Assessment of connectivity patterns from multivariate time series by partial directed coherence

In nature connectivity between systems is a rule rather than an exception. Accordingly, for the analysis of complex physiological or biological systems, a crucial and important problem is to identify the underlying pattern of connectivity between constituent subsystems of a complex system or between multiple complex systems. In real-life this pattern may be transient, dynamic, non-random, or directed. These features cannot easily be detected by the linear measures of synchronization, such as correlation or magnitude squared coherence, nor by the nonlinear measures which are based on phase/generalized synchronization. In this paper, we considered a measure, termed partial directed coherence (PDC), to investigate the connectivity pattern from multivariate signals. PDC is conceptually related to Granger causality, a statistical measure of causality based on comparative prediction. We initially evaluated the performance of PDC by simulated networks of linear and nonlinear chaotic systems and found that PDC is able to detect asymmetrical coupling and directional information flows in a network. We next applied the PDC measure on recorded multivariate EEG signals during an alternative forced choice task involving preferential or non-preferential decision. As compared to non-preferential decision, preferential decision showed a stronger long-range connectivity between posterior-anterior cortical regions at 800 ms before the decision, which is in accordance with a previous psychophysical study.