Measuring frequency domain granger causality for multiple blocks of interacting time series

In the past years, several frequency-domain causality measures based on vector autoregressive time series modeling have been suggested to assess directional connectivity in neural systems. The most followed approaches are based on representing the considered set of multiple time series as a realization of two or three vector-valued processes, yielding the so-called Geweke linear feedback measures, or as a realization of multiple scalar-valued processes, yielding popular measures like the directed coherence (DC) and the partial DC (PDC). In the present study, these two approaches are unified and generalized by proposing novel frequency-domain causality measures which extend the existing meas…

Granger Causality Analysis of Transient Calcium Dynamics in the Honey Bee Antennal Lobe Network

Odorant processing presents multiple parallels across animal species, and insects became relevant models for the study of olfactory coding because of the tractability of the underlying neural circuits. Within the insect brain, odorants are received by olfactory sensory neurons and processed by the antennal lobe network. Such a network comprises multiple nodes, named glomeruli, that receive sensory information and are interconnected by local interneurons participating in shaping the neural representation of an odorant. The study of functional connectivity between the nodes of a sensory network in vivo is a challenging task that requires simultaneous recording from multiple nodes at high temp…

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

In the framework of information dynamics, the temporal evolution of coupled systems can be studied by decomposing the predictive information about an assigned target system into amounts quantifying the information stored inside the system and the information transferred to it. While information storage and transfer are computed through the known self-entropy (SE) and transfer entropy (TE), an alternative decomposition evidences the so-called cross entropy (CE) and conditional SE (cSE), quantifying the cross information and internal information of the target system, respectively. This study presents a thorough evaluation of SE, TE, CE and cSE as quantities related to the causal statistical s…

Synergetic and redundant information flow detected by unnormalized Granger causality: application to resting state fMRI

Objectives: We develop a framework for the analysis of synergy and redundancy in the pattern of information flow between subsystems of a complex network. Methods: The presence of redundancy and/or synergy in multivariate time series data renders difficult to estimate the neat flow of information from each driver variable to a given target. We show that adopting an unnormalized definition of Granger causality one may put in evidence redundant multiplets of variables influencing the target by maximizing the total Granger causality to a given target, over all the possible partitions of the set of driving variables. Consequently we introduce a pairwise index of synergy which is zero when two in…

Causal and Non-Causal Frequency Domain Assessment of Spontaneous Baroreflex Sensitivity after Myocardial Infarction

Acute myocardial infarction (AMI) is thought to alter the baroreflex control of arterial pressure. We tested this hypothesis investigating the changes of the cardiovascular response after AMI in comparison with young and old healthy controls studied at rest and during head-up tilt, using causal and non-causal frequency domain measures of the baroreflex sensitivity. Our results indicate: (i) the importance of using a causal approach that takes into account not only feedback but also feedforward effects in the study of interactions between the heart period and the arterial pressure; (ii) the compromised capacity of baroreceptors to control SAP fluctuations in post-AMI patients, both at rest a…

Redundancy and synergy in interactions among basic cardiovascular oscillations

The cardiovascular control system comprises a complex network of various control mechanisms operating on many time scales resulting in complex and mutually interconnected output signals (e.g. heart rate, systolic and diastolic blood pressures). The analysis of these interconnections could noninvasively provide an information on the regulatory mechanisms involved in cardiovascular control and thus could be potentially applied to better characterize cardiovascular dysregulation in pathological conditions. Our study demonstrates that the strength of interactions among signals changes with the time scale and as a response to changed autonomic state (orthostasis compared to supine rest). Novel i…

An Information-Theoretic Framework to Measure the Dynamic Interaction between Neural Spike Trains

Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as existing methods either do not consider the inherent point process nature of spike trains or are based on parametric assumptions that may lead to wrong inferences if not met. This work presents a framework, grounded in the field of information dynamics, for the model-free, continuous-time estimation of both undirected (symmetric) and directed (causal) interactions between pairs of spike trains. The framework decomposes the overall information exchanged dynami…

An Empirical Mode Decomposition Approach to Assess the Strength of Heart Period-Systolic Arterial Pressure Variability Interactions.

This work proposes an empirical mode decomposition (EMD) method to assess the strength of the interactions between heart period (HP) and systolic arterial pressure (SAP) variability. EMD was exploited to decompose the original series (OR) into its first, and fastest, intrinsic mode function (IMF1) and the residual (RES) computed by subtracting the IMF1 from OR. EMD procedure was applied to both HP and SAP variability series. Then, the cross correlation function (CCF) was computed over OR, IMF1 and RES series derived from HP and SAP variability in 13 healthy subjects (age 27±8 yrs, 5 males) at rest in supine position (REST) and during head-up tilt (TILT). The first CCF maximum at negative ti…

Dynamic cerebrovascular autoregulation in patients prone to postural syncope: Comparison of techniques assessing the autoregulation index from spontaneous variability series

Abstract Three approaches to the assessment of cerebrovascular autoregulation (CA) via the computation of the autoregulation index (ARI) from spontaneous variability of mean arterial pressure (MAP) and mean cerebral blood flow velocity (MCBFV) were applied: 1) a time domain method (TDM); 2) a nonparametric method (nonPM); 3) a parametric method (PM). Performances were tested over matched and surrogate unmatched pairs. Data were analyzed at supine resting (REST) and during the early phase of 60° head-up tilt (TILT) in 13 subjects with previous history of postural syncope (SYNC, age: 28 ± 9 yrs.; 5 males) and 13 control individuals (noSYNC, age: 27 ± 8 yrs.; 5 males). Analysis was completed b…

Determination of Synchronization of Electrical Activity in the Heart by Shannon Entropy Measure

In this paper we propose a new index of synchronization for the study of heart’s electrical activity during atrial fibrillation (AF). The index relies on the measure of the time delays between correspondent activations in two atrial electrograms and on the characterization of their dispersion by a measure of Shannon Entropy. The algorithm was validated on simulated signals mimicking different degree of synchronization. Results showed the index was able to discriminate among different levels of organization, provided that it works on series of at least 50 activations (time resolution of almost 10 sec during AF). Moreover, we applied the algorithm to real bipolar electrograms, obtained from a…

Assessment of mental stress through the analysis of physiological signals acquired from wearable devices

Mental stress is a physiological state that directly correlates to the quality of life of individuals. Generally speaking, but especially true for disabled or elderly subjects, the assessment of such condition represents a very strong indicator correlated to the difficulties, and, in some case, to the frustration that derives from the execution of a task that results troublesome to be accomplished. This article describes a novel procedure for the assessment of the mental stress level through the use of low invasive wireless wearable devices. The information contained in electrocardiogram, respiratory signal, blood volume pulse, and electroencephalogram was extracted to set up an estimator f…

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 Sq…

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls.

We present a framework for the linear parametric analysis of pairwise interactions in bivariate time series in the time and frequency domains, which allows the evaluation of total, causal and instantaneous interactions and connects time- and frequency-domain measures. The framework is applied to physiological time series to investigate the cerebrovascular regulation from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (MAP), and the cardiovascular regulation from the variability of heart period (HP) and systolic arterial pressure (SAP). We analyze time series acquired at rest and during the early and late phase of head-up tilt in subjects developing or…

Information decomposition of short-term cardiovascular and cardiorespiratory variability

We present an entropy decomposition strategy aimed at quantifying how the predictive information (PI) about heart rate (HR) variability is dynamically stored in HR and is transferred to HR from arterial pressure (AP) and respiration (RS) variability according to synergistic or redundant cooperation. The PI is expressed as the sum of the self entropy (SE) of HR plus the transfer entropy (TE) from RS,AP to HR, quantifying respectively the information stored in the cardiac system and transferred to the cardiac system to the vascular and respiratory systems. The information transfer is further decomposed as the sum of the (unconditioned) TE from RS to HR plus the TE from SP to HR conditioned to…

Entropy-Based Detection of Complexity and Nonlinearity in Short-Term Heart Period Variability under different Physiopathological States

We compare different estimators of a popular en-tropy-based nonlinear dynamic measure, i.e. the conditional entropy (CE), as regards their ability to assess the complexity and nonlinearity of short-term heart rate variability (HRV). The CE is computed using binning, kernel and nearest neighbor entropy estimators in HRV time series measured from young, old and post-myocardial infarction patients studied at rest and during orthostatic stress. We find that the three estimators yield similar patterns of CE, but different patterns of nonlinear dynamics, across groups and conditions. These results suggest that the strategy for CE estimation is not crucial for the quantification of complexity, but…

A new framework for the time- and frequency-domain assessment of high-order interactions in networks of random processes

While the standard network description of complex systems is based on quantifying the link between pairs of system units, higher-order interactions (HOIs) involving three or more units often play a major role in governing the collective network behavior. This work introduces a new approach to quantify pairwise and HOIs for multivariate rhythmic processes interacting across multiple time scales. We define the so-called O-information rate (OIR) as a new metric to assess HOIs for multivariate time series, and present a framework to decompose the OIR into measures quantifying Granger-causal and instantaneous influences, as well as to expand all measures in the frequency domain. The framework ex…

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…

Quantification of synchronization during atrial fibrillation by Shannon entropy: Validation in patients and computer model of atrial arrhythmias

Atrial fibrillation (AF), a cardiac arrhythmia classically described as completely desynchronized, is now known to show a certain amount of synchronized electrical activity. In the present work a new method for quantifying the level of synchronization of the electrical activity recorded in pairs of atrial sites during atrial fibrillation is presented. A synchronization index (Sy) was defined by quantifying the degree of complexity of the distribution of the time delays between sites by Shannon entropy estimation. The capability of Sy to discriminate different AF types in patients was assessed on a database of 60 pairs of endocardial recordings from a multipolar basket catheter. The analysis…

Information domain approach to the investigation of cardio-vascular, cardio-pulmonary, and vasculo-pulmonary causal couplings

The physiological mechanisms related to cardio-vascular (CV), cardio-pulmonary (CP), and vasculo-pulmonary (VP) regulation may be probed through multivariate time series analysis tools. This study applied an information domain approach for the evaluation of non-linear causality to the beat-to-beat variability series of heart period (t), systolic arterial pressure (s), and respiration (r) measured during tilt testing and paced breathing (PB) protocols. The approach quantifies the causal coupling from the series i to the series j (C(ij)) as the amount of information flowing from i to j. A measure of directionality is also obtained as the difference between two reciprocal causal couplings (D(i…

Quantification of Different Regulatory Pathways Contributing to Heartbeat Dynamics during Multiple Stimuli: a Proof of the Concept.

The dynamical interplay between brain and heart is mediated by several feedback mechanisms including the central autonomic network and baroreflex loop at a peripheral level, also for a short-term regulation. State of the art focused on the characterization of each regulatory pathway through a single stressor elicitation. However, no studies targeted the actual quantification of different mediating routes leading to the generation of heartbeat dynamics, particularly in case of combined exogenous stimuli. In this study, we propose a new approach based on computational modeling to quantify the contribution of multiple concurrent stimuli in modulating cardiovascular dynamics. In this prelimina…

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 …

Local Granger causality

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the 'local Granger causality', i.e. the profile of the information transfer at each discrete time point in Gaussian processes; in this frame Granger causality is the average of its local version. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear …

Breathing 100% oxygen during water immersion improves postimmersion cardiovascular responses to orthostatic stress

Abstract Physiological compensation to postural stress is weakened after long‐duration water immersion (WI), thus predisposing individuals to orthostatic intolerance. This study was conducted to compare hemodynamic responses to postural stress following exposure to WI alone (Air WI), hyperbaric oxygen alone in a hyperbaric chamber (O 2 HC), and WI combined with hyperbaric oxygen (O 2 WI), all at a depth of 1.35 ATA, and to determine whether hyperbaric oxygen is protective of orthostatic tolerance. Thirty‐two healthy men underwent up to 15 min of 70° head‐up tilt (HUT) testing before and after a single 6‐h resting exposure to Air WI ( N  = 10), O 2 HC ( N  = 12), or O 2 WI ( N  = 10). Heart …

A measure of concurrent neural firing activity based on mutual information

AbstractMultiple methods have been developed in an attempt to quantify stimulus-induced neural coordination and to understand internal coordination of neuronal responses by examining the synchronization phenomena in neural discharge patterns. In this work we propose a novel approach to estimate the degree of concomitant firing between two neural units, based on a modified form of mutual information (MI) applied to a two-state representation of the firing activity. The binary profile of each single unit unfolds its discharge activity in time by decomposition into the state of neural quiescence/low activity and state of moderate firing/bursting. Then, the MI computed between the two binary st…

Wave similarity mapping shows the spatiotemporal distribution of fibrillatory wave complexity in the human right atrium during paroxysmal and chronic atrial fibrillation.

Introduction: The complexity of waveforms during atrial fibrillation may reflect critical activation patterns for the arrhythmia perpetuation. In this study, we introduce a novel concept of map, based on the analysis of the wave morphology, which gives a direct evidence in the human right atrium on the spatiotemporal distribution of fibrillatory wave complexity in paroxysmal (PAF) and chronic (CAF) atrial fibrillation. Methods and Results: Electrograms were recorded from a 64-electrode catheter in the right atrium of 15 patients during PAF (n = 8) and CAF (n = 7). Wave similarity maps were constructed by calculating the degree of morphological similarity of activation waves (S) at each atri…

A silicon photomultiplier-based analog front-end for DC component rejection and pulse wave recording in photoplethysmographic applications

The growing attention towards healthcare and the constant technological innovations in the field of semiconductor components have allowed a widespread availability of smaller devices, suitable to be worn and able to continuously acquire physiological signals. Wearable devices are, however, more prone to yield signals corrupted by artifacts caused by movement. This issue is particularly relevant in photoplethysmographic (PPG) applications where also, to exploit the whole dynamic range of the acquisition device, the DC component of the signal should be removed and the AC component amplified. In this context, we have designed and realized an analog front-end (AFE) suitable to be integrated wit…

A method for quantifying atrial fibrillation organization based on wave-morphology similarity

A new method for quantifying the organization of single bipolar electrograms recorded in the human atria during atrial fibrillation (AF) is presented. The algorithm relies on the comparison between pairs of local activation waves (LAWs) to estimate their morphological similarity, and returns a regularity index (/spl rho/) which measures the extent of repetitiveness over time of the detected activations. The database consisted of endocardial data from a multipolar basket catheter during AF and intraatrial recordings during atrial flutter. The index showed maximum regularity (/spl rho/=1) for all atrial flutter episodes and decreased significantly when increasing AF complexity as defined by W…

Propagation pattern analysis during atrial fibrillation based on the adaptive group LASSO.

