Phase Slope Index Research Articles

Lateralized alpha-band cortical networks regulate volitional modulation of beta-band sensorimotor oscillations

Sensorimotor rhythms (SMRs) are oscillatory brain activities in the α- and β-bands across the sensorimotor regions of the brain. Each frequency band has its own specific function. The α-band oscillations are closely related to intrinsic cortical networks, whereas oscillations in the β-band are relevant for the information transfer between the cortex and periphery, as well as for visual and proprioceptive feedback. This study aimed to investigate the interaction between these two frequency bands, under the premise that the regional modulation of β-band power is linked to a cortical network in the α-band. We therefore designed a procedure to maximize the modulation of β-band activity over the sensorimotor cortex by combining kinesthetic motor-imagery with closed-loop haptic feedback. The cortical network activity during this procedure was estimated via the phase slope index in electroencephalographic recordings. Analysis of effective connectivity within the α-band network revealed an information flow between the precentral (premotor and primary motor), postcentral (primary somatosensory) and parietal cortical areas. The range of β-modulation was connected to a reduction of an ipsilateral sensorimotor and parietal α-network and, consequently, to a lateralization of this network to the contralateral side. These results showed that regional sensorimotor oscillatory activity in the β-band was regulated by cortical coupling of distant areas in the α-band.

Functional and effective connectivity in subthalamic local field potential recordings of patients with Parkinson’s disease

In Parkinson’s disease (PD) levodopa-associated changes in the power and long-range temporal correlations of beta oscillations have been demonstrated, yet the presence and modulation of genuine connectivity in local field potentials (LFP) recorded from the subthalamic nucleus (STN) remains an open question. The present study investigated LFP recorded bilaterally from the STN at wakeful rest in ten patients with PD after overnight withdrawal of levodopa (OFF) and after a single dose levodopa administration (ON). We utilized connectivity measures being insensitive to volume conduction (functional connectivity: non-zero imaginary part of coherency; effective connectivity: phase–slope index). We demonstrated the presence of neuronal interactions in the frequency range of 10–30Hz in STN–LFP without a preferential directionality of interactions between different contacts along the electrode tracks. While the direction of neuronal interactions per se was preserved after levodopa administration, functional connectivity and the ventral–dorsal information flow were modulated by medication. The OFF–ON differences in functional connectivity were correlated with the levodopa-induced improvement in clinical Unified Parkinson’s Disease Rating Scale scores. We hypothesize that regional neuronal interactions, as reflected in STN–LFP connectivity, might represent a basis for the intra-nuclear spatial specificity of deep brain stimulation. Moreover, our results suggest the potential use of volume conduction-insensitive measures of connectivity in STN–LFP as a marker of clinical motor symptoms in PD.

Information source in multiple MEG spike clusters can be identified by effective connectivity in focal cortical dysplasia

It has been reported that patients with a single MEG spike cluster have better postoperative outcomes compared to patients with multiple clusters. However, the problem of identifying a genuine source in the multiple MEG spike clusters remains unsolved. The aim of this study was to determine the focus of the epileptic activity in a situation with multiple MEG spike clusters. Five patients with intractable epilepsy with multiple MEG spike clusters were retrospectively investigated. They had pathologically proven type IA focal cortical dysplasia (FCD) with discordant multimodal presurgical evaluations, and showed a favorable postoperative outcome. MEG spikes were localized and clustered using a hierarchical clustering method. Then, effective connectivity (a phase-slope index method) referring to the causal interaction between distant structures in the brain was applied to the source waveforms extracted from the multiple MEG spike clusters. Finally, the information source, that is, the driver region between multiple clusters, could be identified. We found that 4 of the 5 FCD patients exhibited the driver regions were coincident with the resection area, which was also quite consistent at different epochs. Our results suggest that effective connectivity analysis has a potential value as a presurgical evaluation when multiple MEG spike clusters are found.

