Analyzing the waveshape of brain oscillations with bicoherence

Oscillations are characteristic features of brain activity and have traditionally been categorized into frequency bands. Despite this categorization, brain oscillations have non-sinusoidal waveshape features, which have recently been discussed for their potential to mislead cross-frequency coupling measures. Waveshape characteristics deserve attention in their own right, as they are a direct reflection of the underlying neurophysiology and have shown to be altered in conditions such as Parkinson's disease. Here, we want to contribute to waveshape analysis in three steps: (1) While shape is most intuitively described in the time domain, complementary information is provided by frequency domain. In particular we show, that the bispectrum of an oscillation directly reflects waveshape properties such as differences in the steepness of its rise and decay phases, as well as differences in the duration of its crests and troughs. (2) Methods for the extraction of brain oscillations need to be chosen with care, as the ubiquitous use of bandpass filters causes waveshape distortions. We illustrate common problems and introduce a waveshape-preserving spatial filter for the purpose of waveshape analysis. (3) In an exemplary analysis of resting-state alpha rhythms, bicoherence provides evidence that shape characteristics of alpha rhythms exist on a spectrum. In addition, the bispectral view identifies significant mu rhythm anomalies in schizophrenia and suggests potential causes relating to waveshape.