow (1) during the preictal period from the EZ to the baseline and hyperperfused regions, (2) during the ictal onset from the EZ to all three regions, and (3) during the period of seizure evolution from the area of hypoperfusion to all three regions.

CONCLUSIONS

Hypoperfused brain regions were found to indirectly interact with the EZ during the ictal period.

SIGNIFICANCE

Our unique study, combining intracranial electrophysiology and perfusion imaging, presents compelling evidence of dynamic changes in directional connectivity between brain regions during the transition from interictal to ictal states.

A Method to Assess Granger Causality, Isolation and Autonomy in the Time and Frequency Domains: Theory and Application to Cerebrovascular Variability

OBJECTIVE

Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of clear spectral representation.

METHODS

We embed into the linear parametric framework for computing GC from a driver X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The measures are illustrated in theoretical simulations and applied to time series of arterial pressure and cerebral blood flow obtained in syncope subjects and healthy controls.

RESULTS

Simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to orthostasis in syncope subjects, likely related to impaired cerebral autoregulation.

CONCLUSION AND SIGNIFICANCE

The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect pathophysiological responses to postural stress which cannot be traced in the time domain. The thorough assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled processes in both physiological and clinical investigations.

CardioRVAR: A New R Package and Shiny Application for the Evaluation of Closed-Loop Cardiovascular Interactions

CardioRVAR is a new R package designed for the complete evaluation of closed-loop cardiovascular interactions and baroreflex sensitivity estimated from continuous non-invasive heart rate and blood pressure recordings. In this work, we highlight the importance of this software tool in the context of human cardiovascular and autonomic neurophysiology. A summary of the main algorithms that CardioRVAR uses are reviewed, and the workflow of this package is also discussed. We present the results obtained from this tool after its application in three clinical settings. These results support the potential clinical and scientific applications of this tool. The open-source tool can be downloaded from a public GitHub repository, as well as its specific Shiny application, CardioRVARapp. The open-source nature of the tool may benefit the future continuation of this work.

Sleep Spindle-Related EEG Connectivity in Children with Attention-Deficit/Hyperactivity Disorder: An Exploratory Study

Attention-deficit/hyperactivity disorder (ADHD) is a neurobehavioral disorder with known brain abnormalities but no biomarkers to support clinical diagnosis. Recently, EEG analysis methods such as functional connectivity have rekindled interest in using EEG for ADHD diagnosis. Most studies have focused on resting-state EEG, while connectivity during sleep and spindle activity has been underexplored. Here we present the results of a preliminary study exploring spindle-related connectivity as a possible biomarker for ADHD. We compared sensor-space connectivity parameters in eight children with ADHD and nine age/sex-matched healthy controls during sleep, before, during, and after spindle activity in various frequency bands. All connectivity parameters were significantly different between the two groups in the delta and gamma bands, and Principal Component Analysis (PCA) in the gamma band distinguished ADHD from healthy subjects. Cluster coefficient and path length values in the sigma band were also significantly different between epochs, indicating different spindle-related brain activity in ADHD.

Information-Theoretic Analysis of Cardio-Respiratory Interactions in Heart Failure Patients: Effects of Arrhythmias and Cardiac Resynchronization Therapy

The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy.

Identifying oscillatory brain networks with hidden Gaussian graphical spectral models of MEEG

Identifying the functional networks underpinning indirectly observed processes poses an inverse problem for neurosciences or other fields. A solution of such inverse problems estimates as a first step the activity emerging within functional networks from EEG or MEG data. These EEG or MEG estimates are a direct reflection of functional brain network activity with a temporal resolution that no other in vivo neuroimage may provide. A second step estimating functional connectivity from such activity pseudodata unveil the oscillatory brain networks that strongly correlate with all cognition and behavior. Simulations of such MEG or EEG inverse problem also reveal estimation errors of the functional connectivity determined by any of the state-of-the-art inverse solutions. We disclose a significant cause of estimation errors originating from misspecification of the functional network model incorporated into either inverse solution steps. We introduce the Bayesian identification of a Hidden Gaussian Graphical Spectral (HIGGS) model specifying such oscillatory brain networks model. In human EEG alpha rhythm simulations, the estimation errors measured as ROC performance do not surpass 2% in our HIGGS inverse solution and reach 20% in state-of-the-art methods. Macaque simultaneous EEG/ECoG recordings provide experimental confirmation for our results with 1/3 times larger congruence according to Riemannian distances than state-of-the-art methods.

Brain Connectivity Estimation Pitfall in Multiple Trials of Electroencephalography Data

Introduction

The electroencephalography signal is well suited to calculate brain connectivity due to its high temporal resolution. When the purpose is to compute connectivity from multi-trial electroencephalography (EEG) data, confusion arises about how these trials involved in calculating the connectivity. The purpose of this paper is to study this confusing issue using simulated and experimental data.

Methods

To this end, Granger causality-based connectivity measures were considered. Using simulations, two signals were generated with known AR (auto-regressive) coefficients and then simple multivariate autoregressive (MVAR) models based on different numbers of trials were extracted. For accurate estimation of the MVAR model, the data samples should be sufficient. Two Granger causality-based connectivity, granger causality (GC) and Partial directed coherence (PDC) were estimated.

Results

Estimating connectivity corresponding to small trial numbers (5 and 10 trials) resulted in an average value of connectivity that is significantly higher and also more variable over different estimates. By increasing the number of trials, the MVAR model has fitted more appropriately to the data and the connectivity values were converged. This procedure was implemented on real EEG data. The obtained results agreed well with the findings of simulated data.

