Unified asymptotic theory for all partial directed coherence forms

Parallel Factorization to Implement Group Analysis in Brain Networks Estimation

When dealing with complex functional brain networks, group analysis still represents an open issue. In this paper, we investigated the potential of an innovative approach based on PARAllel FActorization (PARAFAC) for the extraction of the grand average connectivity matrices from both simulated and real datasets. The PARAFAC approach was solved using three different numbers of rank-one tensors (PAR-FACT). Synthetic data were parametrized according to different levels of three parameters: network dimension (NODES), number of observations (SAMPLE-SIZE), and noise (SWAP-CON) in order to investigate the way they affect the grand average estimation. PARAFAC was then tested on a real connectivity dataset, derived from EEG data of 17 healthy subjects performing wrist extension with left and right hand separately. Findings on both synthetic and real data revealed the potential of the PARAFAC algorithm as a useful tool for grand average extraction. As expected, the best performances in terms of FPR, FNR, and AUC were achieved for great values of sample size and low noise level. A crucial role has been revealed for the PAR-FACT parameter, revealing that an increase in the number of rank-one tensors solving the PARAFAC problem leads to an increase in FPR values and, thus, to a worse grand average estimation.

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

Linear and Nonlinear Directed Connectivity Analysis of the Cardio-Respiratory System in Type 1 Diabetes

In this study, we explored the possibility of developing non-invasive biomarkers for patients with type 1 diabetes (T1D) by quantifying the directional couplings between the cardiac, vascular, and respiratory systems, treating them as interconnected nodes in a network configuration. Towards this goal, we employed a linear directional connectivity measure, the directed transfer function (DTF), estimated by a linear multivariate autoregressive modelling of ECG, respiratory and skin perfusion signals, and a nonlinear method, the dynamical Bayesian inference (DBI) analysis of bivariate phase interactions. The physiological data were recorded concurrently for a relatively short time period (5 min) from 10 healthy control subjects and 10 T1D patients. We found that, in both control and T1D subjects, breathing had greater influence on the heart and perfusion with respect to the opposite coupling direction and that, by both employed methods of analysis, the causal influence of breathing on the heart was significantly decreased (p < 0.05) in T1D patients compared to the control group. These preliminary results, although obtained from a limited number of subjects, provide a strong indication for the usefulness of a network-based multi-modal analysis for the development of biomarkers of T1D-related complications from short-duration data, as well as their potential in the exploration of the pathophysiological mechanisms that underlie this devastating and very widespread disease.

Frequency Domain Repercussions of Instantaneous Granger Causality

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC's repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected.

Multivariate model for cooperation: bridging social physiological compliance and hyperscanning

The neurophysiological analysis of cooperation has evolved over the past 20 years, moving towards the research of common patterns in neurophysiological signals of people interacting. Social physiological compliance (SPC) and hyperscanning represent two frameworks for the joint analysis of autonomic and brain signals, respectively. Each of the two approaches allows to know about a single layer of cooperation according to the nature of these signals: SPC provides information mainly related to emotions, and hyperscanning that related to cognitive aspects. In this work, after the analysis of the state of the art of SPC and hyperscanning, we explored the possibility to unify the two approaches creating a complete neurophysiological model for cooperation considering both affective and cognitive mechanisms We synchronously recorded electrodermal activity, cardiac and brain signals of 14 cooperative dyads. Time series from these signals were extracted, and multivariate Granger causality was computed. The results showed that only when subjects in a dyad cooperate there is a statistically significant causality between the multivariate variables representing each subject. Moreover, the entity of this statistical relationship correlates with the dyad’s performance. Finally, given the novelty of this approach and its exploratory nature, we provided its strengths and limitations.

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.

Nonstationary coupling between heart rate and perfusion index in extremely preterm infants in the first day of life

OBJECTIVE

Adaptation to the extra-uterine environment presents many challenges for infants born less than 28 weeks of gestation. Quantitative analysis of readily-available physiological signals at the cotside could provide valuable information during this critical time. We aim to assess the time-varying coupling between heart rate (HR) and perfusion index (PI) over the first 24 hours after birth and relate this coupling to gestational age, inotropic therapy, and short-term clinical outcome.

