Information Decomposition in Multivariate Systems: Definitions, Implementation and Application to Cardiovascular Networks

A Method to Assess Granger Causality, Isolation and Autonomy in the Time and Frequency Domains: Theory and Application to Cerebrovascular Variability

OBJECTIVE

Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of clear spectral representation.

METHODS

We embed into the linear parametric framework for computing GC from a driver X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The measures are illustrated in theoretical simulations and applied to time series of arterial pressure and cerebral blood flow obtained in syncope subjects and healthy controls.

RESULTS

Simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to orthostasis in syncope subjects, likely related to impaired cerebral autoregulation.

CONCLUSION AND SIGNIFICANCE

The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect pathophysiological responses to postural stress which cannot be traced in the time domain. The thorough assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled processes in both physiological and clinical investigations.

A method to assess linear self-predictability of physiologic processes in the frequency domain: application to beat-to-beat variability of arterial compliance

The concept of self-predictability plays a key role for the analysis of the self-driven dynamics of physiological processes displaying richness of oscillatory rhythms. While time domain measures of self-predictability, as well as time-varying and local extensions, have already been proposed and largely applied in different contexts, they still lack a clear spectral description, which would be significantly useful for the interpretation of the frequency-specific content of the investigated processes. Herein, we propose a novel approach to characterize the linear self-predictability (LSP) of Gaussian processes in the frequency domain. The LSP spectral functions are related to the peaks of the power spectral density (PSD) of the investigated process, which is represented as the sum of different oscillatory components with specific frequency through the method of spectral decomposition. Remarkably, each of the LSP profiles is linked to a specific oscillation of the process, and it returns frequency-specific measures when integrated along spectral bands of physiological interest, as well as a time domain self-predictability measure with a clear meaning in the field of information theory, corresponding to the well-known information storage, when integrated along the whole frequency axis. The proposed measure is first illustrated in a theoretical simulation, showing that it clearly reflects the degree and frequency-specific location of predictability patterns of the analyzed process in both time and frequency domains. Then, it is applied to beat-to-beat time series of arterial compliance obtained in young healthy subjects. The results evidence that the spectral decomposition strategy applied to both the PSD and the spectral LSP of compliance identifies physiological responses to postural stress of low and high frequency oscillations of the process which cannot be traced in the time domain only, highlighting the importance of computing frequency-specific measures of self-predictability in any oscillatory physiologic process.

Time-varying information measures: an adaptive estimation of information storage with application to brain-heart interactions

Network Physiology is a rapidly growing field of study that aims to understand how physiological systems interact to maintain health. Within the information theory framework the information storage (IS) allows to measure the regularity and predictability of a dynamic process under stationarity assumption. However, this assumption does not allow to track over time the transient pathways occurring in the dynamical activity of a physiological system. To address this limitation, we propose a time-varying approach based on the recursive least squares algorithm (RLS) for estimating IS at each time instant, in non-stationary conditions. We tested this approach in simulated time-varying dynamics and in the analysis of electroencephalographic (EEG) signals recorded from healthy volunteers and timed with the heartbeat to investigate brain-heart interactions. In simulations, we show that the proposed approach allows to track both abrupt and slow changes in the information stored in a physiological system. These changes are reflected in its evolution and variability over time. The analysis of brain-heart interactions reveals marked differences across the cardiac cycle phases of the variability of the time-varying IS. On the other hand, the average IS values exhibit a weak modulation over parieto-occiptal areas of the scalp. Our study highlights the importance of developing more advanced methods for measuring IS that account for non-stationarity in physiological systems. The proposed time-varying approach based on RLS represents a useful tool for identifying spatio-temporal dynamics within the neurocardiac system and can contribute to the understanding of brain-heart interactions.

Statistical Approaches to Identify Pairwise and High-Order Brain Functional Connectivity Signatures on a Single-Subject Basis

Keeping up with the shift towards personalized neuroscience essentially requires the derivation of meaningful insights from individual brain signal recordings by analyzing the descriptive indexes of physio-pathological states through statistical methods that prioritize subject-specific differences under varying experimental conditions. Within this framework, the current study presents a methodology for assessing the value of the single-subject fingerprints of brain functional connectivity, assessed both by standard pairwise and novel high-order measures. Functional connectivity networks, which investigate the inter-relationships between pairs of brain regions, have long been a valuable tool for modeling the brain as a complex system. However, their usefulness is limited by their inability to detect high-order dependencies beyond pairwise correlations. In this study, by leveraging multivariate information theory, we confirm recent evidence suggesting that the brain contains a plethora of high-order, synergistic subsystems that would go unnoticed using a pairwise graph structure. The significance and variations across different conditions of functional pairwise and high-order interactions (HOIs) between groups of brain signals are statistically verified on an individual level through the utilization of surrogate and bootstrap data analyses. The approach is illustrated on the single-subject recordings of resting-state functional magnetic resonance imaging (rest-fMRI) signals acquired using a pediatric patient with hepatic encephalopathy associated with a portosystemic shunt and undergoing liver vascular shunt correction. Our results show that (i) the proposed single-subject analysis may have remarkable clinical relevance for subject-specific investigations and treatment planning, and (ii) the possibility of investigating brain connectivity and its post-treatment functional developments at a high-order level may be essential to fully capture the complexity and modalities of the recovery.

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.

