Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardio-Respiratory Nonstationary Dynamics

Objective: Measures of Transfer Entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of transfer entropy to provide an im- proved assessment of complex non-stationary cardio-respiratory interactions

Information-Theoretic Analysis of Cardio-Respiratory Interactions in Heart Failure Patients: Effects of Arrhythmias and Cardiac Resynchronization Therapy

The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy

Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be followed. It is based on phase dynamics, with Bayesian inference of the time-evolving parameters achieved by shaping the prior densities to incorporate knowledge of previous samples. The method is tested numerically and applied to reveal and quantify the time-varying nature of cardiorespiratory interactions.Comment: 5 pages, 3 figures, accepted for Physical Review Letter

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

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 X and Y and the terms of its decomposition evidencing either the individual entropy rates of X and Y and their joint entropy rate, or the transfer entropies from X to Y and from Y to X and the instantaneous information shared by X and Y. 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

The cardiorespiratory network in healthy first-degree relatives of schizophrenic patients

Impaired heart rate- and respiratory regulatory processes as a sign of an autonomic dysfunction seems to be obviously present in patients suffering from schizophrenia. Since the linear and non-linear couplings within the cardiorespiratory system with respiration as an important homeostatic control mechanism are only partially investigated so far for those subjects, we aimed to characterize instantaneous cardiorespiratory couplings by quantifying the casual interaction between heart rate (HR) and respiration (RESP). Therefore, we investigated causal linear and non-linear cardiorespiratory couplings of 23 patients suffering from schizophrenia (SZO), 20 healthy first-degree relatives (REL) and 23 healthy subjects, who were age-gender matched (CON). From all participants’ heart rate (HR) and respirations (respiratory frequency, RESP) were investigated for 30 min under resting conditions. The results revealed highly significant increased HR, reduced HR variability, increased respiration rates and impaired cardiorespiratory couplings in SZO in comparison to CON. SZO were revealed bidirectional couplings, with respiration as the driver (RESP → HR), and with weaker linear and non-linear coupling strengths when RESP influencing HR (RESP → HR) and with stronger linear and non-linear coupling strengths when HR influencing RESP (HR → RESP). For REL we found only significant increased HR and only slightly reduced cardiorespiratory couplings compared to CON. These findings clearly pointing to an underlying disease-inherent genetic component of the cardiac system for SZO and REL, and those respiratory alterations are only clearly present in SZO seem to be connected to their mental emotional states

Assessment of Cardiorespiratory Interactions during Apneic Events in Sleep via Fuzzy Kernel Measures of Information Dynamics

Apnea and other breathing-related disorders have been linked to the development of hypertension or impairments of the cardiovascular, cognitive or metabolic systems. The combined assessment of multiple physiological signals acquired during sleep is of fundamental importance for providing additional insights about breathing disorder events and the associated impairments. In this work, we apply information-theoretic measures to describe the joint dynamics of cardiorespiratory physiological processes in a large group of patients reporting repeated episodes of hypopneas, apneas (central, obstructive, mixed) and respiratory effort related arousals (RERAs). We analyze the heart period as the target process and the airflow amplitude as the driver, computing the predictive information, the information storage, the information transfer, the internal information and the cross information, using a fuzzy kernel entropy estimator. The analyses were performed comparing the information measures among segments during, immediately before and after the respiratory event and with control segments. Results highlight a general tendency to decrease of predictive information and information storage of heart period, as well as of cross information and information transfer from respiration to heart period, during the breathing disordered events. The information-theoretic measures also vary according to the breathing disorder, and significant changes of information transfer can be detected during RERAs, suggesting that the latter could represent a risk factor for developing cardiovascular diseases. These findings reflect the impact of different sleep breathing disorders on respiratory sinus arrhythmia, suggesting overall higher complexity of the cardiac dynamics and weaker cardiorespiratory interactions which may have physiological and clinical relevance

Assessment of quadratic nonlinear cardiorespiratory couplings during tilt table test by means of real wavelet biphase

In this paper a method for assessment of Quadratic Phase Coupling (QPC) between respiration and Heart Rate Variability (HRV) is presented. Methods: First, a method for QPC detection is proposed named Real Wavelet Biphase (RWB). Then, a method for QPC quantification is proposed based on the Normalized Wavelet Biamplitude (NWB). A simulation study has been conducted to test the reliability of RWB to identify QPC, even in the presence of constant delays between interacting oscillations, and to discriminate it from Quadratic Phase Uncoupling. Significant QPC was assessed based on surrogate data analysis. Then, quadratic cardiorespiratory couplings were studied during a tilt table test protocol of 17 young healthy subjects. Results: Simulation study showed that RWB is able to detect even weak QPC with delays in the range of 0 - 2 s, which are usual in the Autonomic Nervous System (ANS) control of heart rate. Results from the database revealed a significant reduction (p<0.05) of NWB between respiration and both low and high frequencies of HRV in head-up tilt position compared to early supine. Conclusion: The proposed technique detects and quantifies robustly QPC and is able to track the coupling between respiration and various HRV components during ANS changes. Significance: The proposed method can help to assess alternations of nonlinear cardiorespiratory interactions related to ANS dysfunction and physiological regulation of HRV in cardiovascular diseases

MuTE: a new matlab toolbox for estimating the multivariate transfer entropy in physiological variability series

We present a new time series analysis toolbox, developed in Matlab, for the estimation of the Transfer entropy (TE) between time series taken from a multivariate dataset. The main feature of the toolbox is its fully multivariate implementation, that is made possible by the design of an approach for the non-uniform embedding (NUE) of the observed time series. The toolbox is equipped with parametric (linear) and non-parametric (based on binning or nearest neighbors) entropy estimators. All these estimators, implemented using the NUE approach in comparison with the classical approach based on uniform embedding, are tested on RR interval, systolic pressure and respiration variability series measured from healthy subjects during head-up tilt. The results support the necessity of resorting to NUE for obtaining reliable estimates of the multivariate TE in short-term cardiovascular and cardiorespiratory variability