Investigating High-Order Behaviors in Multivariate Cardiovascular Interactions via Nonlinear Prediction and Information-Theoretic Tools

Objective: Assessing the synergistic high-order behaviors (HOBs) that emerge from underlying structural mechanisms is crucial to characterize complex systems. This work leverages the combined use of predictability and information-theoretic measures to detect and quantify HOBs in synthetic and physiological network systems. Methods: After providing formal definitions of mechanisms and behaviors in a complex system, measures of statistical synergy are defined as the whole-minus-sum (WMS) excess of mutual predictability (∆MP) or mutual information (∆MI) observed when considering the system as a whole rather than as a combination of its units. The two measures are computed using model-free methods based on nonlinear prediction and entropy estimation. Results: The application to simulated linear Gaussian systems and nonlinear deterministic and stochastic dynamic systems shows that ∆MI tends to vanish for target variables influenced by additive effects of single independent source variables and is positive in the presence of group interactions between sources, while ∆MI exhibits a higher propensity to display positive values. Then, the analysis of physiological variables shows significant values of ∆MI when investigating the additive effect of systolic and diastolic arterial pressure on mean arterial pressure, and of both ∆MP and ∆MI when assessing how diastolic pressure is modulated by pre-ejection period and left-ventricular ejection time. Conclusion: HOBs can be more clearly identified by information-theoretic WMS measures, while prediction WMS measures appear more sensitive to synergy arising from the governing rules of the system analyzed rather than from pure statistical dependencies. Significance: Quantifying HOBs through WMS measures sensitive to complex structural mechanisms can provide new biomarkers to assess physio-pathological alterations of cardiovascular networks.