Disentangling cardiovascular control mechanisms during head-down tilt via joint transfer entropy and self-entropy decompositions

Effects of the angle of head-down tilt on dynamic cerebral autoregulation during combined exposure to cephalad fluid shift and mild hypercapnia

Astronauts experience combined exposure to a cephalad fluid shift and mild hypercapnia during space missions, potentially contributing to health problems. Such combined exposure may weaken dynamic cerebral autoregulation. The magnitude of cephalad fluid shift varies between individuals, and dynamic cerebral autoregulation may be affected more by greater cephalad fluid shift during combined exposure. We evaluated the dose-dependent effects of head-down tilt (HDT) on dynamic cerebral autoregulation during acute combined exposure to HDT and 3% CO2 inhalation. Twenty healthy participants were randomly exposed to three angles of HDT (-5°HDT+CO2, -15°HDT+CO2 and -30°HDT+CO2). After 15 min of rest, participants inhaled room air for 10 min in a horizontal body position, then inhaled 3% CO2 for 10 min under HDT. The last 6 min of data were used for analysis in each stage. Arterial pressure waveforms were obtained using finger blood pressure, and blood velocity waveforms in the middle cerebral artery were obtained using transcranial Doppler ultrasonography. Dynamic cerebral autoregulation was evaluated by transfer function analysis between waveforms. Statistical analysis was performed by two-way repeated-measures analysis of variance. The index of transfer function gain in the low-frequency range increased significantly with -15°HDT+CO2 and -30°HDT+CO2, but no changes were seen with -5°HDT+CO2. Phase in the low-frequency range decreased significantly with all three protocols. These results of significant changes in indexes of both gain and phase during combined exposure to steep HDT (-15° to -30°) and 3% CO2 inhalation suggest weakened dynamic cerebral autoregulation with the combination of moderate cephalad fluid shift and mild hypercapnia.

Effects of weightlessness on the cardiovascular system: a systematic review and meta-analysis

Background: The microgravity environment has a direct impact on the cardiovascular system due to the fluid shift and weightlessness that results in cardiac dysfunction, vascular remodeling, and altered Cardiovascular autonomic modulation (CAM), deconditioning and poor performance on space activities, ultimately endangering the health of astronauts. Objective: This study aimed to identify the acute and chronic effects of microgravity and Earth analogues on cardiovascular anatomy and function and CAM. Methods: CINAHL, Cochrane Library, Scopus, Science Direct, PubMed, and Web of Science databases were searched. Outcomes were grouped into cardiovascular anatomic, functional, and autonomic alterations, and vascular remodeling. Studies were categorized as Spaceflight (SF), Chronic Simulation (CS), or Acute Simulation (AS) based on the weightlessness conditions. Meta-analysis was performed for the most frequent outcomes. Weightlessness and control groups were compared. Results: 62 articles were included with a total of 963 participants involved. The meta-analysis showed that heart rate increased in SF [Mean difference (MD) = 3.44; p = 0.01] and in CS (MD = 4.98; p < 0.0001), whereas cardiac output and stroke volume decreased in CS (MD = -0.49; p = 0.03; and MD = -12.95; p < 0.0001, respectively), and systolic arterial pressure decreased in AS (MD = -5.20; p = 0.03). According to the qualitative synthesis, jugular vein cross-sectional area (CSA) and volume were greater in all conditions, and SF had increased carotid artery CSA. Heart rate variability and baroreflex sensitivity, in general, decreased in SF and CS, whereas both increased in AS. Conclusion: This review indicates that weightlessness impairs the health of astronauts during and after spaceflight, similarly to the effects of aging and immobility, potentially increasing the risk of cardiovascular diseases. Systematic Review Registration: https://www.crd.york.ac.uk/prospero/, identifier CRD42020215515.

