Is the Surface Potential Integral of a Dipole in a Volume Conductor Always Zero? A Cloud Over the Average Reference of EEG and ERP

Abstract

Currently, average reference is one of the most widely adopted references in EEG and ERP studies. The theoretical assumption is the surface potential integral of a volume conductor being zero, thus the average of scalp potential recordings might be an approximation of the theoretically desired zero reference. However, such a zero integral assumption has been proved only for a spherical surface. In this short communication, three counter-examples are given to show that the potential integral over the surface of a dipole in a volume conductor may not be zero. It depends on the shape of the conductor and the orientation of the dipole. This fact on one side means that average reference is not a theoretical 'gold standard' reference, and on the other side reminds us that the practical accuracy of average reference is not only determined by the well-known electrode array density and its coverage but also intrinsically by the head shape. It means that reference selection still is a fundamental problem to be fixed in various EEG and ERP studies.

Keywords: Average reference; Gold standard; Spherical head; Volume conductor model; Zero potential.

Fig. 1

Illustration of a dipole in a spherical volume conductor. $\overrightarrow{P}$ is the dipole moment, the grey area is the spherical volume conductor

Fig. 2

Illustration of a dipole in a half-space volume conductor. $\overrightarrow{P}$ is the dipole moment, the grey area is the volume conductor

Fig. 3

Illustration of a dipole in a volume conductor outside of a spherical cave. $\overrightarrow{P}$ is the dipole moment, the grey area is the volume conductor