On the meaning and interpretation of global descriptors of brain electrical activity. Including a reply to X. Pei et al.

Global descriptors of the brain's electrical activity, Σ, Φ, and Ω, provide a comprehensive characterisation of brain functional states. Recently, Pei et al. [Pei, X., Zheng, C., Zhang, A., Duan, F., Bin, G., 2005. Discussion on “Towards a quantitative characterisation of functional states of the brain: from the nonlinear methodology to the global linear description” by J. Wackermann. Int. J. Psychophysiol. 56, 201–207] discussed the effects of signal power on the global measure of spatial complexity, Ω, and suggested a modification consisting in epoch-wise and channel-wise normalisation of input data to unit power. In the present paper, the basic principles of the global approach are reviewed, and the issues of Pei et al.'s approach are assessed. The original and the modified measures of spatial complexity are compared in two case studies. Numerical simulation shows that both methods veridically estimate small numbers of signal sources, but systematically underestimate as the number increases; the modified method yields a minor relative improvement. A study on real EEG data shows that the two measures sensibly differ only where artefactual inhomogeneities in channel variances affect the data; a combined procedure, consisting in record-wise equalisation of channel variances before Ω calculations, is suggested as the optimal strategy. Differences between the original objectives of the global methodology and the proposed modifications are pointed out and critically discussed.