Statistical Analysis of EEG Phase Shift Events

This thesis develops statistical methods for the identification, and analysis of phase shift events, i.e. sudden changes in the timing relationship between coupled oscillators. Phase shifts events occur in many complex systems but here the primary interest is the analysis of electroencephalogram (EEG) recordings where they have been identified as markers of information transmission in the brain; as a secondary example we analyze systems of weakly coupled Rossler attractors. The main result, found in Chapter 2, is a novel method for estimating neural connectivity from EEG recordings based on spatio-temporal patterns of phase shift events. Phase shift events are modelled as a multivariate point process, and the ideas of Granger causality are used to motivate a directed measure of connectivity. The method is demonstrated on EEG recordings from 18 participants during three task conditions; resting, visual vigilance and auditory vigilance. Likelihood ratios are used to test the hypothesis of no Granger causal interaction between signals, and network patterns are analyzed using graph theory. In Chapter 3 the problem of phase shift identification is formulated as a change point in the instantaneous phase. Two estimators are considered, based on the cumulative summation and the instantaneous phase derivative. Block bootstrapping techniques are used to capture the dependency structure in the signals and determine critical values for shift identification. Estimators are evaluated both on their accuracy, and temporal resolution. Finally, detailed simulation studies are performed using realistic head models to investigate the effect of volume conduction (linear spread of electrical activity at the scalp) on phase shift analysis. Specifically, Chapter 4 investigates the effect of volume conduction on the analysis, in order to understand the limitations of the phase shift Granger causality method. Chapter 5 then investigates an approach for reducing the effect of volume conduction by using EEG source reconstruction techniques to estimate neural source activity and then identifying phase shifts with-in the brain directly from the reconstructed sources. The primary impact is the novel method for estimating neural connectivity. Each chapter investigates a different aspect of EEG phase analysis, and together they form a complete package for estimation and interpretation of neural connectivity. Two other areas of impact are in statistical change point analysis, and behavioural psychology

Critical comments on EEG sensor space dynamical connectivity analysis

Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because 1) the channel locations cannot be seen as an approximation of a source's anatomical location and 2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing

Performance comparison of functional and effective brain connectivity methods

Functional and effective connectivity estimates based on electroencephalography (EEG) and magnetoencephalography (MEG) are widely used to understand and reveal new insight into the dynamic behaviour of the brain. However, with a large number of different connectivity methods that are currently available, there is a lack of systematic comparative studies including a statistical evaluation of their performance to understand the strengths and shortcomings of competing methods. Here, we present a simulation framework to evaluate and compare the performance of connectivity estimators on simulated, yet realistic electromagnetic recordings. We assess the ability of various methods to reconstruct cortical networks, while systematically varying specific parameters which are of significant importance during the simulation, preprocessing or inverse source reconstruction of realistic EEG recordings. A decisive advantage of this simulation framework, when compared with models utilised in other studies, is the integration of volume conduction artifacts. This is achieved by modelling the propagation of electric or magnetic fields from an electric primary current source through biological tissue towards measurement sensors. Subsequently, inverse source reconstruction approaches are applied to estimate the temporal activity patterns of underlying network nodes. The implementation of these concepts enabled the analysis of parameters involved during forward modelling and source reconstruction which may affect the estimation of connectivity on the source level. The experiments carried out in this work unfold the behaviour of estimators regarding the effect of signal-to-noise ratio (SNR), length of data sets, various phase shifts between correlated signals, the impact of regularization used in inverse source reconstruction, errors in the localization and varying network sizes. For each simulation, strengths and weaknesses of methods are pointed out. Furthermore, pitfalls and obstacles researchers might come across when applying particular estimators on EEG recordings are discussed. Building on the insight gained from simulation studies, the final part of the thesis analyses the performance of connectivity estimators when applied to resting-state EEG recordings. Network reconstructions with priority on the alpha frequency band reveal a default-mode-network (DMN) with dominant posterior-to-anterior information flow. We detected no significant variations in the amount of correctly identified network links between connectivity methods. However, we discuss differences in connectivity spectra that emerged, which affect the interpretability and applicability of methods

