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

Nonlinear markers of coupling strength are often utilized to typify cardiorespiratory and cerebrovascular regulations. The computation of these indices requires techniques describing nonlinear interactions between respiration (R) and heart period (HP) and between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv). We compared two model-free methods for the assessment of dynamic HP–R and MCBv–MAP interactions, namely the cross-sample entropy (CSampEn) and k-nearest-neighbor cross-unpredictability (KNNCUP). Comparison was carried out first over simulations generated by linear and nonlinear unidirectional causal, bidirectional linear causal, and lag-zero linear noncausal models, and then over experimental data acquired from 19 subjects at supine rest during spontaneous breathing and controlled respiration at 10, 15, and 20 breaths·minute−1 as well as from 13 subjects at supine rest and during 60° head-up tilt. Linear markers were computed for comparison. We found that: (i) over simulations, CSampEn and KNNCUP exhibit different abilities in evaluating coupling strength; (ii) KNNCUP is more reliable than CSampEn when interactions occur according to a causal structure, while performances are similar in noncausal models; (iii) in healthy subjects, KNNCUP is more powerful in characterizing cardiorespiratory and cerebrovascular variability interactions than CSampEn and linear markers. We recommend KNNCUP for quantifying cardiorespiratory and cerebrovascular coupling.

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

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

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 analysis, on daily data recorded during the years 2000 to 2019, allows the identification of the synergistic information that a pair of drivers carry about the target. By studying the influence of the closing returns of drivers on the subsequent overnight changes of target indexes, we find that (i) Korea, Tokyo, Hong Kong, and Singapore are, in order, the most influenced Asian markets; (ii) US indices SP500 and Russell are the strongest drivers with respect to the bivariate Granger causality; and (iii) concerning higher order effects, pairs of European and American stock market indices play a major role as the most synergetic three-variables circuits. Our results show that the Synergy, a proxy of higher order predictive information flow rooted in information theory, provides details that are complementary to those obtained from bivariate and global Granger causality, and can thus be used to get a better characterization of the global financial system.

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

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

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

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 structure of coupled dynamic processes. First, we investigate the theoretical properties of these measures, providing the conditions for their existence and assessing the meaning of the information theoretic quantity that each of them reflects. Then, we present an approach for the exact computation of information dynamics based on the linear Gaussian approximation, and exploit this approach to characterize the behavior of SE, TE, CE and cSE in benchmark systems with known dynamics. Finally, we exploit these measures to study cardiorespiratory dynamics measured from healthy subjects during head-up tilt and paced breathing protocols. Our main result is that the combined evaluation of the measures of information dynamics allows to infer the causal effects associated with the observed dynamics and to interpret the alteration of these effects with changing experimental conditions.

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

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

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 alternative empirical strategies: if IC is deemed as physiologically meaningful, zero-lag effects are assimilated to lagged effects to make them causally relevant; if not, zero-lag effects are incorporated in both CE terms to obtain a compensation. The resulting compensated TE (cTE) estimator is tested on simulated time series, showing that its utilization improves sensitivity (from 61% to 96%) and specificity (from 5/6 to 0/6 false positives) in the detection of information transfer respectively when instantaneous effect are causally meaningful and non-meaningful. Then, it is evaluated on examples of cardiovascular and neurological time series, supporting the feasibility of the proposed framework for the investigation of physiological mechanisms.

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 synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone.

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 amounts eliciting the specific contribution of assigned source systems to the target dynamics, and amounts reflecting information modification through the balance between redundant and synergetic interaction between systems. These decompositions are formulated quantifying information either as the variance or as the entropy of the investigated processes, and their exact computation for the case of linear Gaussian processes is presented. The theoretical properties of the resulting measures are first investigated in simulations of vector autoregressive processes. Then, the measures are applied to assess information dynamics in cardiovascular networks from the variability series of heart period, systolic arterial pressure and respiratory activity measured in healthy subjects during supine rest, orthostatic stress, and mental stress. Our results document the importance of combining the assessment of information storage, transfer and modification to investigate common and complementary aspects of network dynamics; suggest the higher specificity to alterations in the network properties of the measures derived from the decompositions; and indicate that measures of information transfer and information modification are better assessed, respectively, through entropy-based and variance-based implementations of the framework.