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

A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks

Abstracting causal knowledge from process measurements has become an appealing topic for decades, especially for fault root cause analysis (RCA) based on signals recorded by multiple sensors in a complex system. Although many causality detection methods have been developed and applied in different fields, some research communities may have an idiosyncratic implementation of their preferred methods, with limited accessibility to the wider community. Targeting interested experimental researchers and engineers, this paper provides a comprehensive comparison of data-based causality detection methods in root cause diagnosis across two distinct domains. We provide a possible taxonomy of those methods followed by descriptions of the main motivations of those concepts. Of the two cases we investigated, one is a root cause diagnosis of plant-wide oscillations in an industrial process, while the other is the localization of the epileptogenic focus in a human brain network where the connectivity pattern is transient and even more complex. Considering the differences in various causality detection methods, we designed several sets of experiments so that for each case, a total of 11 methods could be appropriately compared under a unified and reasonable evaluation framework. In each case, these methods were implemented separately and in a standard way to infer causal interactions among multiple variables to thus establish the causal network for RCA. From the cross-domain investigation, several findings are presented along with insights into them, including an interpretative pitfall that warrants caution.

Exploring Convolutional Neural Network Architectures for EEG Feature Extraction

The main purpose of this paper is to provide information on how to create a convolutional neural network (CNN) for extracting features from EEG signals. Our task was to understand the primary aspects of creating and fine-tuning CNNs for various application scenarios. We considered the characteristics of EEG signals, coupled with an exploration of various signal processing and data preparation techniques. These techniques include noise reduction, filtering, encoding, decoding, and dimension reduction, among others. In addition, we conduct an in-depth analysis of well-known CNN architectures, categorizing them into four distinct groups: standard implementation, recurrent convolutional, decoder architecture, and combined architecture. This paper further offers a comprehensive evaluation of these architectures, covering accuracy metrics, hyperparameters, and an appendix that contains a table outlining the parameters of commonly used CNN architectures for feature extraction from EEG signals.

Graph Analysis of TMS-EEG Connectivity Reveals Hemispheric Differences following Occipital Stimulation

(1) Background: Transcranial magnetic stimulation combined with electroencephalography (TMS-EEG) provides a unique opportunity to investigate brain connectivity. However, possible hemispheric asymmetries in signal propagation dynamics following occipital TMS have not been investigated. (2) Methods: Eighteen healthy participants underwent occipital single-pulse TMS at two different EEG sites, corresponding to early visual areas. We used a state-of-the-art Bayesian estimation approach to accurately estimate TMS-evoked potentials (TEPs) from EEG data, which has not been previously used in this context. To capture the rapid dynamics of information flow patterns, we implemented a self-tuning optimized Kalman (STOK) filter in conjunction with the information partial directed coherence (iPDC) measure, enabling us to derive time-varying connectivity matrices. Subsequently, graph analysis was conducted to assess key network properties, providing insight into the overall network organization of the brain network. (3) Results: Our findings revealed distinct lateralized effects on effective brain connectivity and graph networks after TMS stimulation, with left stimulation facilitating enhanced communication between contralateral frontal regions and right stimulation promoting increased intra-hemispheric ipsilateral connectivity, as evidenced by statistical test (p < 0.001). (4) Conclusions: The identified hemispheric differences in terms of connectivity provide novel insights into brain networks involved in visual information processing, revealing the hemispheric specificity of neural responses to occipital stimulation.

Improving EEG-Based Driver Distraction Classification Using Brain Connectivity Estimators

This paper discusses a novel approach to an EEG (electroencephalogram)-based driver distraction classification by using brain connectivity estimators as features. Ten healthy volunteers with more than one year of driving experience and an average age of 24.3 participated in a virtual reality environment with two conditions, a simple math problem-solving task and a lane-keeping task to mimic the distracted driving task and a non-distracted driving task, respectively. Independent component analysis (ICA) was conducted on the selected epochs of six selected components relevant to the frontal, central, parietal, occipital, left motor, and right motor areas. Granger-Geweke causality (GGC), directed transfer function (DTF), partial directed coherence (PDC), and generalized partial directed coherence (GPDC) brain connectivity estimators were used to calculate the connectivity matrixes. These connectivity matrixes were used as features to train the support vector machine (SVM) with the radial basis function (RBF) and classify the distracted and non-distracted driving tasks. GGC, DTF, PDC, and GPDC connectivity estimators yielded the classification accuracies of 82.27%, 70.02%, 86.19%, and 80.95%, respectively. Further analysis of the PDC connectivity estimator was conducted to determine the best window to differentiate between the distracted and non-distracted driving tasks. This study suggests that the PDC connectivity estimator can yield better classification accuracy for driver distractions.