The present study introduces sparse modeling for the estimation of propagation patterns in intracardiac atrial fibrillation (AF) signals. The estimation is based on the partial directed coherence (PDC) function, derived from fitting a multivariate autoregressive model to the observed signals. A sparse optimization method is proposed for estimation of the model parameters, namely, the adaptive group least absolute selection and shrinkage operator (aLASSO). In simulations aLASSO was found superior to the commonly used least-squares (LS) estimation with respect to estimation performance. The normalized error between the true and estimated model parameters dropped from 0.200.04 for LS estimatio…

Reliability of Short-Term Heart Rate Variability Indexes Assessed through Photoplethysmography

The gold standard method to monitor heart rate variability (HRV) comprises measuring the time series of interbeat interval durations from electrocardiographic (ECG) recordings. However, due to the widespread use, simplicity and usability of photoplethysmographic (PPG) techniques, monitoring pulse rate variability (PRV) from pulse wave recordings has become a viable alternative to standard HRV analysis. The present study investigates the accuracy of PRV, measured as a surrogate of HRV, for the quantification of descriptive indexes computed in the time domain (mean, variance), frequency domain (low-to-high frequency power ratio LF/HF, HF band central frequency) and information domain (entropy…

Cardiorespiratory information dynamics during mental arithmetic and sustained attention

An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV) were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, alt…

Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique

We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected acc…

Assessing complexity and causality in heart period variability through a model-free data-driven multivariate approach

The aim of this study is to emphasize the importance of model-free data-driven mul- tivariate approaches in describing HP variability and cardiovascular control mechanisms responsible for inducing HP changes via modifications of different cardiovascular vari- ables such as SAP and RESP. The goal was achieved through the application, a previously proposed model-free data-driven multivariate framework devised to assess complexity and causality over a multivariate set composed by several, simultaneously recorded, car- diovascular variability series (Porta et al., 2014). The approach was applied to assess the complexity of the cardiac control, through the evaluation of the amount of irregularit…

Algorithms for the inference of causality in dynamic processes: Application to cardiovascular and cerebrovascular variability

This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the traditional Granger causality analysis, showing that it leads to false detection of causality when instantaneous and time-lagged effects coexist in the process structure. Then, we propose an improved algorithm for causal inference that combines the Granger framework with the approach proposed by Pearl for the study of causality among multiple random variables. This new approach is compared with the traditional one in theoretical and simulated examples of interacting processes, sho…

An Information-Theoretic Framework to Map the Spatiotemporal Dynamics of the Scalp Electroencephalogram

We present the first application of the emerging framework of information dynamics to the characterization of the electroencephalography (EEG) activity. The framework provides entropy-based measures of information storage (self entropy, SE) and information transfer (joint transfer entropy (TE) and partial TE), which are applied here to detect complex dynamics of individual EEG sensors and causal interactions between different sensors. The measures are implemented according to a model-free and fully multivariate formulation of the framework, allowing the detection of nonlinear dynamics and direct links. Moreover, to deal with the issue of volume conduction, a compensation for instantaneous e…

Reliable Paroxysmal Atrial Fibrillation Substrate Assessment During Sinus Rhythm Through Optimal Estimation of Local Activation Waves Dynamics

[EN] The analysis of coronary sinus (CS) electrograms (EGMs) during catheter ablation (CA) of atrial fibrillation (AF) is highly important for AF substrate evaluation. However, channels of the CS catheter may be affected by vigorous cardiac movement and bad contact. This work investigates the most reliable channels in preserving the AF dynamics during sinus rhythm (SR). Local activation waves (LAWs) were detected in 44 bipolar CS recordings of 60-300 seconds duration in 28 paroxysmal AF patients undergoing CA. Recordings consisted of five channels: distal, mid-distal, medial, mid-proximal and proximal. LAW duration, amplitude, area and correlation between dominant morphologies of each chann…

Time-Varying Surrogate Data to Assess Nonlinearity in Nonstationary Time Series: Application to Heart Rate Variability

We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discrimin…

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 …

Impact of Nonstationarities on Short Heart Rate Variability Recordings During Obstructive Sleep Apnea

Obstructive sleep apnea (OSA) is a sleep disorder characterized by breathing pauses due to collapse of the upper airways. During OSA the autonomic modulation, as noninvasively assessed through heart period (HP) variability, is altered in a time-varying way even though time-varying properties of HP fluctuations are often disregarded by HP variability studies. We performed a time domain analysis computed over very short epochs corresponding to the sole OSA events explicitly accounting for HP variability nonstationarities. Length-matched epochs were extracted during OSA and quiet sleep (SLEEP) in 13 subjects suffering from OSA (11 males, age 55±11, apnea-hypopnea index 44±19). Mean HP, varianc…

Mixed predictability and cross-validation to assess non-linear Granger causality in short cardiovascular variability series

A method to evaluate the direction and strength of causal interactions in bivariate cardiovascular and cardiorespiratory series is presented. The method is based on quantifying self and mixed predictability of the two series using nearest-neighbour local linear approximation. It returns two causal coupling indexes measuring the relative improvement in predictability along direct and reverse directions, and a directionality index indicating the preferential direction of interaction. The method was implemented through a cross-validation approach that allowed quantification of directionality without constraining the embedding of the series, and fully exploited the available data to maximise th…

Lag-specific transfer entropy as a tool to assess cardiovascular and cardiorespiratory information transfer

In the study of interacting physiological systems, model-free tools for time series analysis are fundamental to provide a proper description of how the coupling among systems arises from the multiple involved regulatory mechanisms. This study presents an approach which evaluates direction, magnitude, and exact timing of the information transfer between two time series belonging to a multivariate dataset. The approach performs a decomposition of the well-known transfer entropy (TE) which achieves 1) identifying, according to a lag-specific information-theoretic formulation of the concept of Granger causality, the set of time lags associated with significant information transfer, and 2) assig…

A Novel Approach to Propagation Pattern Analysis in Intracardiac Atrial Fibrillation Signals

The purpose of this study is to investigate propagation patterns in intracardiac signals recorded during atrial fibrillation (AF) using an approach based on partial directed coherence (PDC), which evaluates directional coupling between multiple signals in the frequency domain. The PDC is evaluated at the dominant frequency of AF signals and tested for significance using a surrogate data procedure specifically designed to assess causality. For significantly coupled sites, the approach allows also to estimate the delay in propagation. The methods potential is illustrated with two simulation scenarios based on a detailed ionic model of the human atrial myocyte as well as with real data recordi…

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations.

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of …

Need of causal analysis for assessing phase relationships in closed loop interacting cardiovascular variability series

The phase spectra obtained by the classical closed loop autoregressive model (2AR) and by an open loop autoregressive model (ARXAR) were compared to shed light on the need of introducing causality in the assessment of the delay between RR and arterial pressure oscillations. The reliability of the two approaches was tested in simulation and real data setting. In simulation, the coupling strength of a bivariate closed loop process was adjusted to obtain a range of working conditions from open to closed loop. In open loop condition, 2AR and ARXAR phases were comparable and in agreement with the imposed delay. In closed loop condition, ARXAR model returned the imposed delays, while 2AR showed a…

Conditional Entropy-Based Evaluation of Information Dynamics in Physiological Systems

We present a framework for quantifying the dynamics of information in coupled physiological systems based on the notion of conditional entropy (CondEn). First, we revisit some basic concepts of information dynamics, providing definitions of self entropy (SE), cross entropy (CE) and transfer entropy (TE) as measures of information storage and transfer in bivariate systems. We discuss also the generalization to multivariate systems, showing the importance of SE, CE and TE as relevant factors in the decomposition of the system predictive information. Then, we show how all these measures can be expressed in terms of CondEn, and devise accordingly a framework for their data-efficient estimation.…

Mutual information-based feature selection for low-cost BCIs based on motor imagery

In the present study a feature selection algorithm based on mutual information (MI) was applied to electro-encephalographic (EEG) data acquired during three different motor imagery tasks from two dataset: Dataset I from BCI Competition IV including full scalp recordings from four subjects, and new data recorded from three subjects using the popular low-cost Emotiv EPOC EEG headset. The aim was to evaluate optimal channels and band-power (BP) features for motor imagery tasks discrimination, in order to assess the feasibility of a portable low-cost motor imagery based Brain-Computer Interface (BCI) system. The minimal sub set of features most relevant to task description and less redundant to…

A stochastic approach for automatic registration and fusion of left atrial electroanatomic maps with 3D CT anatomical images.

The integration of electroanatomic maps with highly resolved computed tomography cardiac images plays an important role in the successful planning of the ablation procedure of arrhythmias. In this paper, we present and validate a fully-automated strategy for the registration and fusion of sparse, atrial endocardial electroanatomic maps (CARTO maps) with detailed left atrial (LA) anatomical reconstructions segmented from a pre-procedural MDCT scan. Registration is accomplished by a parameterized geometric transformation of the CARTO points and by a stochastic search of the best parameter set which minimizes the misalignment between transformed CARTO points and the LA surface. The subsequent …

Assessing causality in brain dynamics and cardiovascular control

Understanding how different cerebral areas interact to produce an integrated behaviour and disentangling the mechanisms that contribute to cardiovascular control are two of the major challenges of brain and cardiovascular neuroscience. The increasing availability of simultaneous continuous

Measuring High-Order Interactions in Rhythmic Processes Through Multivariate Spectral Information Decomposition

Many complex systems in physics, biology and engineering are modeled as dynamical networks and described using multivariate time series analysis. Recent developments have shown that the emergent dynamics of a network system are significantly affected by interactions involving multiple network nodes which cannot be described using pairwise links. While these higher-order interactions can be probed using information-theoretic measures, a rigorous framework to describe them in the frequency domain is still lacking. This work presents an approach for the spectral decomposition of multivariate information measures, capable of identifying higher-order synergistic and redundant interactions betwee…

Quantifying multidimensional control mechanisms of cardiovascular dynamics during multiple concurrent stressors

Heartbeat regulation is achieved through different routes originating from central autonomic network sources, as well as peripheral control mechanisms. While previous studies successfully characterized cardiovascular regulatory mechanisms during a single stressor, to the best of our knowledge, a combination of multiple concurrent elicitations leading to the activation of different autonomic regulatory routes has not been investigated yet. Therefore, in this study, we propose a novel modeling framework for the quantification of heartbeat regulatory mechanisms driven by different neural routes. The framework is evaluated using two heartbeat datasets gathered from healthy subjects undergoing p…

Nonlinear effects of respiration on the crosstalk between cardiovascular and cerebrovascular control systems.

Cardiovascular and cerebrovascular regulatory systems are vital control mechanisms responsible for guaranteeing homeostasis and are affected by respiration. This work proposes the investigation of cardiovascular and cerebrovascular control systems and the nonlinear influences of respiration on both regulations through joint symbolic analysis (JSA), conditioned or unconditioned on respiration. Interactions between cardiovascular and cerebrovascular regulatory systems were evaluated as well by performing correlation analysis between JSA indexes describing the two control systems. Heart period, systolic and mean arterial pressure, mean cerebral blood flow velocity and respiration were acquired…

Assessing Causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods

We investigated the ability of mutual nonlinear prediction methods to assess causal interactions in short-term cardiovascular variability during normal and impaired conditions. Directional interactions between heart period (RR interval of the ECG) and systolic arterial pressure (SAP) short-term variability series were quantified as the cross-predictability (CP) of one series given the other, and as the predictability improvement (PI) yielded by the inclusion of samples of one series into the prediction of the other series. Nonlinear prediction was performed through global approximation (GA), approximation with locally constant models (LA0) and approximation with locally linear models (LA1) …

An Automatic System for the Analysis and Classification of Human Atrial Fibrillation Patterns from Intracardiac Electrograms

This paper presents an automatic system for the analysis and classification of atrial fibrillation (AF) patterns from bipolar intracardiac signals. The system is made up of: 1) a feature- extraction module that defines and extracts a set of measures potentially useful for characterizing AF types on the basis of their degree of organization; 2) a feature-selection module (based on the Jeffries-Matusita distance and a branch and bound search algorithm) identifying the best subset of features for discriminating different AF types; and 3) a support vector machine technique-based classification module that automatically discriminates the AF types according to the Wells' criteria. The automatic s…

An integrated approach based on uniform quantization for the evaluation of complexity of short-term heart period variability: Application to 24 h Holter recordings in healthy and heart failure humans.

We propose an integrated approach based on uniform quantization over a small number of levels for the evaluation and characterization of complexity of a process. This approach integrates information-domain analysis based on entropy rate, local nonlinear prediction, and pattern classification based on symbolic analysis. Normalized and non-normalized indexes quantifying complexity over short data sequences (∼300 samples) are derived. This approach provides a rule for deciding the optimal length of the patterns that may be worth considering and some suggestions about possible strategies to group patterns into a smaller number of families. The approach is applied to 24 h Holter recordings of …

Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach

In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI) framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently G…

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

The continuously growing framework of information dynamics encompasses a set of tools, rooted in information theory and statistical physics, which allow to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of complex networks. Building on the most recent developments in this field, this work designs a complete approach to dissect the information carried by the target of a network of multiple interacting systems into the new information produced by the system, the information stored in the system, and the information transferred to it from the other systems; information storage and transfer are then further decomposed into amou…

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 delta, theta, alpha, and beta electroencephalographic (EEG) wave amplitudes, and of heart rate, respiration amplitude, and pulse arrival time (PAT) variability. MI is computed: (i) considering all variables in the two subnetworks to evaluate overall brain–body interaction…

Mutual nonlinear prediction of cardiovascular variability series: Comparison between exogenous and autoregressive exogenous models

A model-based approach to perform mutual nonlinear prediction of short cardiovascular variability series is presented. The approach is based on identifying exogenous (X) and autoregressive exogenous (ARX) models by K-nearest neighbors local linear approximation, and estimates the predictability of a series given the other as the squared correlation between original and predicted values of the series. The method was first tested on simulations reproducing different types of interaction between non-identical Henon maps, and then applied to heart rate (HR) and blood pressure (BP) variability series measured in healthy subjects at rest and after head-up tilt. Simulations showed that different c…

Bivariate nonlinear prediction to quantify the strength of complex dynamical interactions in short-term cardiovascular variability.

