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 ($Δ_\textrm{MP}$) or mutual information ($Δ_\textrm{MI}$) 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 $Δ_\textrm{MP}$ 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 $Δ_\textrm{MI}$ exhibits a higher propensity to display positive values. The analysis of physiological variables shows significant values of $Δ_\textrm{MI}$ when investigating the additive effect of systolic and diastolic arterial pressure on mean arterial pressure, and of both $Δ_\textrm{MP}$ and $Δ_\textrm{MI}$ 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.
Summary
This paper investigates high-order behaviors (HOBs) in complex systems, particularly focusing on cardiovascular interactions. The core research question is how to detect and quantify synergistic HOBs using a combination of predictability and information-theoretic measures. The authors propose a "whole-minus-sum" (WMS) approach to quantify statistical synergy, defining measures based on the excess of mutual predictability (ΔMP) or mutual information (ΔMI) when considering the system as a whole versus the sum of its individual parts. They use model-free methods based on nonlinear prediction (k-nearest neighbors) and entropy estimation to compute these measures. The key findings indicate that ΔMP tends to be positive only in the presence of group interactions (high-order mechanisms, HOMs), while ΔMI exhibits positive values more readily, even with additive effects. Application to physiological data shows significant ΔMI values for the effect of systolic and diastolic arterial pressure on mean arterial pressure, and significant ΔMP and ΔMI values for the modulation of diastolic pressure by pre-ejection and left-ventricular ejection times. The authors conclude that information-theoretic WMS measures are better at identifying HOBs, while prediction WMS measures are more sensitive to synergy arising from the system's governing rules (HOMs). This research matters to the field because it provides a framework for quantifying HOBs in complex systems, potentially leading to new biomarkers for assessing physio-pathological alterations in cardiovascular networks.
Key Insights
- •ΔMP tends to vanish in systems with additive effects of independent source variables (no HOMs) but is positive when group interactions exist (HOMs present).
- •ΔMI exhibits a higher propensity to display positive values, even in the absence of HOMs, indicating its sensitivity to general statistical dependencies.
- •Both ΔMP and ΔMI are positive and statistically significant in systems with HOMs (coupled Hénon maps, nonlinearly mixed autoregressive processes).
- •In linear Gaussian systems where r12=0 (sources are uncorrelated), ΔMP = 0 and ΔMI > 0, highlighting that prediction power is additive for independent predictors.
- •The study uses surrogate data analysis with circular shifting to assess the statistical significance of the HOI measures, preserving individual variable statistics while disrupting correlations.
- •The optimal number of neighbors (k) for MP estimation is determined by maximizing the predictability of the target variable given the source.
- •The study acknowledges limitations related to bias and variance in entropy estimation, especially with short data lengths, and suggests future research using Partial Information Decomposition to differentiate synergistic and redundant components.
Practical Implications
- •The proposed framework can be used to analyze other complex physiological systems beyond cardiovascular networks, potentially leading to new biomarkers for disease detection and monitoring.
- •Practitioners and engineers can use the ΔMP and ΔMI measures to quantify the degree of synergy in multivariate systems and identify potential targets for intervention.
- •The findings suggest that information-theoretic measures (ΔMI) are more suitable for detecting general HOBs, while prediction-based measures (ΔMP) may be more useful for identifying HOBs arising from specific structural mechanisms.
- •Future research should focus on extending these methods to higher-dimensional systems and developing techniques to separate synergistic and redundant components of interactions.
- •The analysis of cardiovascular interactions provides insights into the physiological mechanisms underlying arterial pressure regulation and heart timing, which could inform the development of new diagnostic and therapeutic strategies for cardiovascular diseases.