CVRanalysis: a free software for analyzing cardiac, vascular and respiratory interactions

Introduction: Simultaneous beat-to-beat R-R intervals, blood pressure and respiration signals are routinely analyzed for the evaluation of autonomic cardiovascular and cardiorespiratory regulations for research or clinical purposes. The more recognized analyses are i) heart rate variability and cardiac coherence, which provides an evaluation of autonomic nervous system activity and more particularly parasympathetic and sympathetic autonomic arms; ii) blood pressure variability which is mainly linked to sympathetic modulation and myogenic vascular function; iii) baroreflex sensitivity; iv) time-frequency analyses to identify fast modifications of autonomic activity; and more recently, v) time and frequency domain Granger causality analyses were introduced for assessing bidirectional causal links between each considered signal, thus allowing the scrutiny of many physiological regulatory mechanisms. Methods: These analyses are commonly applied in various populations and conditions, including mortality and morbidity predictions, cardiac and respiratory rehabilitation, training and overtraining, diabetes, autonomic status of newborns, anesthesia, or neurophysiological studies. Results: We developed CVRanalysis, a free software to analyze cardiac, vascular and respiratory interactions, with a friendly graphical interface designed to meet laboratory requirements. The main strength of CVRanalysis resides in its wide scope of applications: recordings can arise from beat-to-beat preprocessed data (R-R, systolic, diastolic and mean blood pressure, respiration) or raw data (ECG, continuous blood pressure and respiratory waveforms). It has several tools for beat detection and correction, as well as setting of specific areas or events. In addition to the wide possibility of analyses cited above, the interface is also designed for easy study of large cohorts, including batch mode signal processing to avoid running repetitive operations. Results are displayed as figures or saved in text files that are easily employable in statistical softwares. Conclusion: CVRanalysis is freely available at this website: anslabtools.univ-st-etienne.fr. It has been developed using MATLAB® and works on Windows 64-bit operating systems. The software is a standalone application avoiding to have programming skills and to install MATLAB. The aims of this paper area are to describe the physiological, research and clinical contexts of CVRanalysis, to introduce the methodological approach of the different techniques used, and to show an overview of the software with the aid of screenshots.

Concomitant evaluation of cardiovascular and cerebrovascular controls via Geweke spectral causality to assess the propensity to postural syncope

The evaluation of propensity to postural syncope necessitates the concomitant characterization of the cardiovascular and cerebrovascular controls and a method capable of disentangling closed loop relationships and decomposing causal links in the frequency domain. We applied Geweke spectral causality (GSC) to assess cardiovascular control from heart period and systolic arterial pressure variability and cerebrovascular regulation from mean arterial pressure and mean cerebral blood velocity variability in 13 control subjects and 13 individuals prone to develop orthostatic syncope. Analysis was made at rest in supine position and during head-up tilt at 60°, well before observing presyncope signs. Two different linear model structures were compared, namely bivariate autoregressive and bivariate dynamic adjustment classes. We found that (i) GSC markers did not depend on the model structure; (ii) the concomitant assessment of cardiovascular and cerebrovascular controls was useful for a deeper comprehension of postural disturbances; (iii) orthostatic syncope appeared to be favored by the loss of a coordinated behavior between the baroreflex feedback and mechanical feedforward pathway in the frequency band typical of the baroreflex functioning during the postural challenge, and by a weak cerebral autoregulation as revealed by the increased strength of the pressure-to-flow link in the respiratory band. GSC applied to spontaneous cardiovascular and cerebrovascular oscillations is a promising tool for describing and monitoring disturbances associated with posture modification.

