Reference-Free EEG and Electric Fields: A Multi-Scale Parallax View

To address the reference issue, a refined conceptual framework, a parallax view, clarifies how multi-scale electric potentials, electric fields, current sources, and reference strategies interrelate. Electric potentials, introduced historically to simplify mathematics, are physically meaningful only when expressed as differences. The so-called zero potential at infinity is clarified physically by focusing on the electric field, an unambiguously real physical entity.Measures of functional connectivity like coherence are affected by reference, volume conduction, and the spatial scale of description. Nonetheless, the common average reference (CAVE or CAR) yields robust information, even though coherence between specific electrode pairs is uncertain. CAVE’s strength lies in treating all electrode sites equally, without prior assumptions about brain sources or volume conductor models. CAVE may benefit more from increased electrode density and reduced inter-electrode spacing than from extending electrode array coverage to lower head locations. With average center-to-center spacing below about 2.5 cm, CAVE accurately represents recorded potential relative to the average potential over the underlying scalp—without implying that this average is zero. Electric field measurements can usefully supplement CAVE measurements, the proposed parallax view. High-density recordings enable accurate estimation of scalp tangential electric fields, an extension of simple bipolar recording to the entire array. Such measure provides estimates of electric field magnitudes and directions, expressed as contour maps and streaming vector maps, respectively. Field magnitude maps sometimes resemble Laplacian maps depending on sources; streaming vector maps provide directions and strengths of scalp currents. Because electric fields are inherently reference-free, only volume conduction remains as a barrier distorting coherence and other measures of dynamic source behavior.