[Paper Review] Multiscale Partial Information Decomposition of Dynamic Processes with Short and Long-range correlations: Theory and Application to Cardiovascular Control

Hélder Pinto, Riccardo Pernice+4 more|arXiv (Cornell University)|Apr 29, 2022

Heart Rate Variability and Autonomic Control78 references15 citations

TL;DR

This paper proposes a novel multiscale partial information decomposition (M-PID) framework using Vector Autoregressive Fractionally Integrated (VARFI) models to quantify directed information flow from systolic arterial pressure (S) and respiration (R) to heart period (H), accounting for both short-term dynamics and long-range correlations. The method reveals that postural stress increases redundant information transfer at short scales, while mental stress enhances synergistic information transfer at longer scales, demonstrating distinct physiological mechanisms of stress response.

ABSTRACT

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.

Motivation & Objective

• To develop a method that captures both short-term dynamics and long-range correlations in multiscale information transfer within physiological networks.
• To extend partial information decomposition (PID) to multiscale analysis of coupled physiological processes like heart rate, blood pressure, and respiration.
• To investigate how different types of stress—postural and mental—affect the nature of information transfer in cardiovascular control.
• To provide analytical, parametric solutions for information measures using state space models, enabling reliable analysis on short time series.

Proposed method

• Uses Vector Autoregressive Fractionally Integrated (VARFI) models to represent multivariate physiological processes with both short-term dynamics and long-range correlations.
• Applies state space model theory to derive analytical expressions for multiscale Transfer Entropy (TE) and its decomposition into unique, redundant, and synergistic components.
• Employs Partial Information Decomposition (PID) to decompose joint information transfer from S and R to H into unique, redundant, and synergistic contributions at multiple time scales.
• Utilizes fractional integration in the VARFI model to capture long-range dependence, extending standard VAR models.
• Derives multiscale representations of TE and ITE (Interaction Transfer Entropy) through time-scale aggregation using state space filtering.
• Validates the method on simulated VARFI processes before applying it to experimental H, S, and R time series from healthy subjects under rest, mental stress, and postural stress.

Experimental results

Research questions

• RQ1 How does the balance between short-term dynamics and long-range correlations affect information transfer in cardiovascular control systems?
• RQ2 What is the contribution of redundancy versus synergy in the information transfer from arterial pressure and respiration to heart period across multiple time scales?
• RQ3 How do different stressors—mental and postural—affect the nature and scale of information transfer in the cardiovascular network?
• RQ4 Can a parametric, analytical framework based on VARFI and state space models reliably estimate multiscale information decomposition in short physiological time series?

Key findings

• Postural stress induces significantly larger redundant information transfer from S and R to H at short time scales (0.5–2 seconds), indicating a more synchronized, less differentiated control mechanism.
• Mental stress leads to greater synergistic information transfer at longer time scales (4–8 seconds), suggesting cooperative integration of inputs for adaptive regulation.
• The proposed M-PID with VARFI models successfully captures the interplay between short-term and long-range correlations, which standard methods fail to detect.
• The method reveals distinct physiological signatures of stress: postural stress favors redundancy, while mental stress favors synergy in information processing.
• Analytical derivations via state space models enable accurate and efficient computation of multiscale information measures even on short time series.
• The framework demonstrates that long-range correlations significantly modulate the structure of information transfer, which is obscured when ignored.