An atrioventricular node model incorporating autonomic tone

The response to atrial fibrillation (AF) treatment is differing widely among patients, and a better understanding of the factors that contribute to these differences is needed. One important factor may be differences in the autonomic nervous system (ANS) activity. The atrioventricular (AV) node plays an important role during AF in modulating heart rate. To study the effect of the ANS-induced activity on the AV nodal function in AF, mathematical modelling is a valuable tool. In this study, we present an extended AV node model that incorporates changes in autonomic tone. The extension was guided by a distribution-based sensitivity analysis and incorporates the ANS-induced changes in the refractoriness and conduction delay. Simulated RR series from the extended model driven by atrial impulse series obtained from clinical tilt test data were qualitatively evaluated against clinical RR series in terms of heart rate, RR series variability and RR series irregularity. The changes to the RR series characteristics during head-down tilt were replicated by a 10% decrease in conduction delay, while the changes during head-up tilt were replicated by a 5% decrease in the refractory period and a 10% decrease in the conduction delay. We demonstrate that the model extension is needed to replicate ANS-induced changes during tilt, indicating that the changes in RR series characteristics could not be explained by changes in atrial activity alone.

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

OBJECTIVE

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

APPROACH

We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the decomposition into unique, redundant and synergistic contributions, is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress.

MAIN RESULTS

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

SIGNIFICANCE

The proposed methodology allows to extract useful information about the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations.

Beyond the Baroreflex: A New Measure of Autonomic Regulation Based on the Time-Frequency Assessment of Variability, Phase Coherence and Couplings

For decades the role of autonomic regulation and the baroreflex in the generation of the respiratory sinus arrhythmia (RSA) - modulation of heart rate by the frequency of breathing - has been under dispute. We hypothesized that by using autonomic blockers we can reveal which oscillations and their interactions are suppressed, elucidating their involvement in RSA as well as in cardiovascular regulation more generally. R-R intervals, end tidal CO2, finger arterial pressure, and muscle sympathetic nerve activity (MSNA) were measured simultaneously in 7 subjects during saline, atropine and propranolol infusion. The measurements were repeated during spontaneous and fixed-frequency breathing, and apnea. The power spectra, phase coherence and couplings were calculated to characterise the variability and interactions within the cardiovascular system. Atropine reduced R-R interval variability (p < 0.05) in all three breathing conditions, reduced MSNA power during apnea and removed much of the significant coherence and couplings. Propranolol had smaller effect on the power of oscillations and did not change the number of significant interactions. Most notably, atropine reduced R-R interval power in the 0.145-0.6 Hz interval during apnea, which supports the hypothesis that the RSA is modulated by a mechanism other than the baroreflex. Atropine also reduced or made negative the phase shift between the systolic and diastolic pressure, indicating the cessation of baroreflex-dependent blood pressure variability. This result suggests that coherent respiratory oscillations in the blood pressure can be used for the non-invasive assessment of autonomic regulation.

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 protocols: We applied the C/S test to variability series of respiratory movements, heart period, systolic arterial pressure, mean arterial pressure, and mean cerebral blood flow recorded in 17 pathological individuals (age: 648 yrs; 17 males) before and after induction of propofol-based general anesthesia prior to coronary artery bypass grafting, and in 13 healthy subjects (age: 278 yrs; 5 males) at rest in supine position and during head-up tilt with a table inclination of 60.

RESULTS

Respiration behaved systematically as a confounder for cardiovascular and cerebrovascular controls. In addition, its role was affected by propofol-based general anesthesia but not by a postural stimulus of limited intensity.

CONCLUSION

The C/S test can be fruitfully exploited to categorize the role of respiration over causal variability interactions.

SIGNIFICANCE

The application of the C/S test could favor the comprehension of the role of respiration in cardiovascular and cerebrovascular regulations.

Parasympathetic-Sympathetic Causal Interactions Assessed by Time-Varying Multivariate Autoregressive Modeling of Electrodermal Activity and Heart-Rate-Variability

OBJECTIVE

Most of the bodily functions are regulated by multiple interactions between the parasympathetic (PNS) and sympathetic (SNS) nervous system. In this study, we propose a novel framework to quantify the causal flow of information between PNS and SNS through the analysis of heart rate variability (HRV) and electrodermal activity (EDA) signals.

