Granger causality in cardiovascular variability series: comparison between model-based and model-free approaches

A linear model-based (MB) approach for the evaluation of Granger causality is compared to a nonlinear model-free (MF) one. The MB method is based on the identification of the coefficients of a multivariate linear regression via least-squares procedure. The MF technique is grounded on the concept of local prediction and exploits the k-nearest-neighbors approach. Both the methods optimize the multivariate embedding dimension but MF technique is more parsimonious since the number of components taken from each signal can be different. Both methods were applied to the variability series of heart period (HP), systolic arterial pressure (SAP) and respiration (R) recorded during spontaneous and controlled respiration at 15 breaths/minute (SR and RC15) in 19 healthy humans. Both MB and MF methods revealed the increase of HP predictability during RC15 and the unmodified causality from SAP to HP and from R to HP during RC15, thus suggesting that nonlinear methods are not superior to the linear ones in assessing predictability and causality in healthy humans.