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

Abstract

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 population-level 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 ill-informed 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. We also show that our method can automatically identify subject-level variations in frequency to overcome the limitations of fixed canonical frequency bands.

Novel Cyclic Homogeneous Oscillation Detection Method for High Accuracy and Specific Characterization of Neural Dynamics

“…However, because our CHO method is modular, the FFT-based time-frequency analysis can be replaced with more sophisticated time-frequency estimation methods to improve the sensitivity of neural oscillation detection. Specifically, a state-space model ( Matsuda and Komaki, 2017 ; Beck et al, 2022 ; Brady and Bardouille, 2022 ; He et al, 2023 ) or empirical mode decomposition (EMD, Fabus et al 2022 ; Quinn et al 2021 ) may improve the estimation of the auto-correlation of the harmonic structure underlying non-sinusoidal oscillations. Furthermore, a Gabor transform or matching pursuit-based approach may improve the onset/offset detection of short burst-like neural oscillations ( Kuś et al, 2013 ; Morales and Bowers, 2022 ).…”

Switching state-space modeling of neural signal dynamics

“…Parameters in state-space models of the form in Eq 37 can be subjected to prior distributions to yield MAP instead of ML estimation. We followed [90] to impose priors on the rotation frequency, ω , and the state- and observation-noise variances, σ 2 and R (see S3 Appendix). We used these MAP estimates throughout all the M-steps that involve updating the Gaussian SSM parameters and the observation noise variance.…”

“…We accomplished this by fitting two oscillators (one in slow frequency range, the other in spindle frequency range) to the EEG time series, assuming that both oscillations are present for the entire duration. This fitting was done using a standard EM algorithm [71,90] with the parameters initialized based on our prior knowledge of the typical frequencies of these sleep oscillations: a δ = 0.98 ω δ = 2π 1 Hz 100 Hz (σ 2 ) δ = 1 a ς = 0.98 ω ς = 2π 13 Hz 100 Hz (σ 2 ) ς = 1.…”

A dynamic generative model can extract interpretable oscillatory components from multichannel neurophysiological recordings

“…Multiple oscillations can be readily incorporated in this state space model by simply considering their linear combination. Recently, several investigators [27][28][29] have utilized this state space representation to extract underlying oscillatory time courses from single channel EEG time traces.…”