A nonlinear prediction method for investigating the dynamic interdependence between short length time series is presented. The method is a generalization to bivariate prediction of the univariate approach based on nearest neighbor local linear approximation. Given the input and output series x and y, the relationship between a pattern of samples of x and a synchronous sample of y was approximated with a linear polynomial whose coefficients were estimated from an equation system including the nearest neighbor patterns in x and the corresponding samples in y. To avoid overfitting and waste of data, the training and testing stages of the prediction were designed through a specific out-of-sampl…

Exploring directionality in spontaneous heart period and systolic pressure variability interactions in humans: implications in the evaluation of baroreflex gain

Although in physiological conditions RR interval and systolic arterial pressure (SAP) are likely to interact in a closed loop, the traditional cross-spectral analysis cannot distinguish feedback (FB) from feedforward (FF) influences. In this study, a causal approach was applied for calculating the coherence from SAP to RR ( Ks-r) and from RR to SAP ( Kr-s) and the gain and phase of the baroreflex transfer function. The method was applied, compared with the noncausal one, to RR and SAP series taken from 15 healthy young subjects in the supine position and after passive head-up tilt. For the low frequency (0.04–0.15 Hz) spectral component, the enhanced FF coupling ( Kr-s = 0.59 ± 0.21, signi…

Deterioration of organization in the first minutes of atrial fibrillation: A beat-to-beat analysis of cycle length and wave similarity

Deterioration of AF Organization. Introduction: It has been recently suggested that many episodes of atrial fibrillation (AF) may be partially organized at the onset and thus more suitable for antitachycardia pacing therapy. Nevertheless, the time course of organization in the first minutes of AF has not been quantified yet. Methods and Results: Twenty episodes of paroxysmal AF were studied. Electrograms were recorded from the right atrium (RA), distal (CSd), and proximal coronary sinus (CSp). The time course of AF cycle length (AFCL) and the regularity of wave morphology (similarity index S) were beat-to-beat measured at each recording site during the first 7 minutes of AF. AFCL and S show…

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

Abstract 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 s…

Inclusion of Instantaneous Influences in the Spectral Decomposition of Causality: Application to the Control Mechanisms of Heart Rate Variability

Heart rate variability is the result of several physiological regulation mechanisms, including cardiovascular and cardiorespiratory interactions. Since instantaneous influences occurring within the same cardiac beat are commonplace in this regulation, their inclusion is mandatory to get a realistic model of physiological causal interactions. Here we exploit a recently proposed framework for the spectral decomposition of causal influences between autoregressive processes [2] and generalize it by introducing instantaneous couplings in the vector autoregressive model (VAR). We show the effectiveness of the proposed approach on a toy model, and on real data consisting of heart period (RR), syst…

Multiscale Granger causality

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well-established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer a…

Mutual Information Analysis of Brain-Heart Interactions in Epileptic Children

In this work we apply the network physiology paradigm to retrieve information from central and autonomic nervous systems before focal epileptic seizure, represented respectively by electroencephalogram (EEG) signals and R-R intervals (RRI), and investigate on the presence and strength of brain-heart interactions by computing mutual information (MI) measures. Statistical significance of MI values was tested through surrogate time series generated with the random shuffle approach. Our results suggest that the proposed method for aligning signals representing brain and heart activity measured with different sampling rates, is capable of revealing coupling between RRI representing heart system,…

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 …

Information-theoretic assessment of cardiovascular variability during postural and mental stress

This study was aimed at investigating the individual and combined effects of postural and mental stress on short-term cardiovascular regulation. To this end, we applied measures taken from the emerging framework of information dynamics on the beat-to-beat spontaneous variability of RR interval and systolic arterial pressure (SAP) measured from healthy subjects in the resting supine position and during the separate and simultaneous execution of experimental protocols performing head-up tilt (HUT) and mental arithmetics (MA). The information stored in RR interval variability, a measure inversely related to the complexity of the time series, increased significantly during HUT and HUT+MA compar…

Wiener-Granger Causality in Network Physiology with Applications to Cardiovascular Control and Neuroscience

Since the operative definition given by C. W. J. Granger of an idea expressed by N. Wiener, the Wiener–Granger causality (WGC) has been one of the most relevant concepts exploited by modern time series analysis. Indeed, in networks formed by multiple components, working according to the notion of segregation and interacting with each other according to the principle of integration, inferring causality has opened a window on the effective connectivity of the network and has linked experimental evidences to functions and mechanisms. This tutorial reviews predictability improvement, information-based and frequency domain methods for inferring WGC among physiological processes from multivariate…

A portable multisensor system to assess cardiorespiratory interactions through photoplethysmography

Nowadays, the ever-growing interest to health and quality of life of individuals and the advancements in electronic devices technology are pushing the development of portable and wearable biomedical devices able to pursue a minimally invasive monitoring of physiological parameters in daily-life conditions. Such devices can now carry out a real-time assessment of the subjects’ overall health status and possibly even detect ongoing diseases. In this context, we have designed and implemented a multisensor portable system able to perform synchronous real-time acquisitions of electrocardiographic (ECG), photoplethysmographic (PPG) and airflow breathing signals. We investigated cardiorespiratory …

Causal linear parametric model for baroreflex gain assessment in patients with recent myocardial infarction

Spectral and cross-spectral analysis of R-R interval and systolic arterial pressure (SAP) spontaneous fluctuations have been proposed for noninvasive evaluation of baroreflex sensitivity (BRS). However, results are not in good agreement with clinical measurements. In this study, a bivariate parametric autoregressive model with exogenous input (ARXAR model), able to divide the R-R variability into SAP-related and -unrelated parts, was used to quantify the gain (αARXAR) of the baroreflex regulatory mechanism. For performance assessing, two traditional noninvasive methods based on frequency domain analysis [spectral, baroreflex gain by autogressive model (αAR); cross-spectral, baroreflex gain…

An identifiable model to assess frequency-domain Granger causality in the presence of significant instantaneous interactions

We present a new approach for the investigation of Granger causality in the frequency domain by means of the partial directed coherence (PDC). The approach is based on the utilization of an extended multivariate autoregressive (MVAR) model, including instantaneous effects in addition to the lagged effects traditionally studied, to fit the observed multiple time series prior to PDC computation. Model identification is performed combining standard MVAR coefficient estimation with a recent technique for instantaneous causal modeling based on independent component analysis. The approach is first validated on simulated MVAR processes showing that, in the presence of instantaneous effects, only t…

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 affect…

Estimation of confidence limits for descriptive indexes derived from autoregressive analysis of time series: Methods and application to heart rate variability

The growing interest in personalized medicine requires making inferences from descriptive indexes estimated from individual recordings of physiological signals, with statistical analyses focused on individual differences between/within subjects, rather than comparing supposedly homogeneous cohorts. To this end, methods to compute confidence limits of individual estimates of descriptive indexes are needed. This study introduces numerical methods to compute such confidence limits and perform statistical comparisons between indexes derived from autoregressive (AR) modeling of individual time series. Analytical approaches are generally not viable, because the indexes are usually nonlinear funct…

Selection of blood pressure signal for baroreflex analysis

This study aims to evaluate the strength of the causal coupling among systolic, mean and diastolic blood pressure (SBP, MBP and DBP) with heart period (RR interval) (evaluating cardiac chronotropic baroreflex arm) and peripheral vascular resistance (PVR) (evaluating vascular resistance baroreflex arm) in frequency domain using partial spectral decomposition method. We recorded beat-to-beat RR, SBP, MBP and DBP and PVR values in 39 volunteers during supine rest and head-up tilt. Our results showed that during supine rest the most dominant causal coupling was from DBP to RR in both low and high frequency bands and significantly decreased during orthostasis. The strength of spectral couplings …

Role of causality in the evaluation of coherence and transfer function between heart period and systolic pressure in humans

To elicit the effects of considering causality in the study of the interactions between RR interval and systolic pressure (SP) variability, the traditional noncausal cross-spectral analysis was compared with a causal method able to separate the two arms of the RR-SP regulatory loop. Estimates of coherence (K) and causal coherences from SP to RR (Ksr) and from RR to SP (Krs), and of noncausal (G) and causal (Gsr) baroreflex gain were evaluated at 0.1 Hz in 10 healthy young subjects in the supine position and after head-up tilt. While K was high in both conditions, at rest Ksr was significantly lower than Krs. After tilt, Ksr increased and Krs decreased significantly. With respect to G, Gsr w…

Exploring metrics for the characterization of the cerebral autoregulation during head-up tilt and propofol general anesthesia

Techniques grounded on the simultaneous utilization of Tiecks' second order differential equations and spontaneous variability of mean arterial pressure (MAP) and mean cerebral blood flow velocity (MCBFV), recorded from middle cerebral arteries through a transcranial Doppler device, provide a characterization of cerebral autoregulation (CA) via the autoregulation index (ARI). These methods exploit two metrics for comparing the measured MCBFV series with the version predicted by Tiecks' model: normalized mean square prediction error (NMSPE) and normalized correlation rho. The aim of this study is to assess the two metrics for ARI computation in 13 healthy subjects (age: 27 & PLUSMN; 8 yr…

Towards understanding the complexity of cardiovascular oscillations: Insights from information theory.

Abstract Cardiovascular complexity is a feature of healthy physiological regulation, which stems from the simultaneous activity of several cardiovascular reflexes and other non-reflex physiological mechanisms. It is manifested in the rich dynamics characterizing the spontaneous heart rate and blood pressure variability (HRV and BPV). The present study faces the challenge of disclosing the origin of short-term HRV and BPV from the statistical perspective offered by information theory. To dissect the physiological mechanisms giving rise to cardiovascular complexity in different conditions, measures of predictive information, information storage, information transfer and information modificati…

Measuring the Rate of Information Transfer in Point-Process Data: Application to Cardiovascular Interactions

We present the implementation to cardiovascular variability of a method for the information-theoretic estimation of the directed interactions between event-based data. The method allows to compute the transfer entropy rate (TER) from a source to a target point process in continuous time, thus overcoming the severe limitations associated with time discretization of event-based processes. In this work, the method is evaluated on coupled cardiovascular point processes representing the heartbeat dynamics and the related peripheral pulsation, first using a physiologically-based simulation model and then studying real point-process data from healthy subjects monitored at rest and during postural …

Evidence of unbalanced regulatory mechanism of heart rate and systolic pressure after acute myocardial infarction

The interactions between systolic arterial pressure (SAP) and R-R interval (RR) fluctuations after acute myocardial infarction (AMI) were investigated by measures of synchronization separating the feedback from the feedforward control and capturing both linear and nonlinear contributions. The causal synchronization, evaluating the ability of RR to predict SAP (χs/t) or vice versa (χt/s), and the global synchronization (χ) were estimated at rest and after head-up tilt in 35 post-AMI patients, 20 young and 12 old. Significance and nonlinearity of the coupling were assessed by surrogate data analysis. Tilting increased the number of young subjects in which RR-SAP link was significant (from 17…

Critical comments on EEG sensor space dynamical connectivity analysis

Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because (1) the channel locations canno…

Principal component analysis and cluster analysis for measuring the local organisation of human atrial fibrillation

The distribution of atrial electrogram types has been proposed to characterise human atrial fibrillation. The aim of this study was to provide computer procedures for evaluating the local organisation of intracardiac recordings during AF as an alternative to off-line manual classification. Principal components analysis (PCA) reduced the data set to a few representative activations, and cluster analysis (CA) measured the average dissimilarity between consecutive activations of an intracardiac signal. The data set consisted of 106 bipolar signals recorded on 11 patients during electrophysiological studies for catheter ablation. Performances of PCA and CA in distinguishing between organised (t…

Propagation pattern analysis during atrial fibrillation based on sparse modeling.

In this study, sparse modeling is introduced for the estimation of propagation patterns in intracardiac atrial fibrillation (AF) signals. The estimation is based on the partial directed coherence function, derived from fitting a multivariate autoregressive model to the observed signal using least-squares (LS) estimation. The propagation pattern analysis incorporates prior information on sparse coupling as well as the distance between the recording sites. Two optimization methods are employed for estimation of the model parameters, namely, the adaptive group least absolute selection and shrinkage operator (aLASSO), and a novel method named the distance-adaptive group LASSO (dLASSO). Using si…

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

Heart rate variability (HRV

Partial Information Decomposition in the Frequency Domain: Application to Control Mechanisms of Heart Rate Variability at Rest and During Postural Stress

We exploit a recently proposed framework for assessing causal influences in the frequency domain to construct the partial information decomposition (PID) for informational circuits of three variables, thus obtaining the spectral decomposition of redundancy, synergy and unique information. The approach is applied to heart period (HP), systolic pressure (SP) and respiration (RESP) variability series measured in healthy subjects in baseline and head up tilt conditions. Integrating the informational quantities in the respiratory band, the total influence from RESP to HP does not change in the two conditions. However, we find that in baseline RESP causes HP mostly through the direct pathway desc…

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.…

A framework for assessing frequency domain causality in physiological time series with instantaneous effects.

We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the kno…

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 acti…

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

Abstract 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 re…

Feasibility of Linear Parametric Estimation of Dynamic Information Measures to assess Physiological Stress from Short-Term Cardiovascular Variability

Extensive efforts have been recently devoted to implement fast and reliable algorithms capable of assessing the physiological response of the organism to physiological stress. In this study, we propose the comparison between model-free and linear parametric methods as regards their ability to detect alterations in the dynamics and in the complexity of cardiovascular and respiratory variability evoked by postural and mental stress. Dynamic entropy (DE) and information storage (IS) measures were calculated on three physiological time-series, i.e. heart period, respiratory volume and systolic arterial pressure, on 61 healthy subjects monitored in resting conditions as well as during head-up ti…

Compensating for instantaneous signal mixing in transfer entropy analysis of neurobiological time series

The transfer entropy (TE) has recently emerged as a nonlinear model-free tool, framed in information theory, to detect directed interactions in coupled processes. Unfortunately, when applied to neurobiological time series TE is biased by signal cross-talk due to volume conduction. To compensate for this bias, in this study we introduce a modified TE measure which accounts for possible instantaneous effects between the analyzed time series. The new measure, denoted as compensated TE (cTE), is tested on simulated time series reproducing conditions typical of neuroscience applications, and on real magnetoencephalographic (MEG) multi-trial data measured during a visuo-tactile cognitive experime…

Feasibility of cuff-free measurement of systolic and diastolic arterial blood pressure

We validated a prototype cuff-free device for noninvasive estimation of blood pressure (BP). The system assumed a linear relation between BP values and the inverse of arterial blood pulse transit time, measured as time interval between the R wave on the electrocardiograph and the onset of the peripheral pulse wave on a finger plethysmogram. Thirty-three healthy subjects were analyzed at rest and during increasing stress exercise. To estimate subject-specific linear model parameters, the system was calibrated ad personam with reference to BP measures obtained by a cuff sphygmomanometer. High correlation values (R2= 0.89 and 0.78 for systolic and diastolic BP, respectively) and differences co…

Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions.

The Partial Directed Coherence (PDC) and its generalized formulation (gPDC) are popular tools for investigating, in the frequency domain, the concept of Granger causality among multivariate (MV) time series. PDC and gPDC are formalized in terms of the coefficients of an MV autoregressive (MVAR) model which describes only the lagged effects among the time series and forsakes instantaneous effects. However, instantaneous effects are known to affect linear parametric modeling, and are likely to occur in experimental time series. In this study, we investigate the impact on the assessment of frequency domain causality of excluding instantaneous effects from the model underlying PDC evaluation. M…

Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy

Some previous evidence suggests that postural related syncope is associated with defective mechanisms of cerebrovascular (CB) and cardiovascular (CV) control. We characterized the information processing in short-term CB regulation, from the variability of mean cerebral blood flow velocity (CBFV) and mean arterial pressure (AP), and in CV regulation, from the variability of heart period (HP) and systolic AP (SAP), in ten young subjects developing orthostatic syncope in response to prolonged head-up tilt testing. We exploited a novel information-theoretic approach that decomposes the information associated with a variability series into three amounts: the information stored in the series, the…

Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategies based on k nearest neighbors

We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of $k$-nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application d…

Frequency Domain Information Decomposition: Application to Plateau Waves of Intracranial Pressure

The sustainment and/or resurgence of Plateau Waves (PWs) reveals a borderline cerebral situation of the pressure-volume relationship and is related to increased mortality. The intense systemic stress caused by PWs can be evidenced by the study of Heart Rate Variability (HRV), which is an indicator of the activity of the autonomic nervous system, namely the sympathetic and parasympathetic imbalance. In this work, heart and brain crosstalk interactions will be analyzed using a spectral decomposition of multivariate information measures, which provides frequency-specific quantification of the information shared between a target and two source time series. The spectral measures of information h…

Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach

In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI) framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently G…

Basic cardiovascular variability signals: mutual directed interactions explored in the information domain.

