A framework for assessing frequency domain causality in physiological time series with instantaneous effects

CVRanalysis: a free software for analyzing cardiac, vascular and respiratory interactions

Introduction: Simultaneous beat-to-beat R-R intervals, blood pressure and respiration signals are routinely analyzed for the evaluation of autonomic cardiovascular and cardiorespiratory regulations for research or clinical purposes. The more recognized analyses are i) heart rate variability and cardiac coherence, which provides an evaluation of autonomic nervous system activity and more particularly parasympathetic and sympathetic autonomic arms; ii) blood pressure variability which is mainly linked to sympathetic modulation and myogenic vascular function; iii) baroreflex sensitivity; iv) time-frequency analyses to identify fast modifications of autonomic activity; and more recently, v) time and frequency domain Granger causality analyses were introduced for assessing bidirectional causal links between each considered signal, thus allowing the scrutiny of many physiological regulatory mechanisms. Methods: These analyses are commonly applied in various populations and conditions, including mortality and morbidity predictions, cardiac and respiratory rehabilitation, training and overtraining, diabetes, autonomic status of newborns, anesthesia, or neurophysiological studies. Results: We developed CVRanalysis, a free software to analyze cardiac, vascular and respiratory interactions, with a friendly graphical interface designed to meet laboratory requirements. The main strength of CVRanalysis resides in its wide scope of applications: recordings can arise from beat-to-beat preprocessed data (R-R, systolic, diastolic and mean blood pressure, respiration) or raw data (ECG, continuous blood pressure and respiratory waveforms). It has several tools for beat detection and correction, as well as setting of specific areas or events. In addition to the wide possibility of analyses cited above, the interface is also designed for easy study of large cohorts, including batch mode signal processing to avoid running repetitive operations. Results are displayed as figures or saved in text files that are easily employable in statistical softwares. Conclusion: CVRanalysis is freely available at this website: anslabtools.univ-st-etienne.fr. It has been developed using MATLAB® and works on Windows 64-bit operating systems. The software is a standalone application avoiding to have programming skills and to install MATLAB. The aims of this paper area are to describe the physiological, research and clinical contexts of CVRanalysis, to introduce the methodological approach of the different techniques used, and to show an overview of the software with the aid of screenshots.

Concomitant evaluation of cardiovascular and cerebrovascular controls via Geweke spectral causality to assess the propensity to postural syncope

The evaluation of propensity to postural syncope necessitates the concomitant characterization of the cardiovascular and cerebrovascular controls and a method capable of disentangling closed loop relationships and decomposing causal links in the frequency domain. We applied Geweke spectral causality (GSC) to assess cardiovascular control from heart period and systolic arterial pressure variability and cerebrovascular regulation from mean arterial pressure and mean cerebral blood velocity variability in 13 control subjects and 13 individuals prone to develop orthostatic syncope. Analysis was made at rest in supine position and during head-up tilt at 60°, well before observing presyncope signs. Two different linear model structures were compared, namely bivariate autoregressive and bivariate dynamic adjustment classes. We found that (i) GSC markers did not depend on the model structure; (ii) the concomitant assessment of cardiovascular and cerebrovascular controls was useful for a deeper comprehension of postural disturbances; (iii) orthostatic syncope appeared to be favored by the loss of a coordinated behavior between the baroreflex feedback and mechanical feedforward pathway in the frequency band typical of the baroreflex functioning during the postural challenge, and by a weak cerebral autoregulation as revealed by the increased strength of the pressure-to-flow link in the respiratory band. GSC applied to spontaneous cardiovascular and cerebrovascular oscillations is a promising tool for describing and monitoring disturbances associated with posture modification.

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.

Altered default mode network causal connectivity patterns in autism spectrum disorder revealed by Liang information flow analysis

