Introduction

Experimental and theoretical studies of functional connectivity in healthy humans requires non-invasive techniques such as electroenchaphalography (EEG), magnetoencephalography (MEG), and functional magnetic resonance imaging (fMRI). Among these, EEG and MEG provide the most direct measure of cortical activity with high temporal resolution (< 1 msec), but with spatial resolution (1-10 cm) limited by the locations of sensors on the scalp. In contrast, functional MRI has low temporal resolution (1-10 sec), but high spatial resolution (1-10 mm). To the extent that functional activity among brain regions in the cortex may be conceptualized as a large-scale brain network with diffuse nodes, fMRI may delineate the anatomy of these networks, perhaps most effectively in identifying major network hubs. Much current effort is aimed at the integration of these technologies and others, for the obvious reason: to provide the most complete view of dynamical brain activity both spatially and temporally. This chapter focuses primarily on EEG, but also makes connections with MEG.

The human brain exhibits interesting and relevant dynamics on all spatial scales, ranging from single neurons to the entire cortex. The spatial resolution of a particular measurement technique selects certain physiological processes over others. Much investigation in animals has focussed on the information capacities of single neurons, using direct measurements from implanted electrodes. Although EEG measurements integrate over the activity of 10-100 millions of neurons, there is ample evidence that relevant information is represented at these large scales. Indeed, interactions between remote brain areas must involve large spatial scales. Furthermore, several techniques have been developed for improving the spatial resolution of scalp EEG so that dynamic behavior at the scale of roughly 2-3 cm may be estimated.

The physics and physiology of scalp EEG have been described at length elsewhere (Nunez 1981; Nunez 1995; Nunez and Srinivasan 2006). The goal of this chapter is partly to summarize that material, and partly to extend it. Section 2 describes the physiological genesis of EEG and MEG in terms of cellular currents. Section 3 describes the physical basis of EEG and MEG starting from Maxwell's equations. The remaining chapters focus exclusively on EEG. Section 4 shows how a multipole expansion of the electric potential defines the familiar current dipole. Section 5 adds the effects of head tissue inhomogeneities, which strongly affect the electric potential measured at the scalp. Section 6 reviews EEG measurement principles. Section 7 develops lead field theory, an intuitive way of thinking about the sensitivity of scalp electrodes to brain current sources. Together these sections link concepts of neural activity from the cellular level to the scalp, and provide a basis for the application of scalp EEG to study functional connectivity.

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