METHODS

Our method is based on a time-varying (TV) multivariate autoregressive model of EDA and HRV time-series and incorporates physiologically inspired assumptions by estimating the Directed Coherence in a specific frequency range. The statistical significance of the observed interactions is assessed by a bootstrap procedure purposely developed to infer causalities in the presence of both TV model coefficients and TV model residuals (i.e., heteroskedasticity). We tested our method on two different experiments designed to trigger a sympathetic response, i.e., a hand-grip task (HG) and a mental-computation task (MC).

RESULTS

Our results show a parasympathetic driven interaction in the resting state, which is consistent across different studies. The onset of the stressful stimulation triggers a cascade of events characterized by the presence or absence of the PNS-SNS interaction and changes in the directionality. Despite similarities between the results related to the two tasks, we reveal differences in the dynamics of the PNS-SNS interaction, which might reflect different regulatory mechanisms associated with different stressors.

CONCLUSION

We estimate causal coupling between PNS and SNS through MVAR modeling of EDA and HRV time-series.

SIGNIFICANCE

Our results suggest promising future applicability to investigate more complex contexts such as affective and pathological scenarios.

Causal analyses to study autonomic regulation during acute head-out water immersion, head-down tilt and supine position

NEW FINDINGS

What is the central question of this study? Can Granger causality analysis of R-R intervals, systolic blood pressure and respiration provide evidence for the different physiological mechanisms induced during thermoneutral water immersion, 6 deg head-down tilt and supine position tests that are not accessible using traditional heart rate variability and baroreflex methods? What is the main finding and its importance? The Granger analysis demonstrated a significant difference in the causal link from R-R intervals to respiration between water immersion and head-down tilt. The underlying physiological mechanism explaining this difference could be the variation in peripheral resistances.

ABSTRACT

Thermoneutral head-out water immersion (WI) and 6 deg head-down tilt (HDT) are used to simulate SCUBA diving, swimming and microgravity, because these models induce an increase in central blood volume. Standard methods to analyse autonomic regulation have demonstrated an increase in parasympathetic activity and baroreflex sensitivity during these experimental conditions. However, such methods are not adapted to quantify all closed-loop interactions involved in respiratory and cardiovascular regulation. To overcome this limitation, we used Granger causality analysis between R-R intervals (RR), systolic blood pressure (SBP) and respiration (RE) in eight young, healthy subjects, recorded during 30 min periods in the supine position, WI and HDT. For all experimental conditions, we found a bidirectional causal relationship between RE and RR and between RR and SBP, with a dominant direction from RR to SBP, and a unidirectional causality from RE to SBP. These causal relationships remained unchanged for the three experimental tests. Interestingly, there was a lower causal relationship from RR to RE during WI compared with HDT. This causal link from RR to RE could be modulated by peripheral resistances. These results highlight differences in cardiovascular regulation during WI and HDT and confirm that Granger causality might reveal physiological mechanisms not accessible with standard methods.

Assessing Synergy/Redundancy of Baroreflex and Non-Baroreflex Components of the Cardiac Control during Sleep

Cardiovascular regulation and autonomic function change across sleep stages and compared to wake. Little information is present in literature about cardiac control during sleep especially in relation to new information-theoretic quantities such as synergy and redundancy. In the present work we compute synergy and redundancy of baroreflex and non-baroreflex components of the cardiac control according to two information-theoretic approaches, namely predictive information decomposition (PID) and minimal mutual information (MMI) methods. We applied a bivariate approach to heart period (HP) and systolic arterial pressure (SAP) beat-to-beat variability series during sleep in a healthy subject. PID approach computes the net balance between synergy and redundancy, while MMI calculates the two quantities as separate entities. Results suggested that: i) redundancy was dominant over synergy during NREM phases; ii) redundancy increased during NREM phase; iii) synergy did not change across the sleep stages. We interpret this result as a consequence of the vagal enhancement, slowing and deepening of respiration during NREM phases. These preliminary findings support the potential of assessing redundancy/synergy of baroreflex-related and unrelated regulations during sleep to improve our knowledge about physiological mechanisms.

