The effect of linear mixing in the EEG on Hurst exponent estimation

Although the long-range temporal correlation (LRTC) of the amplitude fluctuations of neuronal EEG/MEG oscillations is widely acknowledged, the majority of studies to date have been performed in sensor space, disregarding the mixing effects implied by volume conduction and confounding noise. While the effect of mixing on the evaluation of evoked responses and connectivity measures has been extensively studied, there are, to date, no studies reporting on the differences in the values of the estimated Hurst exponents when moving between sensor and source space representations of the multivariate data or on the effect of noise. Such differences, if not duly acknowledged, may lead to erroneous data interpretations. We show in simulations and in theory that measuring Hurst exponents in sensor space may lead to an incomplete picture of the LRTC properties of the underlying data and that noise may significantly bias the estimate of the Hurst exponent of the underlying signal. Moreover, these predictions are confirmed in real data, where we analyze the amplitude dynamics of neuronal oscillations in the resting state from EEG data. By moving either to an independent components representation or to a source representation which maximizes the signal to noise ratio in the alpha frequency range, we observe greater variance, skewness and kurtosis over measured Hurst exponents than in sensor space. We confirm the suitability of conventional source separation methodology by introducing a novel algorithm HeMax which obtains a source maximizing the Hurst exponent in the amplitude dynamics of narrow band oscillations. Our findings imply that the long-range correlative properties of the EEG should be studied in source space, in such a way that the SNR is maximized, or at least with spatial decomposition techniques approximating source activities, rather than in sensor space.