Conclusion

The results showed that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. Also, the larger the trial numbers, the MVAR model has fitted more appropriately to the data, and connectivity estimations are more reliable.

Highlights

The average of connectivity values on trials is considered brain connectivity.Connectivity estimations are more reliable for larger trial numbers.Estimations of connectivity for small trial numbers are not valid.

Plain Language Summary

Several different techniques can be utilized to evaluate brain connectivity such as functional magnetic resonance imaging (fMRI), magnetoencephalography (MEG), electroencephalography (EEG) and etc. Connectivity estimation methods are associated with computing the correspondence of neural signals over time, therefore modalities such as EEG due to their fine temporal resolution are well suited to calculate such connectivity. When the purpose is to compute connectivity from multi-trial data, confusion arises about how these trials and how many trials are involved in calculating the connectivity. During calculating brain connectivity from data with many observation epochs, the question arises whether brain connectivity is calculated for each trial and then average or for the averaged trials. The target of this paper is to study the abovementioned issue using simulated data and realistic EEG data. Our analysis indicated that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. It was also found that estimating connectivity corresponding to small trial numbers resulted in an average value of connectivity that is significantly higher and also more variable over different estimates and is not valid. These findings can help us in the correct estimation of brain connectivity.

Granger Causality Analysis of Transient Calcium Dynamics in the Honey Bee Antennal Lobe Network

Odorant processing presents multiple parallels across animal species, and insects became relevant models for the study of olfactory coding because of the tractability of the underlying neural circuits. Within the insect brain, odorants are received by olfactory sensory neurons and processed by the antennal lobe network. Such a network comprises multiple nodes, named glomeruli, that receive sensory information and are interconnected by local interneurons participating in shaping the neural representation of an odorant. The study of functional connectivity between the nodes of a sensory network in vivo is a challenging task that requires simultaneous recording from multiple nodes at high temporal resolutions. Here, we followed the calcium dynamics of antennal lobe glomeruli and applied Granger causality analysis to assess the functional connectivity among network nodes in the presence and absence of an odorous stimulus. This approach revealed the existence of causal connectivity links between antennal lobe glomeruli in the absence of olfactory stimulation, while at odor arrival, the connectivity network's density increased and became stimulus-specific. Thus, such an analytical approach may provide a new tool for the investigation of neural network plasticity in vivo.

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.

Minimizing the distortions in electrophysiological source imaging of cortical oscillatory activity via Spectral Structured Sparse Bayesian Learning

Oscillatory processes at all spatial scales and on all frequencies underpin brain function. Electrophysiological Source Imaging (ESI) is the data-driven brain imaging modality that provides the inverse solutions to the source processes of the EEG, MEG, or ECoG data. This study aimed to carry out an ESI of the source cross-spectrum while controlling common distortions of the estimates. As with all ESI-related problems under realistic settings, the main obstacle we faced is a severely ill-conditioned and high-dimensional inverse problem. Therefore, we opted for Bayesian inverse solutions that posited a priori probabilities on the source process. Indeed, rigorously specifying both the likelihoods and a priori probabilities of the problem leads to the proper Bayesian inverse problem of cross-spectral matrices. These inverse solutions are our formal definition for cross-spectral ESI (cESI), which requires a priori of the source cross-spectrum to counter the severe ill-condition and high-dimensionality of matrices. However, inverse solutions for this problem were NP-hard to tackle or approximated within iterations with bad-conditioned matrices in the standard ESI setup. We introduce cESI with a joint a priori probability upon the source cross-spectrum to avoid these problems. cESI inverse solutions are low-dimensional ones for the set of random vector instances and not random matrices. We achieved cESI inverse solutions through the variational approximations via our Spectral Structured Sparse Bayesian Learning (ssSBL) algorithm https://github.com/CCC-members/Spectral-Structured-Sparse-Bayesian-Learning. We compared low-density EEG (10-20 system) ssSBL inverse solutions with reference cESIs for two experiments: (a) high-density MEG that were used to simulate EEG and (b) high-density macaque ECoG that were recorded simultaneously with EEG. The ssSBL resulted in two orders of magnitude with less distortion than the state-of-the-art ESI methods. Our cESI toolbox, including the ssSBL method, is available at https://github.com/CCC-members/BC-VARETA_Toolbox.

Multiscale partial information decomposition of dynamic processes with short and long-range correlations: theory and application to cardiovascular control

OBJECTIVE

In this work, an analytical framework for the multiscale analysis of multivariate Gaussian processes is presented, whereby the computation of Partial Information Decomposition measures is achieved accounting for the simultaneous presence of short-term dynamics and long-range correlations.

APPROACH

We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the decomposition into unique, redundant and synergistic contributions, is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress.

MAIN RESULTS

We demonstrate the ability of the VARFI modeling approach to account for the coexistence of short-term and long-range correlations in the study of multivariate processes. Physiologically, we show that postural stress induces larger redundant and synergistic effects from S and R to H at short time scales, while mental stress induces larger information transfer from S to H at longer time scales, thus evidencing the different nature of the two stressors.

SIGNIFICANCE

The proposed methodology allows to extract useful information about the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations.

