A comparison of multivariate causality based measures of effective connectivity

A novel method for efficient estimation of brain effective connectivity in EEG

BACKGROUND AND OBJECTIVE

Brain connectivity plays a pivotal role in understanding the brain's information processing functions by providing various details including magnitude, direction, and temporal dynamics of inter-neuron connections. While the connectivity may be classified as structural, functional and causal, a complete in-vivo directional analysis is guaranteed by the latter and is referred to as Effective Connectivity (EC). Two most widely used EC techniques are Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) which are based on multivariate autoregressive models. The drawbacks of these techniques include poor frequency resolution and the requirement for experimental approach to determine signal normalization and thresholding techniques in identifying significant connectivities between multivariate sources.

METHODS

In this study, the drawbacks of DTF and PDC are addressed by proposing a novel technique, termed as Efficient Effective Connectivity (EEC), for the estimation of EC between multivariate sources using AR spectral estimation and Granger causality principle. In EEC, a linear predictive filter with AR coefficients obtained via multivariate EEG is used for signal prediction. This leads to the estimation of full-length signals which are then transformed into frequency domain by using Burg spectral estimation method. Furthermore, the newly proposed normalization method addressed the effect on each source in EEC using the sum of maximum connectivity values over the entire frequency range. Lastly, the proposed dynamic thresholding works by subtracting the first moment of causal effects of all the sources on one source from individual connections present for that source.

RESULTS

The proposed method is evaluated using synthetic and real resting-state EEG of 46 healthy controls. A 3D-Convolutional Neural Network is trained and tested using the PDC and EEC samples. The result indicates that compared to PDC, EEC improves the EEG eye-state classification accuracy, sensitivity and specificity by 5.57%, 3.15% and 8.74%, respectively.

CONCLUSION

Correct identification of all connections in synthetic data and improved resting-state classification performance using EEC proved that EEC gives better estimation of directed causality and indicates that it can be used for reliable understanding of brain mechanisms. Conclusively, the proposed technique may open up new research dimensions for clinical diagnosis of mental disorders.

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.

Evaluation of Directed Causality Measures and Lag Estimations in Multivariate Time-Series

The detection of causal effects among simultaneous observations provides knowledge about the underlying network, and is a topic of interests in many scientific areas. Over the years different causality measures have been developed, each with their own advantages and disadvantages. However, an extensive evaluation study is missing. In this work we consider some of the best-known causality measures i.e., cross-correlation, (conditional) Granger causality index (CGCI), partial directed coherence (PDC), directed transfer function (DTF), and partial mutual information on mixed embedding (PMIME). To correct for noise-related spurious connections, each measure (except PMIME) is tested for statistical significance based on surrogate data. The performance of the causality metrics is evaluated on a set of simulation models with distinct characteristics, to assess how well they work in- as well as outside of their “comfort zone.” PDC and DTF perform best on systems with frequency-specific connections, while PMIME is the only one able to detect non-linear interactions. The varying performance depending on the system characteristics warrants the use of multiple measures and comparing their results to avoid errors. Furthermore, lags between coupled variables are inherent to real-world systems and could hold essential information on the network dynamics. They are however often not taken into account and we lack proper tools to estimate them. We propose three new methods for lag estimation in multivariate time series, based on autoregressive modelling and information theory. One of the autoregressive methods and the one based on information theory were able to reliably identify the correct lag value in different simulated systems. However, only the latter was able to maintain its performance in the case of non-linear interactions. As a clinical application, the same methods are also applied on an intracranial recording of an epileptic seizure. The combined knowledge from the causality measures and insights from the simulations, on how these measures perform under different circumstances and when to use which one, allow us to recreate a plausible network of the seizure propagation that supports previous observations of desynchronisation and synchronisation during seizure progression. The lag estimation results show absence of a relationship between connectivity strength and estimated lag values, which contradicts the line of thinking in connectivity shaped by the neuron doctrine.

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.

