Reconstruction of phase-amplitude dynamics from electrophysiological signals

TL;DR

This paper introduces a new method to reconstruct phase-amplitude dynamics from electrophysiological signals, enabling better estimation of inter-regional brain coupling using Koopman operator-based transformations.

Contribution

It combines phase-amplitude reduction techniques with Koopman operator eigenfunction estimation to directly reconstruct coupled oscillatory systems from electrophysiological data.

Findings

Successfully reconstructs phase-amplitude dynamics from signals.

Provides a framework for estimating coupling functions between brain regions.

Enhances understanding of neural oscillatory interactions.

Abstract

We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates.