Thus the scalp surface Laplacian is proportional to the dura potential. Because the scalp surface Laplacian acts as a spatial high-pass filter (Nunez and Srinivasan 2006), possibly missing some valid information in the data, it is best used in conjunction with the average-referenced potential to study brain dynamics on the scalp.
Another way of eliminating the reference electrode effect is to based studies on bipolar pairs, as is common in clinical practice. Figs. 5(a) and (b) show that the potential difference between nearby electrode pairs have spatial sensitivity that is restricted to their local. The potential difference between all such pairs, or perhaps only nearest-neighbor pairs, may be computed easily and completely eliminates the dependence on the original reference electrode. Whereas the previous two approaches, the average reference and surface Laplacian, eliminated the dependence on the reference electrode, this approach makes explicit use of the reference electrode by effectively moving it around to form local bipolar pairs. Time-domain averages (i.e., event-related potentials) or power spectra computed from these time series are representative of the associated HSV, although the results are difficult to show graphically because each temporal or spectral measure is associated with one electrode rather than two. Time series collected from two bipolar pairs, which are themselves widely separated (e.g., a nearby pair in occipital cortex and a nearby pair in frontal cortex) may also be used for coherence analysis (Nunez 1995).
This goal of this chapter is to provide a rigorous introduction to scalp EEG for research in functional connectivity. We started at the microscopic level and discussed the cellular basis of current sources that generate extracellular fields, and developed the steps in electromagnetic theory that describe macroscopic fields in biological systems. We discussed the solutions to the EEG forward problem in spherical and realistic head models. We also discussed EEG measurement technology, to make clear the reasons why the reference electrode issue arises so frequently in EEG experiments. We developed the concept of the lead field vector L to help visualize the spatial sensitivity patterns of scalp electrode measurements. These arguments lead to the conclusion that the reference electrode acts as a measurement electrode, and this fact must be addressed before drawing conclusions about the activity under any single electrode.
Studies of functional connectivity involve temporal measures of correlation, e.g., coherence and Granger causality, applied to two or more electrodes. Implicitly it is assumed that the time series collected at each electrode detects brain activity near that electrode. Our arguments using lead field theory show that each electrode is sensitive to large tissue volumes, containing perhaps 108-109 cortical neurons. Thus EEG measures of functional connectivity apply only to very large spatial scales, although somewhat smaller scale connectivity may be estimated with high resolution EEG methods like the surface Laplacian.
The reference electrode continues to confound many EEG studies. This chapter presented three practical ways of dealing with the reference electrode issue: adopting the average reference, the scalp surface Laplacian, or bipolar pairs. These data transformations and related concepts are essential to the estimation of temporal and spectral measures that may be used to make inferences about functional connectivity. Other facets of these topics are described elsewhere (e.g., Nunez and Srinivasan 2006).
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