The olfactory bulb modulates entorhinal cortex oscillations during spatial working memory

Cognitive functions such as working memory require integrated activity among different brain regions. Notably, entorhinal cortex (EC) activity is associated with the successful working memory task. Olfactory bulb (OB) oscillations are known as rhythms that modulate rhythmic activity in widespread brain regions during cognitive tasks. Since the OB is structurally connected to the EC, we hypothesized that OB could modulate EC activity during working memory performance. Herein, we explored OB-EC functional connectivity during spatial working memory performance by simultaneous recording local field potentials when rats performed a Y-maze task. Our results showed that the coherence of delta, theta, and gamma-band oscillations between OB and EC was increased during correct trials compared to wrong trials. Cross-frequency coupling analyses revealed that the modulatory effect of OBs low-frequency phase on EC gamma power and phase was enhanced when animals correctly performed working memory task. The influx of information from OB to EC was also increased at delta and gamma bands within correct trials. These findings indicated that the modulatory influence of OB rhythms on EC oscillations might be necessary for successful working memory performance.

Allergic rhinitis impairs working memory in association with drop of hippocampal - Prefrontal coupling

Allergic rhinitis (AR) is a chronic inflammatory disease frequently associated with a deficit in learning and memory. Working memory is an important system for decision making and guidance, which depends on interactions between the ventral hippocampus (vHipp) and the prelimbic prefrontal cortex (plPFC). It is still unclear whether AR influences the activity and coupling of these brain areas, which consequently may impair working memory. The current study aimed to examine alterations of the vHipp-plPFC circuit in a rat model of AR. Our results show decreased working memory performance in AR animals, accompanied by a reduction of theta and gamma oscillations in plPFC. Also, AR reduces coherence between vHipp and plPFC in both theta and gamma frequency bands. Cross-frequency coupling analyses confirmed a reduced interaction between hippocampal theta and plPFC gamma oscillations. Granger causality analysis revealed a reduction in the causal effects of vHipp activity on plPFC oscillations and vice versa. A significant correlation was found between working memory performance with disruption of functional connectivity in AR animals. In summary, our data show that in AR, there is a deficit of functional coupling between hippocampal and prefrontal network, and suggest that this mechanism might contribute to working memory impairment in individuals with AR.

Non-Uniform Embedding Scheme and Low-Dimensional Approximation Methods for Causality Detection

Information causality measures have proven to be very effective in uncovering the connectivity patterns of multivariate systems. The non-uniform embedding (NUE) scheme has been developed to address the “curse of dimensionality”, since the estimation relies on high-dimensional conditional mutual information (CMI) terms. Although the NUE scheme is a dimension reduction technique, the estimation of high-dimensional CMIs is still required. A possible solution is the utilization of low-dimensional approximation (LA) methods for the computation of CMIs. In this study, we aim to provide useful insights regarding the effectiveness of causality measures that rely on NUE and/or on LA methods. In a comparative study, three causality detection methods are evaluated, namely partial transfer entropy (PTE) defined using uniform embedding, PTE using the NUE scheme (PTENUE), and PTE utilizing both NUE and an LA method (LATE). Results from simulations on well known coupled systems suggest the superiority of PTENUE over the other two measures in identifying the true causal effects, having also the least computational cost. The effectiveness of PTENUE is also demonstrated in a real application, where insights are presented regarding the leading forces in financial data.

Evaluation of Granger Causality Measures for Constructing Networks from Multivariate Time Series

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain, and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets.

Evaluation of synchronization measures for capturing the lagged synchronization between EEG channels: A cognitive task recognition approach

During cognitive, perceptual and sensory tasks, connectivity profile changes across different regions of the brain. Variations of such connectivity patterns between different cognitive tasks can be evaluated using pairwise synchronization measures applied to electrophysiological signals, such as electroencephalography (EEG). However, connectivity-based task recognition approaches achieving viable recognition performance have been lacking from the literature. By using several synchronization measures, we identify time lags between channel pairs during different cognitive tasks. We employed mutual information, cross correntropy, cross correlation, phase locking value, cosine similarity and nonlinear interdependence measures. In the training phase, for each type of cognitive task, we identify the time lags that maximize the average synchronization between channel pairs. These lags are used to calculate pairwise synchronization values with which we construct the train and test feature vectors for recognition of the cognitive task carried out using Fisher's linear discriminant (FLD) analysis. We tested our framework in a motor imagery activity recognition scenario on PhysioNet Motor Movement/Imagery and BCI Competition-III Ⅳa datasets. For PhysioNet dataset, average performance results ranging between % 51 and % 61 across 20 subjects. For BCI Competition-Ⅲ dataset, we achieve an average recognition performance of % 76 which is above the minimum reliable communication rate (% 70). We achieved an average accuracy over the minimum reliable communication rate on the BCI Competition-Ⅲ dataset. Performance levels were lower on the PhysioNet dataset. These results indicate that a viable task recognition system is achievable using pairwise synchronization measures evaluated at the proper task specific lags.