Resting State EEG Directed Functional Connectivity Unveils Changes in Motor Network Organization in Subacute Stroke Patients After Rehabilitation

Brain plasticity and functional reorganization are mechanisms behind functional motor recovery of patients after an ischemic stroke. The study of resting-state motor network functional connectivity by means of EEG proved to be useful in investigating changes occurring in the information flow and find correlation with motor function recovery. In the literature, most studies applying EEG to post-stroke patients investigated the undirected functional connectivity of interacting brain regions. Quite recently, works started to investigate the directionality of the connections and many approaches or features have been proposed, each of them being more suitable to describe different aspects, e.g., direct or indirect information flow between network nodes, the coupling strength or its characteristic oscillation frequency. Each work chose one specific measure, despite in literature there is not an agreed consensus, and the selection of the most appropriate measure is still an open issue. In an attempt to shed light on this methodological aspect, we propose here to combine the information of direct and indirect coupling provided by two frequency-domain measures based on Granger’s causality, i.e., the directed coherence (DC) and the generalized partial directed coherence (gPDC), to investigate the longitudinal changes of resting-state directed connectivity associated with sensorimotor rhythms α and β, occurring in 18 sub-acute ischemic stroke patients who followed a rehabilitation treatment. Our results showed a relevant role of the information flow through the pre-motor regions in the reorganization of the motor network after the rehabilitation in the sub-acute stage. In particular, DC highlighted an increase in intra-hemispheric coupling strength between pre-motor and primary motor areas, especially in ipsi-lesional hemisphere in both α and β frequency bands, whereas gPDC was more sensitive in the detection of those connection whose variation was mostly represented within the population. A decreased causal flow from contra-lesional premotor cortex towards supplementary motor area was detected in both α and β frequency bands and a significant reinforced inter-hemispheric connection from ipsi to contra-lesional pre-motor cortex was observed in β frequency. Interestingly, the connection from contra towards ipsilesional pre-motor area correlated with upper limb motor recovery in α band. The usage of two different measures of directed connectivity allowed a better comprehension of those coupling changes between brain motor regions, either direct or mediated, which mostly were influenced by the rehabilitation, revealing a particular involvement of the pre-motor areas in the cerebral functional reorganization.

Depression Diagnosis Modeling With Advanced Computational Methods: Frequency-Domain eMVAR and Deep Learning

Electroencephalogram (EEG)-based automated depression diagnosis systems have been suggested for early and accurate detection of mood disorders. EEG signals are highly irregular, nonlinear, and nonstationary in nature and are traditionally studied from a linear viewpoint by means of statistical and frequency features. Since, linear metrics present certain limitations and nonlinear methods have proven to be an efficient tool in understanding the complexities of the brain in the identification of underlying behavior of biological signals, such as electrocardiogram, EEG and magnetoencephalogram and thus, can be applied to all nonstationary signals. Various nonlinear algorithms can be used in the analysis of EEG signals. In this research paper, we aim to develop a novel methodology for EEG-based depression diagnosis utilizing 2 advanced computational techniques: frequency-domain extended multivariate autoregressive (eMVAR) and deep learning (DL). We proposed a hybrid method comprising a pretrained ResNet-50 and long-short term memory (LSTM) to capture depression-specific information and compared with a strong conventional machine learning (ML) framework having eMVAR connectivity features. The following 8 causality measures, which interpret the interaction mechanisms among spectrally decomposed oscillations, were used to extract features from multivariate EEG time series: directed coherence (DC), directed transfer function (DTF), partial DC (PDC), generalized PDC (gPDC), extended DC (eDC), delayed DC (dDC), extended PDC (ePDC), and delayed PDC (dPDC). The classification accuracies were 84% with DC, 85% with DTF, 95.3% with PDC, 95.1% with gPDC, 84.8% with eDC, 84.6% with dDC, 84.2% with ePDC, and 95.9% with dPDC for the eMVAR framework. Through a DL framework (ResNet-50 + LSTM), the classification accuracy was achieved as 90.22%. The results demonstrate that our DL methodology is a competitive alternative to the strong feature extraction-based ML methods in depression classification.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Coupling feature extraction method of resting state EEG Signals from amnestic mild cognitive impairment with type 2 diabetes mellitus based on weight permutation conditional mutual information

This study aimed to find a good coupling feature extraction method to effectively analyze resting state EEG signals (rsEEG) of amnestic mild cognitive impairment(aMCI) with type 2 diabetes mellitus(T2DM) and normal control (NC) with T2DM. A method of EEG signal coupling feature extraction based on weight permutation conditional mutual information (WPCMI) was proposed in this research. With the WPCMI method, coupling feature strength of two time series in Alpha1, Alpha2, Beta1, Beta2 and Gamma bands for aMCI with T2DM and NC with T2DM could be extracted respectively. Then selected three frequency bands coupling feature matrix with the help of multi-spectral image transformation method to map it as spectral image characteristics. And finally classified these characteristics through the convolution neural network method(CNN). For aMCI with T2DM and NC with T2DM, the highest classification accuracy of 96%, 95%, 95% could be achieved respectively in the combination of three frequency bands (Alpha1, Alpha2, Gamma), (Beta1, Beta2 and Gamma) and (Alpha2, Beta1, Beta2). This WPCMI method highlighted the coupling dynamic characteristics of EEG signals, and its classification performance was better than all previous methods in aMCI with T2DM diagnosis field. WPCMI method could be used as an effective biomarker to distinguish EEG signals of aMCI with T2DM and NC with T2DM. The coupling feature extraction method used in this paper provided a new perspective for the EEG analysis of aMCI with T2DM.

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.