Autism spectrum disorder (ASD) is a pervasive developmental disorder with severe cognitive impairment in social communication and interaction. Previous studies have reported that abnormal functional connectivity patterns within the default mode network (DMN) were associated with social dysfunction in ASD. However, how the altered causal connectivity pattern within the DMN affects the social functioning in ASD remains largely unclear. Here, we introduced the Liang information flow method, widely applied to climate science and quantum mechanics, to uncover the brain causal network patterns in ASD. Compared with the healthy controls (HC), we observed that the interactions among the dorsal medial prefrontal cortex (dMPFC), ventral medial prefrontal cortex (vMPFC), hippocampal formation, and temporo-parietal junction showed more inter-regional causal connectivity differences in ASD. For the topological property analysis, we also found the clustering coefficient of DMN and the In-Out degree of anterior medial prefrontal cortex were significantly decreased in ASD. Furthermore, we found that the causal connectivity from dMPFC to vMPFC was correlated with the clinical symptoms of ASD. These altered causal connectivity patterns indicated that the DMN inter-regions information processing was perturbed in ASD. In particular, we found that the dMPFC acts as a causal source in the DMN in HC, whereas it plays a causal target in ASD. Overall, our findings indicated that the Liang information flow method could serve as an important way to explore the DMN causal connectivity patterns, and it also can provide novel insights into the nueromechanisms underlying DMN dysfunction in ASD.

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls

We present a framework for the linear parametric analysis of pairwise interactions in bivariate time series in the time and frequency domains, which allows the evaluation of total, causal and instantaneous interactions and connects time- and frequency-domain measures. The framework is applied to physiological time series to investigate the cerebrovascular regulation from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (MAP), and the cardiovascular regulation from the variability of heart period (HP) and systolic arterial pressure (SAP). We analyze time series acquired at rest and during the early and late phase of head-up tilt in subjects developing orthostatic syncope in response to prolonged postural stress, and in healthy controls. The spectral measures of total, causal and instantaneous coupling between HP and SAP, and between MAP and CBFV, are averaged in the low-frequency band of the spectrum to focus on specific rhythms, and over all frequencies to get time-domain measures. The analysis of cardiovascular interactions indicates that postural stress induces baroreflex involvement, and its prolongation induces baroreflex dysregulation in syncope subjects. The analysis of cerebrovascular interactions indicates that the postural stress enhances the total coupling between MAP and CBFV, and challenges cerebral autoregulation in syncope subjects, while the strong sympathetic activation elicited by prolonged postural stress in healthy controls may determine an increased coupling from CBFV to MAP during late tilt. These results document that the combination of time-domain and spectral measures allows us to obtain an integrated view of cardiovascular and cerebrovascular regulation in healthy and diseased subjects.

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.

Coherence Coefficient for Official Statistics

One of the quality requirements in official statistics is coherence of statistical information across domains, in time, in national accounts, and internally. However, no measure of its strength is used. The concept of coherence is also met in signal processing, wave physics, and time series. In the current article, the definition of the coherence coefficient for a weakly stationary time series is recalled and discussed. The coherence coefficient is a correlation coefficient between two indicators in time indexed by the same frequency components of their Fourier transforms and shows a degree of synchronicity between the time series for each frequency. The usage of this coefficient is illustrated through the coherence and Granger causality analysis of a collection of numerical economic and social statistical indicators. The coherence coefficient matrix-based non-metric multidimensional scaling for visualization of the time series in the frequency domain is a newly suggested method. The aim of this article is to propose the use of this coherence coefficient and its applications in official statistics.

Measuring Spinal Cord Potentials and Cortico-Spinal Interactions After Wrist Movements Induced by Neuromuscular Electrical Stimulation

Electroencephalographic (EEG) correlates of movement have been studied extensively over many years. In the present work, we focus on investigating neural correlates that originate from the spine and study their connectivity to corresponding signals from the sensorimotor cortex using multivariate autoregressive (MVAR) models. To study cortico-spinal interactions, we simultaneously measured spinal cord potentials (SCPs) and somatosensory evoked potentials (SEPs) of wrist movements elicited by neuromuscular electrical stimulation. We identified directional connections between spine and cortex during both the extension and flexion of the wrist using only non-invasive recording techniques. Our connectivity estimation results are in alignment with various studies investigating correlates of movement, i.e., we found the contralateral side of the sensorimotor cortex to be the main sink of information as well as the spine to be the main source of it. Both types of movement could also be clearly identified in the time-domain signals.

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.

Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate variability

Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of 'instantaneous' effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index of undirected instantaneous causality and (ii) a novel measure of GC including instantaneous effects. An effective procedure to speed up the optimization of parameters in this frame is also presented. After illustrating the proposed formalism in a theoretical example, we apply it to two datasets of cardiovascular and respiratory time series and compare the values obtained within the frequency bands of physiological interest by the proposed total measure of causality with those derived from the standard GC analysis. We find that the inclusion of instantaneous causality allows us to correctly disentangle the baroreflex mechanism from the effects related to cardiorespiratory interactions. Moreover, studying how controlling the respiratory rhythm acts on cardiovascular interactions, we document an increase of the direct (non-baroreflex mediated) influence of respiration on the heart rate in the respiratory frequency band when switching from spontaneous to paced breathing. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

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.

Functional Interactions between Entorhinal Cortical Pathways Modulate Theta Activity in the Hippocampus

Simple Summary

The activity in the hippocampus is characterized by a strong oscillation at theta frequency that organizes the neuronal firing. We have recently shown that different theta oscillations are present in the hippocampus, opening the possibility to multiple interactions between theta rhythms. In this work, we analyzed the functional connectivity between theta generators during the exploration of a known environment with or without a novel stimulus. The directionality of the interactions was determined using tools based on Granger causality and transfer entropy. We found significant interactions between activity components originated in CA3 and in layers II and III of the entorhinal cortex. During exploration with a novel stimulus, the connectivity from the entorhinal cortex layer II increased, while the influence of CA3 decreased. These results suggest that the entorhinal cortex layer II may drive theta interactions and synchronization in the hippocampus during novelty exploration.

Abstract

Theta oscillations organize neuronal firing in the hippocampus during context exploration and memory formation. Recently, we have shown that multiple theta rhythms coexist in the hippocampus, reflecting the activity in their afferent regions in CA3 (Schaffer collaterals) and the entorhinal cortex layers II (EC-II, perforant pathway) and III (EC-III, temporoammonic pathway). Frequency and phase coupling between theta rhythms were modulated by the behavioral state, with synchronized theta rhythmicity preferentially occurring in tasks involving memory updating. However, information transmission between theta generators was not investigated. Here, we used source separation techniques to disentangle the current generators recorded in the hippocampus of rats exploring a known environment with or without a novel stimulus. We applied analytical tools based on Granger causality and transfer entropy to investigate linear and non-linear directed interactions, respectively, between the theta activities. Exploration in the novelty condition was associated with increased theta power in the generators with EC origin. We found a significant directed interaction from the Schaffer input over the EC-III input in CA1, and a bidirectional interaction between the inputs in the hippocampus originating in the EC, likely reflecting the connection between layers II and III. During novelty exploration, the influence of the EC-II over the EC-III generator increased, while the Schaffer influence decreased. These results associate the increase in hippocampal theta activity and synchrony during novelty exploration with an increase in the directed functional connectivity from EC-II to EC-III.

The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey-Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.

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.

Ld-EEG Effective Brain Connectivity in Patients With Cheyne-Stokes Respiration

The characterization of brain cortical activity in heart-failure patients affected by Cheyne-Stokes Respiration might provide relevant information about the mechanism underlying this pathology. Central autonomic network is gaining increasing attention for its role in the regulation of breathing and cardiac functions. In this scenario, evaluating changes in cortical connectivity associated with Cheyne-Stokes Respiration may be of interest in the study of specific brain-activity related to such disease. Nonetheless, the inter subject variability, the temporal dynamics of Central-Apnea/Hyperpnea cycles and the limitations of clinical setups lead to different methodological challenges. To this aim, we present a framework for the assessment of cortico-cortical interactions from Electroencephalographic signals acquired using low-density caps and block-design paradigms, arising from endogenous triggers. The framework combines ICA-decomposition, unsupervised clustering, MVAR modelling and a permutation-bootstrap strategy for evaluating significant connectivity differences between conditions. A common network, lateralized towards the left hemisphere, was depicted across 8 patients exhibiting Cheyne-Stokes Respiration patterns during acquisitions. Significant differences in connectivity at the group level were observed based on patients' ventilatory condition. Interactions were significantly higher during hyperpnea periods with respect to central apneas and occurred mainly in the delta band. Opposite-sign differences were observed for higher frequencies (i.e. beta, low-gamma).

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.

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.