Network perspectives on epilepsy using EEG/MEG source connectivity

The evolution of EEG/MEG source connectivity is both, a promising, and controversial advance in the characterization of epileptic brain activity. In this narrative review we elucidate the potential of this technology to provide an intuitive view of the epileptic network at its origin, the different brain regions involved in the epilepsy, without the limitation of electrodes at the scalp level. Several studies have confirmed the added value of using source connectivity to localize the seizure onset zone and irritative zone or to quantify the propagation of epileptic activity over time. It has been shown in pilot studies that source connectivity has the potential to obtain prognostic correlates, to assist in the diagnosis of the epilepsy type even in the absence of visually noticeable epileptic activity in the EEG/MEG, and to predict treatment outcome. Nevertheless, prospective validation studies in large and heterogeneous patient cohorts are still lacking and are needed to bring these techniques into clinical use. Moreover, the methodological approach is challenging, with several poorly examined parameters that most likely impact the resulting network patterns. These fundamental challenges affect all potential applications of EEG/MEG source connectivity analysis, be it in a resting, spiking, or ictal state, and also its application to cognitive activation of the eloquent area in presurgical evaluation. However, such method can allow unique insights into physiological and pathological brain functions and have great potential in (clinical) neuroscience

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

Influence of time-series normalization, number of nodes, connectivity and graph measure selection on seizure-onset zone localization from intracranial EEG

We investigated the influence of processing steps in the estimation of multivariate directed functional connectivity during seizures recorded with intracranial EEG (iEEG) on seizure-onset zone (SOZ) localization. We studied the effect of (i) the number of nodes, (ii) time-series normalization, (iii) the choice of multivariate time-varying connectivity measure: Adaptive Directed Transfer Function (ADTF) or Adaptive Partial Directed Coherence (APDC) and (iv) graph theory measure: outdegree or shortest path length. First, simulations were performed to quantify the influence of the various processing steps on the accuracy to localize the SOZ. Afterwards, the SOZ was estimated from a 113-electrodes iEEG seizure recording and compared with the resection that rendered the patient seizure-free. The simulations revealed that ADTF is preferred over APDC to localize the SOZ from ictal iEEG recordings. Normalizing the time series before analysis resulted in an increase of 25-35% of correctly localized SOZ, while adding more nodes to the connectivity analysis led to a moderate decrease of 10%, when comparing 128 with 32 input nodes. The real-seizure connectivity estimates localized the SOZ inside the resection area using the ADTF coupled to outdegree or shortest path length. Our study showed that normalizing the time-series is an important pre-processing step, while adding nodes to the analysis did only marginally affect the SOZ localization. The study shows that directed multivariate Granger-based connectivity analysis is feasible with many input nodes (> 100) and that normalization of the time-series before connectivity analysis is preferred

Seizure-onset mapping based on time-variant multivariate functional connectivity analysis of high-dimensional intracranial EEG : a Kalman filter approach

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

Estimating directed connectivity from cortical recordings and reconstructed sources

In cognitive neuroscience, electrical brain activity is most commonly recorded at the scalp. In order to infer the contributions and connectivity of underlying neuronal sources within the brain, it is necessary to reconstruct sensor data at the source level. Several approaches to this reconstruction have been developed, thereby solving the so-called implicit inverse problem Michel et al. (Clin Neurophysiol 115:2195-2222, 2004). However, a unifying premise against which to validate these source reconstructions is seldom available. The dataset provided in this work, in which brain activity is simultaneously recorded on the scalp (non-invasively) by electroencephalography (EEG) and on the cortex (invasively) by electrocorticography (ECoG), can be of a great help in this direction. These multimodal recordings were obtained from a macaque monkey under wakefulness and sedation. Our primary goal was to establish the connectivity architecture between two sources of interest (frontal and parietal), and to assess how their coupling changes over the conditions. We chose these sources because previous studies have shown that the connections between them are modified by anaesthesia Boly et al. (J Neurosci 32:7082-7090, 2012). Our secondary goal was to evaluate the consistency of the connectivity results when analyzing sources recorded from invasive data (128 implanted ECoG sources) and source activity reconstructed from scalp recordings (19 EEG sensors) at the same locations as the ECoG sources. We conclude that the directed connectivity in the frequency domain between cortical sources reconstructed from scalp EEG is qualitatively similar to the connectivity inferred directly from cortical recordings, using both data-driven (directed transfer function) and biologically grounded (dynamic causal modelling) methods. Furthermore, the connectivity changes identified were consistent with previous findings Boly et al. (J Neurosci 32:7082-7090, 2012). Our findings suggest that inferences about directed connectivity based upon non-invasive electrophysiological data have construct validity in relation to invasive recordings