A new Framework for the Spectral Information Decomposition of Multivariate Gaussian Processes

Different information-theoretic measures are available in the literature for the study of pairwise and higher-order interactions in multivariate dynamical systems. While these measures operate in the time domain, several physiological and non-physiological systems exhibit a rich oscillatory content that is typically analyzed in the frequency domain through spectral and cross-spectral approaches. For Gaussian systems, the relation between information and spectral measures has been established considering coupling and causality measures, but not for higher-order interactions. To fill this gap, in this work we introduce an information-theoretic framework in the frequency domain to quantify the information shared between a target process and two sources, even multivariate, and to highlight the presence of redundancy and synergy in the analyzed dynamical system. Firstly, we simulate different linear interacting processes by showing the capability of the proposed framework to retrieve amounts of information shared by the processes in specific frequency bands which are not detectable by the related time-domain measures. Then, the framework is applied on EEG time series representative of the brain activity during a motor execution task in a group of healthy subjects.

Joint Analysis of Eye Blinks and Brain Activity to Investigate Attentional Demand during a Visual Search Task

In several fields, the need for a joint analysis of brain activity and eye activity to investigate the association between brain mechanisms and manifest behavior has been felt. In this work, two levels of attentional demand, elicited through a conjunction search task, have been modelled in terms of eye blinks, brain activity, and brain network features. Moreover, the association between endogenous neural mechanisms underlying attentional demand and eye blinks, without imposing a time-locked structure to the analysis, has been investigated. The analysis revealed statistically significant spatial and spectral modulations of the recorded brain activity according to the different levels of attentional demand, and a significant reduction in the number of eye blinks when a higher amount of attentional investment was required. Besides, the integration of information coming from high-density electroencephalography (EEG), brain source localization, and connectivity estimation allowed us to merge spectral and causal information between brain areas, characterizing a comprehensive model of neurophysiological processes behind attentional demand. The analysis of the association between eye and brain-related parameters revealed a statistically significant high correlation (R > 0.7) of eye blink rate with anterofrontal brain activity at 8 Hz, centroparietal brain activity at 12 Hz, and a significant moderate correlation with the participation of right Intra Parietal Sulcus in alpha band (R = -0.62). Due to these findings, this work suggests the possibility of using eye blinks measured from one sensor placed on the forehead as an unobtrusive measure correlating with neural mechanisms underpinning attentional demand.

Parasympathetic-Sympathetic Causal Interactions Assessed by Time-Varying Multivariate Autoregressive Modeling of Electrodermal Activity and Heart-Rate-Variability

OBJECTIVE

Most of the bodily functions are regulated by multiple interactions between the parasympathetic (PNS) and sympathetic (SNS) nervous system. In this study, we propose a novel framework to quantify the causal flow of information between PNS and SNS through the analysis of heart rate variability (HRV) and electrodermal activity (EDA) signals.

METHODS

Our method is based on a time-varying (TV) multivariate autoregressive model of EDA and HRV time-series and incorporates physiologically inspired assumptions by estimating the Directed Coherence in a specific frequency range. The statistical significance of the observed interactions is assessed by a bootstrap procedure purposely developed to infer causalities in the presence of both TV model coefficients and TV model residuals (i.e., heteroskedasticity). We tested our method on two different experiments designed to trigger a sympathetic response, i.e., a hand-grip task (HG) and a mental-computation task (MC).

RESULTS

Our results show a parasympathetic driven interaction in the resting state, which is consistent across different studies. The onset of the stressful stimulation triggers a cascade of events characterized by the presence or absence of the PNS-SNS interaction and changes in the directionality. Despite similarities between the results related to the two tasks, we reveal differences in the dynamics of the PNS-SNS interaction, which might reflect different regulatory mechanisms associated with different stressors.

CONCLUSION

We estimate causal coupling between PNS and SNS through MVAR modeling of EDA and HRV time-series.

SIGNIFICANCE

Our results suggest promising future applicability to investigate more complex contexts such as affective and pathological scenarios.

A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks

This study introduces a framework for the information-theoretic analysis of brain functional connectivity performed at the level of electroencephalogram (EEG) sources. The framework combines the use of common spatial patterns to select the EEG components which maximize the variance between two experimental conditions, simultaneous implementation of vector autoregressive modeling (VAR) with independent component analysis to describe the joint source dynamics and their projection to the scalp, and computation of information dynamics measures (information storage, information transfer, statistically significant network links) from the source VAR parameters. The proposed framework was tested on simulated EEGs obtained mixing source signals generated under different coupling conditions, showing its ability to retrieve source information dynamics from the scalp signals. Then, it was applied to investigate scalp and source brain connectivity in a group of children manifesting episodes of focal and generalized epilepsy; the analysis was performed on EEG signals lasting 5 s, collected in two consecutive windows preceding and one window following each ictal episode. Our results show that generalized seizures are associated with a significant decrease from pre-ictal to post-ictal periods of the information stored in the signals and of the information transferred among them, reflecting reduced self-predictability and causal connectivity at the level of both scalp and source brain dynamics. On the contrary, in the case of focal seizures the scalp EEG activity was not discriminated across conditions by any information measure, while source analysis revealed a tendency of the measures of information transfer to increase just before seizures and to decrease just after seizures. These results suggest that focal epileptic seizures are associated with a reorganization of the topology of EEG brain networks which is only visible analyzing connectivity among the brain sources. Our findings emphasize the importance of EEG modeling approaches able to deal with the adverse effects of volume conduction on brain connectivity analysis, and their potential relevance to the development of strategies for prediction and clinical treatment of epilepsy.

