[Paper Review] Distinct criticality of phase and amplitude dynamics in the resting brain

Robert Ton, Gustavo Deco+3 more|arXiv (Cornell University)|Dec 8, 2015

Neural dynamics and brain function43 references3 citations

TL;DR

This study investigates criticality in the human resting brain by analyzing power-law scaling in amplitude and phase dynamics of magnetoencephalographic (MEG) signals. Using source-reconstructed MEG data from 10 subjects, it reveals that amplitude fluctuations exhibit persistent, slow-decaying correlations (Hurst exponent H ≈ 0.7), indicating long-term memory, while phase synchronization shows more complex, less structured correlations (H ≈ 0.6), suggesting fast, flexible coding—highlighting distinct functional roles for amplitude and phase in cortical information processing.

ABSTRACT

Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase fluctuations, which may reflect different aspects of cortical functioning. Using source-reconstructed magneto-encephalographic signals, we found power-law scaling for the collective amplitude and for phase synchronization, both capturing whole-brain activity. The temporal changes of the amplitude comprise slow, persistent memory processes, whereas phase synchronization exhibits less temporally structured and more complex correlations, indicating a fast and flexible coding. This distinct temporal scaling supports the idea of different roles of amplitude and phase in cortical functioning.

Motivation & Objective

• To investigate whether amplitude and phase dynamics in the resting brain exhibit different scaling properties, reflecting distinct functional roles in cortical processing.
• To determine if global amplitude and phase synchronization in MEG signals display power-law scaling, indicating criticality.
• To compare the temporal structure of amplitude and phase dynamics to assess their respective roles in information encoding and memory.
• To evaluate whether the observed scaling behavior is robust to volume conduction and reflects intrinsic neural dynamics rather than signal artifacts.

Proposed method

• Source-reconstructed MEG signals from 10 subjects in eyes-closed resting state were analyzed at 250 Hz, with data downsampled and beamformed onto a 90-node brain parcellation.
• Alpha (8–12 Hz) and beta (20–30 Hz) band signals were extracted using bandpass filtering, and the Hilbert transform was applied to compute instantaneous phase and amplitude for each node.
• Global collective variables were defined: phase synchronization (R(t,f)) as the magnitude of the Kuramoto order parameter, and mean amplitude (A(t,f)) as the average across all nodes.
• Z-scoring of R(t,f) and A(t,f) across subjects enabled group-level analysis by reducing inter-individual variability.
• Detrended fluctuation analysis (DFA) was applied to quantify long-range temporal correlations, estimating the Hurst exponent H as a measure of scaling behavior.
• Additional analysis focused on slow amplitude dynamics by extracting low-frequency components of amplitude envelopes, defining new collective variables R^(a)(t,f) and A^(a)(t,f) for further comparison.

Experimental results

Research questions

• RQ1 Do amplitude and phase dynamics in the resting brain exhibit different power-law scaling behaviors?
• RQ2 How do the scaling exponents of amplitude and phase synchronization compare, and what do they imply about their functional roles?
• RQ3 Is the observed power-law scaling robust to volume conduction effects, which can confound encephalographic signal interpretation?
• RQ4 To what extent do amplitude and phase dynamics reflect distinct temporal memory structures—persistent vs. flexible coding?
• RQ5 Can global measures of amplitude and phase synchronization reveal whole-brain criticality in resting-state brain activity?

Key findings

• Amplitude dynamics exhibit strong, persistent long-range temporal correlations with a Hurst exponent H ≈ 0.7, indicating slow decay and high predictability.
• Phase synchronization shows less persistent correlations with H ≈ 0.6, suggesting a more complex, rapidly changing correlation structure.
• The distinct scaling exponents indicate that amplitude dynamics support long-term memory coding, while phase dynamics enable fast, flexible information processing.
• The observed power-law scaling is robust to volume conduction, as linear mixing does not alter the presence of power-law behavior in signals.
• Both amplitude and phase dynamics display power-law scaling over hundreds of seconds, supporting the hypothesis that the brain operates near a critical state.
• The results demonstrate that amplitude and phase dynamics are not interchangeable in information processing, with amplitude reflecting slow, stable states and phase reflecting dynamic, adaptive states.