Cycle-by-cycle analysis of neural oscillations.

Neural oscillations are widely studied using methods based on the Fourier transform, which models data as sums of sinusoids. This has successfully uncovered numerous links between oscillations and cognition or disease. However, neural data are nonsinusoidal, and these nonsinusoidal features are increasingly linked to a variety of behavioral and cognitive states, pathophysiology, and underlying neuronal circuit properties. We present a new analysis framework, one that is complementary to existing Fourier and Hilbert transform-based approaches, that quantifies oscillatory features in the time domain on a cycle-by-cycle basis. We have released this cycle-by-cycle analysis suite as "bycycle," a fully documented, open-source Python package with detailed tutorials and troubleshooting cases. This approach performs tests to assess whether an oscillation is present at any given moment and, if so, quantifies each oscillatory cycle by its amplitude, period, and waveform symmetry, the latter of which is missed with the use of conventional approaches. In a series of simulated event-related studies, we show how conventional Fourier and Hilbert transform approaches can conflate event-related changes in oscillation burst duration as increased oscillatory amplitude and as a change in the oscillation frequency, even though those features were unchanged in simulation. Our approach avoids these errors. Furthermore, we validate this approach in simulation and against experimental recordings of patients with Parkinson's disease, who are known to have nonsinusoidal beta (12-30 Hz) oscillations.