Dynamic causal modelling of phase-amplitude interactions

TL;DR

This paper extends dynamic causal modelling to include both phase and amplitude of neural oscillations, improving the understanding of neural connectivity especially in strongly coupled systems, with validation on simulated and real neuroimaging data.

Contribution

It introduces a phase-amplitude model for neural interactions, surpassing phase-only models in describing complex, strongly coupled neural systems.

Findings

Phase-amplitude models outperform phase-only models in strongly coupled systems.

Amplitudes significantly contribute to neural dynamics in anesthetized brain states.

The model effectively captures multiple neuroimaging metrics.

Abstract

Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that interactions can be described purely in terms of phase differences. Whilst mathematically convenient, the restrictive nature of phase-only models can limit their explanatory power. We therefore propose a generalisation of dynamic causal modelling that incorporates both phase and amplitude. This allows for the separate quantifications of phase and amplitude contributions to the connectivity between neural regions. We establish, using model-generated data and simulations of coupled pendula, that phase-only models perform well only under weak coupling conditions. We also show that, despite their higher complexity, phase-amplitude models can describe strongly coupled systems more effectively than their phase-only counterparts. We relate our findings to four metrics commonly used in neuroimaging: the Kuramoto order parameter, cross-correlation, phase-lag index, and spectral entropy. We find that, with the exception of spectral entropy, the phase-amplitude model is able to capture all metrics more effectively than the phase-only model. We then demonstrate, using local field potential recordings in rodents and functional magnetic resonance imaging in macaque monkeys, that amplitudes in oscillator models play an important role in describing neural dynamics in anaesthetised brain states.