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

Abstract

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 measures to detect and quantify HOBs in synthetic and physiological network systems. After providing formal definitions of mechanisms and behaviors in a complex system, measures of statistical synergy are defined as the whole-minus-sum excess of mutual predictability ($\Delta_\textrm{MP}$) or mutual information ($\Delta_\textrm{MI}$) obtained 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. The application to simulated linear Gaussian systems and nonlinear deterministic and stochastic dynamic systems shows that $\Delta_\textrm{MP}$ 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 $\Delta_\textrm{MI}$ exhibits a higher propensity to display positive values. The analysis of physiological variables shows significant values of $\Delta_\textrm{MI}$ when investigating the additive effect of systolic and diastolic arterial pressure on mean arterial pressure, and of both $\Delta_\textrm{MP}$ and $\Delta_\textrm{MI}$ when assessing how diastolic pressure is modulated by pre-ejection and left-ventricular ejection times. HOBs can be more clearly identified by information-theoretic measures, while prediction measures are more sensitive to synergy arising from the governing rules of the system analyzed rather than from pure statistical dependencies. Quantifying HOBs through measures sensitive to structural mechanisms can provide biomarkers to assess physio-pathological alterations of cardiovascular networks.