Spatio-temporal Granger causality: a new framework

TL;DR

This paper introduces a new spatio-temporal Granger causality framework that improves the estimation of directed information flow in time-varying physiological signals like fMRI, outperforming traditional methods.

Contribution

It redefines Granger causality as a global index for time-varying data and demonstrates its advantages through theoretical analysis and numerical examples.

Findings

Finer spatio-temporal scales yield more accurate causality estimates.

The new framework outperforms traditional methods in consistency across scans.

Granger causality increases monotonically with temporal resolution.

Abstract

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger causality from fMRI, EEG, and other related data.