Clinical EEG standards frequently rely on bipolar montages (i.e., sequentially changing the reference as opposed to relying on a fixed, single reference) to help localize electrographic abnormalities associated with seizures (e.g., Osselton, 1965). This intuitive approach may be generalized by noting that the electric field (E) is a vector quantity defined as the negative gradient (i.e., spatial slope) of the field potential (−∇Φ). The direction of the electric field corresponding to the point source and sink shown in Fig. 1 is normal to the isopotential lines at any location (for additional intuitive and mathematical implications, see Schey, 1997). The use of the gradient, which, at least in theory, represents a continuous difference potential pointing in the direction of greatest potential decrease (i.e., downhill), sidesteps the longstanding controversy over the optimal (or universal) recoding reference for scalp-recorded EEG or ERP. Another notable property of the field potential gradient is that it is approximately constant as large or distributed current generators are approached (i.e., field potential fall-off is approximately linear above a cortical generator; cf. Tenke et al., 1993).