Temporal cardiovascular causality during orthostatic stress by extended partial directed coherence

The aim of this study was to investigate the temporal dynamic behavior of cardiovascular interactions between heart period and systolic blood pressure during a 20-min head-up tilt test at 70° in young women with orthostatic intolerance compared to healthy women. Methods included the lagged and extended partial directed coherence applied to short-term windows shifted by 5 seconds, extracted from a multivariate set of cardiovascular and respiratory time series. Findings revealed significantly increased information flow (p <; 0.01) in patients from: a) heart period to blood pressure during supine position which subsequently decreased and b) blood pressure to heart period during the progression of orthostatic phase. Controls developed balanced cardiovascular interactions with smaller information flows than patients.

Increasing robustness of pairwise methods for effective connectivity in magnetic resonance imaging by using fractional moment series of BOLD signal distributions

Estimating causal interactions in the brain from functional magnetic resonance imaging (fMRI) data remains a challenging task. Multiple studies have demonstrated that all current approaches to determine direction of connectivity perform poorly when applied to synthetic fMRI datasets. Recent advances in this field include methods for pairwise inference, which involve creating a sparse connectome in the first step, and then using a classifier in order to determine the directionality of connection between every pair of nodes in the second step. In this work, we introduce an advance to the second step of this procedure, by building a classifier based on fractional moments of the BOLD distribution combined into cumulants. The classifier is trained on datasets generated under the dynamic causal modeling (DCM) generative model. The directionality is inferred based on statistical dependencies between the two-node time series, for example, by assigning a causal link from time series of low variance to time series of high variance. Our approach outperforms or performs as well as other methods for effective connectivity when applied to the benchmark datasets. Crucially, it is also more resilient to confounding effects such as differential noise level across different areas of the connectome.

Causality analysis reveals the link between cerebrovascular control and acute kidney dysfunction after coronary artery bypass grafting

BACKGROUND

Patients undergoing coronary artery bypass graft (CABG) surgery might experience postoperative complications and some of them, such as acute kidney dysfunction (AKD), are the likely consequence of hypoperfusion. We hypothesized that an impaired cerebrovascular control is a hallmark of a vascular damage that might favor AKD after CABG.

OBJECTIVE

Our aim is to characterize cerebrovascular control in CABG patients through the assessment of the relationship between mean arterial pressure (MAP) and mean cerebral blood flow velocity (MCBFV) and to check whether markers describing MCBFV-MAP dynamical interactions could identify subjects at risk to develop postoperative AKD.

APPROACH

MAP and MCBFV beat-to-beat series were extracted from invasive arterial pressure and transcranial Doppler recordings acquired simultaneously in 23 patients just before CABG after the induction of propofol general anesthesia. Subjects were divided into AKD group (n  =  9, age: 68  ±  9, 8 males) and noAKD group (n  =  14, age: 65  ±  8, 12 males) according to whether they developed postoperative AKD or not after CABG. We computed MAP and MCBFV time-domain and spectral markers as well as MCBFV-MAP cross-spectral indexes in very-low-frequency (VLF, 0.02-0.07 Hz), low-frequency (LF, 0.07-0.15 Hz) and high-frequency (HF, 0.15-0.30 Hz) bands. We also calculated model-based transfer entropy (TE) to quantify the degree of MCBFV dependence on MAP and vice versa. The null hypothesis of MCBFV-MAP uncoupling was tested via a surrogate approach associating MAP and MCBFV in different patients.

MAIN RESULTS

Time, spectral and cross-spectral markers had a limited power in separating AKD from noAKD individuals. Conversely, TE from MAP to MCBFV was significantly above the level set by surrogates only in AKD groups and significantly larger than that computed in noAKD.

SIGNIFICANCE

The reduced cerebrovascular autoregulation in AKD patients suggest a vascular impairment likely making them more at risk of hypoperfusion during CABG and AKD after CABG.

Identification of Hidden Sources by Estimating Instantaneous Causality in High-Dimensional Biomedical Time Series

The study of connectivity patterns of a system’s variables, such as multi-channel electroencephalograms (EEG), is of utmost importance towards a better understanding of its internal evolutionary mechanisms. Here, the problem of estimating the connectivity network from multivariate time series in the presence of prominent unobserved variables is addressed. The causality measure of partial mutual information from mixed embedding (PMIME), designed to estimate direct lag-causal effects in the presence of many observed variables, is adapted to estimate also zero-lag effects, the so-called instantaneous causality. We term the proposed advanced method, PMIME0. The estimation of instantaneous causality by PMIME0 is a signature of the presence of hidden source in the observed system, as demonstrated analytically in a toy model. It is further demonstrated that the PMIME0 identifies the true instantaneous with great accuracy in a variety of high-dimensional dynamical systems. The method is applied to EEG data with epileptiform discharges (EDs), and the results imply a strong impact of unobserved confounders during the EDs. This finding comes as a possible explanation for the increased levels of causality during epileptic seizures estimated by some measures affected by the presence of a common source.

