Abstract
A full decomposition of the predictive entropy (PE) of the spontaneous variations of the heart period (HP) given systolic arterial pressure (SAP) and respiration (R) is proposed. The PE of HP is decomposed into the joint transfer entropy (JTE) from SAP and R to HP and self-entropy (SE) of HP. The SE is the sum of three terms quantifying the synergistic/redundant contributions of HP and SAP, when taken individually and jointly, to SE and one term conditioned on HP and SAP denoted as the conditional SE (CSE) of HP given SAP and R. The JTE from SAP and R to HP is the sum of two terms attributable to SAP or R plus an extra term describing the redundant/synergistic contribution to the JTE. All quantities were computed during cardiopulmonary loading induced by −25° head-down tilt (HDT) via a multivariate linear regression approach. We found that: (i) the PE of HP decreases during HDT; (ii) the decrease of PE is attributable to a lessening of SE of HP, while the JTE from SAP and R to HP remains constant; (iii) the SE of HP is dominant over the JTE from SAP and R to HP and the CSE of HP given SAP and R is prevailing over the SE of HP due to SAP and R both in supine position and during HDT; (iv) all terms of the decompositions of JTE from SAP and R to HP and SE of HP due to SAP and R were not affected by HDT; (v) the decrease of the SE of HP during HDT was attributed to the reduction of the CSE of HP given SAP and R; (vi) redundancy of SAP and R is prevailing over synergy in the information transferred into HP both in supine position and during HDT, while in the HP information storage synergy and redundancy are more balanced. The approach suggests that the larger complexity of the cardiac control during HDT is unrelated to the baroreflex control and cardiopulmonary reflexes and may be related to central commands and/or modifications of the dynamical properties of the sinus node.
Highlights
Head-down tilt (HDT) is an experimental maneuver inducing an increase of the venous return, central blood volume, and central venous pressure (London et al, 1983; Nagaya et al, 1995)
The methodological findings of this study can be summarized as follows: (i) the study proposes a full decomposition of predictive entropy (PE) of y in = {y,x1,x2} that includes the decomposition of SE of y in addition to the known decomposition of joint transfer entropy (JTE) from x1 and x2 to y; (ii) both JTE and SE decompositions include a term are the three synergistic/redundant terms of the SEHP decomposition according to Equation (22)
Describing redundancy/synergy of x1 and x2 in contributing to the information carried by y and the redundant/synergistic term of SE has a more complex structure; (iii) the utility of the JTE and SE decompositions is demonstrated in the field of cardiovascular control analysis to disentangle physiological mechanisms from spontaneous variations and clarify the origin of the increase of respiratory sinus arrhythmia during HDT
Summary
Head-down tilt (HDT) is an experimental maneuver inducing an increase of the venous return, central blood volume, and central venous pressure (London et al, 1983; Nagaya et al, 1995). In the field of information dynamics multivariate tools have been recently devised that allow the quantitative description of the dynamical interactions among time series (McGill, 1954; Schreiber, 2000; Barnett et al, 2009; Faes et al, 2011, 2013, 2015; Lizier et al, 2011; Wibral et al, 2011, 2014; Chicharro and Ledberg, 2012; Stramaglia et al, 2012; Kugiumtzis, 2013; Porta et al, 2014a, 2015; Barrett, 2015) These tools have been successfully applied to disentangle physiological mechanisms from the spontaneous variability of the heart period (HP), systolic arterial pressure (SAP), and respiration (R). Usually the full decomposition of PE is given for bivariate interactions (e.g., HP and R) (Faes et al, 2015) or limited to the TE term (Chicharro and Ledberg, 2012; Stramaglia et al, 2012; Barrett, 2015), while the full decomposition of the self-entropy (SE) has never been investigated
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