Corticomuscular interactions during different movement periods in a multi-joint compound movement

While much is known about motor control during simple movements, corticomuscular communication profiles during compound movement control remain largely unexplored. Here, we aimed at examining frequency band related interactions between brain and muscles during different movement periods of a bipedal squat (BpS) task utilizing regression corticomuscular coherence (rCMC), as well as partial directed coherence (PDC) analyses. Participants performed 40 squats, divided into three successive movement periods (Eccentric (ECC), Isometric (ISO) and Concentric (CON)) in a standardized manner. EEG was recorded from 32 channels specifically-tailored to cover bilateral sensorimotor areas while bilateral EMG was recorded from four main muscles of BpS. We found both significant CMC and PDC (in beta and gamma bands) during BpS execution, where CMC was significantly elevated during ECC and CON when compared to ISO. Further, the dominant direction of information flow (DIF) was most prominent in EEG-EMG direction for CON and EMG-EEG direction for ECC. Collectively, we provide novel evidence that motor control during BpS is potentially achieved through central motor commands driven by a combination of directed inputs spanning across multiple frequency bands. These results serve as an important step toward a better understanding of brain-muscle relationships during multi joint compound movements.

Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

Granger causality analysis of rat cortical functional connectivity in pain

OBJECTIVE

The primary somatosensory cortex (S1) and the anterior cingulate cortex (ACC) are two of the most important cortical brain regions encoding the sensory-discriminative and affective-emotional aspects of pain, respectively. However, the functional connectivity of these two areas during pain processing remains unclear. Developing methods to dissect the functional connectivity and directed information flow between cortical pain circuits can reveal insight into neural mechanisms of pain perception.

APPROACH

We recorded multichannel local field potentials (LFPs) from the S1 and ACC in freely behaving rats under various conditions of pain stimulus (thermal versus mechanical) and pain state (naive versus chronic pain). We applied Granger causality (GC) analysis to the LFP recordings and inferred frequency-dependent GC statistics between the S1 and ACC.

MAIN RESULTS

We found an increased information flow during noxious pain stimulus presentation in both S1[Formula: see text]ACC and ACC[Formula: see text]S1 directions, especially at theta and gamma frequency bands. Similar results were found for thermal and mechanical pain stimuli. The chronic pain state shares common observations, except for further elevated GC measures especially in the gamma band. Furthermore, time-varying GC analysis revealed a negative correlation between the direction-specific and frequency-dependent GC and animal's paw withdrawal latency. In addition, we used computer simulations to investigate the impact of model mismatch, noise, missing variables, and common input on the conditional GC estimate. We also compared the GC results with the transfer entropy (TE) estimates.

SIGNIFICANCE

Our results reveal functional connectivity and directed information flow between the S1 and ACC during various pain conditions. The dynamic GC analysis support the hypothesis of cortico-cortical information loop in pain perception, consistent with the computational predictive coding paradigm.

Toward a cooperation index based on EEG-workload causality: preliminary findings on aerospace-like tasks

According to Human-System Integration analyses, cooperation between humans is one of the most relevant factors in many of today's human activities: do not take it into account in models of working environments is highly farfetched. Although the Human Factor aspects have obtained much benefit from the use of neurophysiological signals to estimate human-machine interaction, very few are the indications about neurophysiological analysis of human cooperation deviating from typical laboratory tasks. Among these, some evidence showed that there is a relationship between the mental workload experienced by the subjects cooperating and some characteristics of the brain network obtained through multi-subjects connectivity analysis. Accordingly, this work aimed to identify common dynamics in time series that describe the EEG-based mental workload of cooperating subjects and to exploit this information to create an index of cooperation. In order to answer the question whether a causality between the workload values of the two subjects can be in some way discerned and related to the cooperation required by the task, Granger's causality test has been performed. This method was applied to two different tasks simulating features of the aerospace domain. The results showed that the causality test was statistically significant for the most collaborating couple. In addition, causality values are modulated by the presence of real couples compared to fake couples. The extension of the experimental sample could open up the possibility for the development of an objective and neurophysiological signals-based cooperation index.

Risk Stratification in Idiopathic Dilated Cardiomyopathy Patients Using Cardiovascular Coupling Analysis

Cardiovascular diseases are one of the most common causes of death; however, the early detection of patients at high risk of sudden cardiac death (SCD) remains an issue. The aim of this study was to analyze the cardio-vascular couplings based on heart rate variability (HRV) and blood pressure variability (BPV) analyses in order to introduce new indices for noninvasive risk stratification in idiopathic dilated cardiomyopathy patients (IDC). High-resolution electrocardiogram (ECG) and continuous noninvasive blood pressure (BP) signals were recorded in 91 IDC patients and 49 healthy subjects (CON). The patients were stratified by their SCD risk as high risk (IDC_HR) when after two years the subject either died or suffered life-threatening complications, and as low risk (IDC_LR) when the subject remained stable during this period. Values were extracted from ECG and BP signals, the beat-to-beat interval, and systolic and diastolic blood pressure, and analyzed using the segmented Poincaré plot analysis (SPPA), the high-resolution joint symbolic dynamics (HRJSD) and the normalized short time partial directed coherence methods. Support vector machine (SVM) models were built to classify these patients according to SCD risk. IDC_HR patients presented lowered HRV and increased BPV compared to both IDC_LR patients and the control subjects, suggesting a decrease in their vagal activity and a compensation of sympathetic activity. Both, the cardio -systolic and -diastolic coupling strength was stronger in high-risk patients when comparing with low-risk patients. The cardio-systolic coupling analysis revealed that the systolic influence on heart rate gets weaker as the risk increases. The SVM IDC_LR vs. IDC_HR model achieved 98.9% accuracy with an area under the curve (AUC) of 0.96. The IDC and the CON groups obtained 93.6% and 0.94 accuracy and AUC, respectively. To simulate a circumstance in which the original status of the subject is unknown, a cascade model was built fusing the aforementioned models, and achieved 94.4% accuracy. In conclusion, this study introduced a novel method for SCD risk stratification for IDC patients based on new indices from coupling analysis and non-linear HRV and BPV. We have uncovered some of the complex interactions within the autonomic regulation in this type of patient.