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.

Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress

In this study, an analysis of brain, cardiovascular and respiratory dynamics was conducted combining information-theoretic measures with the Network Physiology paradigm during different levels of mental stress. Starting from low invasive recordings of electroencephalographic, electrocardiographic, respiratory, and blood volume pulse signals, the dynamical activity of seven physiological systems was probed with one-second time resolution measuring the time series of the δ, θ, α and β brain wave amplitudes, the cardiac period (RR interval), the respiratory amplitude, and the duration of blood pressure wave propagation (pulse arrival time, PAT). Synchronous 5-min windows of these time series, obtained from 18 subjects during resting wakefulness (REST), mental stress induced by mental arithmetic (MA) and sustained attention induced by serious game (SG), were taken to describe the dynamics of the nodes composing the observed physiological network. Network activity and connectivity were then assessed in the framework of information dynamics computing the new information generated by each node, the information dynamically stored in it, and the information transferred to it from the other network nodes. Moreover, the network topology was investigated using directed measures of conditional information transfer and assessing their statistical significance. We found that all network nodes dynamically produce and store significant amounts of information, with the new information being prevalent in the brain systems and the information storage being prevalent in the peripheral systems. The transition from REST to MA was associated with an increase of the new information produced by the respiratory signal time series (RESP), and that from MA to SG with a decrease of the new information produced by PAT. Each network node received a significant amount of information from the other nodes, with the highest amount transferred to RR and the lowest transferred to δ, θ, α and β. The topology of the physiological network underlying such information transfer was node- and state-dependent, with the peripheral subnetwork showing interactions from RR to PAT and between RESP and RR, PAT consistently across states, the brain subnetwork resulting more connected during MA, and the subnetwork of brain–peripheral interactions involving different brain rhythms in the three states and resulting primarily activated during MA. These results have both physiological relevance as regards the interpretation of central and autonomic effects on cardiovascular and respiratory variability, and practical relevance as regards the identification of features useful for the automatic distinction of different mental states.

A Dynamic Regression Approach for Frequency-Domain Partial Coherence and Causality Analysis of Functional Brain Networks

Coherence and causality measures are often used to analyze the influence of one region on another during analysis of functional brain networks. The analysis methods usually involve a regression problem, where the signal of interest is decomposed into a mixture of regressor and a residual signal. In this paper, we revisit this basic problem and present solutions that provide the minimal-entropy residuals for different types of regression filters, such as causal, instantaneously causal, and noncausal filters. Using optimal prediction theory, we derive several novel frequency-domain expressions for partial coherence, causality, and conditional causality analysis. In particular, our solution provides a more accurate estimation of the frequency-domain causality compared with the classical Geweke causality measure. Using synthetic examples and in vivo resting-state functional magnetic resonance imaging data from the human connectome project, we show that the proposed solution is more accurate at revealing frequency-domain linear dependence among high-dimensional signals.

The Effect of Common Signals on Power, Coherence and Granger Causality: Theoretical Review, Simulations, and Empirical Analysis of Fruit Fly LFPs Data

When analyzing neural data it is important to consider the limitations of the particular experimental setup. An enduring issue in the context of electrophysiology is the presence of common signals. For example a non-silent reference electrode adds a common signal across all recorded data and this adversely affects functional and effective connectivity analysis. To address the common signals problem, a number of methods have been proposed, but relatively few detailed investigations have been carried out. As a result, our understanding of how common signals affect neural connectivity estimation is incomplete. For example, little is known about recording preparations involving high spatial-resolution electrodes, used in linear array recordings. We address this gap through a combination of theoretical review, simulations, and empirical analysis of local field potentials recorded from the brains of fruit flies. We demonstrate how a framework that jointly analyzes power, coherence, and quantities based on Granger causality reveals the presence of common signals. We further show that subtracting spatially adjacent signals (bipolar derivations) largely removes the effects of the common signals. However, in some special cases this operation itself introduces a common signal. We also show that Granger causality is adversely affected by common signals and that a quantity referred to as “instantaneous interaction” is increased in the presence of common signals. The theoretical review, simulation, and empirical analysis we present can readily be adapted by others to investigate the nature of the common signals in their data. Our contributions improve our understanding of how common signals affect power, coherence, and Granger causality and will help reduce the misinterpretation of functional and effective connectivity analysis.

