An iterative search algorithm to identify oscillatory dynamics in neurophysiological time series

Neural oscillations have long been recognized for their mechanistic importance in coordinating activity within and between brain circuits. Co-occurring broad-band, non-periodic signals are also ubiquitous in neural data and are thought to reflect the characteristics of populationlevel neuronal spiking activity. Identifying oscillatory activity distinct from broadband signals is therefore an important, yet surprisingly difficult, problem in neuroscience. Commonly-used bandpass filters produce spurious oscillations when applied to broad-band noise and may be illinformed by canonical frequency bands. Curve-fitting procedures have been developed to identify peaks in the power spectrum distinct from broadband noise. Unfortunately, these ad hoc methods are prone to overfitting and are difficult to interpret in the absence of generative models to formally represent oscillatory behavior. Here we present a novel method to identify and characterize neural oscillations distinct from broad-band noise. First, we propose a new conceptual construct that makes clear, from a dynamical systems perspective, when oscillations are present or not. We then use this construct to develop generative models for neural oscillations. We show through extensive analyses of simulated and human EEG data that our approach identifies oscillations and their characteristics far more accurately than widely used methods, achieving near-perfect recovery of the number of oscillations when the SNR exceeds a very modest threshold. We also show that our method can automatically identify subject-level variations in frequency to overcome the limitations of fixed canonical frequency bands. Finally we demonstrate how our method can extract clinically-relevant neurophysiological features with greater statistical efficiency other established methods.