Investigating Dynamic High-Order Interactions in Physiological Networks through Predictive Information Decomposition

We present an approach to assess redundant and synergistic interactions in network systems via the information-theoretic analysis of multivariate physiological processes. The approach sets up a strategy to decompose the information shared between the present states of a group of random processes and their own past states into unique contributions arising from the past of subgroups of processes and redundant and synergistic contributions arising from the dynamic interaction among the subgroups. The method is illustrated in a theoretical example of linearly interacting Gaussian processes, showing that redundancy and synergy are related mostly to unidirectional coupling and to bidirectional coupling with internal dynamics. It is then applied to the network of short-term heart period, arterial pressure and respiratory variability probed in healthy subjects, showing that redundancy and synergy prevail respectively in cardiorespiratory interactions and in cardiovascular interactions in the resting state, and that postural stress increases the predictive information and the redundancy of physiological interactions.

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks.

Multiscale partial information decomposition of dynamic processes with short and long-range correlations: theory and application to cardiovascular control

OBJECTIVE

In this work, an analytical framework for the multiscale analysis of multivariate Gaussian processes is presented, whereby the computation of Partial Information Decomposition measures is achieved accounting for the simultaneous presence of short-term dynamics and long-range correlations.

APPROACH

We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the 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. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. 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.

MAIN RESULTS

We demonstrate the ability of the VARFI modeling approach to account for the coexistence of short-term and long-range correlations in the study of multivariate processes. Physiologically, we show that postural stress induces larger redundant and synergistic effects from S and R to H at short time scales, while mental stress induces larger information transfer from S to H at longer time scales, thus evidencing the different nature of the two stressors.

SIGNIFICANCE

The proposed methodology allows to extract useful information about 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.

Pairwise and higher-order measures of brain-heart interactions in children with temporal lobe epilepsy

OBJECTIVE

While it is well-known that epilepsy has a clear impact on the activity of both the central nervous system (CNS) and the autonomic nervous system (ANS), its role on the complex interplay between CNS and ANS has not been fully elucidated yet. In this work, pairwise and higher-order predictability measures based on the concepts of Granger causality (GC) and Partial Information Decomposition (PID) were applied on time series of electroencephalographic (EEG) brain wave amplitude and heart rate variability (HRV) in order to investigate directed brain-heart interactions associated with the occurrence of focal epilepsy.

APPROACH

HRV and the envelopes of δ and α EEG activity recorded from ipsilateral (ipsi-EEG) and contralateral (contra-EEG) scalp regions were analyzed in 18 children suffering from temporal lobe epilepsy monitored during pre-ictal, ictal and post-ictal periods. After linear parametric model identification, we compared pairwise GC measures computed between HRV and a single EEG component with PID measures quantifying the unique, redundant and synergistic information transferred from ipsi-EEG and contra-EEG to HRV.

MAIN RESULTS

The analysis of GC revealed a dominance of the information transfer from EEG to HRV and negligible transfer from HRV to EEG, suggesting that CNS activities drive the ANS modulation of the heart rhythm, but did not evidence clear differences between δ and α rhythms, ipsi-EEG and contra-EEG, or pre- and post-ictal periods. On the contrary, PID revealed that epileptic seizures induce a reorganization of the interactions from brain to heart, as the unique predictability of HRV originated from the ipsi-EEG for the δ waves and from the contra-EEG for the α waves in the pre-ictal phase, while these patterns were reversed after the seizure.

SIGNIFICANCE

These results highlight the importance of considering higher-order interactions elicited by PID for the study of the neuro-autonomic effects of focal epilepsy, and may have neurophysiological and clinical implications.

Information Dynamics of Electric Field Intensity before and during the COVID-19 Pandemic

This work investigates the temporal statistical structure of time series of electric field (EF) intensity recorded with the aim of exploring the dynamical patterns associated with periods with different human activity in urban areas. The analyzed time series were obtained from a sensor of the EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, Serbia. The sensor performs wideband cumulative EF intensity monitoring of all active commercial EF sources, thus including those linked to human utilization of wireless communication systems. Monitoring was performed continuously during the years 2019 and 2020, allowing us to investigate the effects on the patterns of EF intensity of varying conditions of human mobility, including regular teaching and exam activity within the campus, as well as limitations to mobility related to the COVID-19 pandemic. Time series analysis was performed using both simple statistics (mean and variance) and combining the information-theoretic measure of information storage (IS) with the method of surrogate data to quantify the regularity of EF dynamic patterns and detect the presence of nonlinear dynamics. Moreover, to assess the possible coexistence of dynamic behaviors across multiple temporal scales, IS analysis was performed over consecutive observation windows lasting one day, week, month, and year, respectively coarse grained at time scales of 6 min, 30 min, 2 h, and 1 day. Our results document that the EF intensity patterns of variability are modulated by the movement of people at daily, weekly, and monthly scales, and are blunted during periods of restricted mobility related to the COVID-19 pandemic. Mobility restrictions also affected significantly the regularity of the EF intensity time series, resulting in lower values of IS observed simultaneously with a loss of nonlinear dynamics. Thus, our analysis can be useful to investigate changes in the global patterns of human mobility both during pandemics or other types of events, and from this perspective may serve to implement strategies for safety assessment and for optimizing the design of networks of EF sensors.

Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate variability

Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of 'instantaneous' effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index of undirected instantaneous causality and (ii) a novel measure of GC including instantaneous effects. An effective procedure to speed up the optimization of parameters in this frame is also presented. After illustrating the proposed formalism in a theoretical example, we apply it to two datasets of cardiovascular and respiratory time series and compare the values obtained within the frequency bands of physiological interest by the proposed total measure of causality with those derived from the standard GC analysis. We find that the inclusion of instantaneous causality allows us to correctly disentangle the baroreflex mechanism from the effects related to cardiorespiratory interactions. Moreover, studying how controlling the respiratory rhythm acts on cardiovascular interactions, we document an increase of the direct (non-baroreflex mediated) influence of respiration on the heart rate in the respiratory frequency band when switching from spontaneous to paced breathing. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Cardiopulmonary coupling indices to assess weaning readiness from mechanical ventilation

The ideal moment to withdraw respiratory supply of patients under Mechanical Ventilation at Intensive Care Units (ICU), is not easy to be determined for clinicians. Although the Spontaneous Breathing Trial (SBT) provides a measure of the patients' readiness, there is still around 15-20% of predictive failure rate. This work is a proof of concept focused on adding new value to the prediction of the weaning outcome. Heart Rate Variability (HRV) and Cardiopulmonary Coupling (CPC) methods are evaluated as new complementary estimates to assess weaning readiness. The CPC is related to how the mechanisms regulating respiration and cardiac pumping are working simultaneously, and it is defined from HRV in combination with respiratory information. Three different techniques are used to estimate the CPC, including Time-Frequency Coherence, Dynamic Mutual Information and Orthogonal Subspace Projections. The cohort study includes 22 patients in pressure support ventilation, ready to undergo the SBT, analysed in the 24 h previous to the SBT. Of these, 13 had a successful weaning and 9 failed the SBT or needed reintubation -being both considered as failed weaning. Results illustrate that traditional variables such as heart rate, respiratory frequency, and the parameters derived from HRV do not differ in patients with successful or failed weaning. Results revealed that HRV parameters can vary considerably depending on the time at which they are measured. This fact could be attributed to circadian rhythms, having a strong influence on HRV values. On the contrary, significant statistical differences are found in the proposed CPC parameters when comparing the values of the two groups, and throughout the whole recordings. In addition, differences are greater at night, probably because patients with failed weaning might be experiencing more respiratory episodes, e.g. apneas during the night, which is directly related to a reduced respiratory sinus arrhythmia. Therefore, results suggest that the traditional measures could be used in combination with the proposed CPC biomarkers to improve weaning readiness.

Information Flow Between Heart Rhythm, Repolarization, and the Diastolic Interval Series for Healthy Individuals and LQTS1 Patients

Using information theoretic measures, relations between heart rhythm, repolarization in the tissue of the heart, and the diastolic interval time series are analyzed. These processes are a fragment of the cardiovascular physiological network. A comparison is made between the results for 84 (42 women) healthy individuals and 65 (45 women) long QT syndrome type 1 (LQTS1) patients. Self-entropy, transfer entropy, and joint transfer entropy are calculated for the three time series and their combinations. The results for self-entropy indicate the well-known result that regularity of heart rhythm for healthy individuals is larger than that of QT interval series. The flow of information depends on the direction with the flow from the heart rhythm to QT dominating. In LQTS1 patients, however, our results indicate that information flow in the opposite direction may occur-a new result. The information flow from the heart rhythm to QT dominates, which verifies the asymmetry seen by Porta et al. in the variable tilt angle experiment. The amount of new information and self-entropy for LQTS1 patients is smaller than that for healthy individuals. However, information transfers from RR to QT and from DI to QT are larger in the case of LQTS1 patients.

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.

Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Square (OLS) estimation, a viable alternative is to use Artificial Neural Networks (ANNs) implemented in a simple structure with one input and one output layer and trained in a way such that the weights matrix corresponds to the matrix of VAR parameters. In this work, we introduce an ANN combined with SS models for the computation of GC. The ANN is trained through the Stochastic Gradient Descent L1 (SGD-L1) algorithm, and a cumulative penalty inspired from penalized regression is applied to the network weights to encourage sparsity. Simulating networks of coupled Gaussian systems, we show how the combination of ANNs and SGD-L1 allows to mitigate the strong reduction in accuracy of OLS identification in settings of low ratio between number of time series points and of VAR parameters. We also report how the performances in GC estimation are influenced by the number of iterations of gradient descent and by the learning rate used for training the ANN. We recommend using some specific combinations for these parameters to optimize the performance of GC estimation. Then, the performances of ANN and OLS are compared in terms of GC magnitude and statistical significance to highlight the potential of the new approach to reconstruct causal coupling strength and network topology even in challenging conditions of data paucity. The results highlight the importance of of a proper selection of regularization parameter which determines the degree of sparsity in the estimated network. Furthermore, we apply the two approaches to real data scenarios, to study the physiological network of brain and peripheral interactions in humans under different conditions of rest and mental stress, and the effects of the newly emerged concept of remote synchronization on the information exchanged in a ring of electronic oscillators. The results highlight how ANNs provide a mesoscopic description of the information exchanged in networks of multiple interacting physiological systems, preserving the most active causal interactions between cardiovascular, respiratory and brain systems. Moreover, ANNs can reconstruct the flow of directed information in a ring of oscillators whose statistical properties can be related to those of physiological networks.

Extrinsic noise of the target gene governs abundance pattern of feed-forward loop motifs

Feed-forward loop (FFL) is found to be a recurrent structure in bacterial and yeast gene transcription regulatory networks. In a generic FFL, transcription factor (TF) S regulates production of another TF X while both of these TFs regulate production of final gene-product Y. Depending upon the regulatory programs (activation or repression), FFLs are grouped into two broad classes: coherent (C) and incoherent (I), each class containing four distinct types (C1-C4 and I1-I4). These FFL types are experimentally observed to occur with varied frequencies, C1 and I1 being the abundant ones. Here we present a stochastic framework singling out the absolute value of the normalized covariance of X and Y to be the determining factor behind the abundance of FFLs while considering differential promoter activities of X and Y. Our theoretical construct employs two possible signal integration mechanisms (additive and multiplicative) to synthesize Y while steady-state population level of S remains fixed or becomes tunable reflecting two possible environmental signaling scenarios. Our model categorically points out that abundant FFLs exhibit higher amount of the designated metric which has a biophysical connotation of extrinsic noise for the target gene Y. Our predictions emanating from an overarching analytical expression utilizing biologically plausible parametric conditions are substantiated by stochastic simulation.

