Spherical Harmonics Reveal Standing EEG Waves and Long-Range Neural Synchronization during Non-REM Sleep

Brain states as wave-like motifs

There is ample evidence of wave-like activity in the brain at multiple scales and levels. This emerging literature supports the broader adoption of a wave perspective of brain activity. Specifically, a brain state can be described as a set of recurring, sequential patterns of propagating brain activity, namely a wave. We examine a collective body of experimental work investigating wave-like properties. Based on these works, we consider brain states as waves using a scale-agnostic framework across time and space. Emphasis is placed on the sequentiality and periodicity associated with brain activity. We conclude by discussing the implications, prospects, and experimental opportunities of this framework.

Resting-state EEG topographies: Reliable and sensitive signatures of unilateral spatial neglect

Theoretical advances in the neurosciences are leading to the development of an increasing number of proposed interventions for the enhancement of functional recovery after brain damage. Integration of these novel approaches in clinical practice depends on the availability of reliable, simple, and sensitive biomarkers of impairment level and extent of recovery, to enable an informed clinical-decision process. However, the neuropsychological tests currently in use do not tap into the complex neural re-organization process that occurs after brain insult and its modulation by treatment. Here we show that topographical analysis of resting-state electroencephalography (rsEEG) patterns using singular value decomposition (SVD) could be used to capture these processes. In two groups of subacute stroke patients, we show reliable detection of deviant neurophysiological patterns over repeated measurement sessions on separate days. These patterns generalized across patients groups. Additionally, they maintained a significant association with ipsilesional attention bias, discriminating patients with spatial neglect of different severity levels. The sensitivity and reliability of these rsEEG topographical analyses support their use as a tool for monitoring natural and treatment-induced recovery in the rehabilitation process.

Spherical-harmonics mode decomposition of neural field equations

Large-scale neural networks can be described in the spatial continuous limit by neural field equations. For large-scale brain networks, the connectivity is typically translationally variant and imposes a large computational burden upon simulations. To reduce this burden, we take a semiquantitative approach and study the dynamics of neural fields described by a delayed integrodifferential equation. We decompose the connectivity into spatially variant and invariant contributions, which typically comprise the short- and long-range fiber systems, respectively. The neural fields are mapped on the two-dimensional spherical surface, which is choice consistent with routine mappings of cortical surfaces. Then, we perform mathematically a mode decomposition of the neural field equation into spherical harmonic basis functions. A spatial truncation of the leading orders at low wave number is consistent with the spatially coherent pattern formation of large-scale patterns observed in simulations and empirical brain imaging data and leads to a low-dimensional representation of the dynamics of the neural fields, bearing promise for an acceleration of the numerical simulations by orders of magnitude.

EEG microstates as a tool for studying the temporal dynamics of whole-brain neuronal networks: A review

The present review discusses a well-established method for characterizing resting-state activity of the human brain using multichannel electroencephalography (EEG). This method involves the examination of electrical microstates in the brain, which are defined as successive short time periods during which the configuration of the scalp potential field remains semi-stable, suggesting quasi-simultaneity of activity among the nodes of large-scale networks. A few prototypic microstates, which occur in a repetitive sequence across time, can be reliably identified across participants. Researchers have proposed that these microstates represent the basic building blocks of the chain of spontaneous conscious mental processes, and that their occurrence and temporal dynamics determine the quality of mentation. Several studies have further demonstrated that disturbances of mental processes associated with neurological and psychiatric conditions manifest as changes in the temporal dynamics of specific microstates. Combined EEG-fMRI studies and EEG source imaging studies have indicated that EEG microstates are closely associated with resting-state networks as identified using fMRI. The scale-free properties of the time series of EEG microstates explain why similar networks can be observed at such different time scales. The present review will provide an overview of these EEG microstates, available methods for analysis, the functional interpretations of findings regarding these microstates, and their behavioral and clinical correlates.

Effect of Field Spread on Resting-State Magneto Encephalography Functional Network Analysis: A Computational Modeling Study

A popular way to analyze resting-state electroencephalography (EEG) and magneto encephalography (MEG) data is to treat them as a functional network in which sensors are identified with nodes and the interaction between channel time series and the network connections. Although conceptually appealing, the network-theoretical approach to sensor-level EEG and MEG data is challenged by the fact that EEG and MEG time series are mixtures of source activity. It is, therefore, of interest to assess the relationship between functional networks of source activity and the ensuing sensor-level networks. Since these topological features are of high interest in experimental studies, we address the question of to what extent the network topology can be reconstructed from sensor-level functional connectivity (FC) measures in case of MEG data. Simple simulations that consider only a small number of regions do not allow to assess network properties; therefore, we use a diffusion magnetic resonance imaging-constrained whole-brain computational model of resting-state activity. Our motivation lies behind the fact that still many contributions found in the literature perform network analysis at sensor level, and we aim at showing the discrepancies between source- and sensor-level network topologies by using realistic simulations of resting-state cortical activity. Our main findings are that the effect of field spread on network topology depends on the type of interaction (instantaneous or lagged) and leads to an underestimation of lagged FC at sensor level due to instantaneous mixing of cortical signals, instantaneous interaction is more sensitive to field spread than lagged interaction, and discrepancies are reduced when using planar gradiometers rather than axial gradiometers. We, therefore, recommend using lagged interaction measures on planar gradiometer data when investigating network properties of resting-state sensor-level MEG data.