A new Frequency Domain Measure of Causality based on Partial Spectral Decomposition of Autoregressive Processes and its Application to Cardiovascular Interactions. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2019;2019:4258-4261. [PMID: 31946809 DOI: 10.1109/embc.2019.8857312]

We present a new method to quantify in the frequency domain the strength of directed interactions between linear stochastic processes. This issue is traditionally addressed by the directed coherence (DC), a popular causality measure derived from the spectral representation of vector autoregressive (AR) processes. Here, to overcome intrinsic limitations of the DC when it needs to be objectively quantified within specific frequency bands, we propose an approach based on spectral decomposition, which allows to isolate oscillatory components related to the pole representation of the vector AR process in the Z-domain. Relating the causal and non-causal power content of these components we obtain a new spectral causality measure, denoted as pole-specific spectral causality (PSSC). In this study, PSSC is compared with DC in the context of cardiovascular variability analysis, where evaluation of the spectral causality from arterial pressure to heart period variability is of interest to assess baroreflex modulation in the low frequency band (0.04-0-15 Hz). Using both a theoretical example in which baroreflex interactions are simulated, and real cardiovascular variability series measured from a group of healthy subjects during a postural challenge, we show that - compared with DC- PSSC leads to a frequency-specific evaluation of spectral causality which is more objective and more focused on the frequency band of interest.

Time-Frequency Analysis of Cardiovascular and Cardiorespiratory Interactions During Orthostatic Stress by Extended Partial Directed Coherence

In this study, the linear method of extended partial directed coherence (ePDC) was applied to establish the temporal dynamic behavior of cardiovascular and cardiorespiratory interactions during orthostatic stress at a 70° head-up tilt (HUT) test on young age-matched healthy subjects and patients with orthostatic intolerance (OI), both male and female. Twenty 5-min windows were used to analyze the minute-wise progression of interactions from 5 min in a supine position (baseline, BL) until 18 min of the orthostatic phase (OP) without including pre-syncopal phases. Gender differences in controls were present in cardiorespiratory interactions during OP without compromised autonomic regulation. However in patients, analysis by ePDC revealed considerable dynamic alterations within cardiovascular and cardiorespiratory interactions over the temporal course during the HUT test. Considering the young female patients with OI, the information flow from heart rate to systolic blood pressure (mechanical modulation) was already increased before the tilt-up, the information flow from systolic blood pressure to heart rate (neural baroreflex) increased during OP, while the information flow from respiration to heart rate (respiratory sinus arrhythmia) decreased during the complete HUT test. Findings revealed impaired cardiovascular interactions in patients with orthostatic intolerance and confirmed the usefulness of ePDC for causality analysis.

Multiscale information storage of linear long-range correlated stochastic processes

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then its complexity is evaluated in terms of conditional entropy. Within this framework, our approach makes use of linear fractionally integrated autoregressive (ARFI) models to derive analytical expressions for the information storage computed at multiple timescales. Specifically, we exploit state space models to provide the representation of lowpass filtered and downsampled ARFI processes, from which information storage is computed at any given timescale relating the process variance to the prediction error variance. This enhances the practical usability of multiscale information storage, as it enables a computationally reliable quantification of a complexity measure which incorporates the effects of LRC together with that of short-term dynamics. The proposed measure is first assessed in simulated ARFI processes reproducing different types of autoregressive dynamics and different degrees of LRC, studying both the theoretical values and the finite sample performance. We find that LRC alter substantially the complexity of ARFI processes even at short timescales, and that reliable estimation of complexity can be achieved at longer timescales only when LRC are properly modeled. Then, we assess multiscale information storage in physiological time series measured in humans during resting state and postural stress, revealing unprecedented responses to stress of the complexity of heart period and systolic arterial pressure variability, which are related to the different role played by LRC in the two conditions.

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.

Estimating coupling strength between multivariate neural series with multivariate permutation conditional mutual information

Recently, coupling between groups of neurons or different brain regions has been widely studied to provide insights into underlying mechanisms of brain functions. To comprehensively understand the effect of such coupling, it is necessary to accurately extract the coupling strength information among multivariate neural signals from the whole brain. This study proposed a new method named multivariate permutation conditional mutual information (MPCMI) to quantitatively estimate the coupling strength of multivariate neural signals (MNS). The performance of the MPCMI method was validated on the simulated MNS generated by multi-channel neural mass model (MNMM). The coupling strength feature of simulated MNS extracted by MPCMI showed better performance compared with standard methods, such as permutation conditional mutual information (PCMI), multivariate Granger causality (MVGC), and Granger causality analysis (GCA). Furthermore, the MPCMI was applied to estimate the coupling strengths of two-channel resting-state electroencephalographic (rsEEG) signals from different brain regions of 19 patients with amnestic mild cognitive impairment (aMCI) with type 2 diabetes mellitus (T2DM) and 20 normal control (NC) with T2DM in Alpha1 and Alpha2 frequency bands. Empirical results showed that the MPCMI could effectively extract the coupling strength features that were significantly different between the aMCI and the NC. Hence, the proposed MPCMI method could be an effective estimate of coupling strengths of MNS, and might be a viable biomarker for clinical applications.