Brain Synchronization and Multivariate Autoregressive (MVAR) Modeling in Cognitive Neurodynamics

This paper is a review of cognitive neurodynamics research as it pertains to recent advances in Multivariate Autoregressive (MVAR) modeling. Long-range synchronization between the frontoparietal network (FPN) and forebrain subcortical systems occurs when multiple neuronal actions are coordinated across time (Chafee and Goldman-Rakic, 1998), resulting in large-scale measurable activity in the EEG. This paper reviews the power and advantages of the MVAR method to analyze long-range synchronization between brain regions (Kaminski et al., 2016; Kaminski and Blinowska, 2017). It explores the synchronization expressed in neurocognitive networks that is observable in the local field potential (LFP), an EEG-like signal, and in fMRI time series. In recent years, the surge in MVAR modeling in cognitive neurodynamics experiments has highlighted the effectiveness of the method, particularly in analyzing continuous neural signals such as EEG and fMRI (Pereda et al., 2005). MVAR modeling has been particularly useful in identifying causality, a multichannel time-series measure that can only be consistently computed with multivariate processes. Due to the multivariate nature of neuronal communication, multiple non-linear multivariate-analysis models are successful, presenting results with much greater accuracy and speed than non-linear univariate-analysis methods. Granger’s framework provides causal information about neuronal flow using neural time and frequency analysis, comprising the basis of the MVAR model. Recent advancements in MVAR modeling have included Directed Transfer Function (DTF) and Partial Directed Coherence (PDC), multivariate methods based on MVAR modeling that are capable of determining causal influences and directed propagation of EEG activity. The related Granger causality is an increasingly popular tool for measuring directed functional interactions from time series data.

Time-Varying Effective Connectivity for Describing the Dynamic Brain Networks of Post-stroke Rehabilitation

Hemiplegia is a common motor dysfunction caused by a stroke. However, the dynamic network mechanism of brain processing information in post-stroke hemiplegic patients has not been revealed when performing motor imagery (MI) tasks. We acquire electroencephalography (EEG) data from healthy subjects and post-stroke hemiplegic patients and use the Fugl-Meyer assessment (FMA) to assess the degree of motor function damage in stroke patients. Time-varying MI networks are constructed using the adaptive directed transfer function (ADTF) method to explore the dynamic network mechanism of MI in post-stroke hemiplegic patients. Finally, correlation analysis has been conducted to study potential relationships between global efficiency and FMA scores. The performance of our proposed method has shown that the brain network pattern of stroke patients does not significantly change from laterality to bilateral symmetry when performing MI recognition. The main change is that the contralateral motor areas of the brain damage and the effective connection between the frontal lobe and the non-motor areas are enhanced, to compensate for motor dysfunction in stroke patients. We also find that there is a correlation between FMA scores and global efficiency. These findings help us better understand the dynamic brain network of patients with post-stroke when processing MI information. The network properties may provide a reliable biomarker for the objective evaluation of the functional rehabilitation diagnosis of stroke patients.

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

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

A survey of brain network analysis by electroencephalographic signals

Brain network analysis is one efficient tool in exploring human brain diseases and can differentiate the alterations from comparative networks. The alterations account for time, mental states, tasks, individuals, and so forth. Furthermore, the changes determine the segregation and integration of functional networks that lead to network reorganization (or reconfiguration) to extend the neuroplasticity of the brain. Exploring related brain networks should be of interest that may provide roadmaps for brain research and clinical diagnosis. Recent electroencephalogram (EEG) studies have revealed the secrets of the brain networks and diseases (or disorders) within and between subjects and have provided instructive and promising suggestions and methods. This review summarized the corresponding algorithms that had been used to construct functional or effective networks on the scalp and cerebral cortex. We reviewed EEG network analysis that unveils more cognitive functions and neural disorders of the human and then explored the relationship between brain science and artificial intelligence which may fuel each other to accelerate their advances, and also discussed some innovations and future challenges in the end.

Structure supports function: Informing directed and dynamic functional connectivity with anatomical priors

The dynamic repertoire of functional brain networks is constrained by the underlying topology of structural connections. Despite this intrinsic relationship between structural connectivity (SC) and functional connectivity (FC), integrative and multimodal approaches to combine the two remain limited. Here, we propose a new adaptive filter for estimating dynamic and directed FC using structural connectivity information as priors. We tested the filter in rat epicranial recordings and human event-related EEG data, using SC priors from a meta-analysis of tracer studies and diffusion tensor imaging metrics, respectively. We show that, particularly under conditions of low signal-to-noise ratio, SC priors can help to refine estimates of directed FC, promoting sparse functional networks that combine information from structure and function. In addition, the proposed filter provides intrinsic protection against SC-related false negatives, as well as robustness against false positives, representing a valuable new tool for multimodal imaging in the context of dynamic and directed FC analysis.