Behavior of information flow near criticality

Recent experiments have indicated that many biological systems self-organize near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains unclear how information transmission depends on the dynamics of the input signal, the distance over which the information needs to be transmitted, and the distance to the critical point. Here we employ stochastic simulations of a driven two-dimensional Ising system and study the instantaneous mutual information and the information transmission rate between a driven input spin and an output spin. The instantaneous mutual information varies nonmonotonically with the temperature but increases monotonically with the correlation time of the input signal. In contrast, there exists not only an optimal temperature but also an optimal finite input correlation time that maximizes the information transmission rate. This global optimum arises from a fundamental trade-off between the need to maximize the frequency of independent input messages, the necessity to respond fast to changes in the input, and the need to respond reliably to these changes. The optimal temperature lies above the critical point but moves toward it as the distance between the input and output spin is increased.

Assessment of Outliers and Detection of Artifactual Network Segments Using Univariate and Multivariate Dispersion Entropy on Physiological Signals

Network physiology has emerged as a promising paradigm for the extraction of clinically relevant information from physiological signals by moving from univariate to multivariate analysis, allowing for the inspection of interdependencies between organ systems. However, for its successful implementation, the disruptive effects of artifactual outliers, which are a common occurrence in physiological recordings, have to be studied, quantified, and addressed. Within the scope of this study, we utilize Dispersion Entropy (DisEn) to initially quantify the capacity of outlier samples to disrupt the values of univariate and multivariate features extracted with DisEn from physiological network segments consisting of synchronised, electroencephalogram, nasal respiratory, blood pressure, and electrocardiogram signals. The DisEn algorithm is selected due to its efficient computation and good performance in the detection of changes in signals for both univariate and multivariate time-series. The extracted features are then utilised for the training and testing of a logistic regression classifier in univariate and multivariate configurations in an effort to partially automate the detection of artifactual network segments. Our results indicate that outlier samples cause significant disruption in the values of extracted features with multivariate features displaying a certain level of robustness based on the number of signals formulating the network segments from which they are extracted. Furthermore, the deployed classifiers achieve noteworthy performance, where the percentage of correct network segment classification surpasses 95% in a number of experimental setups, with the effectiveness of each configuration being affected by the signal in which outliers are located. Finally, due to the increase in the number of features extracted within the framework of network physiology and the observed impact of artifactual samples in the accuracy of their values, the implementation of algorithmic steps capable of effective feature selection is highlighted as an important area for future research.

Multivariate Correlation Measures Reveal Structure and Strength of Brain-Body Physiological Networks at Rest and During Mental Stress

In this work, we extend to the multivariate case the classical correlation analysis used in the field of network physiology to probe dynamic interactions between organ systems in the human body. To this end, we define different correlation-based measures of the multivariate interaction (MI) within and between the brain and body subnetworks of the human physiological network, represented, respectively, by the time series of δ, θ, α, and β electroencephalographic (EEG) wave amplitudes, and of heart rate, respiration amplitude, and pulse arrival time (PAT) variability (η, ρ, π). MI is computed: (i) considering all variables in the two subnetworks to evaluate overall brain-body interactions; (ii) focusing on a single target variable and dissecting its global interaction with all other variables into contributions arising from the same subnetwork and from the other subnetwork; and (iii) considering two variables conditioned to all the others to infer the network topology. The framework is applied to the time series measured from the EEG, electrocardiographic (ECG), respiration, and blood volume pulse (BVP) signals recorded synchronously via wearable sensors in a group of healthy subjects monitored at rest and during mental arithmetic and sustained attention tasks. We find that the human physiological network is highly connected, with predominance of the links internal of each subnetwork (mainly η-ρ and δ-θ, θ-α, α-β), but also statistically significant interactions between the two subnetworks (mainly η-β and η-δ). MI values are often spatially heterogeneous across the scalp and are modulated by the physiological state, as indicated by the decrease of cardiorespiratory interactions during sustained attention and by the increase of brain-heart interactions and of brain-brain interactions at the frontal scalp regions during mental arithmetic. These findings illustrate the complex and multi-faceted structure of interactions manifested within and between different physiological systems and subsystems across different levels of mental stress.

Information Dynamics Analysis: A new approach based on Sparse Identification of Linear Parametric Models

The framework of information dynamics allows to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of a complex network. The information transfer from one process to another can be quantified through Transfer Entropy, and under the assumption of joint Gaussian variables it is strictly related to the concept of Granger Causality (GC). According to the most recent developments in the field, the computation of GC entails representing the processes through a Vector Autoregressive (VAR) model and a state space (SS) model typically identified by means of the Ordinary Least Squares (OLS). In this work, we propose a new identification approach for the VAR and SS models, based on Least Absolute Shrinkage and Selection Operator (LASSO), that has the advantages of maintaining good accuracy even when few data samples are available and yielding as output a sparse matrix of estimated information transfer. The performances of LASSO identification were first tested and compared to those of OLS by a simulation study and then validated on real electroencephalographic (EEG) signals recorded during a motor imagery task. Both studies indicated that LASSO, under conditions of data paucity, provides better performances in terms of network structure. Given the general nature of the model, this work opens the way to the use of LASSO regression for the computation of several measures of information dynamics currently in use in computational neuroscience.

