Session SA2.1

Linear and Nonlinear Parametric Model Identification to Assess Granger Causality in Short-Term Cardiovascular Interactions

L Faes, G Nollo*, KH Chon

Università di Trento
Trento, Italy

This work was aimed to assess directional relationships between short heart period (HP) and systolic pressure (SP) variability series according to the concept of Granger causality. We quantified causality as the predictability improvement (PI) of a time series obtained when samples of another series were used for prediction, i.e. moving from autoregressive (AR) prediction to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models, taking the mean squared prediction error as a measure of predictability. Model identification was performed by the optimal parameter search, a recently proposed algorithm allowing accurate coefficient estimation and appropriate model order selection. The approach was validated on simulations involving short realizations of linear and nonlinear time series in which different conditions of interactions were imposed, showing the ability of PI to detect the nature of the coupling (unidirectional or bidirectional) and to reflect the coupling strength in each causal direction. It was then applied on HP and SP series measured from 15 young healthy subjects in the resting supine position and after 60º head-up tilt, yielding measures of the causal coupling from SP to HP (PIh|s) and from HP to SP (PIs|h). Using nonlinear parametric models we found a bilateral causal relationship between the two series, unbalanced towards the HP to SP direction at rest (PIh|s=0.33±0.19; PIs|h=0.46±0.09, p<0.05) and balanced after tilt (PIh|s=0.42±0.08; PIs|h=0.42±0.14). The utilization of linear AR and ARX models led to higher prediction errors and PI values (rest: PIh|s=0.22±0.11, PIs|h=0.31±0.09, p<0.05; tilt: PIh|s=0.25±0.06, PIs|h=0.30±0.10), suggesting that a nonlinear model could be more appropriate to describe HP-SP causality. The reported results were well interpretable according to the known cardiovascular physiology: the difference between PIh|s and PIs|h at rest suggests an unbalancing of the cardiovascular regulation in the supine position with prevalence of the mechanical causal influences from HP to SP, while the increase of PIh|s moving from the supine to the upright position was ascribed to the tilt-induced sympathetic activation.

(Abstract Control Number: 198)