Is the Cushing mechanism a dynamic blood pressure-stabilizing system? Insights from Granger causality analysis of spontaneous blood pressure and cerebral blood flow

Blood pressure (BP) regulation is widely recognized as being integral to the control of end-organ perfusion, but it remains unclear whether end-organ perfusion also plays a role in driving changes in BP. A randomized and placebo-controlled study design was followed to examine feedback relationships between very-low-frequency fluctuations in BP and cerebral blood flow (CBF) in humans under placebo treatment and α₁-adrenergic blockade. To determine the causal relations among hemodynamic variables, BP, middle cerebral artery blood velocity (MCAv), and end-tidal CO ₂ time-series were decimated, low-pass filtered (<0.07 Hz), fitted to vector autoregressive models, and tested for Granger causality in the time domain. Results showed that 1) at baseline, changes in BP and MCAv often interact in a closed-loop; and 2) α₁-adrenergic blockade results in the dominant causal direction from BP to MCAv. These results suggest that, between subjects, cerebral pressure-flow interactions at time scales < 0.07 Hz are frequently bidirectional, and that in the presence of an intact autonomic nervous system BP may be regulated by reflex pathways sensitive to changes in CBF.

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.

Causality analysis of leading singular value decomposition modes identifies rotor as the dominant driving normal mode in fibrillation

Cardiac fibrillation is a major clinical and societal burden. Rotors may drive fibrillation in many cases, but their role and patterns are often masked by complex propagation. We used Singular Value Decomposition (SVD), which ranks patterns of activation hierarchically, together with Wiener-Granger causality analysis (WGCA), which analyses direction of information among observations, to investigate the role of rotors in cardiac fibrillation. We hypothesized that combining SVD analysis with WGCA should reveal whether rotor activity is the dominant driving force of fibrillation even in cases of high complexity. Optical mapping experiments were conducted in neonatal rat cardiomyocyte monolayers (diameter, 35 mm), which were genetically modified to overexpress the delayed rectifier K⁺ channel I_Kr only in one half of the monolayer. Such monolayers have been shown previously to sustain fast rotors confined to the I_Kr overexpressing half and driving fibrillatory-like activity in the other half. SVD analysis of the optical mapping movies revealed a hierarchical pattern in which the primary modes corresponded to rotor activity in the I_Kr overexpressing region and the secondary modes corresponded to fibrillatory activity elsewhere. We then applied WGCA to evaluate the directionality of influence between modes in the entire monolayer using clear and noisy movies of activity. We demonstrated that the rotor modes influence the secondary fibrillatory modes, but influence was detected also in the opposite direction. To more specifically delineate the role of the rotor in fibrillation, we decomposed separately the respective SVD modes of the rotor and fibrillatory domains. In this case, WGCA yielded more information from the rotor to the fibrillatory domains than in the opposite direction. In conclusion, SVD analysis reveals that rotors can be the dominant modes of an experimental model of fibrillation. Wiener-Granger causality on modes of the rotor domains confirms their preferential driving influence on fibrillatory modes.

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.

A Time-Varying Nonparametric Methodology for Assessing Changes in QT Variability Unrelated to Heart Rate Variability

OBJECTIVE

To propose and test a novel methodology to measure changes in QT interval variability (QTV) unrelated to RR interval variability (RRV) in nonstationary conditions.

METHODS

Time-frequency coherent and residual spectra representing QTV related (QTVrRRV) and unrelated (QTVuRRV) to RRV, respectively, are estimated using time-frequency Cohen's class distributions. The proposed approach decomposes the nonstationary output spectrum of any two-input one-output model with uncorrelated inputs into two spectra representing the information related and unrelated to one of the two inputs, respectively. An algorithm to correct for the bias of the time-frequency coherence function between QTV and RRV is proposed to provide accurate estimates of both QTVuRRV and QTVrRRV. Two simulation studies were conducted to assess the methodology in challenging nonstationary conditions and data recorded during head-up tilt in 16 healthy volunteers were analyzed.

