Rhythmicity of neuronal oscillations delineates their cortical and spectral architecture

The study addresses a central limitation in the analysis of neuronal oscillations: prevailing power spectral density (PSD) methods quantify amplitude but do not directly measure rhythmicity, i.e., the temporal stability of oscillatory phase. Neuronal oscillations underpin a wide range of cognitive functions and are implicated across neuropsychiatric and neurological disorders. However, amplitude-based approaches are qualitative indicators of rhythmicity and can be confounded by amplitude distributions, long-range temporal correlations, and non-Gaussian dynamics. The authors propose the phase-autocorrelation function (pACF) as a direct, amplitude-independent measure of rhythmicity that operates in the cycles domain and quantifies phase predictability across lags. The hypothesis is that explicit measurement of rhythmicity reveals a distinct cortical and spectral architecture, is functionally significant (e.g., prerequisite for long-range synchronization), and is dynamically modulated during event-related processing.

Prior work established that oscillations manifest in EEG/MEG and SEEG, with amplitude changes such as the “Berger effect” in alpha power with eyes closed vs open. PSD-based methods identify oscillations via peaks above the aperiodic 1/f component and can be parameterized (e.g., FOOOF) but do not quantify rhythmicity directly. Oscillation amplitudes often have heavy-tailed, non-Gaussian distributions and exhibit power-law long-range correlations, challenging Gaussian assumptions underlying some spectral interpretations. Frequency gradients across cortex have been reported (e.g., posterior-to-anterior increase of alpha peak), and oscillations are typically studied within canonical bands (theta/alpha/beta). Methods operating on signal power require manual selection of central frequencies and can be confounded by frequency leakage and amplitude fluctuations. While autocorrelation methods were historically used to quantify rhythmicity, modern analyses have emphasized PSD; extensions like lagged coherence can bias peak-frequency estimates. These considerations motivate an explicit phase-based rhythmicity measure.

Data: Resting-state SEEG (final cohort: 61 patients with drug-resistant focal epilepsy, non-epileptic zone contacts, ~10 min eyes-closed; 6945 gray-matter contacts) and MEG (resting state eyes-open: 54 healthy participants, 306-channel Triux system; separate eyes-open/closed cohort of 15; TSDT task MEG: 23 participants, 18 analyzed). MRI-based source modeling and Schaefer 400-parcel atlas were used for MEG. Preprocessing: SEEG referenced to closest white matter (cWM), FIR low-pass at 440 Hz; MEG tSSS (Maxfilter), low-pass at 249 Hz, notch for line noise, ICA to remove EOG/ECG/muscle artifacts. FreeSurfer for anatomy; MNE for head models and cortically constrained source modeling (5 mm spacing), fidelity-weighted inverse operators; source time series collapsed to parcels. Signal processing: Complex Morlet wavelets (7.5 cycles) provided narrow-band analytic signals for 81 log-spaced frequencies (2–100 Hz), with notch suppression of 50 Hz harmonics. Upper frequency ensured ≥10 samples per cycle. Phase autocorrelation (pACF): pACF(l) defined as expected cross-spectrum between a complex signal and its lagged copy, operationalized via Phase Locking Value (PLV) across lags from 0 to 20 cycles in 0.1-cycle steps. Instantaneous frequency correction was used to map lags to time samples (using mean instantaneous frequency) to avoid frequency-shifting bias. The pACF curve was normalized to explained variance across lags; rhythmicity lifetime defined non-parametrically as the first lag at which the cumulative function exceeds a threshold (0.9). Surrogate distributions (10,000 pink-noise realizations filtered identically) established frequency-specific significance thresholds (99th percentile; p≤0.01) accounting for filter-induced autocorrelations and scaling exponents. Spectral analyses and clustering: PSD spectra were decomposed into periodic and aperiodic components using FOOOF. pACF lifetime spectra across frequencies were computed per contact/parcel, and hierarchical clustering (Ward’s method) and deep NMF-based community detection grouped frequencies by similarity in anatomical patterns. Peak detection (SciPy) identified oscillatory peaks with minimum height at noise level, width ≥1 Hz, and inter-peak distance ≥3 Hz. Functional connectivity: Inter-areal phase synchrony estimated with PLV (SEEG) and weighted Phase Lag Index (wPLI; MEG). Node strength (mean synchrony with all others) was related to pACF rhythmicity. Modeling: A hierarchical Kuramoto model simulated cortical synchronization dynamics using HCP-derived structural connectomes (Schaefer 400-parcel resolution), with nodes comprising 500 oscillators each, intrinsic and inter-node coupling, and noise. Inter-node weights were log-transformed; K=10. Burstiness (stability index): npACF computed by normalizing pACF to noise-level pACF. The longest npACF segment above threshold (value 2) was extracted; quantiles Q1, Q2, Q3 computed; stability index SI=(Q3+Q1−2Q2)/(Q3−Q1). Simulations varied burst length (3–20 cycles) and inter-burst intervals (5–30 cycles) to validate SI. Time-resolved pACF: PLV computed in moving windows of 2.5 cycles between a signal and delayed versions (lags 1–3 cycles, 0.1-cycle increments), averaged over lags to yield time-frequency pACF representations. Statistics: Surrogate/permutation testing for significance of pACF lifetimes, correlations between pACF and synchrony, predictability of significant synchrony (tp/fn with thresholds: synchrony >3.42surrogate mean, p<0.001 Rayleigh; rhythmicity threshold at 95th percentile of noise pACF lifetime), and TSDT contrasts (10,000 label shuffles, F-max correction).

