Mutual nonlinear prediction of cardiovascular variability series: comparison between exogenous and autoregressive exogenous models

A model-based approach to perform mutual nonlinear prediction of short cardiovascular variability series is presented. The approach is based on identifying exogenous (X) and autoregressive exogenous (ARX) models by K-nearest neighbors local linear approximation, and estimates the predictability of a series given the other as the squared correlation between original and predicted values of the series. The method was first tested on simulations reproducing different types of interaction between non-identical Henon maps, and then applied to heart rate (HR) and blood pressure (BP) variability series measured in healthy subjects at rest and after head-up tilt. Simulations showed that different coupling conditions were always detected by the X model but not by the ARX model. The comparison between X and ARX models suggested the presence of oscillatory sources determining the regularity of HR and BP dynamics independently of their closed-loop mutual regulation. The transition from supine to upright position was associated with an enhancement of the HR and BP mutual regulation, compatible with the activation of the sympathetic nervous system induced by tilt.