Need of causal analysis for assessing phase relationships in closed loop interacting cardiovascular variability series

The phase spectra obtained by the classical closed loop autoregressive model (2AR) and by an open loop autoregressive model (ARXAR) were compared to shed light on the need of introducing causality in the assessment of the delay between RR and arterial pressure oscillations. The reliability of the two approaches was tested in simulation and real data setting. In simulation, the coupling strength of a bivariate closed loop process was adjusted to obtain a range of working conditions from open to closed loop. In open loop condition, 2AR and ARXAR phases were comparable and in agreement with the imposed delay. In closed loop condition, ARXAR model returned the imposed delays, while 2AR showed an intermediate value of delay. Real data were chosen to represent comparable physiological condition. The use of cross spectrum for calculating the delay from arterial pressure to RR oscillations seems adequate only in particular condition of open-loop relationship as it happens during head up tilt in young healthy subjects.