Extended Granger causality: a new tool to identify the structure of physiological networks.

Granger causality (GC) is a very popular tool for assessing the presence of directional interactions between two time series of a multivariate data set. In its original formulation, GC does not account for zero-lag correlations possibly existing between the observed time series. In the present study we compare the GC with a novel measure, termed extended GC (eGC), able to capture instantaneous causal relationships. We present a two-step procedure for the practical estimation of eGC based on first detecting the existence of zero-lag correlations, and then assigning them to one of the two possible causal directions using pairwise measures of non-Gaussianity. The proposed method was validated in a simulation study, showing that the estimation procedure based on the extended representation overcomes the limits of the classic computation of GC, correctly detecting the presence and direction of zero-lag interactions and providing a meaningful causal interpretation based on the eGC. Then, GC and eGC were computed on the physiological variability series of heart period (HP), mean arterial pressure (AP) and cerebral blood flow velocity (FV) in ten subjects with postural related syncope (PRS), during different epochs of an head-up tilt test protocol. We found that both measures reflect the baroreflex impairment and the loss of cerebral autoregulation during pre-syncope. Furthermore, eGC analysis suggests that fast, within-beat effects between AP and FV variability contribute substantially to the mutual regulation of these physiological variables, and may play an important role in the impairment of cerebrovascular regulation associated with PRS.