APPROACH

We develop new nonstationary measures of coupling to summarise both frequency- and direction-dependent coupling. These measures employ a coherence measure capable of measuring time-varying Granger casuality using a short-time information partial directed coherence function. Measures are correlated with gestational age, inotropic therapy (yes/no), and outcome (adverse/normal).

MAIN RESULTS

In a cohort of 99 extremely preterm infants (<28 weeks of gestation), we find weak but significant coupling in both the HR-to-PI and PI-to-HR directions (P<0.05). HR-to-PI coupling increases with maturation (correlation r=0.26; P=0.011); PI-to-HR coupling increases with inotrope administration (r=0.27; P=0.007). And nonstationary features of PI-to-HR coupling are associated with (r=0.27; P=0.009).

SIGNIFICANCE

Nonstationary features are necessary to distinguish different coupling types for complex biomedical systems. Time-varying directional coupling between PI and HR provides objective and independent biomarkers of adverse outcome in extremely preterm infants.

Directional communication during movement execution interferes with tremor in Parkinson's disease

BACKGROUND

Both the cerebello-thalamo-cortical circuit and the basal ganglia/cortical motor loop have been postulated to be generators of tremor in PD. The recent suggestion that the basal ganglia trigger tremor episodes and the cerebello-thalamo-cortical circuitry modulates tremor amplitude combines both competing hypotheses. However, the role of the STN in tremor generation and the impact of proprioceptive feedback on tremor suppression during voluntary movements have not been considered in this model yet.

OBJECTIVES

The objective of this study was to evaluate the role of the STN and proprioceptive feedback in PD tremor generation during movement execution.

METHODS

Local-field potentials of the STN as well as electromyographical and electroencephalographical rhythms were recorded in tremor-dominant and nontremor PD patients while performing voluntary movements of the contralateral hand during DBS surgery. Effective connectivity between these electrophysiological signals were analyzed and compared to electromyographical tremor activity.

RESULTS

There was an intensified information flow between the STN and the muscle in the tremor frequencies (5-8 Hz) for tremor-dominant, in comparison to nontremor, patients. In both subtypes, active movement was associated with an increase of afferent interaction between the muscle and the cortex in the β- and γ-frequencies. The γ-frequency (30-40 Hz) of this communication between muscle and cortex correlated inversely with electromyographical tremor activity.

CONCLUSIONS

Our results indicate an involvement of the STN in propagation of tremor-related activity to the muscle. Furthermore, we provide evidence that increased proprioceptive information flow during voluntary movement interferes with central tremor generation. © 2018 International Parkinson and Movement Disorder Society.

Electrophysiological Brain Connectivity: Theory and Implementation

We review the theory and algorithms of electrophysiological brain connectivity analysis. This tutorial is aimed at providing an introduction to brain functional connectivity from electrophysiological signals, including electroencephalography (EEG), magnetoencephalography (MEG), electrocorticography (ECoG), stereoelectroencephalography (SEEG). Various connectivity estimators are discussed, and algorithms introduced. Important issues for estimating and mapping brain functional connectivity with electrophysiology are discussed.

Connectivity and Centrality Characteristics of the Epileptogenic Focus Using Directed Network Analysis

Accurate epileptogenic focus localization is required prior to surgical resection of brain tissue for the treatment of patients with antiepileptic drug-resistant (intractable) epilepsy. This clinical need is only partially fulfilled through a subjective, and at times inconclusive, the evaluation of the recorded electroencephalogram (EEG) at seizures' onset (the so-called gold standard for focus localization in epilepsy). We herein present a novel method of multivariate analysis of the EEG that appears to be very promising for an objective and robust localization of the epileptogenic focus at seizures' onset. Using the measure of generalized partial directed coherence, combined with surrogate data analysis, we first estimated from multichannel intracranial EEG the statistically significant causal interactions between brain regions at the onset of 92 clinical seizures from nine patients with temporal lobe intractable epilepsy. From the networks that were formed based on the thus derived interactions, a set of centrality metrics was estimated per network node (brain site). Brain sites located anatomically within the epileptogenic focus were shown to be associated with greater inward centrality values than non-focal brain regions at high frequencies ( γ band), and particular inward centrality metrics accurately localized the focus in all nine patients. In addition to focus localization from seizure (ictal) onset, the developed novel framework for analysis of EEG could be employed to identify the changes of the focal network over time, peri-ictally and interictally, and thus shed light onto the dynamics of ictogenesis, which could then have a significant impact on automated prediction and closed-loop control of seizures by neuromodulation.

