Instantaneous transfer entropy for the study of cardio-respiratory dynamics

Measures of transfer entropy have been proposed to quantify the directional coupling and strength between two complex physiological variables. Particular attention has been given to nonlinear interactions within cardiovascular and respiratory dynamics as influenced by the autonomic nervous system. However, standard transfer entropy estimates have shown major limitations in dealing with issues concerning stochastic system modeling, limited observations in time, and the assumption of stationarity of the considered physiological variables. Moreover, standard estimates are unable to track time-varying changes in nonlinear coupling with high resolution in time. Here, we propose a novel definition of transfer entropy linked to inhomogeneous point-process theory. Heartbeat and respiratory dynamics are characterized through discrete time series, and modeled through probability density functions (PDFs) which characterize and predict the time until the occurrence of the next physiological event as a function of the past history. As the derived measures of entropy are instantaneously defined through continuos PDFs, a novel index (the Instantaneous point-process Transfer Entropy, ipT ransfEn) is able to provide instantaneous tracking of the information transfer. The new measure is tested on experimental data gathered from 16 healthy subjects undergoing postural changes, showing fast tracking of the tilting events and low variability during the standing phase.