• Validation: Increasing simulated rhythmicity increased pACF lifetimes without changing power or wavelet amplitude; increasing power changed PSD and amplitudes while pACF lifetimes remained nearly constant, demonstrating amplitude-independent rhythmicity measurement.
• SEEG single-subject: Narrow-band significant rhythmicity detected at low-alpha (~7.9 Hz) and other bands; significant pACF lifetimes identified using p≤0.01 thresholds from surrogates.
• Spectral architecture: pACF spectra in SEEG formed narrow peaks predominantly in alpha and beta bands (e.g., peaks at 7.8 Hz and 22.9 Hz), with anatomical segregation and spectral sparsity (2–3 Hz width). PSD peaks were ~64% wider, elevated between peaks, and clustering of FOOOF’ed PSD did not recover pACF-defined clusters. PSD peak heights above 1/f were poorly correlated with pACF rhythmicity (Pearson r=0.06 at 7.8 Hz; r=−0.001 at 22.9 Hz).
• Population-level prevalence: Significant rhythmicity in theta-alpha bands observed in 29% of SEEG electrodes and 42% of MEG parcels; beta-band rhythmicity significant in 18% of SEEG electrodes and 18% of MEG parcels. Overall, 66% of SEEG contacts and 73% of MEG parcels exhibited oscillations (pACF-defined). Multi-band oscillations were less common: two peaks in 27% (SEEG) and 29% (MEG); >2 peaks in 11% (SEEG) and 7% (MEG).
• Anatomical organization: Highest prevalence of oscillations in dorsal attention, visual, and sensorimotor systems (70–80%); lowest in default and limbic systems and anterior frontal cortex. pACF delineated frequency communities (SEEG: prefrontal theta ~5.6 Hz; posterior low-alpha ~7.1 Hz; visual/sensorimotor high-alpha ~9.1 Hz; low beta ~16.9 Hz; mid beta ~25.5 Hz; high beta ~31.6 Hz). MEG showed co-localized tau/alpha/mu-like components (e.g., superior temporal low-alpha ~8.3 Hz; posterior alpha ~10.1 Hz; sensorimotor high-alpha and beta ~14.6 and ~26.0 Hz).
• Single vs multi-band: Single-band oscillations localized to occipital, temporal, and posterior parietal regions; multi-band most prevalent in central frontoparietal, sensorimotor, and dorsal attention systems. Alpha peak frequencies were significantly higher in multi-band vs single-band alpha oscillations (SEEG p=0.0005; MEG p=0.0001). Beta oscillations were more likely parts of multi-band oscillations (SEEG 26%; MEG 38%) than single-band (SEEG 9%; MEG 6%).
• Rhythmicity vs power: Across frequencies, PSD correlated more strongly with wavelet amplitude than with pACF. In eyes-closed vs eyes-open MEG, all metrics increased with eyes closed, but effect sizes at peak alpha were larger for pACF (Cohen’s d′=1.59) than amplitude (1.05) or PSD (0.76). Partial correlations showed PSD contrasts were more predicted by pACF (alpha 0.42; beta 0.49) than amplitude (alpha 0.28; beta 0.20), indicating the Berger effect reflects changes in rhythmicity more than amplitude.
• Synchronization prerequisite: In a hierarchical Kuramoto model, node strength (PLV) correlated with pACF (R²≈0.95 near central frequency). Empirically, node strengths correlated with pACF in SEEG alpha (6.5–9.5 Hz; R²≈0.57) and MEG alpha (8–13 Hz) and beta (18–26 Hz; R²≈0.87). Strong inter-areal phase synchrony occurred only when both nodes had high rhythmicity. Predictability of significant synchrony from both nodes’ rhythmicity exceeded surrogate levels in alpha (SEEG 6.5–9.5 Hz; MEG 8–13 Hz) and beta bands (SEEG 13–17 Hz; MEG 18–24 Hz).
• Burstiness (stability index): Simulations validated SI distinguishing stable (SI>0.05) vs bursty (SI<−0.05) signals. Cohort analyses showed theta/alpha bands (SEEG 6–11 Hz; MEG 7–15 Hz) had highest average SI and largest fractions of stable oscillations; beta exhibited more burst-like activity. In SEEG, limbic system had highest fraction of stable alpha and highest burst-like beta; MEG showed predominance of stable oscillations overall with relatively more burst-like in beta.
• Event-related modulation (TSDT): Time-resolved pACF revealed significant Hit–Miss differences in four time-frequency windows, with up to 39% of parcels showing significant contrasts. pACF indicated decreased rhythmicity/stability in low-alpha (7.5–10 Hz) in ~27% of recordings (control and attention systems) and decreased stability in beta (20–27 Hz) localized to somatomotor. pACF provided finer frequency resolution than induced responses and PLF, dissociating broadband non-oscillatory responses from genuine changes in oscillatoriness.