Evaluation of connectivity estimates using spiking neuronal network models

The flow of information between different regions of the cortex is fundamental for brain function. Researchers use causality detection techniques, such as Granger causality, to infer connectivity among brain areas from time series. Generalized partial directed coherence (GPDC) is a frequency domain linear method based on vector autoregressive model, which has been applied in electroencephalography, local field potential, and blood oxygenation level-dependent signals. Despite its widespread usage, previous attempts to validate GPDC use oversimplified simulated data, which do not reflect the nonlinearities and network couplings present in biological signals. In this work, we evaluated the GPDC performance when applied to simulated LFP signals, i.e., generated from networks of spiking neuronal models. We created three models, each containing five interacting networks, and evaluated whether the GPDC method could accurately detect network couplings. When using a stronger coupling, we showed that GPDC correctly detects all existing connections from simulated LFP signals in the three models, without false positives. Varying the coupling strength between networks, by changing the number of connections or synaptic strengths, and adding noise in the times series, altered the receiver operating characteristic (ROC) curve, ranging from perfect to chance level retrieval. We also showed that GPDC values correlated with coupling strength, indicating that GPDC values can provide useful information regarding coupling strength. These results reinforce that GPDC can be used to detect causality relationships over neural signals.

The HEURECA method: Tracking multiple phase coupling dynamics on a single trial basis

BACKGROUND

Although acquisition techniques have improved tremendously, the neuroscientific understanding of complex cognitive phenomena is still incomplete. One of the reasons for this shortcoming may be the lack of sophisticated signal processing methods. Complex cognitive phenomena usually involve various mental subprocesses whose temporal occurrence varies from trial to trial. Mostly, these mental subprocesses require large-scale integration processes between multiple brain areas that are most likely mediated by complex, non-linear phase coupling mechanisms. Consequently, a spatiotemporal analysis of complex, multivariate phase synchronization patterns on a single trial basis is necessary.

NEW METHOD

This paper introduces the HEURECA method (How to Evaluate and Uncover Recurring EEG Coupling Arrangements) that enables the dynamic detection of distinguishable multivariate functional connectivity states in the electroencephalogram. HEURECA adaptively divides a trial into segments of quasi-stable phase coupling topographies and assigns similar topographies to the same synchrostate cluster.

RESULTS

HEURECA is evaluated by means of simulated data. The results show that it reliably reconstructs a time series of recurring phase coupling topographies and successfully gathers them into clusters of interpretable neural synchrostates. The advantages and unique features of HEURECA are further illustrated by investigating the popular complex cognitive phenomenon insight.

COMPARISON WITH EXISTING METHODS

Unlike existing methods, HEURECA detects complex phase relationships between more than two signals and is applicable to single trials.

CONCLUSIONS

Since HEURECA is applicable to all kinds of circular data, it not only provides new insights into insight, but also into a variety of other phenomena in neuroscience, physics or other scientific fields.

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

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

New Insights into Signed Path Coefficient Granger Causality Analysis

Granger causality analysis, as a time series analysis technique derived from econometrics, has been applied in an ever-increasing number of publications in the field of neuroscience, including fMRI, EEG/MEG, and fNIRS. The present study mainly focuses on the validity of “signed path coefficient Granger causality,” a Granger-causality-derived analysis method that has been adopted by many fMRI researches in the last few years. This method generally estimates the causality effect among the time series by an order-1 autoregression, and defines a positive or negative coefficient as an “excitatory” or “inhibitory” influence. In the current work we conducted a series of computations from resting-state fMRI data and simulation experiments to illustrate the signed path coefficient method was flawed and untenable, due to the fact that the autoregressive coefficients were not always consistent with the real causal relationships and this would inevitablely lead to erroneous conclusions. Overall our findings suggested that the applicability of this kind of causality analysis was rather limited, hence researchers should be more cautious in applying the signed path coefficient Granger causality to fMRI data to avoid misinterpretation.

