A Dynamical Systems and System Identification Framework for Phase Amplitude Coupling Analysis

TL;DR

This paper introduces a novel dynamical systems-based method for detecting and characterizing phase-amplitude coupling (PAC) in neural signals, addressing limitations of existing techniques by improving robustness and interpretability.

Contribution

It proposes a nonlinear system identification approach for PAC analysis that captures underlying dynamics and reduces false detections, enhancing accuracy over traditional methods.

Findings

Method accurately detects PAC in simulated data

Robust to noise and power variations in real data

Outperforms existing PAC detection techniques

Abstract

Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is essential for understanding its role in processes such as memory and attention. However, this remains a significant challenge. Most existing methods rely on variations in the temporal profile to detect PAC, but they often suffer from key limitations, most notably, their sensitivity to filter bandwidth selection and their susceptibility to detecting spurious couplings. Previous studies have suggested that approaches grounded in the actual generative dynamics of PAC may offer improved accuracy. In this study, we adopt a dynamical systems perspective and propose a novel method for PAC detection and characterisation based on nonlinear system identification. This approach involves identifying a nonlinear dynamical model that captures the temporal dynamics underlying PAC. The resulting generative model enables noise-free simulation of estimated PAC signals, facilitating detailed analysis of modulation strength and the low-frequency phase at which the high-frequency bursts occur. The proposed method accounts for harmonic-induced spurious couplings through empirically derived criteria and remains robust to high noise levels and variations in slow-frequency power, offering an accurate and interpretable framework for PAC analysis. The performance of the proposed approach is illustrated using several simulated examples and a real case using local field potentials (LFP) data. The results are compared with several popular methods.