Intracortical Causal Information Flow of Oscillatory Activity (Effective Connectivity) at the Sleep Onset Transition

We investigated the sleep onset transition in humans from an effective connectivity perspective in a baseline condition (approx. 16 h of wakefulness) and after sleep deprivation (40 h of sustained wakefulness). Using EEG recordings (27 derivations), source localization (LORETA) allowed us to reconstruct the underlying patterns of neuronal activity in various brain regions, e.g., the default mode network (DMN), dorsolateral prefrontal cortex and hippocampus, which were defined as regions of interest (ROI). We applied isolated effective coherence (iCOH) to assess effective connectivity patterns at the sleep onset transition [2 min prior to and 10 min after sleep onset (first occurrence of stage 2)]. ICOH reveals directionality aspects and resolves the spectral characteristics of information flow in a given network of ROIs. We observed an anterior-posterior decoupling of the DMN, and moreover, a prominent role of the posterior cingulate cortex guiding the process of the sleep onset transition, particularly, by transmitting information in the low frequency range (delta and theta bands) to other nodes of DMN (including the hippocampus). In addition, the midcingulate cortex appeared as a major cortical relay station for spindle synchronization (originating from the thalamus; sigma activity). The inclusion of hippocampus indicated that this region might be functionally involved in sigma synchronization observed in the cortex after sleep onset. Furthermore, under conditions of increased homeostatic pressure, we hypothesize that an anterior-posterior decoupling of the DMN occurred at a faster rate compared to baseline overall indicating weakened connectivity strength within the DMN. Finally, we also demonstrated that cortico-cortical spindle synchronization was less effective after sleep deprivation than in baseline, thus, reflecting the reduction of spindles under increased sleep pressure.

Evaluation on Directed Functional Brain Connectivity during the Expert Rifle Pre-shot Period

Experts require long-term and intense practice to acquire extraordinary motor skills that be known as the brain function regulator. However, the brain function network mechanism of rifle shooters is still unclear. The generalized orthogonalized partial directed coherence (gOPDC) algorithm and local efficiency significance analysis method (LESA) was applied to quantify the difference in directed functional networks between expert and novice rifle shooters during the pre-shot period. The more directed functional connections were observed in alpha and low-beta frequency bands as compared to other bands. Moreover, comparing with the novice's fluctuant connection, the values of connection (P3→C3) strength were increasing steadily in the experts during the pre-shot period. Fewer connections in left hemisphere networks were obtained in the experts than in the novices. The results validated the "neural efficiency" hypothesis in experts. Moreover, the strength of the functional connection (P3→C3) in the alpha and beta bands serves as a distinguishing feature between experts and novices.

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.

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.

A Comparative Study of the Robustness of Frequency-Domain Connectivity Measures to Finite Data Length

In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time-series. We assume that the neural sources follow a stable MultiVariate AutoRegressive model, and consider three connectivity metrics: imaginary part of coherency (IC), generalized partial directed coherence (gPDC) and frequency-domain granger causality (fGC). In order to assess the statistical significance of the estimated values, we use the surrogate data test by generating phase-randomized and autoregressive surrogate data. We first consider the ideal case where we know the source time courses exactly. Here we show how, expectedly, even exact knowledge of the source time courses is not sufficient to provide reliable estimates of the connectivity when the number of samples gets small; however, while gPDC and fGC tend to provide a larger number of false positives, the IC becomes less sensitive to the presence of connectivity. Then we proceed with more realistic simulations, where the source time courses are estimated using eLORETA, and the EEG signal is affected by biological noise of increasing intensity. Using the ideal case as a reference, we show that the impact of biological noise on IC estimates is qualitatively different from the impact on gPDC and fGC.

On the interpretability and computational reliability of frequency-domain Granger causality

This Correspondence article is a comment which directly relates to the paper "A study of problems encountered in Granger causality analysis from a neuroscience perspective" ( Stokes and Purdon, 2017). We agree that interpretation issues of Granger causality (GC) in neuroscience exist, partially due to the historically unfortunate use of the name "causality", as described in previous literature. On the other hand, we think that Stokes and Purdon use a formulation of GC which is outdated (albeit still used) and do not fully account for the potential of the different frequency-domain versions of GC; in doing so, their paper dismisses GC measures based on a suboptimal use of them. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even if written in good faith, became a wildcard against all possible applications of GC, regardless of the large body of work recently published which aims to address faults in methodology and interpretation. In order to provide a balanced view, we replicate the simulations of Stokes and Purdon, using an updated GC implementation and exploiting the combination of spectral and causal information, showing that in this way the pitfalls are mitigated or directly solved.

Robust Nonlinear Causality Analysis of Nonstationary Multivariate Physiological Time Series

GOAL

An important research area in biomedical signal processing is that of quantifying the relationship between simultaneously observed time series and to reveal interactions between the signals. Since biomedical signals are potentially nonstationary and the measurements may contain outliers and artifacts, we introduce a robust time-varying generalized partial directed coherence (rTV-gPDC) function.

METHODS

The proposed method, which is based on a robust estimator of the time-varying autoregressive (TVAR) parameters, is capable of revealing directed interactions between signals. By definition, the rTV-gPDC only displays the linear relationships between the signals. We therefore suggest to approximate the residuals of the TVAR process, which potentially carry information about the nonlinear causality by a piece-wise linear time-varying moving-average model.

RESULTS

The performance of the proposed method is assessed via extensive simulations. To illustrate the method's applicability to real-world problems, it is applied to a neurophysiological study that involves intracranial pressure, arterial blood pressure, and brain tissue oxygenation level (PtiO2) measurements.

