Statistical analysis of multichannel scalp field data

High density spatial and temporal sampling of EEG data enhances the quality of results of electrophysiological experiments. Because EEG sources typically produce widespread electric fields (see Chapter 3) and operate at frequencies well below the sampling rate, increasing the number of electrodes and time samples will not necessarily increase the number of observed processes, but mainly increase the accuracy of the representation of these processes. This is namely the case when inverse solutions are computed. As a consequence, increasing the sampling in space and time increases the redundancy of the data (in space, because electrodes are correlated due to volume conduction, and time, because neighboring time points are correlated), while the degrees of freedom of the data change only little. This has to be taken into account when statistical inferences are to be made from the data. However, in many ERP studies, the intrinsic correlation structure of the data has been disregarded. Often, some electrodes or groups of electrodes are a priori selected as the analysis entity and considered as repeated (within subject) measures that are analyzed using standard univariate statistics. The increased spatial resolution obtained with more electrodes is thus poorly represented by the resulting statistics. In addition, the assumptions made (e.g. in terms of what constitutes a repeated measure) are not supported by what we know about the properties of EEG data. From the point of view of physics (see Chapter 3), the natural “atomic” analysis entity of EEG and ERP data is the scalp electric field

BOLD correlates of EEG alpha phase-locking and the fMRI default mode network

Phase locking or synchronization of brain areas is a key concept of information processing in the brain. Synchronous oscillations have been observed and investigated extensively in EEG during the past decades. EEG oscillations occur over a wide frequency range. In EEG, a prominent type of oscillations is alpha-band activity, present typically when a subject is awake, but at rest with closed eyes. The spectral power of alpha rhythms has recently been investigated in simultaneous EEG/fMRI recordings, establishing a wide-range cortico-thalamic network. However, spectral power and synchronization are different measures and little is known about the correlations between BOLD effects and EEG synchronization. Interestingly, the fMRI BOLD signal also displays synchronous oscillations across different brain regions. These oscillations delineate so-called resting state networks (RSNs) that resemble the correlation patterns of simultaneous EEG/fMRI recordings. However, the nature of these BOLD oscillations and their relations to EEG activity is still poorly understood. One hypothesis is that the subunits constituting a specific RSN may be coordinated by different EEG rhythms. In this study we report on evidence for this hypothesis. The BOLD correlates of global EEG synchronization (GFS) in the alpha frequency band are located in brain areas involved in specific RSNs, e.g. the 'default mode network'. Furthermore, our results confirm the hypothesis that specific RSNs are organized by long-range synchronization at least in the alpha frequency band. Finally, we could localize specific areas where the GFS BOLD correlates and the associated RSN overlap. Thus, we claim that not only the spectral dynamics of EEG are important, but also their spatio-temporal organization.

Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.

Shifted Coupling of EEG Driving Frequencies and fMRI Resting State Networks in Schizophrenia Spectrum Disorders

INTRODUCTION: The cerebral resting state in schizophrenia is altered, as has been demonstrated separately by electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state networks (RSNs). Previous simultaneous EEG/fMRI findings in healthy controls suggest that a consistent spatiotemporal coupling between neural oscillations (EEG frequency correlates) and RSN activity is necessary to organize cognitive processes optimally. We hypothesized that this coupling is disorganized in schizophrenia and related psychotic disorders, in particular regarding higher cognitive RSNs such as the default-mode (DMN) and left-working-memory network (LWMN). METHODS: Resting state was investigated in eleven patients with a schizophrenia spectrum disorder (n = 11) and matched healthy controls (n = 11) using simultaneous EEG/fMRI. The temporal association of each RSN to topographic spectral changes in the EEG was assessed by creating Covariance Maps. Group differences within, and group similarities across frequencies were estimated for the Covariance Maps. RESULTS: The coupling of EEG frequency bands to the DMN and the LWMN respectively, displayed significant similarities that were shifted towards lower EEG frequencies in patients compared to healthy controls. CONCLUSIONS: By combining EEG and fMRI, each measuring different properties of the same pathophysiology, an aberrant relationship between EEG frequencies and altered RSNs was observed in patients. RSNs of patients were related to lower EEG frequencies, indicating functional alterations of the spatiotemporal coupling. SIGNIFICANCE: The finding of a deviant and shifted coupling between RSNs and related EEG frequencies in patients with a schizophrenia spectrum disorder is significant, as it might indicate how failures in the processing of internal and external stimuli, as commonly seen during this symptomatology (i.e. thought disorders, hallucinations), arise.