The findings demonstrate that rhythmicity, quantified via the phase-autocorrelation lifetime, is a distinct construct from amplitude and is double-dissociable in simulations and empirical SEEG/MEG data. pACF improves spectral and anatomical specificity, revealing narrow-band true oscillations and fine-grained frequency communities that power-based analyses blur. Rhythmicity explains classical functional phenomena (e.g., Berger effect) more strongly than amplitude, indicating functional relevance. Critically, strong inter-areal phase synchrony emerges predominantly among nodes with high rhythmicity, positioning rhythmicity as a mechanistic prerequisite for network communication. The pACF-based stability index captures burst-like vs sustained oscillations, uncovering system- and band-specific patterns (stable alpha, bursty beta). Event-related analyses show rhythmicity is dynamically modulated by task demands, offering complementary insights to amplitude and phase-locking measures by isolating changes in oscillatoriness from broadband activity.

This work introduces pACF as an amplitude-independent, cycle-domain measure of rhythmicity that delineates the cortical and spectral architecture of neuronal oscillations. pACF reveals sparse, narrow-band oscillations with distinct anatomical communities, shows that rhythmicity drives functional phenomena (e.g., Berger effect) and is a prerequisite for long-range synchronization, and enables characterization of burstiness as well as fine-grained event-related dynamics. These contributions suggest pACF as a versatile tool for multiscale neuroscience. Future research can apply pACF across diverse tasks and clinical populations, integrate with multimodal data (e.g., fMRI, DWI-based connectomes), refine thresholds and modeling for stability and burst detection, and probe causal mechanisms linking rhythmicity to cognition and pathology.

• SEEG cohort comprised patients with drug-resistant focal epilepsy (non-epileptic zones analyzed), which may limit generalizability relative to fully healthy populations.
• Wavelet-based narrow-band filtering induces autocorrelations; although surrogate-based thresholds and instantaneous-frequency correction mitigate biases, residual filter effects may influence pACF estimates.
• The choice of parameters (e.g., wavelet cycles, cumulative threshold at 0.9, npACF threshold for stability index) may affect lifetime and stability estimates; alternative parameterizations could yield different sensitivities.
• PSD vs pACF comparisons depend on specific decomposition and parameterization (e.g., FOOOF settings), potentially influencing the degree of observed dissociation.
• MEG source reconstruction and parcel collapsing introduce assumptions and potential spatial leakage; wPLI reduces volume-conduction bias but does not fully eliminate it.
• Data sharing restrictions (privacy) limit external replication with raw datasets, though code and derived data for reproducing main findings are available.