A Dynamic Mutual Information Measure of Phase Amplitude Coupling.

Phase-amplitude coupling (PAC) is a fundamental neural phenomenon in which the phase of a slow oscillation modulates the amplitude of a faster oscillation. PAC has been implicated in various cognitive and clinical conditions, including Parkinson's disease, epilepsy, and depression. Traditional methods for quantifying PAC compute a single summary statistic over an entire time series, limiting their ability to capture dynamic fluctuations. Growing interest in time-varying PAC has led to methods that rely on windowed time-series analysis, but these approaches struggle to track rapid changes in coupling at single-sample resolution. To address this limitation, we propose a novel dynamic mutual information measure of PAC, leveraging a state-space modeling approach based on a Gamma generalized linear model (GLM). By introducing a Gauss-Markov process on the regression weights, our method enables dynamic, interpretable PAC estimation at each time point. We validate our approach using synthetic phase-amplitude coupled signals with time-varying coupling coefficients and demonstrate superior performance in smoothly tracking PAC over time and distinguishing coupled from uncoupled states. Additionally, we apply our technique to sleep EEG data, successfully identifying PAC during sleep spindles, which may serve as a biomarker for neurophysiological conditions such as Alzheimer's disease. Our findings suggest that this dynamic PAC measure is a powerful tool for neuroscientific and clinical research, with potential applications in real-time brain-computer interfaces and neurostimulation protocols.Clinical relevanceThis work demonstrates a new technique for quantifying time-varying electrophysiological coupling. This may allow for understanding transient neural dynamics in disease states and may help more robustly inform electrical stimulation protocols for patients with neurodegenerative disorders.