Lag-specific transfer entropy as a tool to assess cardiovascular and cardiorespiratory information transfer.

In the study of interacting physiological systems, model-free tools for time series analysis are fundamental to provide a proper description of how the coupling among systems arises from the multiple involved regulatory mechanisms. This study presents an approach which evaluates direction, magnitude, and exact timing of the information transfer between two time series belonging to a multivariate dataset. The approach performs a decomposition of the well-known transfer entropy (TE) which achieves 1) identifying, according to a lag-specific information-theoretic formulation of the concept of Granger causality, the set of time lags associated with significant information transfer, and 2) assigning to these delays an amount of information transfer such that the total contribution yields the aggregate TE. The approach is first validated on realizations of simulated linear and nonlinear multivariate processes interacting at different time lags and with different strength, reporting a high accuracy in the detection of imposed delays, and showing that the estimated lag-specific TE follows the imposed coupling strength. The subsequent application to heart period, systolic arterial pressure and respiration variability series measured from healthy subjects during a tilt test protocol illustrated how the proposed approach quantifies the modifications in the involvement and latency of important mechanisms of short-term physiological regulation, like the baroreflex and the respiratory sinus arrhythmia, induced by the orthostatic stress.