Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions

We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral interaction between the two series, unbalanced towards the mechanical direction at rest and balanced after tilt. The utilization of linear AR and ARX models led to higher prediction accuracy but comparable trends of predictability and causality measures.