Identifying causal networks of neuronal sources from EEG/MEG data with the phase slope index: a simulation study

The investigation of functional neuronal synchronization has recently become a growing field of research. With high temporal resolution, electroencephalography and magnetoencephalography are well-suited measurement techniques to identify networks of interacting sources underlying the recorded data. The analysis of the data in terms of effective connectivity, nevertheless, contains intrinsic issues such as the problem of volume conduction and the non-uniqueness of the inverse solution. Here, we briefly introduce a series of existing methods assessing these problems. To determine the locations of interacting brain sources robust to volume conduction, all computations are solely based on the imaginary part of the cross-spectrum as a trustworthy source of information. Furthermore, we demonstrate the feasibility of estimating causal relationships of systems of neuronal sources with the phase slope index in realistically simulated data. Finally, advantages and drawbacks of the applied methodology are highlighted and discussed.

Granger causality is designed to measure effect, not mechanism

Granger causality is designed to measure effect, not mechanism

A critical assessment of connectivity measures for EEG data: A simulation study

Information flow between brain areas is difficult to estimate from EEG measurements due to the presence of noise as well as due to volume conduction. We here test the ability of popular measures of effective connectivity to detect an underlying neuronal interaction from simulated EEG data, as well as the ability of commonly used inverse source reconstruction techniques to improve the connectivity estimation. We find that volume conduction severely limits the neurophysiological interpretability of sensor-space connectivity analyses. Moreover, it may generally lead to conflicting results depending on the connectivity measure and statistical testing approach used. In particular, we note that the application of Granger-causal (GC) measures combined with standard significance testing leads to the detection of spurious connectivity regardless of whether the analysis is performed on sensor-space data or on sources estimated using three different established inverse methods. This empirical result follows from the definition of GC. The phase-slope index (PSI) does not suffer from this theoretical limitation and therefore performs well on our simulated data. We develop a theoretical framework to characterize artifacts of volume conduction, which may still be present even in reconstructed source time series as zero-lag correlations, and to distinguish their time-delayed brain interaction. Based on this theory we derive a procedure which suppresses the influence of volume conduction, but preserves effects related to time-lagged brain interaction in connectivity estimates. This is achieved by using time-reversed data as surrogates for statistical testing. We demonstrate that this robustification makes Granger-causal connectivity measures applicable to EEG data, achieving similar results as PSI. Integrating the insights of our study, we provide a guidance for measuring brain interaction from EEG data. Software for generating benchmark data is made available.

Detecting information flow direction in multivariate linear and nonlinear models

In this paper we present an approach to analyze the direction of information flow between time series involving bidirectional relations. The intuitive idea comes from a first study dedicated to the so-called phase slope index, which is a measure originally developed to detect unidirectional relations and is based on the complex coherence function. In order to detect bidirectional flows, we propose two new causality indices supplying the previous index with two other functions, the directed coherence function and the directed transfer function. Moreover, to cope with the inability of the approaches based on coherence (ordinary or directed) or on directed transfer function to distinguish between direct and indirect relations, we propose another causality index based on the partial directed coherence to identify only direct relations. Experimental results show that some challenges have promising solutions through the use of this new indicator dealing with both linear and nonlinear multivariate models.

Experimental comparison of connectivity measures with simulated EEG signals

Directional connectivity measures exist with different theoretical backgrounds, i.e., information theoretic, parametric-modeling based or phase related. In this paper, we perform the first comparison in this extend of a set of conventional and directed connectivity measures [cross-correlation, coherence, phase slope index (PSI), directed transfer function (DTF), partial-directed coherence (PDC) and transfer entropy (TE)] with eight-node simulation data based on real resting closed eye electroencephalogram (EEG) source signal. The ability of the measures to differentiate the direct causal connections from the non-causal connections was evaluated with the simulated data. Also, the effects of signal-to-noise ratio (SNR) and decimation were explored. All the measures were able to distinguish the direct causal interactions from the non-causal relations. PDC detected less non-causal connections compared to the other measures. Low SNR was tolerated better with DTF and PDC than with the other measures. Decimation affected most the results of TE, DTF and PDC. In conclusion, parametric-modeling-based measures (DTF, PDC) had the highest sensitivity of connections and tolerance to SNR in simulations based on resting closed eye EEG. However, decimation of data has to be carefully considered with these measures.