The study of short-term cardiovascular interactions is classically performed through the bivariate analysis of the interactions between the beat-to-beat variability of heart period (RR interval from the ECG) and systolic blood pressure (SBP). Recent progress in the development of multivariate time series analysis methods is making it possible to explore how directed interactions between two signals change in the context of networks including other coupled signals. Exploiting these advances, the present study aims at assessing directional cardiovascular interactions among the basic variability signals of RR, SBP and diastolic blood pressure (DBP), using an approach which allows direct compar…

Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models

The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE) and refined MSE (RMSE) measures. In spite of their popularity, MSE and RMSE lack an analytical framework allowing their calculation for known dynamic processes and cannot be reliably computed over short time series. To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state-space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the co…

Nonlinear brain-heart interactions in children with focal epilepsy assessed by mutual information of EEG and heart rate variability

Network physiology is a recent approach describing the human body as an integrated network composed of several organ systems which continuously interact to produce healthy and diseased states. In this work, we apply the network physiology paradigm to study dynamical interactions between EEG activity and heart rate variability in children suffering from focal epilepsy. We aim to study the characteristics of brainheart coupling between, before, and after seizures to better understand the physiological mechanisms underlying seizure onset in the pre-ictal phase and the recovery of normal autonomic function in the post-ictal phase. In perspective, linking the dynamic information of brain-heart c…

Assessing High-Order Interdependencies Through Static O-Information Measures Computed on Resting State fMRI Intrinsic Component Networks

Resting state brain networks have reached a strong popularity in recent scientific endeavors due to their feasibility to characterize the metabolic mechanisms at the basis of neural control when the brain is not engaged in any task. The evaluation of these states, consisting in complex physiological processes employing a large amount of energy, is carried out from diagnostic images acquired through resting-state functionalmagnetic resonance (RS-fMRI) on different populations of subjects. In the present study, RS-fMRI signals from the WU-MinnHCP 1200 Subjects Data Release of the Human Connectome Project were studied with the aim of investigating the high order organizational structure of the…

Causal cross-spectral analysis of heart rate and blood pressure variability for describing the impairment of the cardiovascular control in neurally mediated syncope

A causal approach to the calculation of coherence and transfer function between systolic pressure (SP) and RR interval variability was applied in eight patients and eight control subjects during prolonged tilt test for investigating the impairment of cardiovascular control related to neurally mediated syncope. The causal analysis showed a depressed baroreflex regulation in resting patients, with reduced gain and increased latency from SP to RR, and a drop of the baroreflex coupling immediately before syncope. These findings, which were not elicited by traditional cross-spectral analysis, strongly suggest the use of the causal approach for the study of syncope mechanisms. © 2006 IEEE.

Correlation between Baroreflex Sensitivity and Cerebral Autoregulation Index in Healthy Subjects

Despite the acknowledged interaction between baroreflex and cerebral autoregulation (CA), their functional relationship remains controversial. The study investigates this relationship in a healthy population undergoing an orthostatic challenge. Thirteen healthy subjects (age: 27pm 8 yrs; 5 males) underwent electrocardiogram, arterial pressure (AP) and cerebral blood flow velocity (CBFV) recordings at supine resting (REST) and during 60° head-up tilt (TILT). CA was assessed via the autoregulation index (ARI) from spontaneous variations of mean AP and mean CBFV. The cardiac control and baroreflex were evaluated via frequency domain and transfer function analyses applied to systolic AP and hea…

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…

Cardiovascular control and time domain granger causality: Insights from selective autonomic blockade

We studied causal relations among heart period (HP), systolic arterial pressure (SAP) and respiration (R) according to the definition of Granger causality in the time domain. Autonomic pharmacological challenges were used to alter the complexity of cardiovascular control. Atropine (AT), propranolol and clonidine (CL) were administered to block muscarinic receptors, β-adrenergic receptors and centrally sympathetic outflow, respectively. We found that: (i) at baseline, HP and SAP interacted in a closed loop with a dominant causal direction from HP to SAP; (ii) pharmacological blockades did not alter the bidirectional closed-loop interactions between HP and SAP, but AT reduced the dominance of…

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 mea…

Assessment of Granger causality by nonlinear model identification: application to short-term cardiovascular variability.

A method for assessing Granger causal relationships in bivariate time series, based on nonlinear autoregressive (NAR) and nonlinear autoregressive exogenous (NARX) models is presented. The method evaluates bilateral interactions between two time series by quantifying the predictability improvement (PI) of the output time series when the dynamics associated with the input time series are included, i.e., moving from NAR to NARX prediction. The NARX model identification was performed by the optimal parameter search (OPS) algorithm, and its results were compared to the least-squares method to determine the most appropriate method to be used for experimental data. The statistical significance of…

Nonlinear coupling is absent in acute myocardial patients but not healthy subjects.

We investigated whether autonomic nervous system imbalance imposed by pharmacological blockades and associated with acute myocardial infarction (AMI) is manifested as modifications of the nonlinear interactions in heart rate variability signal using a statistically based bispectrum method. The statistically based bispectrum method is an ideal approach for identifying nonlinear couplings in a system and overcomes the previous limitation of determining in an ad hoc way the presence of such interactions. Using the improved bispectrum method, we found significant nonlinear interactions in healthy young subjects, which were abolished by the administration of atropine but were still present afte…

Cerebrovascular and cardiovascular variability interactions investigated through conditional joint transfer entropy in subjects prone to postural syncope.

Objective: A model-based conditional transfer entropy approach was exploited to quantify the information transfer in cerebrovascular (CBV) and cardiovascular (CV) systems in subjects prone to develop postural syncope. Approach: Spontaneous beat-to-beat variations of mean cerebral blood flow velocity (MCBFV) derived from a transcranial Doppler device, heart period (HP) derived from surface electrocardiogram, mean arterial pressure (MAP) and systolic arterial pressure (SAP) derived from finger plethysmographic arterial pressure device were monitored at rest in supine position (REST) and during 60° head-up tilt (TILT) in 13 individuals (age mean ± standard deviation: 28 ± 9 years, min-max r…

Synergistic and Redundant Brain-Heart Information in Patients with Focal Epilepsy

In this work, partial information decomposition (PID) was applied to the time series of heart rate and EEG amplitude variability to investigate the dynamical interactions in brain-heart coupling before and after epileptic seizures. From ECG and EEG signals collected on 23 children suffering from focal epilepsy, the RR intervals and the EEG variance at ipsilateral and contralateral temporal electrodes were computed in four different time windows before and after the seizures. Static PID was used to obtain redundant, unique and synergistic components of the total information shared between the series of RR and EEG variance. Results highlight, in the progression from preictal to postictal stat…

Cardiovascular and autonomic responses to physiological stressors before and after six hours of water immersion

The physiological responses to water immersion (WI) are known; however, the responses to stress following WI are poorly characterized. Ten healthy men were exposed to three physiological stressors before and after a 6-h resting WI (32–33°C): 1) a 2-min cold pressor test, 2) a static handgrip test to fatigue at 40% of maximum strength followed by postexercise muscle ischemia in the exercising forearm, and 3) a 15-min 70° head-up-tilt (HUT) test. Heart rate (HR), systolic and diastolic blood pressure (SBP and DBP), cardiac output (Q̇), limb blood flow (BF), stroke volume (SV), systemic and calf or forearm vascular resistance (SVR and CVR or FVR), baroreflex sensitivity (BRS), and HR variabili…

Assessing directional interactions among multiple physiological time series: The role of instantaneous causality

This paper deals with the assessment of frequency domain causality in multivariate (MV) time series with significant instantaneous interactions. After providing different causality definitions, we introduce an extended MV autoregressive modeling approach whereby each definition is described in the time domain in terms of the model coefficients, and is quantified in the frequency domain by means of novel measures of directional connectivity. These measures are illustrated in a theoretical example showing how they reduce to known indexes when instantaneous causality is trivial, while they describe peculiar aspects of directional interaction in the presence of instantaneous causality. The appl…

Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions

We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral i…

Model-Based Evaluation of Methods for Respiratory Sinus Arrhythmia Estimation

OBJECTIVE: Respiratory sinus arrhythmia (RSA) refers to heart rate oscillations synchronous with respiration, and it is one of the major representations of cardiorespiratory coupling. Its strength has been suggested as a biomarker to monitor different conditions, and diseases. Some approaches have been proposed to quantify the RSA, but it is unclear which one performs best in specific scenarios. The main objective of this study is to compare seven state-of-the-art methods for RSA quantification using data generated with a model proposed to simulate, and control the RSA. These methods are also compared, and evaluated on a real-life application, for their ability to capture changes in cardior…

Information decomposition of multichannel EMG to map functional interactions in the distributed motor system

AbstractThe central nervous system needs to coordinate multiple muscles during postural control. Functional coordination is established through the neural circuitry that interconnects different muscles. Here we used multivariate information decomposition of multichannel EMG acquired from 14 healthy participants during postural tasks to investigate the neural interactions between muscles. A set of information measures were estimated from an instantaneous linear regression model and a time-lagged VAR model fitted to the EMG envelopes of 36 muscles. We used network analysis to quantify the structure of functional interactions between muscles and compared them across experimental conditions. Co…

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 TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions. Methods: We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characteriz…

Low-invasive multisensor real-time acquisition system for the assessment of cardiorespiratory and skin conductance parameters

In recent years, the attention to the health and comfort of the individual, together with the electronic miniaturization progress, have led to an increased interest in the development of biomedical devices that are able to acquire a multitude of biomedical signals. Such devices should be wearable and comfortable during daily use, to be thus suitable for continuously monitoring psychophysical health states. In this context, we have designed and realized a portable biomedical device capable of real-time acquisition of electrocardiographic (ECG), photoplethysmographic (PPG), breathing and galvanic skin response (GSR) signals, for a noninvasive monitoring of multiple physiological parameters. T…

Analysis of Cardiac Pulse Arrival Time Series at Rest and during Physiological Stress

The study of cardiovascular dynamics is pivotal in the prevention and monitoring of cardiovascular diseases. Pulse Arrival Time (PAT) series contain information concerning not only the dynamics of the Autonomic Nervous System (ANS), but of all the systems involved in the regulation of cardiovascular homeostasis. This study aims to highlight how indexes extracted from PAT series in time-, frequency- and information-domain allow to discriminate among different physiological conditions. Analyses were carried out on 76 young healthy subjects, at rest and during orthostatic or mental stress. Our results show that PAT indexes vary according to the ANS condition, and may thus be useful parameters …

Inferring directionality of coupled dynamical systems using Gaussian process priors: Application on neurovascular systems

Dynamical system theory has recently shown promise for uncovering causality and directionality in complex systems, particularly using the method of convergent cross mapping (CCM). In spite of its success in the literature, the presence of process noise raises concern about CCM's ability to uncover coupling direction. Furthermore, CCM's capacity to detect indirect causal links may be challenged in simulated unidrectionally coupled Rossler-Lorenz systems. To overcome these limitations, we propose a method that places a Gaussian process prior on a cross mapping function (named GP-CCM) to impose constraints on local state space neighborhood comparisons. Bayesian posterior likelihood and…

Low invasive multisensor acquisition system for real-time monitoring of cardiovascular and respiratory parameters

The recent advances in multiparametric monitoring of biosignals and management of big data prompt for the development of devices and techniques for the extraction of indicators with physiological relevance. In this context, we have designed and realized a portable electronic system, equipped with simple biomedical sensors, able to synchronously record multiple electrocardiographic (ECG), photoplethysmographic (PPG) and breathing signals, for carrying out a non-invasive monitoring of several cardiovascular parameters. In this work, we show the results of preliminary measurements performed following a specific physiological protocol (i.e., deep breathing with 10 s per cycle). The system allow…

Organization measures of atrial activity during fibrillation

The present chapter summarizes the state-of-art of how to quantify the degree of atrial organization during AF through a review of the main signal processing techniques employed for the analysis of atrial electrical activity. As the concept of atrial organization may assume different meanings in the context of AF, particular attention is paid to stress those peculiar characters of organization probed and captured by each method.

Assessing Transfer Entropy in cardiovascular and respiratory time series under long-range correlations.

Heart Period (H) results from the activity of several coexisting control mechanisms, involving Systolic Arterial Pressure (S) and Respiration (R), which operate across multiple time scales encompassing not only short-term dynamics but also long-range correlations. In this work, multiscale representation of Transfer Entropy (TE) and of its decomposition in the network of these three interacting processes is obtained by extending the multivariate approach based on linear parametric VAR models to the Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This approach allows to dissect the different contributions to cardiac dynamics accounting for the simultane…

A Multi-Variate Predictability Framework to Assess Invasive Cardiac Activity and Interactions during Atrial Fibrillation

Objective: This study introduces a predictability framework based on the concept of Granger causality (GC), in order to analyze the activity and interactions between different intracardiac sites during atrial fibrillation (AF). Methods: GC-based interactions were studied using a three-electrode analysis scheme with multi-variate autoregressive models of the involved preprocessed intracardiac signals. The method was evaluated in different scenarios covering simulations of complex atrial activity as well as endocardial signals acquired from patients. Results: The results illustrate the ability of the method to determine atrial rhythm complexity and to track and map propagation during AF. Conc…

Complexity and Nonlinearity Analysis of the Time Series of Electric Field Intensity

In this work, the conditional entropy (CE) and the method of surrogate data are applied on time series of electric field (EF) intensity to explore their degree of complexity and the possible presence of nonlinear dynamics. The time series were obtained during the wide-band cumulative EF intensity monitoring, performed by one sensor of the Serbian EMF RATEL monitoring system installed in the campus area of the University of Novi Sad, and are re-sampled at one sample per two hours over consecutive time epochs of one month duration. The field intensity measurements during the years 2019 and 2020 allowed us to explore the effects of mobility restrictions related to the COVID-19 pandemic on the …

ANALYSIS OF RESPIRATORY SINUS ARRHYTHMIA MECHANISMS IN INFORMATION DOMAIN

Testing different methodologies for Granger causality estimation: A simulation study

Granger causality (GC) is a method for determining whether and how two time series exert causal influences one over the other. As it is easy to implement through vector autoregressive (VAR) models and can be generalized to the multivariate case, GC has spread in many different areas of research such as neuroscience and network physiology. In its basic formulation, the computation of GC involves two different regressions, taking respectively into account the whole past history of the investigated multivariate time series (full model) and the past of all time series except the putatively causal time series (restricted model). However, the restricted model cannot be represented through a finit…

Vector Autoregressive Fractionally Integrated Models to Assess Multiscale Complexity in Cardiovascular and Respiratory Time Series

Cardiovascular variability is the result of the activity of several physiological control mechanisms, which involve different variables and operate across multiple time scales encompassing short term dynamics and long range correlations. This study presents a new approach to assess the multiscale complexity of multivariate time series, based on linear parametric models incorporating autoregressive coefficients and fractional integration. The approach extends to the multivariate case recent works introducing a linear parametric representation of multiscale entropy, and is exploited to assess the complexity of cardiovascular and respiratory time series in healthy subjects studied during postu…

A new Frequency Domain Measure of Causality based on Partial Spectral Decomposition of Autoregressive Processes and its Application to Cardiovascular Interactions

We present a new method to quantify in the frequency domain the strength of directed interactions between linear stochastic processes. This issue is traditionally addressed by the directed coherence (DC), a popular causality measure derived from the spectral representation of vector autoregressive (AR) processes. Here, to overcome intrinsic limitations of the DC when it needs to be objectively quantified within specific frequency bands, we propose an approach based on spectral decomposition, which allows to isolate oscillatory components related to the pole representation of the vector AR process in the Z-domain. Relating the causal and non-causal power content of these components we obtain…

