EEG coherence and reference signals: experimental results and mathematical explanations

Coherence has become an essential tool in the description of functional relationships between EEG signals generated within various brain areas. In EEG coherence analysis, the reference signal has an important influence, as an improper reference can distort the results and make them impossible to interpret. In the study, EEG are recorded from one volunteer in 11 sessions, with electrodes selected according to the international 10-20 system against FCz. Additional electrodes are placed on the nose, chin and left and right ear lobes, and recordings are made also against FCz. This enables re-referencing of the stored EEG signals for different reference sites, averaged reference signals, common average reference, Laplacian and bipolar. Coherence values using single reference electrodes depend on the reference site to a large extent. Reliable results are obtained using averaged non-cephalic signals as reference ([A1 + A2]/2). Coherence based on FCz yields slightly lower or higher values than that based on non-cephalic reference sites. Completely different results yield common average reference recordings, Laplacian and bipolar recordings, probably owing to the cancellation effect of essential signal portions using these techniques. A mathematical model for coherence based on signal-to-noise ratios is introduced to explain the experimental findings: the model demonstrates that noisy reference signals lead to coherence increase, whereas a coherent amount in the reference signal leads to coherence decrease.