  Heart rate variability results from the combined activity of several
physiological systems, including the cardiac, vascular, and respiratory systems
which have their own internal regulation, but also interact with each other to
preserve the homeostatic function. These control mechanisms operate across
multiple temporal scales, resulting in the simultaneous presence of short-term
dynamics and long-range correlations. The Network Physiology framework provides
statistical tools based on information theory able to quantify structural
aspects of multivariate and multiscale interconnected mechanisms driving the
dynamics of complex physiological networks. In this work, the multiscale
representation of Transfer Entropy from Systolic Arterial Pressure (S) and
Respiration (R) to Heart Period (H) and of its decomposition into unique,
redundant and synergistic contributions is obtained using a Vector
AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian
processes. This novel approach allows to quantify the directed information flow
accounting for the simultaneous presence of short-term dynamics and long-range
correlations among the analyzed processes. The approach is first illustrated in
simulated VARFI processes and then applied to H, S and R time series measured
in healthy subjects monitored at rest and during mental and postural stress.
Our results highlight the dependence of the information transfer on the balance
between short-term and long-range correlations in coupled dynamical systems,
which cannot be observed using standard methods that do not consider long-range
correlations. The proposed methodology shows that postural stress induces
larger redundant effects at short time scales and mental stress induces larger
cardiovascular information transfer at longer time scales.