Local electrical characterisation of human atrial fibrillation

The rate of success of radio-frequency catheter ablation in the treatment of atrial fibrillation may be significantly improved by evaluating the local electrical properties of the atrial tissue. The aim of this study is the development of an automatic procedure for the characterisation of the local electrical activity during atrial fibrillation and the comparison of its performance with the manual analysis. The adopted procedures were the semi-automatic measurement of the local fibrillation intervals (A-A intervals) and the manual electrogram classification following the criteria suggested by Wells (1978) or Konings (1997). Two methods have been used: Principal Component Analysis and Cluste…

Methodological advances in brain connectivity

Determining how distinct neurons or brain regions are connected and communicate with each other is a crucial point in neuroscience, as it allows to investigate how the functional integration of specialized neural populations enables the emergence of coherent cognitive and behavioral states. The general concept of brain connectivity encompasses different aspects: structural connectivity is related to the description of anatomical pathways and synaptic connections; functional connectivity investigates statistical dependencies between spatially separated brain regions; effective connectivity refers to models aimed at elucidating driver-response relationships. The study of these different modes…

Instantaneous transfer entropy for the study of cardio-respiratory dynamics

Measures of transfer entropy have been proposed to quantify the directional coupling and strength between two complex physiological variables. Particular attention has been given to nonlinear interactions within cardiovascular and respiratory dynamics as influenced by the autonomic nervous system. However, standard transfer entropy estimates have shown major limitations in dealing with issues concerning stochastic system modeling, limited observations in time, and the assumption of stationarity of the considered physiological variables. Moreover, standard estimates are unable to track time-varying changes in nonlinear coupling with high resolution in time. Here, we propose a novel definitio…

Multiscale Granger causality analysis by à trous wavelet transform

Since interactions in neural systems occur across multiple temporal scales, it is likely that information flow will exhibit a multiscale structure, thus requiring a multiscale generalization of classical temporal precedence causality analysis like Granger's approach. However, the computation of multiscale measures of information dynamics is complicated by theoretical and practical issues such as filtering and undersampling: to overcome these problems, we propose a wavelet-based approach for multiscale Granger causality (GC) analysis, which is characterized by the following properties: (i) only the candidate driver variable is wavelet transformed (ii) the decomposition is performed using the…

Causal transfer function analysis to describe closed loop interactions between cardiovascular and cardiorespiratory variability signals

Although the concept of transfer function is intrinsically related to an input-output relationship, the traditional and widely used estimation method merges both feedback and feedforward interactions between the two analyzed signals. This limitation may endanger the reliability of transfer function analysis in biological systems characterized by closed loop interactions. In this study, a method for estimating the transfer function between closed loop interacting signals was proposed and validated in the field of cardiovascular and cardiorespiratory variability. The two analyzed signals x and y were described by a bivariate autoregressive model, and the causal transfer function from x to y w…

Information dynamics of brain-heart physiological networks during sleep

This study proposes an integrated approach, framed in the emerging fields of network physiology and information dynamics, for the quantitative analysis of brain-heart interaction networks during sleep. With this approach, the time series of cardiac vagal autonomic activity and brain wave activities measured respectively as the normalized high frequency component of heart rate variability and the EEG power in the δ, θ, σ, and β bands, are considered as realizations of the stochastic processes describing the dynamics of the heart system and of different brain sub-systems. Entropy-based measures are exploited to quantify the predictive information carried by each (sub)system, and to dissec…

Measuring postural-related changes of spontaneous baroreflex sensitivity after repeated long-duration diving: Frequency domain approaches

Sustained water immersion is thought to modulate orthostatic tolerance to an extent dependent on the duration and repetition over consecutive days of the diving sessions. We tested this hypothesis investigating in ten healthy subjects the potential changes in the cardiovascular response to head-up tilt induced by single and multiple resting air dives. Parametric cross-spectral analysis of spontaneous RR interval and systolic arterial pressure variability was performed in three experimental sessions: before diving (BD), after single 6-hour dive (ASD), and after multiple 6-hour dives (AMD, 5 consecutive days with 18-hour surface interval). From this analysis, baroreflex sensitivity (BRS) was …

Categorizing the Role of Respiration in Cardiovascular and Cerebrovascular Variability Interactions

Objective: Respiration disturbs cardiovascular and cerebrovascular controls but its role is not fully elucidated. Methods: Respiration can be classified as a confounder if its observation reduces the strength of the causal relationship from source to target. Respiration is a suppressor if the opposite situation holds. We prove that a confounding/suppression (C/S) test can be accomplished by evaluating the sign of net redundancy/synergy balance in the predictability framework based on multivariate autoregressive modelling. In addition, we suggest that, under the hypothesis of Gaussian processes, the C/S test can be given in the transfer entropy decomposition framework as well. Experimental p…

Investigating the level of significance of the coherence function in cardiovascular variability analysis

Although the presence of significant coupling between cardiovascular variability series is usually verified according to the threshold value of 0.5 in the coherence function (CF), spectral estimator parameters should also be considered. In this study, the surrogate data technique was introduced to define the level of significance of the CF. The proposed method determined a frequency-dependent threshold over which the hypothesis of zero coherence was rejected. The weighted covariance method and the autoregressive method were used to estimate the CF on simulated series with different degrees of linear coupling and on real cardiovascular data. The threshold was dependent on the type and parame…

Information dynamics in cardiorespiratory time series during mental stress testing

In this study, we assessed the information dynamics of respiration and heart rate variability during mental stress testing by means of the cross-entropy, a measure of cardiorespiratory coupling, and the self-entropy of the tachogram conditioned to the knowledge of respiration. Although stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when 5 minutes of rest and stress were compared. The conditional self-entropy, on the other hand, showed significantly higher values during stress, indicating a higher predictability of the tachogram. These results show that entropy analyses of cardiorespiratory data reveal new information that could not …

Information Transfer Between Respiration and Heart Rate During Sleep Apnea

It is well-known that sleep apnea affects the respiration and the heart rate (HR), and studies have shown that the cardiorespiratory coupling is also compromised during obstructive sleep apnea (OSA). Furthermore, the classification of hypopneas is challenging, in particular when only ECG-derived features are used. In this context, this study investigates how different ECG-derived respiratory (EDR) signals resemble the respiratory effort during different types of apneas, and how the amount of information transferred from respiration to HR varies according to the respiratory signal used, real or ECG-derived. ECG and respiratory signals of 10 patients suffering from sleep apnea were analysed, …

Multilevel assessment of mental stress via network physiology paradigm using consumer wearable devices

Mental stress is a physiological condition that has a strong negative impact on the quality of life, affecting both the physical and the mental health. For such a reason, accurate measurements of stress level can be helpful to provide mechanisms for prevention and treatment. This paper proposes a procedure for the classification of different mental stress levels by using physiological signals provided by low invasive wearable devices. 17 healthy volunteers participated in this study. Three different mental states were elicited in them: a resting condition, a stressful cognitive state, and a sustained attention task. The acquired physiological signals were: a one lead electrocardiogram (ECG)…

Block partial directed coherence: a new tool for the structural analysis of brain Networks

Isolation of the left atrial surface from cardiac multi-detector CT images based on marker controlled watershed segmentation

The delineation of left atrium (LA) and pulmonary veins (PVs) anatomy from high resolution images holds importance for atrial fibrillation (AF) investigation and treatment. In this study, a semiautomatic segmentation procedure for LA and PVs inner surface from contrast enhanced CT data was developed. The procedure consists of a three dimensional marker controlled watershed segmentation applied to the external morphological gradient, followed by variable threshold surface extraction from the original intensity image. A preliminary anisotropic non-linear filtering was implemented to improve the S/N ratio of CT images. The performance of segmentation was evaluated on cardiac CT scans of 12 AF …

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&ndash

Information-theoretic assessment of cardiovascular-brain networks during sleep

This study was aimed at detecting the structure of the physiological network underlying the regulation of the cardiovascular and brain systems during normal sleep. To this end, we measured from the polysomnographic recordings of 10 healthy subjects the normalized spectral power of heart rate variability in the high frequency band (HF) and the EEG power in the δ, θ, α, σ, and β bands. Then, the causal statistical dependencies within and between these six time series were assessed in terms of internal information (conditional self entropy, CSE) and information transfer (transfer entropy, TE) computed via a linear method exploiting multiple regression models and a nonlinear method combining ne…

A validity and reliability study of Conditional Entropy Measures of Pulse Rate Variability

In this work, we present the feasibility to use a simpler methodological approach for the assessment of the short-term complexity of Heart Rate Variability (HRV). Specifically, we propose to exploit Pulse Rate Variability (PRV) recorded through photoplethysmography in place of HRV measured from the ECG, and to compute complexity via a linear Gaussian approximation in place of the standard model-free methods (e.g., nearest neighbor entropy estimates) usually applied to HRV. Linear PRV-based and model-free HRV-based complexity measures were compared via statistical tests, correlation analysis and Bland-Altman plots, demonstrating an overall good agreement. These results support the applicabil…

Assessment of Cardiorespiratory Interactions During Spontaneous and Controlled Breathing: Linear Parametric Analysis

In this work, we perform a linear parametric analysis of cardiorespiratory interactions in bivariate time series of heart period (HP) and respiration (RESP) measured in 19 healthy subjects during spontaneous breathing and controlled breathing at varying breathing frequency. The analysis is carried out computing measures of the total and causal interaction between HP and RESP variability in both time and frequency domains (low- and high-frequency, LF and HF). Results highlight strong cardiorespiratory interactions in the time domain and within the HF band that are not affected by the paced breathing condition. Interactions in the LF band are weaker and prevalent along the direction from HP t…

Neural networks with non-uniform embedding and explicit validation phase to assess Granger causality

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of assumptions in modeling the relevant features of the data. We tried to overcome those pitfalls using a neural network approach in which a model is built without any a priori assumptions. In this sense this method can be seen as a bridge between model-free and model-based approaches. The experiments perfo…

Information domain analysis of respiratory sinus arrhythmia mechanisms.

Ventilation related heart rate oscillations – respiratory sinus arrhythmia (RSA) – originate in human from several mechanisms. Two most important of them – the central mechanism (direct communication between respiratory and cardiomotor centers), and the peripheral mechanism (ventilation-associated blood pressure changes transferred to heart rate via baroreflex) have been described in previous studies. The major aim of this study was to compare the importance of these mechanisms in the generation of RSA non-invasively during various states by quantifying the strength of the directed interactions between heart rate, systolic blood pressure and respiratory volume signals. Seventy-eight healthy…

Compensated transfer entropy as a tool for reliably estimating information transfer in physiological time series

We present a framework for the estimation of transfer entropy (TE) under the conditions typical of physiological system analysis, featuring short multivariate time series and the presence of instantaneous causality (IC). The framework is based on recognizing that TE can be interpreted as the difference between two conditional entropy (CE) terms, and builds on an efficient CE estimator that compensates for the bias occurring for high dimensional conditioning vectors and follows a sequential embedding procedure whereby the conditioning vectors are formed progressively according to a criterion for CE minimization. The issue of IC is faced accounting for zero-lag interactions according to two a…

Redundant and synergistic information transfer in cardiovascular and cardiorespiratory variability

In the framework of information dynamics, new tools are emerging which allow one to quantify how the information provided by two source processes about a target process results from the contribution of each source and from the interaction between the sources. We present the first implementation of these tools in the assessment of short-term cardiovascular and cardiorespiratory variability, by introducing two strategies for the decomposition of the information transferred to heart period (HP) variability from systolic arterial pressure (SAP) and respiration flow (RF) variability. Several measures based on the notion of transfer entropy (TE) are defined to quantify joint, individual and redun…

Strength and Latency of the HP-SAP Closed Loop Variability Interactions in Subjects Prone to Develop Postural Syncope

The coupling and latency between heart period (HP) and systolic arterial pressure (SAP) variability can be investigated along the two arms of the HP-SAP closed loop, namely along the baroreflex feedback from SAP to HP, and along the feedforward pathway from HP to SAP. This study investigates the HP-SAP closed loop variability interactions through cross-correlation function (CCF). Coupling strength and delay between HP and SAP variability series were monitored in 13 subjects prone to develop orthostatic syncope (SYNC, 28±9 yrs, 5 males) and in 13 subjects with no history of postural syncope (noSYNC, age: 27±8 yrs, 5 males). Analysis was carried out at rest in supine position (REST) and durin…

Granger causality analysis of sleep brain-heart interactions

We studied the networks of Granger causality (GC) between the time series of cardiac vagal autonomic activity and brain wave activities, measured respectively as the normalized high frequency (HF) component of heart rate variability and EEG power in the δ, θ, α, σ, β bands, computed in 10 healthy subjects during sleep. GC analysis was performed by vector autoregressive modeling, and significance of each link in the network was assessed using F-statistics. The whole-night analysis revealed the existence of a fully connected network of brain-heart and brain-brain interactions, with the ß EEG power acting as a hub which conveys the largest number of GC links between the heart and brain n…

Assessment Of Driving Stress Through SVM And KNN Classifiers On Multi-Domain Physiological Data

We propose an objective stress assessment method based on the extraction of features from physiological time series and their classification using Support Vector Machine and K-Nearest Neighbors algorithms. For this purpose, we used an open dataset consisting of multiparametric physiological signals (electrocardiogram, electromyogram, galvanic skin response and breath signal) obtained during the execution of a driving route within the city of Boston with restful, highway and city driving periods indicative of three different stress states. To predict the driver stress level, 21 features were extracted from 122 chunks of raw signals and were subsequently managed by classification algorithms. …

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 …

Measuring the Rate of Information Exchange in Point-Process Data With Application to Cardiovascular Variability

The amount of information exchanged per unit of time between two dynamic processes is an important concept for the analysis of complex systems. Theoretical formulations and data-efficient estimators have been recently introduced for this quantity, known as the mutual information rate (MIR), allowing its continuous-time computation for event-based data sets measured as realizations of coupled point processes. This work presents the implementation of MIR for point process applications in Network Physiology and cardiovascular variability, which typically feature short and noisy experimental time series. We assess the bias of MIR estimated for uncoupled point processes in the frame of surrogate…

Causal analysis of short-term cardiovascular variability: state-dependent contribution of feedback and feedforward mechanisms.

Baroreflex function is usually assessed from spontaneous oscillations of blood pressure (BP) and cardiac RR interval assuming a unidirectional influence from BP to RR. However, the interaction of BP and RR is bidirectional—RR also influences BP. Novel methods based on the concept of Granger causality were recently developed for separate analysis of feedback (baroreflex) and feedforward (mechanical) interactions between RR and BP. We aimed at assessing the proportion of the two causal directions of the interactions between RR and systolic BP (SBP) oscillations during various conditions, and at comparing causality measures from SBP to RR with baroreflex gain indexes. Arterial BP and ECG sig…

Robust estimation of partial directed coherence by the vector optimal parameter search algorithm

We propose a method for the accurate estimation of Partial Directed Coherence (PDC) from multichannel time series. The method is based on multivariate vector autoregressive (MVAR) model identification performed through the recently proposed Vector Optimal Parameter Search (VOPS) algorithm. Using Monte Carlo simulations generated by different MVAR models, the proposed VOPS algorithm is compared with the traditional Vector Least Squares (VLS) identification method. We show that the VOPS provides more accurate PDC estimates than the VLS (either overall and single-arc errors) in presence of interactions with long delays and missing terms, and for noisy multichannel time series. ©2009 IEEE.

