Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics

Abstract

Non-sinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time-series using masked Empirical Mode Decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency and phase) using instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase-grid space, makes it possible to compare cycles of different durations and shapes. 'Normalised shapes' can then be constructed with high temporal detail whilst accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks non-sinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average, yet exhibiting high variability on a cycle-by-cycle basis. We show how Principal Components Analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of enquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.

Automatic decomposition of electrophysiological data into distinct nonsinusoidal oscillatory modes

“…There is however increasing recognition that individual bursts and cycles may give us additional information about the brain's functions (16,17). As such, we recommend making use of trial-specific information EMD produces, such as building a General Linear Model with the instantaneous frequency and amplitude associated with each cycle (see (11) for an example of such an analysis and Figure 7D-G to compare HHT with a wavelet transform).…”

“…The IMFs are constructed to have locally symmetric upper and lower envelopes with no peaks below zero or troughs above zero. A smooth signal with these features is well-behaved during instantaneous frequency analysis, allowing for a full description of nonsinusoidal waveform shape ( 11 ).…”

“…Unlike Fourier or wavelet methods, EMD does not a priori assume the shape of its functions. It is, therefore, believed that IMFs can capture nonsinusoidal oscillations and may better reflect the underlying processes in physical and physiological signals ( 3 , 10 , 11 ). This can especially aid analyses sensitive to waveform shape, such as calculations of phase and cross-frequency coupling ( 4 , 12 ).…”

“…Mask frequency selection can be done semiautomatically by choosing an initial frequency based on the number of zero-crossings in the first IMF and dividing this successively by two for later IMFs ( 21 ). If the approximate frequency content of the signal is known, then mask frequencies may be directly selected to isolate the specific components of interest ( 11 ). Though effective, the semiautomatic method is relatively inflexible, and the direct specification method can be manually intensive to validate.…”

An Impending Paradigm Shift in Motor Imagery Based Brain-Computer Interfaces

“…This activity is typically analyzed using time-frequency decomposition techniques, which assume that the underlying signal is sinusoidal. However, there is now growing consensus that oscillatory neural activity is often non-sinusoidal ( Cole and Voytek, 2017 , 2019 ; Donoghue et al, 2021 ; Fabus et al, 2021 ), and that the raw waveform shape can be informative of movement ( Quinn et al, 2021 ; Figure 2 ). Future efforts could take advantage of this possibility by using recently developed non-parametric cycle-by-cycle analyzes ( Cole and Voytek, 2019 ).…”