A Framework to Assess the Information Dynamics of Source EEG Activity and Its Application to Epileptic Brain Networks

This study introduces a framework for the information-theoretic analysis of brain functional connectivity performed at the level of electroencephalogram (EEG) sources. The framework combines the use of common spatial patterns to select the EEG components which maximize the variance between two experimental conditions, simultaneous implementation of vector autoregressive modeling (VAR) with independent component analysis to describe the joint source dynamics and their projection to the scalp, and computation of information dynamics measures (information storage, information transfer, statistically significant network links) from the source VAR parameters. The proposed framework was tested on simulated EEGs obtained mixing source signals generated under different coupling conditions, showing its ability to retrieve source information dynamics from the scalp signals. Then, it was applied to investigate scalp and source brain connectivity in a group of children manifesting episodes of focal and generalized epilepsy; the analysis was performed on EEG signals lasting 5 s, collected in two consecutive windows preceding and one window following each ictal episode. Our results show that generalized seizures are associated with a significant decrease from pre-ictal to post-ictal periods of the information stored in the signals and of the information transferred among them, reflecting reduced self-predictability and causal connectivity at the level of both scalp and source brain dynamics. On the contrary, in the case of focal seizures the scalp EEG activity was not discriminated across conditions by any information measure, while source analysis revealed a tendency of the measures of information transfer to increase just before seizures and to decrease just after seizures. These results suggest that focal epileptic seizures are associated with a reorganization of the topology of EEG brain networks which is only visible analyzing connectivity among the brain sources. Our findings emphasize the importance of EEG modeling approaches able to deal with the adverse effects of volume conduction on brain connectivity analysis, and their potential relevance to the development of strategies for prediction and clinical treatment of epilepsy.

Information Transfer in Linear Multivariate Processes Assessed through Penalized Regression Techniques: Validation and Application to Physiological Networks

The framework of information dynamics allows the dissection of the information processed in a network of multiple interacting dynamical systems into meaningful elements of computation that quantify the information generated in a target system, stored in it, transferred to it from one or more source systems, and modified in a synergistic or redundant way. The concepts of information transfer and modification have been recently formulated in the context of linear parametric modeling of vector stochastic processes, linking them to the notion of Granger causality and providing efficient tools for their computation based on the state-space (SS) representation of vector autoregressive (VAR) models. Despite their high computational reliability these tools still suffer from estimation problems which emerge, in the case of low ratio between data points available and the number of time series, when VAR identification is performed via the standard ordinary least squares (OLS). In this work we propose to replace the OLS with penalized regression performed through the Least Absolute Shrinkage and Selection Operator (LASSO), prior to computation of the measures of information transfer and information modification. First, simulating networks of several coupled Gaussian systems with complex interactions, we show that the LASSO regression allows, also in conditions of data paucity, to accurately reconstruct both the underlying network topology and the expected patterns of information transfer. Then we apply the proposed VAR-SS-LASSO approach to a challenging application context, i.e., the study of the physiological network of brain and peripheral interactions probed in humans under different conditions of rest and mental stress. Our results, which document the possibility to extract physiologically plausible patterns of interaction between the cardiovascular, respiratory and brain wave amplitudes, open the way to the use of our new analysis tools to explore the emerging field of Network Physiology in several practical applications.

Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

Risk Stratification in Idiopathic Dilated Cardiomyopathy Patients Using Cardiovascular Coupling Analysis

Cardiovascular diseases are one of the most common causes of death; however, the early detection of patients at high risk of sudden cardiac death (SCD) remains an issue. The aim of this study was to analyze the cardio-vascular couplings based on heart rate variability (HRV) and blood pressure variability (BPV) analyses in order to introduce new indices for noninvasive risk stratification in idiopathic dilated cardiomyopathy patients (IDC). High-resolution electrocardiogram (ECG) and continuous noninvasive blood pressure (BP) signals were recorded in 91 IDC patients and 49 healthy subjects (CON). The patients were stratified by their SCD risk as high risk (IDC_HR) when after two years the subject either died or suffered life-threatening complications, and as low risk (IDC_LR) when the subject remained stable during this period. Values were extracted from ECG and BP signals, the beat-to-beat interval, and systolic and diastolic blood pressure, and analyzed using the segmented Poincaré plot analysis (SPPA), the high-resolution joint symbolic dynamics (HRJSD) and the normalized short time partial directed coherence methods. Support vector machine (SVM) models were built to classify these patients according to SCD risk. IDC_HR patients presented lowered HRV and increased BPV compared to both IDC_LR patients and the control subjects, suggesting a decrease in their vagal activity and a compensation of sympathetic activity. Both, the cardio -systolic and -diastolic coupling strength was stronger in high-risk patients when comparing with low-risk patients. The cardio-systolic coupling analysis revealed that the systolic influence on heart rate gets weaker as the risk increases. The SVM IDC_LR vs. IDC_HR model achieved 98.9% accuracy with an area under the curve (AUC) of 0.96. The IDC and the CON groups obtained 93.6% and 0.94 accuracy and AUC, respectively. To simulate a circumstance in which the original status of the subject is unknown, a cascade model was built fusing the aforementioned models, and achieved 94.4% accuracy. In conclusion, this study introduced a novel method for SCD risk stratification for IDC patients based on new indices from coupling analysis and non-linear HRV and BPV. We have uncovered some of the complex interactions within the autonomic regulation in this type of patient.