Autonomic cardiovascular adaptations to acute head-out water immersion, head-down tilt and supine position

PURPOSE

Thermoneutral head-out water immersion (WI) and 6° head-down tilt (HDT) have been considered as suitable models to increase central blood volume and simulate autonomic cardiovascular adaptations to microgravity, swimming or scuba diving. However, any differences in autonomic cardiovascular adaptations are still unclear. In this study, we hypothesized that WI induces a higher activation of arterial baroreceptors and the parasympathetic system.

METHODS

Ten healthy men underwent 30 min of WI, HDT, and a supine position (SP). RR intervals (RRI) and blood pressure (BP) were continuously monitored. High frequency power (HF), low frequency power (LF) and LF/HF ratio were calculated to study sympathetic and parasympathetic activities, and a spontaneous baroreflex method was used to study arterial baroreflex sensitivity (aBRS). Lung transfer of nitric oxide and carbon monoxide (TLNO/TLCO), vital capacity and alveolar volume (Vc/VA) were measured to study central blood redistribution.

RESULTS

We observed (1) a similar increase in RRI and decrease in BP; (2) a similar increase in HF power during all experimental conditions, whereas LF increased after; (3) a similar rise in aBRS; (4) a similar increase in Vc/VA and decrease in TLNO/TLCO in all experimental conditions.

CONCLUSIONS

These results showed a cardiac parasympathetic dominance to the same extent, underpinned by a similar arterial baroreflex activation during WI and HDT as well as control SP. Future studies may address their association with cold or hyperoxia to assess their ability to replicate autonomic cardiovascular adaptations to microgravity, swimming or scuba diving.

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.

Short-Term Model-Based Multiscale Complexity Analysis of Cardiac Control Provides Complementary Information to Single-Scale Approaches

The study compares a recently proposed shortterm model-based linear multiscale complexity approach to a single-scale application of the same method and to a model-free nonlinear one based on the computation of conditional entropy with the aim at assessing the complementary information. Comparison was carried out over 24 hours Holter recordings of heart period variability during daytime and nighttime in 12 healthy men (age: 34-55 years). Single-scale methods were able to detect the increased complexity of the cardiac control during nighttime. Multiscale complexity analysis showed that this increase was due to an increase of complexity in the low frequency band (from 0.04 to 0.15 Hz), while complexity in the range of frequencies typical of the respiratory rate was unmodified. Regardless of the method (i.e. linear or nonlinear) single-scale complexity indexes were uncorrelated to the multiscale ones. We conclude that short-term model-based linear multiscale complexity approach provides complementary information to single-scale methods in an application devoted to the analysis of cardiac control from 24 hours Holter recordings.

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

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

Differential Entropy Preserves Variational Information of Near-Infrared Spectroscopy Time Series Associated With Working Memory

Neuroscience research shows a growing interest in the application of Near-Infrared Spectroscopy (NIRS) in analysis and decoding of the brain activity of human subjects. Given the correlation that is observed between the Blood Oxygen Dependent Level (BOLD) responses that are exhibited by the time series data of functional Magnetic Resonance Imaging (fMRI) and the hemoglobin oxy/deoxy-genation that is captured by NIRS, linear models play a central role in these applications. This, in turn, results in adaptation of the feature extraction strategies that are well-suited for discretization of data that exhibit a high degree of linearity, namely, slope and the mean as well as their combination, to summarize the informational contents of the NIRS time series. In this article, we demonstrate that these features are inefficient in capturing the variational information of NIRS data, limiting the reliability and the adequacy of the conclusion on their results. Alternatively, we propose the linear estimate of differential entropy of these time series as a natural representation of such information. We provide evidence for our claim through comparative analysis of the application of these features on NIRS data pertinent to several working memory tasks as well as naturalistic conversational stimuli.

Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardiorespiratory 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 characterized through discrete time series, and modeled with probability density functions predicting the time of the next physiological event as a function of the past history. Likewise, nonstationary interactions between heartbeat and blood pressure dynamics are characterized as well. Furthermore, we propose a new measure of information transfer, the instantaneous point-process information transfer (ipInfTr), which is directly derived from point-process-based definitions of the Kolmogorov-Smirnov distance.

RESULTS AND CONCLUSION

Analysis on synthetic data, as well as on experimental data gathered from healthy subjects undergoing postural changes confirms that ipTE, as well as ipInfTr measures are able to dynamically track changes in physiological systems coupling.

SIGNIFICANCE

This novel approach opens new avenues in the study of hidden, transient, nonstationary physiological states involving multivariate autonomic dynamics in cardiovascular health and disease. The proposed method can also be tailored for the study of complex multisystem physiology (e.g., brain-heart or, more in general, brain-body interactions).

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 nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Cardiovascular interactions assessed via conditional joint transfer entropy in patients developing atrial fibrillation after coronary artery bypass graft surgery

Assigned the universe of knowledge Ω as composed by one target and two exogenous signals, the conditional joint transfer entropy (CJTE), assessing the amount of information jointly transferred from the two sources to the target that can be uniquely linked to one of the two sources, was found useful to study cardiovascular control. We propose the assessment of CJTE from systolic arterial pressure (SAP) and respiration (R) to heart period (HP) conditioned on R (CJTESAP, R→HP|R) along the baroreflex, and from HP and R to SAP conditioned on R (CJTEHP, R→SAP|R) along the feedforward mechanical pathway, in 134 patients undergoing coronary artery bypass graft surgery before (PRE) and after (POST) the induction of general anesthesia. In this group 38 patients developed atrial fibrillation (AF) after surgery, while the remaining individuals did not (noAF, n=96). Both CJTESAP, R→HP|R and CJTEHP, R→SAP|R distinguished AF from noAF individuals in the PRE condition, suggesting an impairment of HP-SAP closed-loop regulation in AF group and the possibility to identify subjects at higher risk to develop post-surgery AF.

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Interactions in nature can be described by their coupling strength, direction of coupling, and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems; however, there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here: synchronization transition occurs only due to the time variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brain waves extracted from the electroencephalography recording of a healthy human subject in a free-running resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions, and it should be taken into account when detecting biological or other interactions from data.

Assessing the evolution of redundancy/synergy of spontaneous variability regulation with age

OBJECTIVE

We exploited a model-based Wiener-Granger causality method in the information domain for the evaluation of the transfer entropy (TE) and interaction TE (ITE), the latter taken as a measure of the net balance between redundancy and synergy, to describe the interactions between the spontaneous variability of heart period (HP) and systolic arterial pressure (SAP) and the effect of respiration (R) on both variables.

APPROACH

Cardiac control was typified via the genuine TE from SAP to HP, that from R to HP, and the ITE from SAP and R to HP, while vascular control was characterized via the genuine TE from HP to SAP, that from R to SAP, and the ITE from HP and R to SAP. The approach was applied to study age-related modifications of cardiac and vascular controls in a cohort of 100 healthy humans (age from 21 to 70 years, 54 males) recorded at supine rest (REST) and during active standing (STAND). A surrogate approach was exploited to test the significance of the computed quantities.

MAIN RESULTS

Trends of the genuine information transfer with age, already present in literature, were here confirmed. We originally found that: (i) at REST redundancy was predominant over synergy in both vascular and cardiac controls; (ii) the predominance of redundancy of the cardiac control was not affected by postural challenge, while STAND reduced redundancy of vascular control; (iii) the net redundancy of the cardiac control at REST gradually decreased with age, while that of vascular control remained stable; (iv) during STAND net redundancy of both cardiac and vascular controls was stable with age.

SIGNIFICANCE

The study confirms the relevance of computing genuine information transfer in cardiovascular control analysis and stresses the importance of evaluating the ITE to quantify the degree of redundancy of physiological mechanisms operating to maintain cardiovascular homeostasis.