RESULTS

In the simulation studies, QTVuRRV changes were tracked with only a minor delay due to the filtering necessary to estimate the nonstationary spectra. The correlation coefficient between theoretical and estimated patterns was even for extremely noisy recordings (signal to noise ratio (SNR) in QTV dB). During head-up tilt, QTVrRRV explained the largest proportion of QTV, whereas QTVuRRV showed higher relative increase than QTV or QTVrRRV in all spectral bands ( for most pairwise comparisons).

CONCLUSION

The proposed approach accurately tracks changes in QTVuRRV. Head-up tilt induced a slightly greater increase in QTVuRRV than in QTVrRRV.

SIGNIFICANCE

The proposed index QTVuRRV may represent an indirect measure of intrinsic ventricular repolarization variability, a marker of cardiac instability associated with sympathetic ventricular modulation and sudden cardiac death.

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

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

OBJECTIVE

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

APPROACH

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

MAIN RESULTS

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

SIGNIFICANCE

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

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.

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.

Effect of autonomic blocking agents on the respiratory-related oscillations of ventricular action potential duration in humans

Ventricular action potential repolarization is critical to electrical stability and arrhythmogenesis. Oscillations at the respiratory frequency were investigated in humans by combining endocardial electrophysiological recordings, controlled respiration with adrenergic blocking agents. Results are consistent with a partial role of the sympathetic nervous system combined with additional mechanisms, possibly involving mechano-electric feedback.

Ventricular action potential duration (APD) is an important component of many physiological functions including arrhythmogenesis. APD oscillations have recently been reported in humans at the respiratory frequency. This study investigates the contribution of the autonomic nervous system to these oscillations. In 10 patients undergoing treatment for supraventricular arrhythmias, activation recovery intervals (ARI; a conventional surrogate for APD) were measured from multiple left and right ventricular (RV) endocardial sites, together with femoral artery pressure. Respiration was voluntarily regulated and heart rate clamped by RV pacing. Sympathetic and parasympathetic blockade was achieved using intravenous metoprolol and atropine, respectively. Metroprolol reduced the rate of pressure development (maximal change in pressure over time): 1,271 (± 646) vs. 930 (± 433) mmHg/s; P < 0.01. Systolic blood pressure (SBP) showed a trend to decrease after metoprolol, 133 (± 21) vs. 128 (± 25) mmHg; P = 0.06, and atropine infusion, 122 (± 26) mmHg; P < 0.05. ARI and SBP exhibited significant cyclical variations (P < 0.05) with respiration in all subjects with peak-to-peak amplitudes ranging between 0.7 and 17.0 mmHg and 1 and 16 ms, respectively. Infusion of metoprolol reduced the mean peak-to-peak amplitude [ARI, 6.2 (± 1.4) vs. 4.4 (± 1.0) ms, P = 0.008; SBP, 8.4 (± 1.6) vs. 6.2 (± 2.0) mmHg, P = 0.002]. The addition of atropine had no significant effect. ARI, SBP, and respiration showed significant coupling (P < 0.05) at the breathing frequency in all subjects. Directed coherence from respiration to ARI was high and reduced after metoprolol infusion [0.70 (± 0.17) vs. 0.50 (± 0.23); P < 0.05]. These results suggest a role of respiration in modulating the electrophysiology of ventricular myocardium in humans, which is partly, but not totally, mediated by β-adrenergic mechanisms.

Algorithms for the inference of causality in dynamic processes: Application to cardiovascular and cerebrovascular variability

This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the traditional Granger causality analysis, showing that it leads to false detection of causality when instantaneous and time-lagged effects coexist in the process structure. Then, we propose an improved algorithm for causal inference that combines the Granger framework with the approach proposed by Pearl for the study of causality among multiple random variables. This new approach is compared with the traditional one in theoretical and simulated examples of interacting processes, showing its ability to retrieve the correct structure of instantaneous and time-lagged interactions. These approaches for causal inference are then tested on the physiological variability series of heart period, arterial pressure and cerebral blood flow variability obtained in subjects with postural-related syncope during a tilt-test protocol.

