A Framework for the Time- and Frequency-Domain Assessment of High-Order Interactions in Brain and Physiological Networks

TL;DR

This paper introduces the O-information rate (OIR), a new metric for quantifying high-order interactions in multivariate rhythmic processes across multiple time scales, with applications in neuroscience and physiology.

Contribution

It presents a novel framework to decompose and analyze high-order interactions in time and frequency domains using spectral representations of models.

Findings

Spectral OIR highlights frequency-specific redundant and synergistic interactions.

Application to physiological data reveals circuits related to cardiovascular oscillations.

Application to brain signals identifies rhythms linked to consciousness and anesthesia.

Abstract

While the standard network description of complex systems is based on quantifying links between pairs of system units, higher-order interactions (HOIs) involving three or more units play a major role in governing the collective network behavior. This work introduces an approach to quantify pairwise and HOIs for multivariate rhythmic processes interacting across multiple time scales. We define the so-called O-information rate (OIR) as a new metric to assess HOIs for multivariate time series, and propose a framework to decompose it into measures quantifying Granger-causal and instantaneous influences, as well as to expand it in the frequency domain. The framework exploits the spectral representation of vector autoregressive and state-space models to assess synergistic and redundant interactions among groups of processes, both in specific bands and in the time domain after whole-band integration. Validation on simulated networks illustrates how the spectral OIR can highlight redundant and synergistic HOIs emerging at specific frequencies but not using time-domain measures. The application to physiological networks described by heart period, arterial pressure and respiration measured in healthy subjects during paced breathing, and to brain networks described by ECoG signals acquired in an animal experiment during anesthesia, document the capability of our approach to identify informational circuits relevant to well-defined cardiovascular oscillations and brain rhythms and related to specific physiological mechanisms of autonomic control and altered consciousness. The proposed framework allows a hierarchically-organized evaluation of time- and frequency-domain interactions in networks mapped by multivariate time series, and its high flexibility and scalability make it suitable to investigate networks beyond pairwise interactions in neuroscience, physiology and other fields.