A realistic neuronal network and neurovascular coupling model for the study of multivariate directed connectivity in fMRI data

The use of Multivariate Granger Causality (MVGC) in estimating directed Blood-Oxygen-Level- Dependant (BOLD) connectivity is still controversial. This is mostly due to the short data Ienghts typically available in func- tional MRI (fMRI) acquisitions, to the very nature of the BOLD acquisition strategy (which yields extremely low signal- to-noise-ratio) and importantly to the fact that neuronal activi- ty is convolved with a slow-varying haemodynamic response function (HRF) which therefore generates a temporal confound which is arduous to account for when basing MVGC estimates on vector autoregressive models (VAR). In this paper, we em- ploy realistic complex network models based on Izhikevich neuronal populations, interlinked by realistic neuronal fiber bundles which exert compounded directed influences and cas- cade into Baloon-model-like neurovascular coupling, to explore and validate the MVGC approach to directed connectivity es- timation in realistic fMRI conditions and in a complex directed network setting. In particular, we show in silico that the top 1 percentile of a BOLD connectivity matrix estimated with MVGC from BOLD data similar to the one provided by the Human Connectome Project (HCP) has a Positive Predictive Value very close to 1, hence corroborating the evidence that the "strongest" connections can be safely studied with this method in fMRI.

Multivariate Granger causality unveils directed parietal to prefrontal cortex connectivity during task-free MRI

While a large body of research has focused on the study of functional brain "connectivity", few investigators have focused on directionality of brain-brain interactions which, in spite of the mostly bidirectional anatomical substrates, cannot be assumed to be symmetrical. We employ a multivariate Granger Causality-based approach to estimating directed in-network interactions and quantify its advantages using extensive realistic synthetic BOLD data simulations to match Human Connectome Project (HCP) data specification. We then apply our framework to resting state functional MRI (rs-fMRI) data provided by the HCP to estimate the directed connectome of the human brain. We show that the functional interactions between parietal and prefrontal cortices commonly observed in rs-fMRI studies are not symmetrical, but consists of directional connectivity from parietal areas to prefrontal cortices rather than vice versa. These effects are localized within the same hemisphere and do not generalize to cross-hemispheric functional interactions. Our data are consistent with neurophysiological evidence that posterior parietal cortices involved in processing and integration of multi-sensory information modulate the function of more anterior prefrontal regions implicated in action control and goal-directed behaviour. The directionality of functional connectivity can provide an additional layer of information in interpreting rs-fMRI studies both in health and disease.

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.

Assessing the strength of cardiac and sympathetic baroreflex controls via transfer entropy during orthostatic challenge

The study assesses the strength of the causal relation along baroreflex (BR) in humans during an incremental postural challenge soliciting the BR. Both cardiac BR (cBR) and sympathetic BR (sBR) were characterized via BR sequence approaches from spontaneous fluctuations of heart period (HP), systolic arterial pressure (SAP), diastolic arterial pressure (DAP) and muscle sympathetic nerve activity (MSNA). A model-based transfer entropy method was applied to quantify the strength of the coupling from SAP to HP and from DAP to MSNA. The confounding influences of respiration were accounted for. Twelve young healthy subjects (20-36 years, nine females) were sequentially tilted at 0°, 20°, 30° and 40°. We found that (i) the strength of the causal relation along the cBR increases with tilt table inclination, while that along the sBR is unrelated to it; (ii) the strength of the causal coupling is unrelated to the gain of the relation; (iii) transfer entropy indexes are significantly and positively associated with simplified causality indexes derived from BR sequence analysis. The study proves that causality indexes are complementary to traditional characterization of the BR and suggests that simple markers derived from BR sequence analysis might be fruitfully exploited to estimate causality along the BR.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Backward renormalization-group inference of cortical dipole sources and neural connectivity efficacy

