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

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

Entropy Information of Cardiorespiratory Dynamics in Neonates during Sleep

Abstract: Sleep is a central activity in human adults and characterizes most of the newborn infant life. During sleep, autonomic control acts to modulate heart rate variability (HRV) and respiration. Mechanisms underlying cardiorespiratory interactions in different sleep states have been studied but are not yet fully understood. Signal processing approaches have focused on cardiorespiratory analysis to elucidate this co-regulation. This manuscript proposes to analyze heart rate (HR), respiratory variability and their interrelationship in newborn infants to characterize cardiorespiratory interactions in different sleep states (active vs. quiet). We are searching for indices that could detect regulation alteration or malfunction, potentially leading to infant distress. We have analyzed inter-beat (RR) interval series and respiration in a population of 151 newborns, and followed up with 33 at 1 month of age. RR interval series were obtained by recognizing peaks of the QRS complex in the electrocardiogram (ECG), corresponding to the ventricles depolarization. Univariate time domain, frequency domain and entropy measures were applied. In addition, Transfer Entropy was considered as a bivariate approach able to quantify the bidirectional information flow from one signal (respiration) to another (RR series). Results confirm the validity of the proposed approach. Overall, HRV is higher in active sleep, while high frequency (HF) power characterizes more quiet sleep. Entropy analysis provides higher indices for SampEn and Quadratic Sample entropy (QSE) in quiet sleep. Transfer Entropy values were higher in quiet sleep and point to a major influence of respiration on the RR series. At 1 month of age, time domain parameters show an increase in HR and a decrease in variability. No entropy differences were found across ages. The parameters employed in this study help to quantify the potential for infants to adapt their cardiorespiratory responses as they mature. Thus, they could be useful as early markers of risk for infant cardiorespiratory vulnerabilities

Multivariate assessment of linear and non-linear causal coupling pathways within the central-autonomic-network in patients suffering from schizophrenia

