Canonical Granger causality between regions of interest

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure, termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Stiefel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortexes in cases where standard Granger causality is unable to identify statistically significant interactions.