Proper neural connectivity inference has become essential for understanding cognitive processes associated with human brain function. Its efficacy is often hampered by the curse of dimensionality. In the electroencephalogram case, which is a noninvasive electrophysiological monitoring technique to record electrical activity of the brain, a possible way around this is to replace multichannel electrode information with dipole reconstructed data. We use a method based on maximum entropy and the renormalization group to infer the position of the sources, whose success hinges on transmitting information from low- to high-resolution representations of the cortex. The performance of this method compares favorably to other available source inference algorithms, which are ranked here in terms of their performance with respect to directed connectivity inference by using artificially generated dynamic data. We examine some representative scenarios comprising different numbers of dynamically connected dipoles over distinct cortical surface positions and under different sensor noise impairment levels. The overall conclusion is that inverse problem solutions do not affect the correct inference of the direction of the flow of information as long as the equivalent dipole sources are correctly found.

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 Power of Connecting Dots: Advanced Techniques to Evaluate Brain Functional Connectivity in Humans

Brain functional connectivity estimation allows us to depict patterns of cerebral activity not understandable otherwise with the standard brain imaging techniques such as functional magnetic resonance imaging (fMRI) as well as electro or magnetoencephalography (hr-EEG, MEG). This special issue of the IEEE Transactions on Biomedical Engineering reports a range of methodological innovations toward the estimation of functional connectivity from brain activity data, with emphasis on neuroelectric and hemodynamic imaging modalities. Functional connectivity methodologies enable "connecting of the dots" derived from brain activity observations over multiple distributed sites, as depicted by such fMRI and hr-EEG/MEG devices.

Testing the Significance of Connectivity Networks: Comparison of Different Assessing Procedures

Despite the well-established use of partial directed coherence (PDC) to estimate interactions between brain signals, the assessment of its statistical significance still remains controversial. Commonly used approaches are based on the generation of empirical distributions of the null case, implying a considerable computational time, which may become a serious limitation in practical applications. Recently, rigorous asymptotic distributions for PDC were proposed. The aim of this work is to compare the performances of the asymptotic statistics with those of an empirical approach, in terms of both accuracy and computational time.

METHODS

Indices of performance were derived for the two approaches by a simulation study implementing different ground-truth networks under different levels of signal-to-noise ratio and amount of data available for the estimate. The two approaches were then applied to the resting-state EEG data acquired in a group of minimally conscious state and vegetative state/unresponsive wakefulness syndrome patients.

RESULTS

The performances of the asymptotic statistics in simulations matched those obtained by the empirical approach, with a considerable reduction of the computational time. Results of the application to real data showed that the asymptotic statistics led to the extraction of connectivity-based indices able to discriminate patients in different disorders of consciousness conditions and to correlate significantly with clinical scales. Such results were similar to those obtained by the empirical assessment, but with a considerable time economy.

SIGNIFICANCE

Asymptotic statistics provide an approach to the assessment of PDC significance with comparable performances with respect to the previously used empirical approaches but with a substantial advantage in terms of computational time.

Partial directed coherence statistical performance characteristics in frequency domain

In this work we show the asymptotic behavior of information partial directed coherence estimator via the Monte Carlo simulation of a particular toy model taken from the literature. We show that the control of false positive rate tends to the chosen significance level if detection decision is made at specific frequency values.

