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Figure 1: Image from C.M. Michel et al., 2004: The top row with color shows how interpretation of voltage distribution (EEG) varies by choice of reference. In contrast, the bottom row shows how the actual gradients of the voltage potential (scalp topography) across the scalp at a given moment does not change, regardless of the choice of reference. Although the choice of reference changes how the EEG is interpreted, source analysis is not affected by choice of reference.

The consequence of this problem is that when the value at the reference electrode is arbitrarily assumed to have a fixed value across time (but in reality is always in flux), combined with the fact that potentials recorded at each electrode are relative to the potential recorded at reference, a change in potential at the reference electrode at a given moment induces what appears to be a change at a recording electrode ...when in fact there may have been no change at the recording electrode at that given moment! This can lead to a misinterpretation of the data collected at the scalp, and therefore a misinterpretation of the underlying cortical sources.

This illustrates the need for a reference-independent measure of potential for accurately capturing the changes in EEG over time that make up the scalp topography. To address this need, consider that the electrical potentials integrated over the entire surface of the body is a constant, and as a whole is inactive across time, regardless of the activity and distribution of brain electric sources. Therefore, this means that the average reference of all electrodes (the mean of all recording channels at each time point) can be used to approximate the inactive reference.

The inactive reference can also be thought of as the “zero surface integral”. This concept describes that for a single dipole occurring at a patch of active cortex and projecting to the scalp surface, the positive fields of the dipole measured at the scalp surface must equal the negative fields of the dipole measured at the scalp surface where the resulting value, if added together, is zero. This is the zero surface integral. Further, if this holds true for a single cortical dipole, then it also holds true for any number of simultaneously occurring cortical sources (M. Junghöfer et al., 1999; O. Bertrand et al., 1985).

We begin to see then, that the zero surface integral can only be achieved with adequate spatial sampling across the entire scalp surface in order to measure all the positive and negative potentials.

Adequate spatial sampling requires a sufficient electrode density and full coverage of the head's surface, and it has been shown that inter-electrode distances of around 2–3 cm are needed to avoid distortions of the scalp potential distribution (Gevins et al., 1990; Spitzer et al., 1989; Srinivasan et al., 1996, 1998).

To achieve a spatial sampling with 2 cm inter-electrode distances, about 256 recording channels are required (https://www.egi.com/research-division/research-division-why-dense-array-eeg).

In conclusion, we see that the zero surface integral is necessary for accurate interpretation of EEG data. Achieving this requires an average reference calculation from an adequate number of electrodes evenly covering the entire head surface. With 256-channel EEG sampling, dense array EEG now approximates adequate spatial sampling.  With EGI's technology, this accuracy is now available to researchers and clinicians alike.