Dissecting Spectral Granger Causality Through Partial Information Decomposition

Granger causality (GC), a popular statistical method for the inference of directional influences between time series measured from a complex network, is sensitive to high-order (non-pairwise) interactions which fundamentally shape the collective network dynamics. This work introduces Partial Decomposition of Granger Causality (PDGC), a tool to elicit redundant and synergistic causal interactions among the subsystems of physiological networks.

We use the framework of partial information decomposition to dissect the multivariate GC from a set of driver random processes to a target process into unique effects carried exclusively by each driver, redundant effects carried identically by more drivers, and synergistic effects carried jointly by some drivers but not by any of them individually. Computation is based on multivariate state-space models expanded in the frequency domain to assess PDGC both in specific bands and in the time domain after whole-band integration.

The validation on benchmark simulations demonstrates that the measures of unique, redundant, and synergistic GC reflect the underlying causal mechanisms and are computationally reliable. The application to arterial pressure, respiration, cerebral blood velocity and heart period variability reveals striking differences in the response to postural stress of patients prone to neurally-mediated syncope compared to healthy controls.

PDGC elicits unprecedented modes of physiological interaction, related to the sympathetic control of low-frequency cardiovascular and cerebrovascular oscillations, characterizing distinctive patterns of autonomic dysfunction.

The extraction of high-order causality patterns from the spectral GC allows dissecting the mechanisms of causal influence underlying multivariate physiological interactions, potentially providing new biomarkers for the assessment of patho-physiological states.