Cortical network and connectivity underlying hedonic olfactory perception

Objective.The emotional response to olfactory stimuli implies the activation of a complex cascade of events triggered by structures lying in the limbic system. However, little is known about how this activation is projected up to cerebral cortex and how different cortical areas dynamically interact each other.Approach.In this study, we acquired EEG from human participants performing a passive odor-perception task with odorants conveying positive, neutral and negative valence. A novel methodological pipeline integrating global field power (GFP), independent component analysis (ICA), dipole source localization was applied to estimate effective connectivity in the challenging scenario of single-trial low-synchronized stimulation.Main results.We identified the brain network and the neural paths, elicited at different frequency bands, i.e.θ(4-7Hz),α(8-12Hz)andβ(13-30Hz), involved in odor valence processing. This brain network includes the orbitofrontal cortex (OFC), the cingulate gyrus (CgG), the superior temporal gyrus (STG), the posterior cingulate cortex/precuneus (PCC/PCu) and the parahippocampal gyrus (PHG). It was analyzed using a time-varying multivariate autoregressive model to resolve time-frequency causal interactions. Specifically, the OFC acts as the main node for odor perception and evaluation of pleasant and unpleasant stimuli, whereas no specific path was observed for a neutral stimulus.Significance.The results introduce new evidences on the role of the OFC during hedonic perception and underpin its specificity during the odor valence assessment. Our findings suggest that, after the odor onset different, bidirectional interactions occur between the OFC and other brain regions associated with emotion recognition/categorization and memory according to the stimulus valence. This outcome unveils how the hedonic olfactory network dynamically changes based on odor valence.

Stimulus evoked causality estimation in stereo-EEG

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

Functional and directed connectivity of the cortico-limbic network in mice in vivo

Higher cognitive processes and emotional regulation depend on densely interconnected telencephalic and limbic areas. Central structures of this cortico-limbic network are ventral hippocampus (vHC), medial prefrontal cortex (PFC), basolateral amygdala (BLA) and nucleus accumbens (NAC). Human and animal studies have revealed both anatomical and functional alterations in specific connections of this network in several psychiatric disorders. However, it is often not clear whether functional alterations within these densely interconnected brain areas are caused by modifications in the direct pathways, or alternatively through indirect interactions. We performed multi-site extracellular recordings of spontaneous activity in three different brain regions to study the functional connectivity in the BLA-NAC-PFC-vHC network of the lightly anesthetized mouse in vivo. We show that BLA, NAC, PFC and vHC are functionally connected in distinct frequency bands and determined the influence of a third brain region on this connectivity. In addition to describing mutual synchronicity, we determined the strength of functional connectivity for each region in the BLA-NAC-PFC-vHC network. We find a region-specificity in the strength of feedforward and feedback connections for each region in its interaction with other areas in the network. Our results provide insights into functional and directed connectivity in the cortico-limbic network of adult wild-type mice, which may be helpful to further elucidate the pathophysiological changes of this network in psychiatric disorders and to develop target-specific therapeutic interventions.

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.

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.

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

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

SimMEEG software for simulating event-related MEG and EEG data with underlying functional connectivity

BACKGROUND

Simulating electromagnetic brain signals is becoming more and more prevalent because of the need to verify and validate electrophysiological analysis methods, especially with regards to measurements of functional connectivity and phase-amplitude coupling (PAC).

NEW METHOD

A Matlab software package with a graphical user interface, called SimMEEG, was developed so that novice and expert users could input basic signal parameters (e.g., multiple frequencies, amplitudes, durations, phase interactions, and phase-amplitude couplings) in order to simulate signals that approximate event-related brain activity. A major objective for developing this software was to create software to simulate interacting brain signals that could be used to verify functional connectivity analyses, specifically phase-locking value (PLV), phase-lag index (PLI) algorithms, and PAC. SimMEEG simulates three sources with various parameters defined by users. Users can define, multiple frequencies, event-related changes in amplitude, synchronizations (i.e., PLV and PLI), and PAC.

RESULTS

SimMEEG simulated signals that estimated the signal input parameters within specific target limits for PLV, PLI, and PAC. In addition, SimMEEG's synthetic signals closely approximated real human visual event-related responses. The Monte-Carlo module was used to simulate ten MEG and EEG datasets, conduct function connectivity analyses for comparison among several inverse solutions, and generate errors from ground truth. SimMEEG identified inverse solutions that had good and poor performances for functional connectivity analyses.

COMPARISON WITH EXISTING METHODS

Comparison between other simulation methods and SimMEEG are discussed.

CONCLUSION

SimMEEG software could be used to simulate real human EEG and MEG to aid in verification of analysis pipelines by comparing analyzed results to the simulated ground truth of the user-defined event-related brain signals. A core program within SimMEEG, called SimSignals, might also be used in other fields that would benefit from simulations of three interacting signals.

Seizure-onset regions demonstrate high inward directed connectivity during resting-state: An SEEG study in focal epilepsy

OBJECTIVE

In patients with medically refractory focal epilepsy, stereotactic-electroencephalography (SEEG) can aid in localizing epileptogenic regions for surgical treatment. SEEG, however, requires long hospitalizations to record seizures, and ictal interpretation can be incomplete or inaccurate. Our recent work showed that non-directed resting-state analyses may identify brain regions as epileptogenic or uninvolved. Our present objective is to map epileptogenic networks in greater detail and more accurately identify seizure-onset regions using directed resting-state SEEG connectivity.

METHODS

In 25 patients with focal epilepsy who underwent SEEG, 2 minutes of resting-state, artifact-free, SEEG data were selected and functional connectivity was estimated. Using standard clinical interpretation, brain regions were classified into four categories: ictogenic, early propagation, irritative, or uninvolved. Three non-directed connectivity measures (mutual information [MI] strength, and imaginary coherence between and within regions) and four directed measures (partial directed coherence [PDC] and directed transfer function [DTF], inward and outward strength) were calculated. Logistic regression was used to generate a predictive model of ictogenicity.

RESULTS

Ictogenic regions had the highest and uninvolved regions had the lowest MI strength. Although both PDC and DTF inward strengths were highest in ictogenic regions, outward strengths did not differ among categories. A model incorporating directed and nondirected connectivity measures demonstrated an area under the receiver-operating characteristic (ROC) curve (AUC) of 0.88 in predicting ictogenicity of individual regions. The AUC of this model was 0.93 when restricted to patients with favorable postsurgical seizure outcomes.

SIGNIFICANCE

Directed connectivity measures may help identify epileptogenic networks without requiring ictal recordings. Greater inward but not outward connectivity in ictogenic regions at rest may represent broad inhibitory input to prevent seizure generation.

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

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

Modeling time-varying brain networks with a self-tuning optimized Kalman filter

Brain networks are complex dynamical systems in which directed interactions between different areas evolve at the sub-second scale of sensory, cognitive and motor processes. Due to the highly non-stationary nature of neural signals and their unknown noise components, however, modeling dynamic brain networks has remained one of the major challenges in contemporary neuroscience. Here, we present a new algorithm based on an innovative formulation of the Kalman filter that is optimized for tracking rapidly evolving patterns of directed functional connectivity under unknown noise conditions. The Self-Tuning Optimized Kalman filter (STOK) is a novel adaptive filter that embeds a self-tuning memory decay and a recursive regularization to guarantee high network tracking accuracy, temporal precision and robustness to noise. To validate the proposed algorithm, we performed an extensive comparison against the classical Kalman filter, in both realistic surrogate networks and real electroencephalography (EEG) data. In both simulations and real data, we show that the STOK filter estimates time-frequency patterns of directed connectivity with significantly superior performance. The advantages of the STOK filter were even clearer in real EEG data, where the algorithm recovered latent structures of dynamic connectivity from epicranial EEG recordings in rats and human visual evoked potentials, in excellent agreement with known physiology. These results establish the STOK filter as a powerful tool for modeling dynamic network structures in biological systems, with the potential to yield new insights into the rapid evolution of network states from which brain functions emerge.

During normal behavior, brains transition between functional network states several times per second. This allows humans to quickly read a sentence, and a frog to catch a fly. Understanding these fast network dynamics is fundamental to understanding how brains work, but up to now it has proven very difficult to model fast brain dynamics for various methodological reasons. To overcome these difficulties, we designed a new Kalman filter (STOK) by innovating on previous solutions from control theory and state-space modelling. We show that STOK accurately models fast network changes in simulations and real neural data, making it an essential new tool for modelling fast brain networks in the time and frequency domain.

