Previous studies have shown that synchronized beta frequency (14 -30 Hz) oscillations in the primary motor cortex are involved in maintaining steady contractions of contralateral arm and hand muscles. However, little is known about the role of postcentral cortical areas in motor maintenance and their patterns of interaction with motor cortex. We investigated the functional relations of beta-synchronized neuronal assemblies in pre-and postcentral areas of two monkeys as they pressed a hand lever during the wait period of a visual discrimination task. By using power and coherence spectral analysis, we identified a beta-synchronized largescale network linking pre-and postcentral areas. We then used Granger causality spectra to measure directional influences among recording sites. In both monkeys, strong Granger causal influences were observed from primary somatosensory cortex to both motor cortex and inferior posterior parietal cortex, with the latter area also exerting Granger causal influences on motor cortex. Granger causal influences from motor cortex to postcentral sites, however, were weak in one monkey and not observed in the other. These results are the first, to our knowledge, to demonstrate in awake monkeys that synchronized beta oscillations bind multiple sensorimotor areas into a large-scale network during motor maintenance behavior and carry Granger causal influences from primary somatosensory and inferior posterior parietal cortices to motor cortex.cerebral cortex ͉ motor maintenance ͉ parietal ͉ local field potential ͉ coherence O scillatory activity in the beta frequency range (14-30 Hz) is widely observed in sensorimotor cortex in relation to motor behavior in both humans (1, 2) and nonhuman primates (3-6). Specifically, beta oscillations in monkeys appear in local field potential (LFP) and spiking activity during tactile exploratory forelimb movements (4, 7, 8), movement preparation (5, 6, 9), and steady-state isometric contractions (10). Beta oscillatory activity is often observed to be synchronized between different parts of sensorimotor cortex (4,5,7,(9)(10)(11), between motor cortical LFPs and descending pyramidal tract neuron discharge (10, 12), between single motor units (13,14), and between motor cortical activity and muscle activity (1,4,10,12,15,16).Although the role of beta oscillations in the outflow of activity from motor cortex to muscles is relatively well characterized for certain types of behavior, the relation of beta oscillations in postcentral areas and motor cortex remains poorly understood. This article addresses the functional relations between beta oscillations in pre-and postcentral cortical areas in premovement motor maintenance behavior. It has long been proposed that behavior of this type depends on a corticoperipheral cortical sensorimotor loop (17, 18), and more recently that this loop is supported by oscillatory neuronal activity (19). Reports of beta oscillations in both somatosensory and motor cortices during premovement maintenance behavior (3, 5, 6, 9), taken toge...

We consider the question of evaluating causal relations among neurobiological signals. In particular, we study the relation between the directed transfer function (DTF) and the well-accepted Granger causality, and show that DTF can be interpreted within the framework of Granger causality. In addition, we propose a method to assess the significance of causality measures. Finally, we demonstrate the applications of these measures to simulated data and actual neurobiological recordings.

The human brain has evolved for group living [1]. Yet we know so little about how it supports dynamic group interactions that the study of real-world social exchanges has been dubbed the "dark matter of social neuroscience" [2]. Recently, various studies have begun to approach this question by comparing brain responses of multiple individuals during a variety of (semi-naturalistic) tasks [3-15]. These experiments reveal how stimulus properties [13], individual differences [14], and contextual factors [15] may underpin similarities and differences in neural activity across people. However, most studies to date suffer from various limitations: they often lack direct face-to-face interaction between participants, are typically limited to dyads, do not investigate social dynamics across time, and, crucially, they rarely study social behavior under naturalistic circumstances. Here we extend such experimentation drastically, beyond dyads and beyond laboratory walls, to identify neural markers of group engagement during dynamic real-world group interactions. We used portable electroencephalogram (EEG) to simultaneously record brain activity from a class of 12 high school students over the course of a semester (11 classes) during regular classroom activities (Figures 1A-1C; Supplemental Experimental Procedures, section S1). A novel analysis technique to assess group-based neural coherence demonstrates that the extent to which brain activity is synchronized across students predicts both student class engagement and social dynamics. This suggests that brain-to-brain synchrony is a possible neural marker for dynamic social interactions, likely driven by shared attention mechanisms. This study validates a promising new method to investigate the neuroscience of group interactions in ecologically natural settings.

Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus a highly desired capability for understanding the cooperative nature of neural computation. Research over the last few years has shown that Granger causality is a key technique to furnish this capability. The main goal of this article is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both bivariate Granger causality and conditional Granger causality are developed in detail with particular emphasis on their spectral representations. The technique is demonstrated in numerical examples where the exact answers of causal influences are known.It is then applied to analyze multichannel local field potentials recorded from monkeys performing a visuomotor task. Our results are shown to be physiologically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks.

In this article we consider the application of parametric spectral analysis to multichannel event-related potentials (ERPs) during cognitive experiments. We show that with proper data preprocessing, Adaptive MultiVariate AutoRegressive (AMVAR) modeling is an effective technique for dealing with nonstationary ERP time series. We propose a bootstrap procedure to assess the variability in the estimated spectral quantities. Finally, we apply AMVAR spectral analysis to a visuomotor integration task, revealing rapidly changing cortical dynamics during different stages of task processing.

Field potential oscillations at ϳ10 Hz (alpha rhythm) are widely noted in the visual cortices, but their physiological mechanisms and significance are poorly understood. In vitro studies have implicated pyramidal neurons in both infragranular and supragranular layers as pacemakers. The generality of these observations for the intact brain in the behaving subject is unknown. We analyzed laminar profiles of spontaneous local field potentials and multiunit activity (MUA) recorded with linear array multielectrodes from visual areas V2, V4, and inferotemporal (IT) cortex of two macaque monkeys during performance of a sensory discrimination task. Current source density (CSD) analysis was combined with CSD-MUA coherence to identify intracortical alpha current generators and their potential for alpha pacemaking. The role of each alpha current generator was further delineated by Granger causality analyses. In V2 and V4, alpha current generators were found in all layers, with the infragranular generator acting as primary local pacemaking generator. In contrast, in IT, alpha current generators were found only in supragranular and infragranular layers, with the supragranular generator acting as primary local pacemaking generator. The amplitude of alpha activity in V2 and V4 was negatively correlated with behavioral performance, whereas the opposite was true in IT. The alpha rhythm in IT thus appears to differ from that in the lower-order cortices, both in terms of its underlying physiological mechanism and its behavioral correlates. This work may help to reconcile some of the diverse findings and conclusions on the functional significance of alpha band oscillations in the visual system.

Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

Field potential oscillations in the ~10 Hz range are known as the alpha rhythm. The genesis and function of alpha has been the subject of intense investigation for the past 80 years. Whereas early work focused on the thalamus as the pacemaker of alpha rhythm, subsequent slice studies revealed that pyramidal neurons in the deep layers of sensory cortices are capable of oscillating in the alpha frequency range independently. How thalamic and cortical generating mechanisms in the intact brain might interact to shape the organization and function of alpha oscillations remains unclear. We addressed this problem by analyzing laminar profiles of local field potential (LFP) and multi-unit activity (MUA) recorded with linear array multielectrodes from the striate cortex of two macaque monkeys performing an intermodal selective attention task. Current source density (CSD) analysis was combined with CSD-MUA coherence to identify intracortical alpha current generators and assess their potential for pacemaking. Coherence and Granger causality analysis was applied to delineate the patterns of interaction among different alpha current generators. We found that: (1) separable alpha current generators are located in superficial, granular and deep layers, with both layer 4C and deep layers containing primary local pacemaking generators, suggesting the involvement of the thalamocortical network, and (2) visual attention reduces the magnitude of alpha oscillations as well as the level of alpha interactions, consistent with numerous reports of occipital alpha reduction with visual attention in human EEG. There is also indication that alpha oscillations in the lateral geniculate cohere with those in V1.