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

This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes X and Y and the terms of its decomposition evidencing either the individual entropy rates of X and Y and their joint entropy rate, or the transfer entropies from X to Y and from Y to X and the instantaneous information shared by X and Y. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality.

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

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

On the Different Abilities of Cross-Sample Entropy and K-Nearest-Neighbor Cross-Unpredictability in Assessing Dynamic Cardiorespiratory and Cerebrovascular Interactions.

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.

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 postural and mental stress. Standard time-domain indices are computed, together with entropy-based measures able to assess the regularity and complexity of cardiovascular dynamics, on time series lasting down to 60 samples, employing either a faster linear parametric estimator or a more reliable but time-consuming model-free method based on nearest neighbor estimates. Our results are evidence that shorter time series down to 120 samples still exhibit an acceptable agreement with the ST reference and can also be exploited to discriminate between stress and rest. Moreover, despite neglecting nonlinearities inherent to short-term cardiovascular dynamics, the faster linear estimator is still capable of detecting differences among the conditions, thus resulting in its suitability to be implemented on wearable devices.

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

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

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 specific focus on cardiovascular control physiology and pathology. This includes the development and adaptation of complex signal processing methods, multivariate cardiovascular models, multiscale and nonlinear models for central-peripheral dynamics, as well as deep and transfer learning algorithms applied to large datasets. The width of this perspective highlights the issues of specificity in heartbeat-related features and supports the need for an imminent transition from the black-box paradigm to explainable and personalized clinical models in cardiovascular research. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

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

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

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

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

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

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

Assessing Complexity in Physiological Systems through Biomedical Signals Analysis.

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

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

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

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 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.

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

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

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

The 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. Conditional mutual information and transfer entropy revealed sparse networks dominated by local connections between muscles. We observed significant changes in muscle networks across postural tasks localized to the muscles involved in performing those tasks. Information decomposition revealed distinct patterns in task-related changes: unimanual and bimanual pointing were associated with reduced transfer to the pectoralis major muscles, but an increase in total information compared to no pointing, while postural instability resulted in increased information, information transfer and information storage in the abductor longus muscles compared to normal stability. These findings show robust patterns of directed interactions between muscles that are task-dependent and can be assessed from surface EMG recorded during static postural tasks. We discuss directed muscle networks in terms of the neural circuitry involved in generating muscle activity and suggest that task-related effects may reflect gain modulations of spinal reflex pathways.

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

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

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 cannot be seen as an approximation of a source's anatomical location and (2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing.

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 subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt. The method of surrogate data is employed to detect the presence and quantify the contribution of nonlinear dynamics to HRV. We find that the three measures differ both in their variations across groups and conditions and in the percentage and strength of nonlinear HRV dynamics. NCI and IS displayed opposite variations, suggesting more complex dynamics in O and MI compared to Y and less complex dynamics during tilt. The strength of nonlinear dynamics is reduced by tilt using all measures in Y, while only GLC detects a significant strengthening of such dynamics in MI. A large percentage of detected nonlinear dynamics is revealed only by the IS measure in the Y group at rest, with a decrease in O and MI and during T, while NCI and GLC detect lower percentages in all groups and conditions. While these results suggest that distinct dynamic structures may lie beneath short-term HRV in different physiological states and pathological conditions, the strong dependence on the measure adopted and on their implementation suggests that physiological interpretations should be provided with caution.

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

In this study, an analysis of brain, cardiovascular and respiratory dynamics was conducted combining information-theoretic measures with the Network Physiology paradigm during different levels of mental stress. Starting from low invasive recordings of electroencephalographic, electrocardiographic, respiratory, and blood volume pulse signals, the dynamical activity of seven physiological systems was probed with one-second time resolution measuring the time series of the δ , θ , α and ß 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 ß . The topology of the physiological network underlying such information transfer was node- and state-dependent, with the peripheral subnetwork showing interactions from RR to PAT and between RESP and RR, PAT consistently across states, the brain subnetwork resulting more connected during MA, and the subnetwork of brain-peripheral interactions involving different brain rhythms in the three states and resulting primarily activated during MA. These results have both physiological relevance as regards the interpretation of central and autonomic effects on cardiovascular and respiratory variability, and practical relevance as regards the identification of features useful for the automatic distinction of different mental states.

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

Heart rate variability (HRV; variability of the RR interval of the electrocardiogram) results from the activity of several coexisting control mechanisms, which involve the influence of respiration (RESP) and systolic blood pressure (SBP) oscillations operating across multiple temporal scales and changing in different physiological states. In this study, multiscale information decomposition is used to dissect the physiological mechanisms related to the genesis of HRV in 78 young volunteers monitored at rest and during postural and mental stress evoked by head-up tilt (HUT) and mental arithmetics (MA). After representing RR, RESP and SBP at different time scales through a recently proposed method based on multivariate state space models, the joint information transfer 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.

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 resembling standard amplitude modulation, wherein the lower sideband and the demodulated baseband signals spectrally overlap. Due to a spatially-dependent phase relationship, at a certain distance near-complete destructive interference occurs between them, causing the observed dip. Methods suitable for detecting non-trivial entrainment, such as transfer entropy and the auxiliary system approach, nevertheless, reveal that synchronization and causality actually decrease with distance monotonically. Remoteness is, therefore, arguably only apparent, as also reflected in the propagation of external perturbations. These results demonstrate a complex mechanism of dynamical interdependence, and exemplify how it can lead to incorrectly inferring synchronization and causality.