Lateralization of directional brain-heart information transfer during visual emotional elicitation

Previous studies have characterized the physiological interactions between central nervous system (brain) and peripheral cardiovascular system (heart) during affective elicitation in healthy subjects; however, questions related to the directionality of this functional interplay have been gaining less attention from the scientific community. Here, we explore brain-heart interactions during visual emotional elicitation in healthy subjects using measures of Granger causality (GC), a widely used descriptor of causal influences between two dynamical systems. The proposed approach inferences causality between instantaneous cardiovagal dynamics estimated from inhomogeneous point-process models of the heartbeat and high-density electroencephalogram (EEG) dynamics in 22 healthy subjects who underwent pleasant/unpleasant affective elicitation by watching pictures from the International Affective Picture System database. Particularly, we calculated the GC indexes between the EEG spectrogram in the canonical θ-, α-, β-, and γ-bands and both the instantaneous mean heart rate and its continuous parasympathetic modulations (i.e., the instantaneous HF power). Thus we looked for significant statistical differences among GC values estimated during the resting state, neutral elicitation, and pleasant/unpleasant arousing elicitation. As compared with resting state, coupling strength increases significantly in the left hemisphere during positive stimuli and in the right hemisphere during negative stimuli. Our results further reveal a correlation between emotional valence and lateralization of the dynamical information transfer going from brain-to-heart, mainly localized in the prefrontal, somatosensory, and posterior cortexes, and of the information transfer from heart-to-brain, mainly reflected into the fronto-parietal cortex oscillations in the γ-band (30 −45 Hz).

A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested

One of the pillars of experimental science is sampling. Based on the analysis of samples, estimations for populations are made. There is an entire science based on sampling. Distribution of the population, of the sample, and the connection among those two (including sampling distribution) provides rich information for any estimation to be made. Distributions are split into two main groups: continuous and discrete. The present study applies to continuous distributions. One of the challenges of sampling is its accuracy, or, in other words, how representative the sample is of the population from which it was drawn. To answer this question, a series of statistics have been developed to measure the agreement between the theoretical (the population) and observed (the sample) distributions. Another challenge, connected to this, is the presence of outliers - regarded here as observations wrongly collected, that is, not belonging to the population subjected to study. To detect outliers, a series of tests have been proposed, but mainly for normal (Gauss) distributions—the most frequently encountered distribution. The present study proposes a statistic (and a test) intended to be used for any continuous distribution to detect outliers by constructing the confidence interval for the extreme value in the sample, at a certain (preselected) risk of being in error, and depending on the sample size. The proposed statistic is operational for known distributions (with a known probability density function) and is also dependent on the statistical parameters of the population—here it is discussed in connection with estimating those parameters by the maximum likelihood estimation method operating on a uniform U(0,1) continuous symmetrical distribution.

Multivariate information processing characterizes fitness of a cascaded gene-transcription machinery

We report that a genetic two-step activation cascade processes diverse flavors of information, e.g., synergy, redundancy, and unique information. Our computations measuring reduction in Shannon entropies and reduction in variances produce differently behaving absolute magnitudes of these informational flavors. We find that similarity can be brought in if these terms are evaluated in fractions with respect to corresponding total information. Each of the input signal and final gene-product is found to generate common or redundant information fractions (mostly) to predict each other, whereas they also complement one another to harness synergistic information fraction, predicting the intermediate biochemical species. For an optimally growing signal to maintain fixed steady-state abundance of activated downstream gene-products, the interaction information fractions for this cascade module shift from net-redundancy to information-independence.

Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress

Heart rate variability (HRV; variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer TRESP,SBP→RR is decomposed into unique, redundant and synergistic components, describing the strength of baroreflex modulation independent of respiration (USBP→RR), nonbaroreflex (URESP→RR) and baroreflex-mediated (RRESP,SBP→RR) respiratory influences, and simultaneous presence of baroreflex and nonbaroreflex respiratory influences (SRESP,SBP→RR), respectively. We find that fast (short time scale) HRV oscillations—respiratory sinus arrhythmia—originate from the coexistence of baroreflex and nonbaroreflex (central) mechanisms at rest, with a stronger baroreflex involvement during HUT. Focusing on slower HRV oscillations, the baroreflex origin is dominant and MA leads to its higher involvement. Respiration influences independent on baroreflex are present at long time scales, and are enhanced during HUT.

Information Dynamics of the Brain, Cardiovascular and Respiratory Network during Different Levels of Mental Stress

In this study, an analysis of brain, cardiovascular and respiratory dynamics was conducted combining information-theoretic measures with the Network Physiology paradigm during different levels of mental stress. Starting from low invasive recordings of electroencephalographic, electrocardiographic, respiratory, and blood volume pulse signals, the dynamical activity of seven physiological systems was probed with one-second time resolution measuring the time series of the δ, θ, α and β brain wave amplitudes, the cardiac period (RR interval), the respiratory amplitude, and the duration of blood pressure wave propagation (pulse arrival time, PAT). Synchronous 5-min windows of these time series, obtained from 18 subjects during resting wakefulness (REST), mental stress induced by mental arithmetic (MA) and sustained attention induced by serious game (SG), were taken to describe the dynamics of the nodes composing the observed physiological network. Network activity and connectivity were then assessed in the framework of information dynamics computing the new information generated by each node, the information dynamically stored in it, and the information transferred to it from the other network nodes. Moreover, the network topology was investigated using directed measures of conditional information transfer and assessing their statistical significance. We found that all network nodes dynamically produce and store significant amounts of information, with the new information being prevalent in the brain systems and the information storage being prevalent in the peripheral systems. The transition from REST to MA was associated with an increase of the new information produced by the respiratory signal time series (RESP), and that from MA to SG with a decrease of the new information produced by PAT. Each network node received a significant amount of information from the other nodes, with the highest amount transferred to RR and the lowest transferred to δ, θ, α and β. The topology of the physiological network underlying such information transfer was node- and state-dependent, with the peripheral subnetwork showing interactions from RR to PAT and between RESP and RR, PAT consistently across states, the brain subnetwork resulting more connected during MA, and the subnetwork of brain–peripheral interactions involving different brain rhythms in the three states and resulting primarily activated during MA. These results have both physiological relevance as regards the interpretation of central and autonomic effects on cardiovascular and respiratory variability, and practical relevance as regards the identification of features useful for the automatic distinction of different mental states.