A portable electronic system for non-invasive real-time acquisition of multiple physiological signals

In this work, we have designed and realised a portable and compact electronic system for the synchronous acquisition of multiple physiological signals. The system employs a Texas Instruments ADS1298 front-end with 24-bit resolution for data acquisition and supports up to 8 channels and 4 kHz sampling rate. The front-end communicates via SPI with a STM32 microcontroller which pre-processes the data and sends them through USB or Bluetooth to a suitable PC application. The system has been realized for the simultaneous acquisition of electrocardiographic (ECG) and photoplethysmographic (PPG) signals, but it can also be employed for acquiring other typologies of signals, e.g. breathing or electr…

Linear and non-linear brain-heart and brain-brain interactions during sleep.

In this study, the physiological networks underlying the joint modulation of the parasympathetic component of heart rate variability (HRV) and of the different electroencephalographic (EEG) rhythms during sleep were assessed using two popular measures of directed interaction in multivariate time series, namely Granger causality (GC) and transfer entropy (TE). Time series representative of cardiac and brain activities were obtained in 10 young healthy subjects as the normalized high frequency (HF) component of HRV and EEG power in the δ, θ, α, σ, and β bands, measured during the whole duration of sleep. The magnitude and statistical significance of GC and TE were evaluated between each …

Assessment of Cardiorespiratory Interactions During Spontaneous and Controlled Breathing: Non-linear Model-free Analysis

In this work, nonlinear model-free methods for bivariate time series analysis have been applied to study cardiorespiratory interactions. Specifically, entropy-based (i.e. Transfer Entropy and Cross Entropy) and Convergent Cross Mapping asymmetric coupling measures have been computed on heart rate and breathing time series extracted from electrocardiographic (ECG) and respiratory signals acquired on 19 young healthy subjects during an experimental protocol including spontaneous and controlled breathing conditions. Results evidence a bidirectional nature of cardiorespiratory interactions, and highlight clear similarities and differences among the three considered measures.

A Measure of Concurrent Neural Firing Activity Based on Mutual Information

Multiple methods have been developed in an attempt to quantify stimulus-induced neural coordination and to understand internal coordination of neuronal responses by examining the synchronization phenomena in neural discharge patterns. In this work we propose a novel approach to estimate the degree of concomitant firing between two neural units, based on a modified form of mutual information (MI) applied to a two-state representation of the firing activity. The binary profile of each single unit unfolds its discharge activity in time by decomposition into the state of neural quiescence/low activity and state of moderate firing/bursting. Then, the MI computed between the two binary streams is…

Information – theoretic characterization of concurrent activity of neural spike trains

The analysis of massively parallel spike train recordings facilitates investigation of communications and synchronization in neural networks. In this work we develop and evaluate a measure of concurrent neural activity, which is based on intrinsic firing properties of the recorded neural units. An overall single neuron activity is unfolded in time and decomposed into working and non-firing state, providing a coarse, binary representation of the neurons functional state. We propose a modified measure of mutual information to reflect the degree of simultaneous activation and concurrency in neural firing patterns. The measure is shown to be sensitive to both correlations and anti-correlations,…

Small-sample characterization of stochastic approximation staircases in forced-choice adaptive threshold estimation

Despite the widespread use of up—down staircases in adaptive threshold estimation, their efficiency and usability in forced-choice experiments has been recently debated. In this study, simulation techniques were used to determine the small-sample convergence properties of stochastic approximation (SA) staircases as a function of several experimental parameters. We found that satisfying some general requirements (use of the accelerated SA algorithm, clear suprathreshold initial stimulus intensity, large initial step size) the convergence was accurate independently of the spread of the underlying psychometric function. SA staircases were also reliable for targeting percent-correct levels far …

Predictability decomposition detects the impairment of brain-heart dynamical networks during sleep disorders and their recovery with treatment

This work introduces a framework to study the network formed by the autonomic component of heart rate variability (cardiac process η ) and the amplitude of the different electroencephalographic waves (brain processes δ , θ , α , σ , β ) during sleep. The framework exploits multivariate linear models to decompose the predictability of any given target process into measures of self-, causal and interaction predictability reflecting respectively the information retained in the process and related to its physiological complexity, the information transferred from the other source processes, and the information modified during the transfer according to redundant or synergistic interaction betwee…

On the interpretability and computational reliability of frequency-domain Granger causality

This Correspondence article is a comment which directly relates to the paper “A study of problems encountered in Granger causality analysis from a neuroscience perspective” (Stokes and Purdon, 2017). We agree that interpretation issues of Granger causality (GC) in neuroscience exist, partially due to the historically unfortunate use of the name “causality”, as described in previous literature. On the other hand, we think that Stokes and Purdon use a formulation of GC which is outdated (albeit still used) and do not fully account for the potential of the different frequency-domain versions of GC; in doing so, their paper dismisses GC measures based on a suboptimal use of them. Furthermore, s…

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 targ…

Feasibility of Ultra-Short-Term Analysis of Heart Rate and Systolic Arterial Pressure Variability at Rest and during Stress via Time-Domain and Entropy-Based Measures

Heart Rate Variability (HRV) and Blood Pressure Variability (BPV) are widely employed tools for characterizing the complex behavior of cardiovascular dynamics. Usually, HRV and BPV analyses are carried out through short-term (ST) measurements, which exploit ~five-minute-long recordings. Recent research efforts are focused on reducing the time series length, assessing whether and to what extent Ultra-Short-Term (UST) analysis is capable of extracting information about cardiovascular variability from very short recordings. In this work, we compare ST and UST measures computed on electrocardiographic R-R intervals and systolic arterial pressure time series obtained at rest and during both post…

Information flow in EEG source networks in epileptic children with focal seizure activity

Scalp electroencephalographic (EEG) signals are influenced by several factors, including volume conduction and low spatial resolution, which can jeopardize the validity of brain connectivity analysis performed on the raw recordings. One possible solution is to identify, starting from scalp EEG signals, the underlying cortical source activations, and to apply connectivity metrics on the reconstructed source time series. In this work, the dynamics of information flow between cortical EEG signals obtained after source reconstruction were assessed in children suffering from focal epilepsy. In a group of 10 children with focal seizures, 5-second windows of the 19-channel EEG were obtained in the…

Quantitative assessment of regularity and synchronization of intracardiac recordings during human atrial fibrillation

This study proposes the morphology-based evaluation of the regularity (R) and the synchronization (S) of intra-atrial electrograms acquired during atrial fibrillation (AF). R is defined as the degree of repetitiveness over time of the shapes of the activation waves detected in single atrial recordings. S accounts for the simultaneous presence of morphologically similar activation waves in two atrial electrograms, and for the dispersion of the propagation delays between the two sites. Both R and S resulted unitary for normal sinus rhythm and decreased significantly moving from atrial flutter (R=0.93, S=0.88) to AF of increasing complexity class (type I AF: R=0.75, S=0.66; type II AF: R=0.32,…

Towards Disentangling the Contribution of Different Pathways for the Regulation of Cardiac Activity: A Pilot Study

Heartbeat is dynamically regulated through mediating routes associated with central and peripheral feedback mechanisms. Previous studies focused on the quantification of these mechanisms in the presence of a single stressor. In this pilot study we propose a model aimed to quantify the contribution of different heartbeat regulatory routes while multiple stressors are administrated to the subject. The model is tested with Heart rate Variability (HRV) series from 26 subjects undergoing physical and affective stressors. Results show that the physical stressor prevalently (74%) contributes in mediating cardiac vagal control dynamics in case of concurrent affective elicitation. These results may …

Morphology-based measurement of activation time in human atrial fibrillation

The measurement of the activation time is crucial to allow the correct automatic analysis and classification of intracardiac electrograms recorded in the human atria during atrial fibrillation (AF). This study proposes a method which accounts for the morphology of bipolar signals. After ventricular artifact removal and activation wave recognition, the fiducial point of the activation wave was set at its local barycentre (LB). The method was tested on a set of 30 AF bipolar recordings of increasing complexity class; its performance was compared with that of the traditional methods of maximum peak (MP) or maximum slope (MS) estimation, taking the manual measurements performed by an expert car…

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a compr…

Extended Granger causality: a new tool to identify the structure of physiological networks.

Granger causality (GC) is a very popular tool for assessing the presence of directional interactions between two time series of a multivariate data set. In its original formulation, GC does not account for zero-lag correlations possibly existing between the observed time series. In the present study we compare the GC with a novel measure, termed extended GC (eGC), able to capture instantaneous causal relationships. We present a two-step procedure for the practical estimation of eGC based on first detecting the existence of zero-lag correlations, and then assigning them to one of the two possible causal directions using pairwise measures of non-Gaussianity. The proposed method was validated …

Surrogate data approaches to assess the significance of directed coherence: Application to EEG activity propagation

This paper addresses the topic of evaluating the significance of frequency domain measures of causal coupling in multivariate time series through generation of surrogate data. The considered approaches are the traditional Fourier Transform (FT) algorithm and a new causal FT (CFT) algorithm for surrogate data generation. Both algorithms preserve the FT modulus of the original series; differences are in the phase relationships, that are completely destroyed for FT surrogates and imposed after switching off the link over the considered causal direction for CFT surrogates. The ability of the algorithms to assess causality in the frequency domain was tested using the directed coherence as discri…

k-Nearest neighbour local linear prediction of scalp EEG activity during intermittent photic stimulation

The characterization of the EEG response to photic stimulation (PS) is an important issue with significant clinical relevance. This study aims to quantify and map the complexity of the EEG during PS, where complexity is measured as the degree of unpredictability resulting from local linear prediction. EEG activity was recorded with eyes closed (EC) and eyes open (EO) during resting and PS at 5, 10, and 15. Hz in a group of 30 healthy subjects and in a case-report of a patient suffering from cerebral ischemia. The mean squared prediction error (MSPE) resulting from k-nearest neighbour local linear prediction was calculated in each condition as an index of EEG unpredictability. The linear or …

Task-induced deactivation in diverse brain systems correlates with interindividual differences in distinct autonomic indices

AbstractNeuroimaging research has shown that different cognitive tasks induce relatively specific activation patterns, as well as less task-specific deactivation patterns. Here we examined whether individual differences in Autonomic Nervous System (ANS) activity during task performance correlate with the magnitude of task-induced deactivation. In an fMRI study, participants performed a continuous mental arithmetic task in a task/rest block design, while undergoing combined fMRI and heart / respiration rate acquisitions using photoplethysmograph and respiration belt. As expected, task performance increased heart-rate and reduced the RMSSD, a cardiac index related to vagal tone. Across partic…

Transfer Entropy Analysis of Pulse Arrival Time - Heart Period Interactions during Physiological Stress

Although Heart Period (HP) variability is the most widely used measure to assess cardiovascular oscillations, its evaluation combined with that of Pulse Arrival Time (PAT) variability may provide additional information about cardiac dynamics and cardiovascular interactions. In this study, we computed the transfer entropy from PAT to HP in 76 subjects monitored at rest and during orthostatic and mental stress using both a model-free (k- Nearest Neighbors) and a linear parametric estimator. Our results show how the information flow between these two variables depends on the physiological condition and how the nonlinear measure captures more information than the linear one during orthostatic s…

Causal relationships in the variability of cardiovascular system evoked by orthostatic stress by transfer entropy.

The coupling between cardiac and vascular systems in healthy volunteers, elicited by the head-up tilt test is estimated by means of transfer entropy with non-uniform embedding. The method applied to beat-to-beat recordings with heart periods and systolic blood pressure, supports the commonly accepted model, that baroreflex is the key factor in maintaining homeostatic blood distribution after tilting. However the method applied to changes of heart periods and changes of blood pressure, display switches in the driving system, from vascular in the early tilt, to cardiac just after the early tilt and back to vascular in the late tilt.

Information-Theoretic Analysis of Cardiorespiratory Interactions during Apneic Events in Sleep

In this work, measures of information dynamics are used to describe the dynamics of heart rate and cardiorespiratory interaction associated to sleep breathing disorders. In a large group of patients reporting repeated episodes of hypopneas, apneas (central, obstructive, mixed) and respiratory effort related arousals (RERA), we computed information storage of heart period variability and information transfer from heart period to airflow amplitude before, during and after each event. We find a general tendency to decrease of the information storage, suggesting higher complexity of the cardiac dynamics. The information transfer decreased during apneic events, and increased during milder disord…

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…

A method for the time-varying nonlinear prediction of complex nonstationary biomedical signals

A method to perform time-varying (TV) nonlinear prediction of biomedical signals in the presence of nonstationarity is presented in this paper. The method is based on identification of TV autoregressive models through expansion of the TV coefficients onto a set of basis functions and on k -nearest neighbor local linear approximation to perform nonlinear prediction. The approach provides reasonable nonlinear prediction even for TV deterministic chaotic signals, which has been a daunting task to date. Moreover, the method is used in conjunction with a TV surrogate method to provide statistical validation that the presence of nonlinearity is not due to nonstationarity itself. The approach is t…

Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks.

Objective: Indexes assessing the balance between redundancy and synergy were hypothesized to be helpful in characterizing cardiovascular control from spontaneous beat-to-beat variations of heart period (HP), systolic arterial pressure (SAP), and respiration (R). Methods: Net redundancy/synergy indexes were derived according to predictability and transfer entropy decomposition strategies via a multivariate linear regression approach. Indexes were tested in two protocols inducing modifications of the cardiovascular regulation via baroreflex loading/unloading (i.e., head-down tilt at −25° and graded head-up tilt at 15°, 30°, 45°, 60°, 75°, and 90°, respectively). The net redundancy/synergy of …

Experimental approach for testing the uncoupling between cardiovascular variability series

In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parame…

Registration and fusion of segmented left atrium CT images with CARTO electrical maps for the ablative treatment of atrial fibrillation

This study aims to extract the interior surface of the left atrium (LA) and pulmonary veins (PVs) from threedimensional tomographic data and to integrate it with LA CARTO electrical maps. The separation of LA and PVs from other overlapping structures of the heart was performed processing 3D CT data by marker-controlled watershed segmentation and surface extraction. CARTO maps were then registered on the L A internal surface by a stochastic optimization algorithm based on simulated annealing. The residual registration error resulted inferior to 3 mm. The integration between electrophysiological and high resolved anatomic information of LA results feasible and may constitute a significant sup…

Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by prevalently redundant or sy…

Respiratory Sinus Arrhythmia Mechanisms in Young Obese Subjects

Autonomic nervous system (ANS) activity and imbalance between its sympathetic and parasympathetic components are important factors contributing to the initiation and progression of many cardiovascular disorders related to obesity. The results on respiratory sinus arrhythmia (RSA) magnitude changes as a parasympathetic index were not straightforward in previous studies on young obese subjects. Considering the potentially unbalanced ANS regulation with impaired parasympathetic control in obese patients, the aim of this study was to compare the relative contribution of baroreflex and non-baroreflex (central) mechanisms to the origin of RSA in obese vs. control subjects. To this end, we applied…

Investigating cardiac and respiratory determinants of heart rate variability in an information-theoretic framework.

