Inclusion of instantaneous influences in the spectral decomposition of causality: Application to the control mechanisms of heart rate variability

Heart rate variability is the result of several physiological regulation mechanisms, including cardiovascular and cardiorespiratory interactions. Since instantaneous influences occurring within the same cardiac beat are commonplace in this regulation, their inclusion is mandatory to get a realistic model of physiological causal interactions. Here we exploit a recently proposed framework for the spectral decomposition of causal influences between autoregressive processes [2] and generalize it by introducing instantaneous couplings in the vector autoregressive model (VAR). We show the effectiveness of the proposed approach on a toy model, and on real data consisting of heart period (RR), systolic pressure (SAP) and respiration (RESP) variability series measured in healthy subjects in baseline and head up tilt conditions. In particular, we show that our framework allows one to highlight patterns of frequency domain causality that are consistent with well-interpretable physiological interaction mechanisms like the weakening of respiratory sinus arrhythmia at high frequencies and the activation of the baroreflex control at lower frequencies, in response to postural stress.