CONCLUSION AND SIGNIFICANCE

The rTV-gPDC reveals causal patterns that are in accordance with expected cardiosudoral meachanisms and potentially provides new insights regarding traumatic brain injuries. The rTV-gPDC is not restricted to the above problem but can be useful in revealing interactions in a broad range of applications.

The Concept of Effective Inflow: Application to Interictal Localization of the Epileptogenic Focus From iEEG

GOAL

Accurate determination of the epileptogenic focus is of paramount diagnostic and therapeutic importance in epilepsy. The current gold standard for focus localization is from ictal (seizure) onset and thus requires the occurrence and recording of multiple typical seizures of a patient. Localization of the focus from seizure-free (interictal) periods remains a challenging problem, especially in the absence of interictal epileptiform activity.

METHODS

By exploring the concept of effective inflow, we developed a focus localization algorithm (FLA) based on directed connectivity between brain sites. Subsequently, using the measure of generalized partial directed coherence over a broad frequency band in FLA for the analysis of interictal periods from long-term (days) intracranial electroencephalographic signals, we identified the brain region that is the most frequent receiver of maximal effective inflow from other brain regions.

RESULTS

In six out of nine patients with temporal lobe epilepsy, the thus identified brain region was a statistically significant outlier (p < 0.01) and coincided with the clinically assessed epileptogenic focus. In the remaining three patients, the clinically assessed focus still exhibited the highest inflow, but it was not deemed an outlier (p > 0.01).

CONCLUSIONS

These findings suggest that the epileptogenic focus is a region of intense influence from other regions interictally, possibly as a mechanism to keep it under control in seizure-free periods.

SIGNIFICANCE

The developed framework is expected to assist with the accurate epileptogenic focus localization, reduce hospital stay and healthcare cost, and provide guidance to treatment of epilepsy via resective surgery or neuromodulation.

An Information-Theoretic Framework to Map the Spatiotemporal Dynamics of the Scalp Electroencephalogram

We present the first application of the emerging framework of information dynamics to the characterization of the electroencephalography (EEG) activity. The framework provides entropy-based measures of information storage (self entropy, SE) and information transfer (joint transfer entropy (TE) and partial TE), which are applied here to detect complex dynamics of individual EEG sensors and causal interactions between different sensors. The measures are implemented according to a model-free and fully multivariate formulation of the framework, allowing the detection of nonlinear dynamics and direct links. Moreover, to deal with the issue of volume conduction, a compensation for instantaneous effects is introduced in the computation of joint and partial TE. The framework is applied to resting state EEG measured from healthy subjects in the eyes open (EO) and eyes closed (EC) conditions, evidencing condition-dependent patterns indicative of how information is distributed in the EEG sensor space. The SE was uniformly low during EO and significantly higher in the posterior areas during EC. The joint and partial TE were saturated by instantaneous effects, documenting how volume conduction blurs the detection of information flow in the EEG. However, the use of compensated TE measures led us to evidence meaningful patterns like the presence of local sinks of information flow and propagation motifs, and the emergence of prevalent front-to-back EEG propagation during EC. These findings support the feasibility of our information-theoretic approach to assess the spatiotemporal dynamics of the scalp EEG in different conditions.

Redundant and synergistic information transfer in cardiovascular and cardiorespiratory variability

In the framework of information dynamics, new tools are emerging which allow one to quantify how the information provided by two source processes about a target process results from the contribution of each source and from the interaction between the sources. We present the first implementation of these tools in the assessment of short-term cardiovascular and cardiorespiratory variability, by introducing two strategies for the decomposition of the information transferred to heart period (HP) variability from systolic arterial pressure (SAP) and respiration flow (RF) variability. Several measures based on the notion of transfer entropy (TE) are defined to quantify joint, individual and redundant/synergistic information transfer, and are then estimated from the series of HP, SAP and RF obtained from healthy subjects during head-up tilt and paced breathing protocols. Our results show that the proposed information decomposition methods provide an enhanced view on cardiovascular and cardiorespiratory regulation.

Detection of Coupling in Short Physiological Series by a Joint Distribution Entropy Method

OBJECTIVE

In this study, we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series.

METHODS

The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rössler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography data from rats and RR interval and diastolic time interval series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison.

RESULTS

Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short datasets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data.

CONCLUSION

This study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.

Advanced Insights into Functional Brain Connectivity by Combining Tensor Decomposition and Partial Directed Coherence

Quantification of functional connectivity in physiological networks is frequently performed by means of time-variant partial directed coherence (tvPDC), based on time-variant multivariate autoregressive models. The principle advantage of tvPDC lies in the combination of directionality, time variance and frequency selectivity simultaneously, offering a more differentiated view into complex brain networks. Yet the advantages specific to tvPDC also cause a large number of results, leading to serious problems in interpretability. To counter this issue, we propose the decomposition of multi-dimensional tvPDC results into a sum of rank-1 outer products. This leads to a data condensation which enables an advanced interpretation of results. Furthermore it is thereby possible to uncover inherent interaction patterns of induced neuronal subsystems by limiting the decomposition to several relevant channels, while retaining the global influence determined by the preceding multivariate AR estimation and tvPDC calculation of the entire scalp. Finally a comparison between several subjects is considerably easier, as individual tvPDC results are summarized within a comprehensive model equipped with subject-specific loading coefficients. A proof-of-principle of the approach is provided by means of simulated data; EEG data of an experiment concerning visual evoked potentials are used to demonstrate the applicability to real data.