Seizure Detection Using the Phase-Slope Index and Multichannel ECoG

Detection and analysis of epileptic seizures is of clinical and research interest. We propose a novel seizure detection and analysis scheme based on the phase-slope index (PSI) of directed influence applied to multichannel electrocorticogram data. The PSI metric identifies increases in the spatio-temporal interactions between channels that clearly distinguish seizure from interictal activity. We form a global metric of interaction between channels and compare this metric to a threshold to detect the presence of seizures. The threshold is chosen based on a moving average of recent activity to accommodate differences between patients and slow changes within each patient over time. We evaluate detection performance over a challenging population of five patients with different types of epilepsy using a total of 47 seizures in nearly 258 h of recorded data. Using a common threshold procedure, we show that our approach detects all of the seizures in four of the five patients with a false detection rate less than two per hour. A variation on the global metric is proposed to identify which channels are strong drivers of activity in each patient. These metrics are computationally efficient and suitable for real-time application.

Identifying brain effective connectivity patterns from EEG: performance of Granger Causality, DTF, PDC and PSI on simulated data

Background High temporal resolution and relatively low cost make electroencephalography (EEG) the most suitable noninvasive tool for studying brain dynamics. One of the major challenges is the determination of effective connectivity, i.e., directed (causal) information flow between brain areas. The common definition of effective connectivity is based on Granger’s argument, that “the cause must precede the effect” [1], which is implemented by the original Granger Causality (GC) score [1], the Directed Transfer Function (DTF) [3], Partial Directed Coherence (PDC) [2] and the Phase-slope Index (PSI) [4], all of which have been applied to EEG data previously. However, due to volume conduction in the head, the original causallyrelated sources are mixed into EEG channels. We conducted a realistic simulation study to investigate how volume conduction affects EEG sensor-space effective connectivity estimation.

Decreased cortical connectivity and information flow in type 1 diabetes

Objective To investigate the effect of type 1 diabetes on EEG connectivity and information flow and study the relationship between these parameters and electrophysiological, neuropsychological and clinical variables. Methods Connectivity was assessed using several measures (phase coherence, phase lag index, synchronization likelihood and phase slope index) on 119 patients and 61 healthy controls over several frequency bands (between 0.5 and 45 Hz). Data was further correlated to EEG power, event related potentials, neuropsychological function and demographic variables. Results Multivariate test on the connectivity data showed a difference between patients and controls both with mastoid reference ( p < 0.01) and current source density estimates ( p < 0.04). Connectivity and information flow correlated with EEG power but not with event related potentials or neuropsychological function. Conclusions Connectivity and information flow are decreased in diabetes. These variables assess other functions of the brain than captured by the present cognitive tests. Several tests need to be performed in order to monitor the effect of diabetes on brain function. Significance The decrease in connectivity and cortical information flow are EEG abnormalities that add to the previously described EEG and ERP abnormalities described for type 1 diabetes.

Extracting Information on Flow Direction in Multivariate Time Series

Phase slope index is a measure which aims at detecting causal relation of interdependence in multivariate time series. One drawback of this approach relies in its incapability to distinguish the direct and indirect relations. So, in order to identify only direct relations, we propose to replace the ordinary coherence function used in the phase slope index with the partial coherence. Furthermore, we consider and compare two estimators of the coherence functions, the first one based on Fourier transform and the second one on an autoregressive model. In order to cope with the difficult issue of bidirectional flow, which cannot be addressed by the coherence based phase slope index, we propose another index based on the directed transfer function. Experimental results support the relevance of the new indices, both based on autoregressive modeling, in multivariate time series.

Estimating directions of information flow between cortical activities using phase-slope index

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Robustly Estimating the Flow Direction of Information in Complex Physical Systems

We propose a new measure (phase-slope index) to estimate the direction of information flux in multivariate time series. This measure (a) is insensitive to mixtures of independent sources, (b) gives meaningful results even if the phase spectrum is not linear, and (c) properly weights contributions from different frequencies. These properties are shown in extended simulations and contrasted to Granger causality which yields highly significant false detections for mixtures of independent sources. An application to electroencephalography data (eyes-closed condition) reveals a clear front-to-back information flow.