Comparison of discretization strategies for the model-free information-theoretic assessment of short-term physiological interactions

Abstract

This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes [Formula: see text] and [Formula: see text] and the terms of its decomposition evidencing either the individual entropy rates of [Formula: see text] and [Formula: see text] and their joint entropy rate, or the transfer entropies from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] and the instantaneous information shared by [Formula: see text] and [Formula: see text]. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality.

Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate data analysis

“…The analysis of the coupling of the bivariate system S = { RR , RESP } using MIR highlights that the coupling between RR and RESP is not lost during different paced breathing rates ( Mary et al, 2018 ), being the slight decrease observed in Figure 9 from the SB to the C10 phase not significant, and is followed by a complete recovery in C15 and C20. Such results are similar to what was reported in ( Barà et al, 2023 ). A decrease in nonlinearities was observed in the C10 phase when compared with the other experimental conditions.…”

“…The MIR of the bivariate process S = { X , Y } is defined as the limit, if it exists, of the rate at which the MI between dynamic sequences taken from X and Y increases over time ( Komaee, 2020 ; Miao et al, 2020 ) The MIR serves as a dynamic measure for the information shared per unit of time between two dynamical systems and was adopted in various forms to quantify dynamic interactions among physiological processes ( Baptista and Kurths, 2008 ; Mijatovic et al, 2021 ; Faes et al, 2022 ). This measure of dynamic coupling can be decomposed in terms of other information-theoretic measures, offering valuable insights into the dynamics of each process and the coupling relationships within the bivariate system ( Barà et al, 2023 ). A possible decomposition of MIR is where H X and H Y denote the entropy rate of X and Y , respectively, and H X , Y their joint entropy rate.…”

“…The MIR serves as a dynamic measure for the information shared per unit of time between two dynamical systems and was adopted in various forms to quantify dynamic interactions among physiological processes (Baptista and Kurths, 2008;Mijatovic et al, 2021;Faes et al, 2022). This measure of dynamic coupling can be decomposed in terms of other information-theoretic measures, offering valuable insights into the dynamics of each process and the coupling relationships within the bivariate system (Barà et al, 2023). A possible decomposition of MIR is…”

“…These measures assess complexity ( Pincus, 1991 ; Faes et al, 2017 ) and information stored within a process ( Faes et al, 2019b ), as well as directed information transfer between processes ( Porta and Faes, 2013 ). Another key characteristic to assess in physiological interactions is the dynamic coupling between two processes which can be evaluated through the computation of the Mutual Information Rate (MIR) ( Barà et al, 2023 ; Pinto et al, 2023 ). This information-theoretic measure quantifies the degree of information shared between two systems, providing a measure of their dynamic coupling strength and revealing the interdependencies within their dynamic behavior.…”

Gradients of O-information highlight synergy and redundancy in physiological applications

“…The emergence of new tools for the quantification of high order interactions is opening new possibilities in the field of network physiology, which aims to address the fundamental question of how physiological networks collectively behave to maintain human body in healthy conditions (Bashan et al, 2012;Lin et al, 2020;Ivanov 2021). Historically, the study of physiological time series has seen a shift from the univariate analysis of individual time series, where measures such as the approximate entropy (Pincus, 1991), the sample entropy (Richman and Moorman, 2000) and the corrected conditional entropy (Porta et al, 1998) have been introduced to characterize the predictable dynamics of a physiological system, to the bivariate analysis of two time series, where symmetric or causal measures based on cross-entropies (Porta et al, 1999;Faes et al, 2011), mutual information (Valderas, 2019) and its rate (Barà et al, 2023), directed information (Massey, 1990) or transfer entropy (Schreiber, 2000;Faes et al, 2014) have been used extensively to quantify the information shared and transferred between pairs of physiological systems. Multivariate analyses involving more than two physiological time series have been then introduced to quantify how the information transferred between processes is affected by the rest of the network.…”