Children with well controlled epilepsy possess different spatio-temporal patterns of causal network connectivity during a visual working memory task

Using spectral Granger causality (GC) we identified distinct spatio-temporal causal connectivity (CC) patterns in groups of control and epileptic children during the execution of a one-back matching visual discrimination working memory task. Differences between control and epileptic groups were determined for both GO and NOGO conditions. The analysis was performed on a set of 19-channel EEG cortical activity signals. We show that for the GO task, the highest brain activity in terms of the density of the CC networks is observed in α band for the control group while for the epileptic group the CC network seems disrupted as reflected by the small number of connections. For the NOGO task, the denser CC network was observed in θ band for the control group while widespread differences between the control and the epileptic group were located bilaterally at the left temporal-midline and parietal areas. In order to test the discriminative power of our analysis, we performed a pattern analysis approach based on fuzzy classification techniques. The performance of the classification scheme was evaluated using permutation tests. The analysis demonstrated that, on average, 87.6 % of the subjects were correctly classified in control and epileptic. Thus, our findings may provide a helpful insight on the mechanisms pertaining to the cognitive response of children with well controlled epilepsy and could potentially serve as "functional" biomarkers for early diagnosis.

Causality networks from multivariate time series and application to epilepsy

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. For this, realizations on high dimensional coupled dynamical systems are considered and the performance of the Granger causality measures is evaluated, seeking for the measures that form networks closest to the true network of the dynamical system. In particular, the comparison focuses on Granger causality measures that reduce the state space dimension when many variables are observed. Further, the linear and nonlinear Granger causality measures of dimension reduction are compared to a standard Granger causality measure on electroencephalographic (EEG) recordings containing episodes of epileptiform discharges.

On the statistical performance of Granger-causal connectivity estimators

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

Statistical pitfalls in the comparison of multivariate causality measures for effective causality

The study of Wu et al. (2011) compared the performance of six different causality measures when the autoregressive process was estimated with the Dynamic Autoregressive Neuromagnetic Causal Imaging (DANCI) algorithm to help applied researchers in choosing the best method to estimate effective connectivity. This letter to the editor argues that four methodological restrictions limit the applicability of the results to actual applied research. First, there is no formal test for the significance of a connection between two channels. Second, the simulation results are affected by sizeable sampling variability. Third, only overestimation of the true model order is considered. Fourth, the comparison between methods always involves a joint hypothesis test. The letter discusses the limitations for applied researchers resulting from those restrictions and points to future research directions to overcome them.

Laterality of temporoparietal causal connectivity during the prestimulus period correlates with phonological decoding task performance in dyslexic and typical readers

We examined how effective connectivity into and out of the left and right temporoparietal areas (TPAs) to/from other key cortical areas affected phonological decoding in 7 dyslexic readers (DRs) and 10 typical readers (TRs) who were young adults. Granger causality was used to compute the effective connectivity of the preparatory network 500 ms prior to presentation of nonwords that required phonological decoding. Neuromagnetic activity was analyzed within the low, medium, and high beta and gamma subbands. A mixed-model analysis determined whether connectivity to or from the left and right TPAs differed across connectivity direction (in vs. out), brain areas (right and left inferior frontal and ventral occipital–temporal and the contralateral TPA), reading group (DR vs. TR), and/or task performance. Within the low beta subband, better performance was associated with increased influence of the left TPA on other brain areas across both reading groups and poorer performance was associated with increased influence of the right TPA on other brain areas for DRs only. DRs were also found to have an increase in high gamma connectivity between the left TPA and other brain areas. This study suggests that hierarchal network structure rather than connectivity per se is important in determining phonological decoding performance.