Linear and non-linear brain–heart and brain–brain interactions during sleep

In this study, the physiological networks underlying the joint modulation of the parasympathetic component of heart rate variability (HRV) and of the different electroencephalographic (EEG) rhythms during sleep were assessed using two popular measures of directed interaction in multivariate time series, namely Granger causality (GC) and transfer entropy (TE).Time series representative of cardiac and brain activities were obtained in 10 young healthy subjects as the normalized high frequency (HF) component of HRV and EEG power in the δ, θ, α, σ, and β bands, measured during the whole duration of sleep.The magnitude and statistical significance of GC and TE were evaluated between each pair of series, conditional on the remaining series, using respectively a linear model-based approach exploiting regression models, and a nonlinear model-free approach combining nearestneighbor entropy estimation with a procedure for dimensionality reduction.The contribution of nonlinear dynamics to the TE was also assessed using surrogate data.GC and TE consistently detected structured networks of physiological interactions, with links directed predominantly from HRV to the EEG waves in the brain-heart network, and from the σ and β EEG waves to the δ, θ, and α waves in the brain-brain network.While these common patterns supported the suitability of a linear model-based analysis, we also found a significant contribution of nonlinear dynamics, particularly involving the information transferred out of the δ node in the two networks.This suggested the importance of nonparametric TE estimation for evidencing the fine structure of the physiological networks underlying the autonomic regulation of cardiac and brain functions during sleep.