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. Electrocardiogram was recorded in 17 healthy subjects at rest in supine position and during head-up tilt with table angles of 15°, 30°, 45°, 60°, and 75°. Heart period (HP) was derived as the temporal distance between two consecutive R-wave peaks and analysis was carried out over stationary sequences of 256 successive HPs.

RESULTS

The performance of the MB method in following the progressive decrease of HP complexity with tilt table angles was in line with those of MF approaches and the MB index was remarkably correlated with the MF ones.

CONCLUSION

The MB approach can be utilized to monitor the changes of the complexity of the cardiac control, thus speeding up dramatically the CE calculation.

SIGNIFICANCE

The remarkable performance of the MB approach challenges the notion, generally assumed in cardiac control complexity analysis based on CE, about the need of MF techniques and could allow real-time applications.

Effect of salt intake on beat-to-beat blood pressure nonlinear dynamics and entropy in salt-sensitive versus salt-protected rats

Blood pressure exhibits substantial short- and long-term variability (BPV). We assessed the hypothesis that the complexity of beat-to-beat BPV will be differentially altered in salt-sensitive hypertensive Dahl rats (SS) versus rats protected from salt-induced hypertension (SSBN13) maintained on high-salt versus low-salt diet. Beat-to-beat systolic and diastolic BP series from nine SS and six SSBN13 rats (http://www.physionet.org) were analyzed following 9 weeks on low salt and repeated after 2 weeks on high salt. BP complexity was quantified by detrended fluctuation analysis (DFA), short- and long-range scaling exponents (αS and αL), sample entropy (SampEn), and traditional standard deviation (SD) and coefficient of variation (CV(%)). Mean systolic and diastolic BP increased on high-salt diet (P < 0.01) particularly for SS rats. SD and CV(%) were similar across groups irrespective of diet. Salt-sensitive and -protected rats exhibited similar complexity indices on low-salt diet. On high salt, (1) SS rats showed increased scaling exponents or smoother, systolic (P = 0.007 [αL]) and diastolic (P = 0.008 [αL]) BP series; (2) salt-protected rats showed lower SampEn (less complex) systolic and diastolic BP (P = 0.046); and (3) compared to protected SSBN13 rats, SS showed higher αL for systolic (P = 0.01) and diastolic (P = 0.005) BP Hypertensive SS rats are more susceptible to high salt with a greater rise in mean BP and reduced complexity. Comparable mean pressures in sensitive and protective rats when on low-salt diet coupled with similar BPV dynamics suggest a protective role of low-salt intake in hypertensive rats. This effect likely reflects better coupling of biologic oscillators.

Nonlinear identification of the total baroreflex arc: chronic hypertension model

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). Its linear dynamic functioning has been shown to be preserved in spontaneously hypertensive rats (SHR). However, the system is known to exhibit nonlinear dynamic behaviors. The aim of this study was to establish nonlinear dynamic models of the total arc (and its subsystems) in hypertensive rats and to compare these models with previously published models for normotensive rats. Hypertensive rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned. The carotid sinus regions were isolated and attached to a servo-controlled piston pump. AP and sympathetic nerve activity were measured while CSP was controlled via the pump using Gaussian white noise stimulation. Second-order, nonlinear dynamics models were developed by application of nonparametric system identification to a portion of the measurements. The models of the total arc predicted AP 21-43% better (P < 0.005) than conventional linear dynamic models in response to a new portion of the CSP measurement. The linear and nonlinear terms of these validated models were compared with the corresponding terms of an analogous model for normotensive rats. The nonlinear gains for the hypertensive rats were significantly larger than those for the normotensive rats [-0.38 ± 0.04 (unitless) vs. -0.22 ± 0.03, P < 0.01], whereas the linear gains were similar. Hence, nonlinear dynamic functioning of the sympathetically mediated total arc may enhance baroreflex buffering of AP increases more in SHR than normotensive rats.