Spatial neuronal synchronization and the waveform of oscillations: Implications for EEG and MEG

Neuronal oscillations are ubiquitous in the human brain and are implicated in virtually all brain functions. Although they can be described by a prominent peak in the power spectrum, their waveform is not necessarily sinusoidal and shows rather complex morphology. Both frequency and temporal descriptions of such non-sinusoidal neuronal oscillations can be utilized. However, in non-invasive EEG/MEG recordings the waveform of oscillations often takes a sinusoidal shape which in turn leads to a rather oversimplified view on oscillatory processes. In this study, we show in simulations how spatial synchronization can mask non-sinusoidal features of the underlying rhythmic neuronal processes. Consequently, the degree of non-sinusoidality can serve as a measure of spatial synchronization. To confirm this empirically, we show that a mixture of EEG components is indeed associated with more sinusoidal oscillations compared to the waveform of oscillations in each constituent component. Using simulations, we also show that the spatial mixing of the non-sinusoidal neuronal signals strongly affects the amplitude ratio of the spectral harmonics constituting the waveform. Finally, our simulations show how spatial mixing can affect the strength and even the direction of the amplitude coupling between constituent neuronal harmonics at different frequencies. Validating these simulations, we also demonstrate these effects in real EEG recordings. Our findings have far reaching implications for the neurophysiological interpretation of spectral profiles, cross-frequency interactions, as well as for the unequivocal determination of oscillatory phase. Author summary The electrical activity in the human brain demonstrates oscillations of intricate complexity. Interestingly, such complex waveforms are primarily visible in invasive recordings but not so much when neuronal activity is recorded with non-invasive methods such as electroencephalography. Yet a specific waveform is informative about the postsynaptic processes which are at the core of our understanding of cortical excitability and information transfer in neuronal networks. In our study, we show with simulations and real EEG data, how temporal delays between different cortical sources can contribute to a more sinusoidal or non-sinusoidal shape of neuronal oscillations. We illustrate how, depending on the temporal delays, low- and high-frequency components of oscillations can be enhanced or attenuated to a different degree thus affecting the shape of oscillations and corresponding spectra which are often associated with specific functional consequences. We further show how this phenomenon can challenge our understanding of the link between neuronal oscillations and motor function, cognition and perception.