Dynamic changes of brain networks during feedback-related processing of reinforcement learning in schizophrenia

Previous studies have reported that schizophrenia (SZ) patients showed selective reinforcement learning deficits and abnormal feedback-related event-related potential (ERP) components. However, how the brain networks and their topological properties evolve over time during transient feedback-related cognition processing in SZ patients has not been investigated so far. In this paper, using publicly available feedback-related ERP data which were recorded from SZ patients and healthy controls (HC) when they performed a reinforcement learning task, we carried out an event-related network analysis where topology of brain functional networks was characterized with some graph measures including clustering coefficient (C), global efficiency (E_global) and local efficiency (E_local) on a millisecond timescale. Our results showed that the brain functional networks displayed rapid rearrangements of topological properties during transient feedback-related cognition process for both two groups. More importantly, we found that SZ patients exhibited significantly reduced theta-band (time window of 170-350 ms after stimuli onset) brain functional connectivity strength, E_global, E_local and C in response to negative feedback stimuli compared to HC group. The network based statistic (NBS) analysis detected one significantly decreased theta-band subnetwork in SZ patients mainly involving in frontal-occipital and temporal-occipital connections compared to HC group. In addition, clozapine treatment seemed to greatly reduce theta-band power and topological measures of brain networks in SZ patients. Finally, the theta-band power, graph measures and functional connectivity were extracted to train a support vector machine classifier for classification of HC from SZ, or Cloz + SZ or Cloz- SZ, and a relatively good classification accuracy of 84.48%, 89.47% and 78.26% was obtained, respectively. The above results suggested a less optimal organization of theta-band brain network in SZ patients, and studying the topological parameters of brain networks evolve over time during transient feedback-related processing could be useful for understanding the pathophysiologic mechanisms underlying reinforcement learning deficits in SZ patients.

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

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

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

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

A Parametric Time-Frequency Conditional Granger Causality Method Using Ultra-Regularized Orthogonal Least Squares and Multiwavelets for Dynamic Connectivity Analysis in EEGs

OBJECTIVE

This study proposes a new parametric time-frequency conditional Granger causality (TF-CGC) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source electroencephalogram (EEG) signals to reveal dynamic interaction patterns in oscillatory neocortical sensorimotor networks.

METHODS

The Geweke's spectral measure is combined with the time-varying autoregressive with exogenous input (TVARX) modeling approach, which uses multiwavelet-based ultra-regularized orthogonal least squares (UROLS) algorithm, aided by adjustable prediction error sum of squares (APRESS), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves, but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems.

RESULTS

The proposed method is validated on two simulations, and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cortical networks.

CONCLUSION

Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks.

SIGNIFICANCE

The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition.

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.

Directed functional connections underlying spontaneous brain activity

Neuroimaging studies have shown that spontaneous brain activity is characterized as changing networks of coherent activity across multiple brain areas. However, the directionality of functional interactions between the most active regions in our brain at rest remains poorly understood. Here, we examined, at the whole-brain scale, the main drivers and directionality of interactions that underlie spontaneous human brain activity by applying directed functional connectivity analysis to electroencephalography (EEG) source signals. We found that the main drivers of electrophysiological activity were the posterior cingulate cortex (PCC), the medial temporal lobes (MTL), and the anterior cingulate cortex (ACC). Among those regions, the PCC was the strongest driver and had both the highest integration and segregation importance, followed by the MTL regions. The driving role of the PCC and MTL resulted in an effective directed interaction directed from posterior toward anterior brain regions. Our results strongly suggest that the PCC and MTL structures are the main drivers of electrophysiological spontaneous activity throughout the brain and suggest that EEG-based directed functional connectivity analysis is a promising tool to better understand the dynamics of spontaneous brain activity in healthy subjects and in various brain disorders.

Assessing the performance of Granger-Geweke causality: Benchmark dataset and simulation framework

Nonparametric methods based on spectral factorization offer well validated tools for estimating spectral measures of causality, called Granger–Geweke Causality (GGC). In Pagnotta et al. (2018) [1] we benchmarked nonparametric GGC methods using EEG data recorded during unilateral whisker stimulations in ten rats; here, we include detailed information about the benchmark dataset. In addition, we provide codes for estimating nonparametric GGC and a simulation framework to evaluate the effects on GGC analyses of potential problems, such as the common reference problem, signal-to-noise ratio (SNR) differences between channels, and the presence of additive noise. We focus on nonparametric methods here, but these issues also affect parametric methods, which can be tested in our framework as well. Our examples allow showing that time reversal testing for GGC (tr-GGC) mitigates the detrimental effects due to SNR imbalance and presence of mixed additive noise, and illustrate that, when using a common reference, tr-GGC unambiguously detects the causal influence׳s dominant spectral component, irrespective of the characteristics of the common reference signal. Finally, one of our simulations provides an example that nonparametric methods can overcome a pitfall associated with the implementation of conditional GGC in traditional parametric methods.