Multiscale information storage of linear long-range correlated stochastic processes

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our analysis is performed in the popular framework of multiscale entropy, whereby a time series is first "coarse grained" at the chosen timescale through low-pass filtering and downsampling, and then its complexity is evaluated in terms of conditional entropy. Within this framework, our approach makes use of linear fractionally integrated autoregressive (ARFI) models to derive analytical expressions for the information storage computed at multiple timescales. Specifically, we exploit state space models to provide the representation of lowpass filtered and downsampled ARFI processes, from which information storage is computed at any given timescale relating the process variance to the prediction error variance. This enhances the practical usability of multiscale information storage, as it enables a computationally reliable quantification of a complexity measure which incorporates the effects of LRC together with that of short-term dynamics. The proposed measure is first assessed in simulated ARFI processes reproducing different types of autoregressive dynamics and different degrees of LRC, studying both the theoretical values and the finite sample performance. We find that LRC alter substantially the complexity of ARFI processes even at short timescales, and that reliable estimation of complexity can be achieved at longer timescales only when LRC are properly modeled. Then, we assess multiscale information storage in physiological time series measured in humans during resting state and postural stress, revealing unprecedented responses to stress of the complexity of heart period and systolic arterial pressure variability, which are related to the different role played by LRC in the two conditions.

Comparison of short-term heart rate variability indexes evaluated through electrocardiographic and continuous blood pressure monitoring

Heart rate variability (HRV) analysis represents an important tool for the characterization of complex cardiovascular control. HRV indexes are usually calculated from electrocardiographic (ECG) recordings after measuring the time duration between consecutive R peaks, and this is considered the gold standard. An alternative method consists of assessing the pulse rate variability (PRV) from signals acquired through photoplethysmography, a technique also employed for the continuous noninvasive monitoring of blood pressure. In this work, we carry out a thorough analysis and comparison of short-term variability indexes computed from HRV time series obtained from the ECG and from PRV time series obtained from continuous blood pressure (CBP) signals, in order to evaluate the reliability of using CBP-based recordings in place of standard ECG tracks. The analysis has been carried out on short time series (300 beats) of HRV and PRV in 76 subjects studied in different conditions: resting in the supine position, postural stress during 45° head-up tilt, and mental stress during computation of arithmetic test. Nine different indexes have been taken into account, computed in the time domain (mean, variance, root mean square of the successive differences), frequency domain (low-to-high frequency power ratio LF/HF, HF spectral power, and central frequency), and information domain (entropy, conditional entropy, self entropy). Thorough validation has been performed using comparison of the HRV and PRV distributions, robust linear regression, and Bland-Altman plots. Results demonstrate the feasibility of extracting HRV indexes from CBP-based data, showing an overall relatively good agreement of time-, frequency-, and information-domain measures. The agreement decreased during postural and mental arithmetic stress, especially with regard to band-power ratio, conditional, and self-entropy. This finding suggests to use caution in adopting PRV as a surrogate of HRV during stress conditions.

Paced Breathing Increases the Redundancy of Cardiorespiratory Control in Healthy Individuals and Chronic Heart Failure Patients

Synergy and redundancy are concepts that suggest, respectively, adaptability and fault tolerance of systems with complex behavior. This study computes redundancy/synergy in bivariate systems formed by a target X and a driver Y according to the predictive information decomposition approach and partial information decomposition framework based on the minimal mutual information principle. The two approaches assess the redundancy/synergy of past of X and Y in reducing the uncertainty of the current state of X. The methods were applied to evaluate the interactions between heart and respiration in healthy young subjects (n = 19) during controlled breathing at 10, 15 and 20 breaths/minute and in two groups of chronic heart failure patients during paced respiration at 6 (n = 9) and 15 (n = 20) breaths/minutes from spontaneous beat-to-beat fluctuations of heart period and respiratory signal. Both methods suggested that slowing respiratory rate below the spontaneous frequency increases redundancy of cardiorespiratory control in both healthy and pathological groups, thus possibly improving fault tolerance of the cardiorespiratory control. The two methods provide markers complementary to respiratory sinus arrhythmia and the strength of the linear coupling between heart period variability and respiration in describing the physiology of the cardiorespiratory reflex suitable to be exploited in various pathophysiological settings.

Coupling of local muscle deoxygenation and autonomic control depends on exercise intensity-insights from transfer entropy analysis

OBJECTIVE

We analyzed the driving component between the periods of adjacent heartbeats (R-R intervals) and vastus lateralis-deoxygenation (%HHb) during incremental cycling. Considering a tight matching of local metabolism with systemic and local perfusion, a coupling between indices of cardiovascular control (R-R variability) and %HHb is suggested. Further, an intensity-dependent coupling between R-R variability and %HHb was hypothesized, because a multitude of feedback and feedforward mechanisms to autonomic cardiovascular control as well as local vasodilating mechanisms are associated with muscle metabolism and thus exercise intensity.

APPROACH

Ten male triathletes (age: 34  ±  8 years) completed a test, including baseline (BAS, 50 W), a 25 W * min^-1 ramp incremental phase until exhaustion and a recovery period (REC, 50 W). R-R intervals, %HHb and respiratory responses were simultaneously recorded. Five corresponding data segments were selected: BAS, before the first ventilatory threshold (preGET), between GET and the respiratory compensation point (preRCP), above RCP (postRCP), and REC. Bivariate transfer entropy (BTE) was applied to determine the signal coupling between R-R and %HHb.

MAIN RESULTS

During preGET and preRCP, the analysis yielded the dominating direction from %HHb to R-R intervals, while for postRCP the direction was reversed. No significant signal coupling was detectable for the BAS and REC segments.