This study was aimed at comparing two alternative information-theoretic approaches for the combined analysis of heart rate variability (HRV) and respiration variability (RV). The approaches decompose the predictive information about HRV in two terms, quantifying respectively the information stored into HRV and that transferred to HRV from RV. Storage and transfer were assessed by the popular self entropy (SE) and transfer entropy (TE) measures, as well as by the alternative conditional SE (cSE) and cross entropy (CE) measures. The comparison was performed at a theoretical level, computing the exact values of the four measures for simulated cardiorespiratory dynamics, and on real data, estim…

Mutual Information Analysis of Brain-Body Interactions during different Levels of Mental stress

In this work, we analyze brain-heart interactions during different mental states computing mutual information (MI) between the dynamic activity of different physiological systems. In 18 healthy subjects monitored in a relaxed resting state and during a mental arithmetic and a serious game task, multichannel EEG, one lead ECG, respiration and blood volume pulse were collected via wireless non-invasive biosensors. From these signals, synchronous 300-second time series were extracted measuring brain activity via the δ, θ, α, and β EEG power, and activity of the body district via the ECG R-R interval η, the respiratory amplitude ϱ and the pulse arrival time π. MI was computed using a linear est…

Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series

The complexity of the short-term cardiovascular control prompts for the introduction of multivariate (MV) nonlinear time series analysis methods to assess directional interactions reflecting the underlying regulatory mechanisms. This study introduces a new approach for the detection of nonlinear Granger causality in MV time series, based on embedding the series by a sequential, non-uniform procedure, and on estimating the information flow from one series to another by means of the corrected conditional entropy. The approach is validated on short realizations of linear stochastic and nonlinear deterministic processes, and then evaluated on heart period, systolic arterial pressure and respira…

Multiscale analysis of information dynamics for linear multivariate processes.

In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic approaches to the multiscale analysis of complex dynamics are being increasingly used, the theoretical properties of the applied measures are poorly understood. This study introduces for the first time a framework for the analytical computation of information dynamics for linear multivariate stochastic processes explored at different time scales. After showing that the multiscale processing of a vector autoregressive (VAR) process introduces a moving aver…

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 [Formula: see text] and [Formula: see text] and the terms of its decomposition evidencing either the individual entropy rates of [Formula: see text] and [Formula: see text] and their joint entropy rate, or the transfer entropies from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] and the instantaneous information shared by [Formula: see text] and [Formula: see…

Quantifying High-Order Interactions in Cardiovascular and Cerebrovascular Networks

We present a method to analyze the dynamics of physiological networks beyond the framework of pairwise interactions. Our method defines the so-called O-information rate (OIR) as a measure of the higher-order interaction among several physiological variables. The OIR measure is computed from the vector autoregressive representation of multiple time series, and is applied to the network formed by heart period, systolic and diastolic arterial pressure, respiration and cerebral blood flow variability series measured in healthy subjects at rest and after head-up tilt. Our results document that cardiovascular, cerebrovascular and respiratory interactions are highly redundant, and that redundancy …

Cardiovascular and respiratory variability during orthostatic and mental stress: A comparison of entropy estimators

The aim of this study is to characterize cardiovascular and respiratory signals during orthostatic and mental stress as reflected in indices of entropy and complexity, providing a comparison between the performance of different estimators. To this end, the heart rate variability, systolic blood pressure, diastolic blood pressure and respiration time series were extracted from the recordings of 61 healthy volunteers undergoing a protocol consisting of supine rest, head-up tilt test and mental arithmetic task. The analysis was performed in the information domain using measures of entropy and conditional entropy, estimated through model-based (linear) and model-free (binning, nearest neighbor)…

Assessing Frequency Domain Causality in Cardiovascular Time Series with Instantaneous Interactions

Summary Background: The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series. Objectives: We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series. Methods: A procedure for the identif…

Minimally Invasive Assessment of Mental Stress based on Wearable Wireless Physiological Sensors and Multivariate Biosignal Processing

The development of connected health technologies for the continuous monitoring of the psychophysical state of individuals performing daily life activities requires the aggregation of non-intrusive sensors and the availability of methods and algorithms for extracting the relevant physiological information. The present study proposes an integrated approach for the objective assessment of mental stress which combines wirelessly connected low invasive biosensors with multivariate physiological time series analysis. In a group of 18 healthy subjects monitored in a relaxed resting state and during two experimental conditions inducing mental stress and sustained attention (respectively, mental ari…

Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series

A common way of obtaining information about a physiological system is to measure one or more signals from the system, consider their temporal evolution in the form of numerical time series, and obtain quantitative indexes through the application of time series analysis techniques. While historical approaches to time series analysis were addressed to the study of single signals, recent advances have made it possible to study collectively the behavior of several signals measured simultaneously from the considered system. In fact, multivariate (MV) time series analysis is nowadays extensively used to characterize interdependencies among multiple signals collected from dynamical physiological s…

Investigating cardiovascular and cerebrovascular variability in postural syncope by means of extended Granger causality

The patterns of Granger causality (GC) between heart period (HP), mean arterial pressure (AP) and cerebral blood flow velocity (FV) were investigated in ten subjects with postural related syncope (PRS). The classic GC measure based on vector autoregressive (VAR) modeling was compared with a novel extended GC (eGC) measure derived from VAR models incorporating instantaneous causal effects among the series. The analysis was performed in the supine and in the upright position during early (ET) and late (LT, close to presyncope) epochs of head-up tilt. Moving from ET to LT, both GC and eGC decreased from AP to HP, and increased from AP to FV, reflecting baroreflex impairment and loss of cerebra…

Comparison of Methods for the Assessment of Nonlinearity in Short-Term Heart Rate Variability under different Physiopathological States

Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy su…

Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis

This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence) and causality (directed coherence, partial directed coherence) from the parametric representation of linear multivariate (MV) processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR) processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition an…

Comparison of frequency domain measures based on spectral decomposition for spontaneous baroreflex sensitivity assessment after Acute Myocardial Infarction

Abstract The objective of this study is to present a new method to assess in the frequency domain the directed interactions between the spontaneous variability of systolic arterial pressure (SAP) and heart period (HP) from their linear model representation, and to apply it for studying the baroreflex control of arterial pressure in healthy physiological states and after acute myocardial infarction (AMI). The method is based on pole decomposition of the model transfer function and on the following evaluation of causal measures of coupling and gain from the poles associated to low frequency (0.04−0.15 Hz) oscillatory components. It is compared with traditional non-causal approaches for the sp…

Assisting Electrophysiological Substrate Quantification in Atrial Fibrillation Ablation

[EN] Catheter ablation (CA) is the most popular treatment of atrial fibrillation (AF) with good results in paroxysmal AF, while its efficiency is significantly reduced in persistent AF. With the equipment used for CA strongly depending on electro-gram (EGM) fractionation quantification, the use of a reliable fractionation estimator is crucial to reduce the high recurrence rates in persistent AF. This work introduces a non-linear EGM fractionation quantification technique, which is based on coarse-grained correlation dimension (CGCD) computed over epochs of 1 second. Recordings were firstly normalized, denoised and lowpass filtered. The final CGCD value was calculated by the median CGCD valu…

MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy.

A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different ap…

Information Decomposition: A Tool to Dissect Cardiovascular and Cardiorespiratory Complexity

This chapter reports some recent developments of information-theoretic concepts applied to the description of coupled dynamical systems, which allow to decompose the entropy of an assigned target system into components reflecting the information stored in the system and the information transferred to it from the other systems, as well as the nature (synergistic or redundant) of the information transferred to the target. The decomposition leads to well-defined measures of information dynamics which in the chapter will be defined theoretically, computed in simulations of linear Gaussian systems and implemented in practice through the application to heart period, arterial pressure and respirat…

Detecting nonlinear causal interactions between dynamical systems by non-uniform embedding of multiple time series.

This study introduces a new approach for the detection of nonlinear Granger causality between dynamical systems. The approach is based on embedding the multivariate (MV) time series measured from the systems X and Y by means of a sequential, non-uniform procedure, and on using the corrected conditional entropy (CCE) as unpredictability measure. The causal coupling from X to Y is quantified as the relative decrease of CCE measured after allowing the series of X to enter the embedding procedure for the description of Y. The ability of the approach to quantify nonlinear causality is assessed on MV time series measured from simulated dynamical systems with unidirectional coupling (the Rössler-…

Time, frequency and information domain analysis of short-term heart rate variability before and after focal and generalized seizures in epileptic children

OBJECTIVE In this work we explore the potential of combining standard time and frequency domain indexes with novel information measures, to characterize pre- and post-ictal heart rate variability (HRV) in epileptic children, with the aim of differentiating focal and generalized epilepsy regarding the autonomic control mechanisms. APPROACH We analyze short-term HRV in 37 children suffering from generalized or focal epilepsy, monitored 10 s, 300 s, 600 s and 1800 s both before and after seizure episodes. Nine indexes are computed in time (mean, standard deviation of normal-to-normal intervals, root mean square of the successive differences (RMSSD)), frequency (low-to-high frequency power rati…

Bridging the gap between the development of advanced biomedical signal processing tools and clinical practice

In the last twenty years the eld of the biomedical signal processing has known an upsurge, as witnessed by the progressively increasing number of peer-review international journals and sessions in biomedical meetings.

Assessing connectivity in the presence of instantaneous causality

This chapter is devoted to a discussion of the impact of instantaneous causality on the computation of frequency domain connectivity measures. Instantaneous causality (IC) refers to interactions between two observed time series which occur within the same time lag.

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…

Effect of age on complexity and causality of the cardiovascular control: comparison between model-based and model-free approaches.

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related…

Noninvasive assessment of baroreflex sensitivity in post-MI patients by an open loop parametric model of RR-systolic pressure interactions

Noninvasive evaluation of baroreflex sensitivity is considered an important goal for diagnosis and prognosis in post-MI patients. Methodological approach and physiological measure conditions may be the main causes for the differences found with respect to the standard Phenylephrine test. In this study, three linear parametric models, describing variability and mutual interactions of RR interval and systolic arterial pressure (SAP), were compared in relation to their ability to quantify baroreflex gain, using the Phenylephrine test index (Phe/sub BRS/) as reference. By monovariate autoregressive (AR) model, bivariate AR model and open loop ARXAR model, specific gain indexes (/spl alpha//sub …

Adaptive scheduling of acceleration and gyroscope for motion artifact cancelation in photoplethysmography

Background and objective: Recently, various algorithms have been introduced using wrist-worn photo-plethysmography (PPG) to provide high accuracy of instantaneous heart rate (HR) estimation, including during high-intensity exercise. Most studies focus on using acceleration and/or gyroscope signals for the motion artifact (MA) reference, which attenuates or cancels out noise from the MA-corrupted PPG signals. We aim to open and pave the path to find an appropriate MA reference selection for MA cancelation in PPG.Methods: We investigated how the acceleration and gyroscope reference signals correlate with the MAs of the distorted PPG signals and derived both mathematically and experimentally a…

Advanced computation in cardiovascular physiology: New challenges and opportunities

Recent developments in computational physiology have successfully exploited advanced signal processing and artificial intelligence tools for predicting or uncovering characteristic features of physiological and pathological states in humans. While these advanced tools have demonstrated excellent diagnostic capabilities, the high complexity of these computational 'black boxes’ may severely limit scientific inference, especially in terms of biological insight about both physiology and pathological aberrations. This theme issue highlights current challenges and opportunities of advanced computational tools for processing dynamical data reflecting autonomic nervous system dynamics, with a speci…

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…

Synergistic Information Transfer in the Global System of Financial Markets.

Uncovering dynamic information flow between stock market indices has been the topic of several studies which exploited the notion of transfer entropy or Granger causality, its linear version. The output of the transfer entropy approach is a directed weighted graph measuring the information about the future state of each target provided by the knowledge of the state of each driving stock market index. In order to go beyond the pairwise description of the information flow, thus looking at higher order informational circuits, here we apply the partial information decomposition to triplets consisting of a pair of driving markets (belonging to America or Europe) and a target market in Asia. Our …

Quantifying the complexity of short-term heart period variability through K nearest neighbor local linear prediction

The complexity of short-term heart period (HP) variability was quantified exploiting the paradigm that associates the degree of unpredictability of a time series to its dynamical complexity. Complexity was assessed through k-nearest neighbor local linear prediction. A proper selection of the parameter k allowed us to perform either linear or nonlinear prediction, and the comparison of the two approaches to infer the presence of nonlinear dynamics. The method was validated on simulations reproducing linear and nonlinear time series with varying levels of predictability. It was then applied to HP variability series measured from healthy subjects during head-up tilt test, showing that short-te…

Partial Information Decomposition of Brain-Heart Interactions in Temporal Lobe Epilepsy in the Childhood

We apply information decomposition methods to elicit unique, redundant and synergistic causal contributions of ipsilateral and contralateral EEG activity to heart rate dynamics in epileptic children. We find that information flows from brain to heart according to opposite lateralization effects for the delta and alpha rhythms, suggesting that different neuroautonomic mechanisms take place in the pre- and post-ictal phases of temporal lobe seizures.

Spectral analysis of the beat-to-beat variability of arterial compliance

Arterial compliance is an important parameter influencing ventricular-arterial coupling, depending on structural and functional mechanics of arteries. In this study, the spontaneous beat-to-beat variability of arterial compliance was investigated in time and frequency domains in thirty-nine young and healthy subjects monitored in the supine resting state and during head-up tilt. Spectral decomposition was applied to retrieve the spectral content of the time series associated to low (LF) and high frequency (HF) oscillatory components. Our results highlight: (i) a decrease of arterial compliance with tilt, in agreement with previous studies; (ii) an increase of the LF power content concurrent…

Assessing Complexity in Physiological Systems through Biomedical Signals Analysis

The idea that most physiological systems are complex has become increasingly popular in recent decades [...]

Apparent remote synchronization of amplitudes: A demodulation and interference effect

A form of "remote synchronization" was recently described, wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and mutual information, synchronization and causality dip at a certain distance, then recover before eventually fading. Here, the underlying mechanism is finally elucidated through novel experiments and simulations. The system non-linearity is found to have a dual role: it supports chaotic dynamics, and it enables the energy exchange between the lower and higher sidebands of a predominant frequency. This frequency acts as carrier signal in an arrangement rese…

Entropy characteristics of heart rate wavelet multiscale components in epileptic children before and after seizures

In this work, we analyze the information content of the multiple time scale components of heart rate variability (HRV) in children with focal epilepsy. HRV components are extracted from 30 pediatric patients, monitored 10 min and 10 s before and after focal epileptic seizures, using wavelet multiscale decomposition (with 5, 15, 30, 60, 120, 180 s time scale), and then characterized computing Entropy (E), permutation entropy (PE), conditional entropy (CE) and information storage (IS). Moving from preictal to postictal windows, we find statistically significant differences in the CE and IS values of HRV components at short time scales, which reflect autonomic imbalance and appear as potential…

Multivariate EEG spectral analysis evidences the functional link between motor and visual cortex during integrative sensorimotor tasks

The identification of the networks connecting brain areas and the understanding of their role in executing complex tasks is a crucial issue in cognitive neuroscience. In this study, specific visuomotor tasks were devised to reveal the functional network underlying the cooperation process between visual and motor regions. Electroencephalography (EEG) data were recorded from twelve healthy subjects during a combined visuomotor task, which integrated precise grip motor commands with sensory visual feedback (VM). This condition was compared with control tasks involving pure motor action (M), pure visual perception (V) and visuomotor performance without feedback (V + M). Multivariate parametric …

Directed coherence analysis in patients with severe autonomic dysfunction

Many different approaches have been applied to analyse the coupling between cardiovascular signals. This study evaluated the use of directed coherence, based on multivariate autoregressive modelling, for analysis of cardiovascular signals in patients with transthyretin amyloidosis, a rare disease where severe autonomic dysfunction is common. © 2014 IEEE.