Seizure-Onset Mapping Based on Time-Variant Multivariate Functional Connectivity Analysis of High-Dimensional Intracranial EEG: A Kalman Filter Approach

The visual interpretation of intracranial EEG (iEEG) is the standard method used in complex epilepsy surgery cases to map the regions of seizure onset targeted for resection. Still, visual iEEG analysis is labor-intensive and biased due to interpreter dependency. Multivariate parametric functional connectivity measures using adaptive autoregressive (AR) modeling of the iEEG signals based on the Kalman filter algorithm have been used successfully to localize the electrographic seizure onsets. Due to their high computational cost, these methods have been applied to a limited number of iEEG time-series (<60). The aim of this study was to test two Kalman filter implementations, a well-known multivariate adaptive AR model (Arnold et al. 1998) and a simplified, computationally efficient derivation of it, for their potential application to connectivity analysis of high-dimensional (up to 192 channels) iEEG data. When used on simulated seizures together with a multivariate connectivity estimator, the partial directed coherence, the two AR models were compared for their ability to reconstitute the designed seizure signal connections from noisy data. Next, focal seizures from iEEG recordings (73-113 channels) in three patients rendered seizure-free after surgery were mapped with the outdegree, a graph-theory index of outward directed connectivity. Simulation results indicated high levels of mapping accuracy for the two models in the presence of low-to-moderate noise cross-correlation. Accordingly, both AR models correctly mapped the real seizure onset to the resection volume. This study supports the possibility of conducting fully data-driven multivariate connectivity estimations on high-dimensional iEEG datasets using the Kalman filter approach.

Distinguishing between direct and indirect directional couplings in large oscillator networks: Partial or non-partial phase analyses?

We investigate the relative merit of phase-based methods for inferring directional couplings in complex networks of weakly interacting dynamical systems from multivariate time-series data. We compare the evolution map approach and its partialized extension to each other with respect to their ability to correctly infer the network topology in the presence of indirect directional couplings for various simulated experimental situations using coupled model systems. In addition, we investigate whether the partialized approach allows for additional or complementary indications of directional interactions in evolving epileptic brain networks using intracranial electroencephalographic recordings from an epilepsy patient. For such networks, both direct and indirect directional couplings can be expected, given the brain's connection structure and effects that may arise from limitations inherent to the recording technique. Our findings indicate that particularly in larger networks (number of nodes ≫10), the partialized approach does not provide information about directional couplings extending the information gained with the evolution map approach.

Statistically significant time-varying neural connectivity estimation using generalized partial directed coherence

This paper illustrates the effectiveness of generalized partial directed coherence (gPDC) in characterizing time-varying neural connectivity by properly extrapolating its single trial asymptotic statistical results to a multi trial setting. Time-varying estimation is performed with a sliding-window procedure based on the proposal in [1], whereby a time-frequency map of the connectivity between channels is built. The technique is validated on a non-linear toy model generating simulated EEG and then applied to a publicly available real EEG dataset for benchmarking purposes.

Source and sink nodes in absence seizures

As opposed to focal epilepsy, absence seizures do not exhibit a clear seizure onset zone or focus since its ictal activity rapidly engages both brain hemispheres. Yet recent graph theoretical analysis applied to absence seizures EEG suggests the cortical focal presence, an unexpected feature for this type of epilepsy. In this study, we explore the characteristics of absence seizure by classifying the nodes as to their source/sink natures via weighted directed graph analysis based on connectivity direction and strength estimation using information partial directed coherence (iPDC). By segmenting the EEG signals into relatively short 5-sec-long time windows we studied the evolution of coupling strengths from both sink and source nodes, and the network dynamics of absence seizures in eight patients.

Globally conditioned Granger causality in brain-brain and brain-heart interactions: a combined heart rate variability/ultra-high-field (7 T) functional magnetic resonance imaging study