SIGNIFICANCE

Assuming that %HHb is related to the metabolic state of the working muscle, BTE results support the role of metaboreceptors in the systemic blood flow regulation at lower exercise intensities, while other mechanisms (e.g. baroreceptor and mechanoreceptor feedback, central command) that modulate cardiovascular control may override this coupling at higher intensities.

Univariate and multivariate conditional entropy measures for the characterization of short-term cardiovascular complexity under physiological stress

OBJECTIVE

A defining feature of physiological systems under the neuroautonomic regulation is their dynamical complexity. The most common approach to assess physiological complexity from short-term recordings, i.e. to compute the rate of entropy generation of an individual system by means of measures of conditional entropy (CE), does not consider that complexity may change when the investigated system is part of a network of physiological interactions. This study aims at extending the concept of short-term complexity towards the perspective of network physiology, defining multivariate CE measures whereby multiple physiological processes are accounted for in the computation of entropy rates.

APPROACH

Univariate and multivariate CE measures are computed using state-of-the-art methods for entropy estimation and applied to time series of heart period (H), systolic (S) and diastolic (D) arterial pressure, and respiration (R) variability measured in healthy subjects monitored in a resting state and during conditions of postural and mental stress.

MAIN RESULTS

Compared with the traditional univariate metric of short-term complexity, multivariate measures provide additional information with plausible physiological interpretation, such as (i) the dampening of respiratory sinus arrhythmia and activation of the baroreflex control during postural stress; (ii) the increased complexity of heart period and blood pressure variability during mental stress, reflecting the effect of respiratory influences and upper cortical centers; (iii) the strong influence of D on S, mediated by left ventricular ejection fraction and vascular properties; (iv) the role of H in reducing the complexity of D, related to cardiac run-off effects; and (v) the unidirectional role of R in influencing cardiovascular variability.

SIGNIFICANCE

Our results document the importance of employing a network perspective in the evaluation of the short-term complexity of cardiovascular and respiratory dynamics across different physiological states.

Information transfer and information modification to identify the structure of cardiovascular and cardiorespiratory networks

To fully elucidate the complex physiological mechanisms underlying the short-term autonomic regulation of heart period (H), systolic and diastolic arterial pressure (S, D) and respiratory (R) variability, the joint dynamics of these variables need to be explored using multivariate time series analysis. This study proposes the utilization of information-theoretic measures to measure causal interactions between nodes of the cardiovascular/cardiorespiratory network and to assess the nature (synergistic or redundant) of these directed interactions. Indexes of information transfer and information modification are extracted from the H, S, D and R series measured from healthy subjects in a resting state and during postural stress. Computations are performed in the framework of multivariate linear regression, using bootstrap techniques to assess on a single-subject basis the statistical significance of each measure and of its transitions across conditions. We find patterns of information transfer and modification which are related to specific cardiovascular and cardiorespiratory mechanisms in resting conditions and to their modification induced by the orthostatic stress.

Causal brain-heart information transfer during visual emotional elicitation in healthy subjects: Preliminary evaluations and future perspectives

Complex heartbeat dynamics is known to reflect subject's emotional state, thanks to numerous links to brain cortical and subcortical regions. Likewise, specific brain regions are deeply involved in vagally-mediated emotional processing and regulation. Nevertheless, although the brain-heart interplay has been studied during visual emotion elicitation, directional interactions have not been investigated so far. To fill this gap, in this study we investigate brain-heart dynamics during emotional elicitation in healthy subjects through measures of Granger causality (GC) between the two physiological systems. Data were gathered from 22 healthy volunteers who underwent pleasant/ unpleasant affective elicitation using pictures from the International Affective Picture System. Neutral emotional stimuli were elicited as well. High density electroencephalogram (EEG) signals were processed to obtain time-varying maps of cortical activation, whereas the associated instantaneous cardiovascular dynamics was estimated through inhomogeneous point-process models. Concerning the information transfer brain-to-heart, GE highlighted significant valence-dependent lateralization with respect to resting states. Furthermore, as a proof of concept, the study of heart-to-brain dynamics considering EEG oscillations in the γ band (30-45 Hz) highlighted differential information transfer between neutral and positive elicitations directed to the prefrontal cortex.

Complexity of cardiovascular rhythms during head-up tilt test by entropy of patterns

OBJECTIVE

The head-up tilt (HUT) test, which provokes transient dynamical alterations in the regulation of cardiovascular system, provides insights into complex organization of this system. Based on signals with heart period intervals (RR-intervals) and/or systolic blood pressure (SBP), differences in the cardiovascular regulation between vasovagal patients (VVS) and the healthy people group (CG) are investigated.

APPROACH

Short-term relations among signal data represented symbolically by three-beat patterns allow to qualify and quantify the complexity of the cardiovascular regulation by Shannon entropy. Four types of patterns: permutation, ordinal, deterministic and dynamical, are used, and different resolutions of signal values in the the symbolization are applied in order to verify how entropy of patterns depends on a way in which values of signals are preprocessed.

MAIN RESULTS

At rest, in the physiologically important signal resolution ranges, independently of the type of patterns used in estimates, the complexity of SBP signals in VVS is different from the complexity found in CG. Entropy of VVS is higher than CG what could be interpreted as substantial presence of noisy ingredients in SBP of VVS. After tilting this relation switches. Entropy of CG occurs significantly higher than VVS for SBP signals. In the case of RR-intervals and large resolutions, the complexity after the tilt becomes reduced when compared to the complexity of RR-intervals at rest for both groups. However, in the case of VVS patients this reduction is significantly stronger than in CG.

SIGNIFICANCE

Our observations about opposite switches in entropy between CG and VVS might support a hypothesis that baroreflex in VVS affects stronger the heart rate because of the inefficient regulation (possibly impaired local vascular tone alternations) of the blood pressure.