CNS*2020 Online

Rick Evertz, Damien Hicks, David Liley

Dynamical and physiological basis of alpha band activity and 1/f noise subject of continued speculation. Here we conjecture, on the basis of empirical data analysis, that both of these features can be dynamically unified if resting EEG is conceived of being the sum of multiple stochastically perturbed alpha band oscillatory relaxation processes. The modulation of alpha-band and 1/f noise activity by dynamic damping is explored in eyes closed (EC) and eyes open (EO) resting state Magneto/Electroencephalography (M/EEG). We assume that the resting M/EEG being recorded is composed of a superposition of stochastically perturbed alpha-band relaxation processes with a distribution of dampings, the functional form of which is unknown. We perform the inverse problem and take measured M/EEG power spectra and compute the distribution of dampings using Tikhonov regularization methods. The characteristics of the damping distribution are examined across subjects, sensors and recording condition (EC/EO).

We find that there is robust changes in the estimated damping distribution between EC/EO recording conditions across participants. Our findings suggest that alpha-blocking and the 1/f noise structure are both explicable through a singular process of dynamically damped alpha-band activity. The estimated damping distributions are typically found to be bimodal or trimodal (Fig. 1). The number and position of the modes is related to the sharpness of the alpha resonance (amplitude, FWHM) and the slope of the power spectrum. The results suggest that there exists an intimate relationship between resting state alpha activity and 1/f noise with changes in both governed by changes to the damping of the underlying alpha relaxation processes. In particular, alpha-blocking is observed to be the result of the most weakly damped distribution mode (peak at 0.4 - 0.6s^-1) becoming more heavily damped (peak at 1.0 - 1.5s^-1). Reductions in the slope of the 1/f noise are the result of the alpha relaxation processes becoming more broadly distributed in their respective dampings with more weighting towards heavily damped alpha activity. The results suggest a novel way of characterizing resting M/EEG power spectra and provides new insight into the central role that damped alpha-band activity may play in the interesting spatio-temporal features of resting state M/EEG.

Future work will explore the more complex case where we expect a distribution over both frequency and damping for the stochastic relaxation processes, elucidating any frequency dependent damping effects between conditions. The inverse problem can be solved via gradient descent methods where we estimate the 2-dimensional probability density function over frequency and damping from a given power spectrum.