A Dynamic Mutual Information Measure of Phase-Amplitude Coupling With Uncertainty Quantification

Phase-amplitude coupling (PAC)-in which the phase of a low-frequency rhythm modulates the amplitude of a higher-frequency oscillation-is widely observed across the brain and linked to cognition and neurological disorders including Parkinson's disease, epilepsy, and depression. Standard PAC metrics aggregate over long windows and return a single summary statistic, obscuring transient structure. We introduce a dynamic PAC framework that captures fast, sample-level fluctuations in coupling strength while supporting multi-trial estimation and uncertainty quantification.

We develop a state space model with a latent Gaussian process for regression weights and a Gamma generalized linear model for measurements, yielding a mutual-information-based PAC measure at every time point. To tune key hyperparameters, we introduce an expectation-maximization (EM) algorithm using a Laplace-approximated posterior. We extend the framework to accommodate multi-trial analyses and derive Bayesian credible intervals for every PAC trajectory via the Laplace approximation.

On synthetic data with ground-truth time-varying coupling, the proposed method more accurately tracks rapid changes and discriminates coupled from uncoupled periods. Applied to human sleep EEG, the approach reliably detects PAC during spindle events and identifies repeatable coupling phenomena across trials.

This dynamic PAC framework provides a flexible, statistically grounded tool for basic and clinical neuroscience, with interpretable, smoothly evolving coupling trajectories and principled uncertainty estimates.

By enabling sample-level, uncertainty-aware PAC estimation, this framework may support biomarkers for neurophysiological disorders such as Alzheimer's disease and future applications in adaptive neurostimulation and brain-computer interfaces.