The causal, directed interactions between brain regions at rest (brain-brain networks) and between resting-state brain activity and autonomic nervous system (ANS) outflow (brain-heart links) have not been completely elucidated. We collected 7 T resting-state functional magnetic resonance imaging (fMRI) data with simultaneous respiration and heartbeat recordings in nine healthy volunteers to investigate (i) the causal interactions between cortical and subcortical brain regions at rest and (ii) the causal interactions between resting-state brain activity and the ANS as quantified through a probabilistic, point-process-based heartbeat model which generates dynamical estimates for sympathetic and parasympathetic activity as well as sympathovagal balance. Given the high amount of information shared between brain-derived signals, we compared the results of traditional bivariate Granger causality (GC) with a globally conditioned approach which evaluated the additional influence of each brain region on the causal target while factoring out effects concomitantly mediated by other brain regions. The bivariate approach resulted in a large number of possibly spurious causal brain-brain links, while, using the globally conditioned approach, we demonstrated the existence of significant selective causal links between cortical/subcortical brain regions and sympathetic and parasympathetic modulation as well as sympathovagal balance. In particular, we demonstrated a causal role of the amygdala, hypothalamus, brainstem and, among others, medial, middle and superior frontal gyri, superior temporal pole, paracentral lobule and cerebellar regions in modulating the so-called central autonomic network (CAN). In summary, we show that, provided proper conditioning is employed to eliminate spurious causalities, ultra-high-field functional imaging coupled with physiological signal acquisition and GC analysis is able to quantify directed brain-brain and brain-heart interactions reflecting central modulation of ANS outflow.

Directed Transfer Function: Unified Asymptotic Theory and Some of Its Implications

OBJECTIVE

To present a unified mathematical derivation of the frequency-dependent asymptotic behavior of the three main forms of directed transfer function (DTF).

METHODS

A synthesis of the results (proved in an extended Appendix) is followed by a series of Monte Carlo simulations of representative examples.

RESULTS

DTF estimators are asymptotically normal when the true values are different from zero. Under the null hypothesis H₀: DTF=0, the estimator is distributed as a linear combination of independent χ²₁ variables.

CONCLUSIONS

Null DTF rejection is shown to be achievable with identical performance irrespective of which DTF form is adopted.

SIGNIFICANCE

Together with recent allied partial directed coherence results, this paper rounds up connectivity inference tools for a class of frequency-domain connectivity estimators.

A new algorithm for neural connectivity estimation of EEG event related potentials

We propose a new algorithm for estimating neural connectivity during event related potentials (ERP) in EEG. It is composed of two steps: the estimation of a time-varying multivariate-autoregressive (MVAR) model and the calculation of the generalized partial directed coherence (gPDC) for assessing the connectivities between channels where MVAR estimation is done via an adapted version of the Nuttall-Strand algorithm, a multivariate generalization of Burg's spectral estimation algorithm. Successful algorithm validation was performed through simulations using toys model with physiologically ERP inspired features.

On neural connectivity estimation problems

After briefly recapping and reframing the problem of neural connectivity and its implications for today's brain mapping efforts, we argue that supplementing/replacing traditional conservative correlation based analysis methods requires active user understanding of the aims and limitations of the newly proposed multivariate analysis frameworks before the new methods can gain general acceptance and full profit can be made from the expanded descriptive opportunities they offer.

Kernel-nonlinear-PDC extends Partial Directed Coherence to detecting nonlinear causal coupling

Here we investigate a new concept, kernel-nonlinear-Partial Directed Coherence, whereby a kernel feature space representation of the data allows detecting nonlinear causal links that are otherwise undetectable through linear modeling. We show that adequate connectivity detection is achievable by applying asympotic decision criteria similar to the ones developed for linear models.

On the statistical performance of Granger-causal connectivity estimators

In this article, we extend the statistical detection performance evaluation of linear connectivity from Sameshima et al. (in: Slezak et al. (eds.) Lecture Notes in Computer Science, 2014) via brand new Monte Carlo simulations of three widely used toy models under different data record lengths for a classic time domain multivariate Granger causality test, information partial directed coherence, information directed transfer function, and include conditional multivariate Granger causality whose behaviour was found to be anomalous.

Local dimension-reduced dynamical spatio-temporal models for resting state network estimation

To overcome the limitations of independent component analysis (ICA), today’s most popular analysis tool for investigating whole-brain spatial activation in resting state functional magnetic resonance imaging (fMRI), we present a new class of local dimension-reduced dynamical spatio-temporal model which dispenses the independence assumptions that severely limit deeper connectivity descriptions between spatial components. The new method combines novel concepts of group sparsity with contiguity-constrained clusterization to produce physiologically consistent regions of interest in illustrative fMRI data whose causal interactions may then be easily estimated, something impossible under the usual ICA assumptions.