Synchronization index for quantifying nonlinear causal coupling between RR interval and systolic arterial pressure after myocardial infarction

The analysis of nonlinear couplings among cardiovascular variability series can improve the knowledge of the cardioregulatory mechanism and help to understand how it can be affected by pathologies. In this study, the influences of acute myocardial infarction (AMI) on the causal relationships between the heart period and the arterial pressure were investigated by a nonlinear dynamic approach based on the corrected cross-conditional entropy. Whereas the global synchronization index did not differentiate the post-AMI patients from the young and old control groups, the causal indexes evidenced the impairment of the baroreflex control and showed an increase of the mechanical driving of the RR in…

Quantifying the contribution of arm postural tremor to the outcome of goal-directed pointing task by displacement measures.

A method for quantifying the outcome of goal-directed postural pointing was presented and used for relating the tremor output to the oscillations of single arm landmarks. The displacement of reflective markers placed on shoulder, upper arm, forearm, and hand were measured by an optoelectronic motion capture system in nine subjects holding a laser penlight pointed at a target. The high signal-to-noise ratio of the measured displacement series (from 7:1 for shoulder marker to 30:1 for hand marker) demonstrated the feasibility of the proposed system to carry out tremor analysis. The track of the laser emission on the target, reconstructed from penlight displacements, was studied as the outcome…

Vascular resistance arm of the baroreflex: methodology and comparison with the cardiac chronotropic arm.

Baroreflex response consists of cardiac chronotropic (effect on heart rate), cardiac inotropic (on contractility), venous (on venous return) and vascular (on vascular resistance) arms. Because of its measurement simplicity, cardiac chronotropic arm is most often analysed. The aim was to introduce a method to assess vascular baroreflex arm, and to characterize its changes during stress. We evaluated the effect of orthostasis and mental arithmetics (MA) in 39 (22 female, median age: 18.7 yrs.) and 36 (21 female, 19.2 yrs.) healthy volunteers, respectively. We recorded systolic and mean blood pressure (SBP and MBP) by volume-clamp method and R-R interval (RR) by ECG. Cardiac output (CO) was re…

Spectral decomposition of RR-variability obtained by an open loop parametric model for the diagnosis of neuromediate syncope

The role of the cardiovascular regulatory mechanism in patients with neuromediate syncope (NS) is poorly understood. The aim of this study was to accomplish continuous non-invasive analysis of the baroreflex mechanism in patients during a head-tip tilt-table test (HTT) using an open-loop autoregressive model with exogenous input. The model describes the causal dependence of the RR interval on the systolic arterial pressure (SAP) variability. Thus, RR variability results as the linear composition of SAP-dependent (Pdep) and SAP-independent parts of the RR power (P). Further, the model allows the estimation of the baroreflex gain using the modulus of the transfer function (G) from SAP to RR i…

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 …

Testing Frequency-Domain Causality in Multivariate Time Series

We introduce a new hypothesis-testing framework, based on surrogate data generation, to assess in the frequency domain, the concept of causality among multivariate (MV) time series. The approach extends the traditional Fourier transform (FT) method for generating surrogate data in a MV process and adapts it to the specific issue of causality. It generates causal FT (CFT) surrogates with FT modulus taken from the original series, and FT phase taken from a set of series with causal interactions set to zero over the direction of interest and preserved over all other directions. Two different zero-setting procedures, acting on the parameters of a MV autoregressive (MVAR) model fitted on the ori…

Multiscale Decomposition of Cardiovascular and Cardiorespiratory Information Transfer under General Anesthesia∗

The analysis of short-term cardiovascular and cardiorespiratory regulation during altered conscious states, such as those induced by anesthesia, requires to employ time series analysis methods able to deal with the multivariate and multiscale nature of the observed dynamics. To meet this requirement, the present study exploits the extension to multiscale analysis of recently proposed information decomposition methods which allow to quantify, from short realizations, the amounts of joint, unique, redundant and synergistic information transferred within multivariate time series. These methods were applied to the spontaneous variability of heart period (HP), systolic arterial pressure (SAP) an…

Mechanisms of causal interaction between short-term RR interval and systolic arterial pressure oscillations during orthostatic challenge

The transition from the supine to the upright position requires a reorganization of the mechanisms of cardiovascular control that, if not properly accomplished, may lead to neurally mediated syncope. We investigated how the patterns of causality between systolic arterial pressure (SAP) and cardiac RR interval were modified by prolonged head-up tilt using a novel nonlinear approach based on corrected conditional entropy (CCE) compared with the standard approach exploiting the cross-correlation function (CCF). Measures of coupling strength and delay of the causal interactions from SAP to RR and from RR to SAP were obtained in 10 patients with recurrent, neurally mediated syncope (RNMS) and 10…

Pre- and post-ictal brain activity characterization using combined source decomposition and connectivity estimation in epileptic children

In this research, the study of functional connectivity between sources of electroencephalogram (EEG) activity assessed for different classes (well before seizure, preictal and post-ictal) was performed. EEG recordings were acquired from 12 subjects with focal epilepsy. Then, ten common spatial patterns (CSP) were obtained for EEG segments describing 95% of Riemannian distance between pairs of classes, followed by estimation of multivariate autoregressive (MVAR) models’ coefficients. The MVAR models were further used to extract coherence as a functional connectivity measures. Our results show that the coherence between CSP sources differs between baseline and pre-ictal segments: it has the l…

Surrogate Data Analysis for Assessing the Significance of the Coherence Function

In cardiovascular variability analysis, the significance of the coupling between two time series is commonly assessed by setting a threshold level in the coherence function. While traditionally used statistical tests consider only the parameters of the adopted estimator, the required zero-coherence level may be affected by some features of the observed series. In this study, three procedures, based on the generation of surrogate series sharing given properties with the original but being structurally uncoupled, were considered: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR). IID surrogates maintained the distribution of the original series, while …

A portable system for multiple parameters monitoring: towards assessment of health conditions and stress level in the automotive field

In this work, an electronic portable combo system able to synchronously acquire multiple signals, e.g. electrocardiographic (ECG), photoplethysmographic (PPG) and breathing waveforms, is presented. The realized system is also capable of showing in real time some physiological parameters which can be used for assessing health/stress status of the volunteer, such as heart rate and breathing frequency and their trends over time. Thanks to the use of non-invasive PPG probes, of batteries as power supply, and to the possibility to add in the future additional sensors to acquire other signals, the system could also be employed inside vehicles for assessing the status of the driver. Finally, the r…

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predom…

Information dynamics in cardiorespiratory analyses: application to controlled breathing

Voluntary adjustment of the breathing pattern is widely used to deal with stress-related conditions. In this study, effects of slow and fast breathing with a low and high inspiratory to expiratory time on heart rate variability (HRV) are evaluated by means of information dynamics. Information transfer is quantified both as the traditional transfer entropy as well as the cross entropy, where the latter does not condition on the past of HRV, thereby taking the highly unidirectional relation between respiration and heart rate into account. The results show that the cross entropy is more suited to quantify cardiorespiratory information transfer as this measure increases during slow breathing, i…

Quantifying changes in EEG complexity induced by photic stimulation.

Summary Objectives: This study aims to characterize EEG complexity, measured as the prediction error resulting from nonlinear prediction, in healthy humans during photic stimulation. Methods: EEGs were recorded from 15 subjects with eyes closed (EC) and eyes open (EO), during the baseline condition and during stroboscopic photic stimulation (PS) at 5, 10, and 15 Hz. The mean squared prediction error (MSPE) resulting from nearest neighbor local linear prediction was taken as complexity index. Complexity maps were generated interpolating the MSPE index over a schematic scalp representation. Results: Statistical analysis revealed that: i) EEG shows good predictability in all conditions and see…

Parametric and nonparametric methods to generate time-varying surrogate data.

We present both nonparametric and parametric approaches to generating time-varying surrogate data. Nonparametric and parametric approaches are based on the use of the short-time Fourier transform and a time-varying autoregressive model, respectively. Time-varying surrogate data (TVSD) can be used to determine the statistical significance of the linear and nonlinear coherence function estimates. Two advantages of the TVSD are that it keeps one from having to make an arbitrary decision about the significance of the coherence value, and it properly takes into account statistical significance levels, which may change with time. Our simulation examples and experimental results on blood pressure …

Decomposing the transfer entropy to quantify lag-specific Granger causality in cardiovascular variability.

We present a modification of the well known transfer entropy (TE) which makes it able to detect, besides the direction and strength of the information transfer between coupled processes, its exact timing. The approach follows a decomposition strategy which identifies--according to a lag-specific formulation of the concept of Granger causality--the set of time delays carrying significant information, and then assigns to each of these delays an amount of information transfer such that the total contribution yields the overall TE. We propose also a procedure for the practical estimation from time series data of the relevant delays and lag-specific TE in both bivariate and multivariate settings…

Studying brain visuo-tactile integration through cross-spectral analysis of human MEG recordings

An important aim in cognitive neuroscience is to identify the networks connecting different brain areas and their role in executing complex tasks. In this study, visuo-tactile tasks were employed to assess the functional correlation underlying the cooperation process between visual and tactile regions. MEG data were recorded from eight healthy subjects while performing a visual, a tactile, and a visuo-tactile task. To define regions of interest (ROIs), event-related fields (ERFs) were estimated from MEG data related to visual and tactile areas. The ten channels with the highest increase in ERF variance, moving from rest to task, were selected. Cross-spectral analysis was then performed to a…

Letter by Masè et al Regarding Article, "Granger Causality-Based Analysis for Classification of Fibrillation Mechanisms and Localization of Rotational Drivers".

Estimating the decomposition of predictive information in multivariate systems

In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…

A new Framework for the Spectral Information Decomposition of Multivariate Gaussian Processes

: Different information-theoretic measures are available in the literature for the study of pairwise and higher-order interactions in multivariate dynamical systems. While these measures operate in the time domain, several physiological and non-physiological systems exhibit a rich oscillatory content that is typically analyzed in the frequency domain through spectral and cross-spectral approaches. For Gaussian systems, the relation between information and spectral measures has been established considering coupling and causality measures, but not for higher-order interactions. To fill this gap, in this work we introduce an information-theoretic framework in the frequency domain to quantify t…

Reliability of Local Activation Waves Features to Characterize Paroxysmal Atrial Fibrillation Substrate During Sinus Rhythm

[EN] Analysis of coronary sinus (CS) electrograms (EGMs) is vastly used for the assessment of the atrial fibrillation (AF) substrate. As a catheter consists of five dipoles (distal, mid-distal, medial, mid-proximal, proximal), results may vary upon the employed channel: myocardial contraction and bad contact are unavoidable factors affecting the recording. This work aims to specify the most reliable channels in catching AF dynamics, using 44 multichannel bipolar CS recordings in sinus rhythm (SR) of paroxysmal AF with 1-5 minutes duration. Local activation waves (LAWs) were detected and main features obtained: duration, amplitude, area and correlation between dominant morphologies of each c…

Feasibility of Ultra-short Term Complexity Analysis of Heart Rate Variability in Resting State and During Orthostatic Stress

In this work, we study ultra-short term (UST) complexity of Heart Rate Variability (HRV) and its agreement with analysis of standard short-term (ST) HRV recordings obtained at rest and during orthostatic stress. Conditional Entropy (CE) measures have been computed using both a linear Gaussian approximation and a more accurate model-free approach based on nearest neighbors. The agreement between UST and ST indices has been compared via statistical tests and correlation analysis, suggesting the feasibility of exploiting faster algorithms and shorter time series for detecting changes in cardiovascular control during various states.

Conditional Self-Entropy and Conditional Joint Transfer Entropy in Heart Period Variability during Graded Postural Challenge.

Self-entropy (SE) and transfer entropy (TE) are widely utilized in biomedical signal processing to assess the information stored into a system and transferred from a source to a destination respectively. The study proposes a more specific definition of the SE, namely the conditional SE (CSE), and a more flexible definition of the TE based on joint TE (JTE), namely the conditional JTE (CJTE), for the analysis of information dynamics in multivariate time series. In a protocol evoking a gradual sympathetic activation and vagal withdrawal proportional to the magnitude of the orthostatic stimulus, such as the graded head-up tilt, we extracted the beat-to-beat spontaneous variability of heart per…

Interictal cardiorespiratory variability in temporal lobe and absence epilepsy in childhood

It is well known that epilepsy has a profound effect on the autonomic nervous system, especially on the autonomic control of heart rate and respiration. This effect has been widely studied during seizure activity, but less attention has been given to interictal (i.e. seizure-free) activity. The studies that have been done on this topic, showed that heart rate and respiration can be affected individually, even without the occurrence of seizures. In this work, the interactions between these two individual physiological variables are analysed during interictal activity in temporal lobe and absence epilepsy in childhood. These interactions are assessed by decomposing the predictive information …

Quantitative assessment of synchronization during atrial fibrillation by Shannon Entropy characterization of propagation delays

This study introduced a new method for the quantification of the synchronization (S) and the causal verse of activation (S12) in couples of atrial electrograms recorded during atrial fibrillation (AF). The synchronization indexes S and S12 relied on the measure of the propagation delays between coupled activation times in two atrial signals and on the characterization of their dispersion by Shannon-Entropy (SE). S and S12 were validated both on simulated activation time series and endocavitary signals in patients. In simulation, S and S12 were equal to 1 for propagation of one single wavefront in a fully excitable tissue, while they decreased for reentries in partially excitable tissue (S =…

Model-Based Transfer Entropy Analysis of Brain-Body Interactions with Penalized regression techniques

The human body can be seen as a functional network depicting the dynamical interactions between different organ systems. This exchange of information is often evaluated with information-theoretic approaches which comprise the use of vector autoregressive (VAR) and state space (SS) models, normally identified with the Ordinary Least Squares (OLS). However, the number of time series to be included in the model is strictly related to the length of data recorded thus limiting the use of the classical approach. In this work, a new method based on penalized regressions, the so-called LASSO, was compared with OLS on physiological time-series extracted from 18 subjects during different stress condi…

Wearable Multisensor Ring-Shaped Probe for Assessing Stress and Blood Oxygenation: Design and Preliminary Measurements

The increasing interest in innovative solutions for health and physiological monitoring has recently fostered the development of smaller biomedical devices. These devices are capable of recording an increasingly large number of biosignals simultaneously, while maximizing the user’s comfort. In this study, we have designed and realized a novel wearable multisensor ring-shaped probe that enables synchronous, real-time acquisition of photoplethysmographic (PPG) and galvanic skin response (GSR) signals. The device integrates both the PPG and GSR sensors onto a single probe that can be easily placed on the finger, thereby minimizing the device footprint and overall size. The system enables the e…

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 &delta

A morphology-based approach to the evaluation of atrial fibrillation organization.

Are nonlinear model-free conditional entropy approaches for the assessment of cardiac control complexity superior to the linear model-based one?

Objective : We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals. Methods : An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electroca…