The amplitude-amplitude cross-frequency coupling method: a step-by-step guide to quantifying physiological network interactions.

Abstract

The human organism operates as an integrated network in which multiple physiological systems dynamically coordinate across spatial and temporal scales. Quantifying these interactions requires analytical frameworks that move beyond single-system measures and capture multisystem coordination. Here, we present a detailed, step-by-step description of the Amplitude-Amplitude Cross-Frequency Coupling (ACFC) method, a network-based approach designed to quantify coordination among skeletomuscular, cardiovascular, and respiratory systems using simultaneous electrophysiological recordings. ACFC evaluates how the amplitudes of oscillatory components across specific frequency bands co-vary over time, producing three network-based markers: inter-muscular, cardio-muscular, and respiratory-muscular coupling. The method combines spectral decomposition, cross-correlation analyses, and network dynamics to characterize global network organization and coupling strength for distinct physiological states, and the temporal variability in systems coordination and network interactions at short timescales. Beyond quantifying average coupling and network link strength over extended period of time associated with a given physiological state, ACFC enables probing the temporal coordination of physiological rhythms embedded in systems dynamics, as well as the variability and evolution of their network interactions across timescales and states in response to internal and external demands. Using a bodyweight squat protocol as an illustrative example, we outline all analytical steps, parameter choices, and practical considerations required to implement the ACFC method to quantify physiological systems coupling and network interactions. This Methods article provides a reproducible guide for applying ACFC analyses and is intended to facilitate the adoption, adaptation, and extension of network-based approaches to study multisystem coordination in exercise, aging, and broader physiological or clinical contexts in Network Physiology.