Assessing dynamic spectral causality by lagged adaptive directed transfer function and instantaneous effect factor

It is of significance to assess the dynamic spectral causality among physiological signals. Several practical estimators adapted from spectral Granger causality have been exploited to track dynamic causality based on the framework of time-varying multivariate autoregressive (tvMVAR) models. The nonzero covariance of the model's residuals has been used to describe the instantaneous effect phenomenon in some causality estimators. However, for the situations with Gaussian residuals in some autoregressive models, it is challenging to distinguish the directed instantaneous causality if the sufficient prior information about the "causal ordering" is missing. Here, we propose a new algorithm to assess the time-varying causal ordering of tvMVAR model under the assumption that the signals follow the same acyclic causal ordering for all time lags and to estimate the instantaneous effect factor (IEF) value in order to track the dynamic directed instantaneous connectivity. The time-lagged adaptive directed transfer function (ADTF) is also estimated to assess the lagged causality after removing the instantaneous effect. In this study, we first investigated the performance of the causal-ordering estimation algorithm and the accuracy of IEF value. Then, we presented the results of IEF and time-lagged ADTF method by comparing with the conventional ADTF method through simulations of various propagation models. Statistical analysis results suggest that the new algorithm could accurately estimate the causal ordering and give a good estimation of the IEF values in the Gaussian residual conditions. Meanwhile, the time-lagged ADTF approach is also more accurate in estimating the time-lagged dynamic interactions in a complex nervous system after extracting the instantaneous effect. In addition to the simulation studies, we applied the proposed method to estimate the dynamic spectral causality on real visual evoked potential (VEP) data in a human subject. Its usefulness in time-variant spectral causality assessment was demonstrated through the mutual causality investigation of brain activity during the VEP experiments.

Assessing direct paths of intracortical causal information flow of oscillatory activity with the isolated effective coherence (iCoh)

Functional connectivity is of central importance in understanding brain function. For this purpose, multiple time series of electric cortical activity can be used for assessing the properties of a network: the strength, directionality, and spectral characteristics (i.e., which oscillations are preferentially transmitted) of the connections. The partial directed coherence (PDC) of Baccala and Sameshima (2001) is a widely used method for this problem. The three aims of this study are: (1) To show that the PDC can misrepresent the frequency response under plausible realistic conditions, thus defeating the main purpose for which the measure was developed; (2) To provide a solution to this problem, namely the "isolated effective coherence" (iCoh), which consists of estimating the partial coherence under a multivariate autoregressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest; and (3) To show that adequate iCoh estimators can be obtained from non-invasively computed cortical signals based on exact low resolution electromagnetic tomography (eLORETA) applied to scalp EEG recordings. To illustrate the severity of the problem with the PDC, and the solution achieved by the iCoh, three examples are given, based on: (1) Simulated time series with known dynamics; (2) Simulated cortical sources with known dynamics, used for generating EEG recordings, which are then used for estimating (with eLORETA) the source signals for the final connectivity assessment; and (3) EEG recordings in rats. Lastly, real human recordings are analyzed, where the iCoh between six cortical regions of interest are calculated and compared under eyes open and closed conditions, using 61-channel EEG recordings from 109 subjects. During eyes closed, the posterior cingulate sends alpha activity to all other regions. During eyes open, the anterior cingulate sends theta-alpha activity to other frontal regions.

Cardiovascular control and time domain Granger causality: insights from selective autonomic blockade

We studied causal relations among heart period (HP), systolic arterial pressure (SAP) and respiration (R) according to the definition of Granger causality in the time domain. Autonomic pharmacological challenges were used to alter the complexity of cardiovascular control. Atropine (AT), propranolol and clonidine (CL) were administered to block muscarinic receptors, β-adrenergic receptors and centrally sympathetic outflow, respectively. We found that: (i) at baseline, HP and SAP interacted in a closed loop with a dominant causal direction from HP to SAP; (ii) pharmacological blockades did not alter the bidirectional closed-loop interactions between HP and SAP, but AT reduced the dominance of the causal direction from HP to SAP; (iii) at baseline, bidirectional interactions between HP and R were frequently found; (iv) the closed-loop relation between HP and R was unmodified by the administration of drugs; (v) at baseline, unidirectional interactions from R to SAP were often found; and (vi) while AT induced frequently an uncoupling between R and SAP, CL favoured bidirectional interactions. These results prove that time domain measures of Granger causality can contribute to the description of cardiovascular control by suggesting the temporal direction of the interactions and by separating different causality schemes (e.g. closed loop versus unidirectional relations).