Im Bereich der Zeitreihenanalyse richtet sich das Interesse zunehmend darauf, wie Einblicke in die Interaktions- und Regulationsprozesse von pathophysiologischen- und physiologischen Zuständen erlangt werden können. Neuste Fortschritte in der nichtlinearen Dynamik, der Informationstheorie und der Netzwerktheorie liefern dabei fundiertes Wissen über Kopplungswege innerhalb (patho)physiologischer (Sub)Systeme. Kopplungsanalysen zielen darauf ab, ein besseres Verständnis dafür zu erlangen, wie die verschiedenen integrierten regulatorischen (Sub)Systeme mit ihren komplexen Strukturen und Regulationsmechanismen das globale Verhalten und die unterschiedlichen physiologischen Funktionen auf der Ebene des Organismus beschreiben. Insbesondere die Erfassung und Quantifizierung der Kopplungsstärke und -richtung sind wesentliche Aspekte für ein detaillierteres Verständnis physiologischer Regulationsprozesse. Ziel dieser Arbeit war die Charakterisierung kurzfristiger unmittelbarer zentral-autonomer Kopplungspfade (top-to-bottom und bottom to top) durch die Kopplungsanalysen der Herzfrequenz, des systolischen Blutdrucks, der Atmung und zentraler Aktivität (EEG) bei schizophrenen Patienten und Gesunden. Dafür wurden in dieser Arbeit neue multivariate kausale und nicht-kausale, lineare und nicht-lineare Kopplungsanalyseverfahren (HRJSD, mHRJSD, NSTPDC) entwickelt, die in der Lage sind, die Kopplungsstärke und -richtung, sowie deterministische regulatorische Kopplungsmuster innerhalb des zentralen-autonomen Netzwerks zu quantifizieren und zu klassifizieren. Diese Kopplungsanalyseverfahren haben ihre eigenen Besonderheiten, die sie einzigartig machen, auch im Vergleich zu etablierten Kopplungsverfahren. Sie erweitern das Spektrum neuartiger Kopplungsansätze für die Biosignalanalyse und tragen auf ihre Weise zur Gewinnung detaillierter Informationen und damit zu einer verbesserten Diagnostik/Therapie bei. Die Hauptergebnisse dieser Arbeit zeigen signifikant schwächere nichtlineare zentral-kardiovaskuläre und zentral-kardiorespiratorische Kopplungswege und einen signifikant stärkeren linearen zentralen Informationsfluss in Richtung des Herzkreislaufsystems auf, sowie einen signifikant stärkeren linearen respiratorischen Informationsfluss in Richtung des zentralen Nervensystems in der Schizophrenie im Vergleich zu Gesunden. Die detaillierten Erkenntnisse darüber, wie die verschiedenen zentral-autonomen Netzwerke mit paranoider Schizophrenie assoziiert sind, können zu einem besseren Verständnis darüber führen, wie zentrale Aktivierung und autonome Reaktionen und/oder Aktivierung in physiologischen Netzwerken unter pathophysiologischen Bedingungen zusammenhängen.In the field of time series analysis, increasing interest focuses on insights gained how the coupling pathways of regulatory mechanisms work in healthy and ill states. Recent advances in non-linear dynamics, information theory and network theory lead to a new sophisticated body of knowledge about coupling pathways within (patho)physiological (sub)systems. Coupling analyses aim to provide a better understanding of how the different integrated physiological (sub)systems, with their complex structures and regulatory mechanisms, describe the global behaviour and distinct physiological functions at the organism level. In particular, the detection and quantification of the coupling strength and direction are important aspects for a more detailed understanding of physiological regulatory processes. This thesis aimed to characterize short-term instantaneous central-autonomic-network coupling pathways (top-to-bottom and bottom to top) by analysing the coupling of heart rate, systolic blood pressure, respiration and central activity (EEG) in schizophrenic patients and healthy participants. Therefore, new multivariate causal and non-causal linear and non-linear coupling approaches (HRJSD, mHRJSD, NSTPDC) that are able to determine the coupling strength and direction were developed. Whereby, the HRJSD and mHRJSD approaches allow the quantification and classification of deterministic regulatory coupling patterns within and between the cardiovascular- the cardiorespiratory system and the central-autonomic-network were developed. These coupling approaches have their own unique features, even as compared to well-established coupling approaches. They expand the spectrum of novel coupling approaches for biosignal analysis and thus contribute in their own way to detailed information obtained, and thereby contribute to improved diagnostics/therapy. The main findings of this thesis revealed significantly weaker non-linear central-cardiovascular and central-cardiorespiratory coupling pathways, and significantly stronger linear central information flow in the direction of the cardiac- and vascular system, and a significantly stronger linear respiratory information transfer towards the central nervous system in schizophrenia in comparison to healthy participants. This thesis provides an enhanced understanding of the interrelationship of central and autonomic regulatory mechanisms in schizophrenia. The detailed findings on how variously-pronounced, central-autonomic-network pathways are associated with paranoid schizophrenia may enable a better understanding on how central activation and autonomic responses and/or activation are connected in physiology networks under pathophysiological conditions

Bits from Biology for Computational Intelligence

Computational intelligence is broadly defined as biologically-inspired computing. Usually, inspiration is drawn from neural systems. This article shows how to analyze neural systems using information theory to obtain constraints that help identify the algorithms run by such systems and the information they represent. Algorithms and representations identified information-theoretically may then guide the design of biologically inspired computing systems (BICS). The material covered includes the necessary introduction to information theory and the estimation of information theoretic quantities from neural data. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely, or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is decomposed into component processes of information storage, transfer, and modification -- locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems

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

Entropy Analysis of Univariate Biomedical Signals:Review and Comparison of Methods

International audienc

Local and global measures of information storage for the assessment of heartbeat-evoked cortical responses

Objective: Brain–heart interactions involve bidirectional effects produced by bottom-up input at each heartbeat, and top-down neural regulatory responses of the brain. While the cortical processing of the heartbeat is usually investigated through the analysis of the Heartbeat Evoked Potential, in this study we propose an alternative approach based on the variability in the predictability of the brain dynamics induced by the heartbeat. Methods: In a group of eighteen subjects in whom simultaneous recording of the electroencephalogram (EEG) and electrocardiogram was performed in a resting-state, we analyzed the temporal profile of the local Information Storage (IS) to detect changes in the regularity of EEG signals in time windows associated with different phases of the cardiac cycle at rest. Results: The average values of the local IS were significantly higher in the parieto-occipital areas of the scalp, suggesting an activation of the Default Mode Network, regardless of the cardiac cycle phase. In contrast, the variability of the local IS showed marked differences across the cardiac cycle phases. Conclusion: Our results suggest that cardiac activity influences the predictive information of EEG dynamics differently in the various phases of the cardiac cycle. Significance: The variability of local IS measures can represent a useful index to identify spatio-temporal dynamics within the neurocardiac system, which generally remain overlooked by the more widely employed global measures