Mutual information function assesses autonomic information flow of heart rate dynamics at different time scales

The autonomic information flow (AIF) represents the complex communication within the Autonomic Nervous System (ANS). It can be assessed by the mutual information function (MIF) of heart rate fluctuations (HRF). The complexity of HRF is based on several interacting physiological mechanisms operating at different time scales. Therefore one prominent time scale for HRF complexity analysis is not given a priori. The MIF reflects the information flow at different time scales. This approach is defined and evaluated in the present paper. In order to aggregate relevant physiological time scales, the MIF of HRF obtained from eight adult Lewis rats during the awake state, under general anesthesia, with additional vagotomy, and additional beta1-adrenergic blockade are investigated. Physiologically relevant measures of the MIF were assessed with regard to the discrimination of these states. A simulation study of a periodically excited pendulum is performed to clarify the influence of the time scale of MIF in comparison to the Kolmogorov Sinai entropy (KSE) of that well defined system. The general relevance of the presented AIF approach was confirmed by comparing mutual information, approximate entropy, and sample entropy at their respective time scales.