Bivariate nonlinear prediction to quantify the strength of complex dynamical interactions in short-term cardiovascular variability

A nonlinear prediction method for investigating the dynamic interdependence between short length time series is presented. The method is a generalization to bivariate prediction of the univariate approach based on nearest neighbor local linear approximation. Given the input and output series x and y, the relationship between a pattern of samples of x and a synchronous sample of y was approximated with a linear polynomial whose coefficients were estimated from an equation system including the nearest neighbor patterns in x and the corresponding samples in y. To avoid overfitting and waste of data, the training and testing stages of the prediction were designed through a specific out-of-sample cross validation. The robustness of the method was assessed on short realizations of simulated processes interacting either linearly or nonlinearly. The predictor was then used to characterize the dynamical interaction between the short-term spontaneous fluctuations of heart period (RR interval) and systolic arterial pressure (SAP) in healthy young subjects. In the supine position, the predictability of RR given SAP was low and influenced by nonlinear dynamics. After head-up tilt the predictability increased significantly and was mostly due to linear dynamics. These findings were related to the larger involvement of the baroreflex regulation from SAP to RR in upright than in supine humans, and to the simplification of the RR–SAP coupling occurring with the tilt-induced alteration of the neural regulation of the cardiovascular rhythms.