Identification of coupling direction: application to cardiorespiratory interaction

The Effects of Resonance Frequency Breathing on Cardiovascular System and Brain-Cardiopulmonary Interactions

Resonance frequency (RF) is characterized as the specific frequency at which a system, equipped with delayed self-correction or negative feedback mechanisms, exhibits maximal amplitude oscillations in response to an external stimulus of a particular frequency. Emerging evidence suggests that the cardiovascular system has an inherent RF, and that breathing at this frequency can markedly enhance health and cardiovascular function. However, the efficacy of resonance frequency breathing (RFB) and the specific responses of the cardiovascular, respiratory, and central nervous systems during RFB remain unclear. In this study, we recruited 27 healthy young male subjects (aged 20-30 years) and used the corrected sliding method to accurately determine each subject's RF. We then investigated cardiovascular activity, cardiorespiratory coupling, and the brain-cardiovascular network to clarify the effects and mechanisms associated with RFB. Our results indicate that: (a) the corrected sliding method can precisely evaluate RF; (b) the reduction in blood pressure is unique to RFB and not observed in other slow-paced breathing patterns (RF + 1 and 6 breaths per minute), which we attribute to the α-wave and parasympathetic-BRS pathway; (c) during slow-paced breathing, cardiorespiratory coupling predominantly favors the respiration-to-heart direction, with the RF stage eliciting the most significant response, while brain-cardiopulmonary information transfer increases across all tasks. These findings offer valuable insights into the impact of RFB on the cardiovascular, respiratory, and central nervous systems, potentially laying the groundwork for future research to optimize respiratory training protocols and improve health outcomes.

Characterization of cardiorespiratory coupling via a variability-based multi-method approach: Application to postural orthostatic tachycardia syndrome

There are several mechanisms responsible for the dynamical link between heart period (HP) and respiration (R), usually referred to as cardiorespiratory coupling (CRC). Historically, diverse signal processing techniques have been employed to study CRC from the spontaneous fluctuations of HP and respiration (R). The proposed tools differ in terms of rationale and implementation, capturing diverse aspects of CRC. In this review, we classify the existing methods and stress differences with the aim of proposing a variability-based multi-method approach to CRC evaluation. Ten methodologies for CRC estimation, namely, power spectral decomposition, traditional and causal squared coherence,\;information transfer, cross-conditional entropy, mixed prediction, Shannon entropy of the latency between heartbeat and inspiratory/expiratory onset, conditional entropy of the phase dynamics, synchrogram-based analysis, pulse-respiration quotient, and joint symbolic dynamics, are considered. The ability of these techniques was exemplified over recordings acquired from patients suffering from postural orthostatic tachycardia syndrome (POTS) and healthy controls. Analyses were performed at rest in the supine position (REST) and during head-up tilt (HUT). Although most of the methods indicated that at REST, the CRC was lower in POTS patients and decreased more evidently during HUT in POTS, peculiar differences stressed the complementary value of the approaches. The multiple perspectives provided by the variability-based multi-method approach to CRC evaluation help the characterization of a pathological state and/or the quantification of the effect of a postural challenge. The present work stresses the need for the application of multiple methods to derive a more complete evaluation of the CRC in humans.

Cardio-respiratory coupling and myocardial recovery in heart failure with reduced ejection fraction

INTRODUCTION

The interaction between the cardiovascular and respiratory systems in healthy subjects is determined by the autonomic nervous system and reflected in respiratory sinus arrhythmia. Recently, another pattern of cardio-respiratory coupling (CRC) has been proposed linking synchronization of heart and respiratory system. However, CRC has not been studied precisely in heart failure (HF) with reduced ejection fraction (EF) (HFrEF) according to the myocardial recovery.

METHODS

10-min resting electrocardiography measurements were performed in persistent HFrEF patients (n=40) who had a subsequent left ventricular EF (LVEF) of ≤ 40 %, HF with recovered EF patients (HFrecEF) (n=41) who had a subsequent LVEF of > 40 % and healthy controls (n=40). Respiratory frequency, respiratory rate, CRC index, time-domain, frequency-domain and nonlinear heart rate variability indices were obtained using standardized software-Kubios™. CRC index was defined as respiratory high-frequency peak minus heart rate variability high-frequency peak.

RESULTS

Respiratory rate was positively correlated with high-frequency (HF) peak (Hz) in both persistent HFrEF group (p<0.001) and HFrecEF group (p<0.001), while respiratory rate was negatively correlated with HF power (ms2) in the healthy controls (p<0.05). CRC index was lowest in the persistent HFrEF group followed by HFrecEF and was high in healthy controls (0.008 vs 0.012 vs 0.056 Hz, p=0.03).

CONCLUSION

CRC index was lowest in patients with impaired myocardial recovery, which indicates that cardio-respiratory synchrony is stronger in persistent HFrEF. This may represent a higher HF peak (Hz)/lower HF power (ms2) and abnormal sympathovagal balance in persistent HFrEF group compared to healthy controls. Further work is underway to tests this hypothesis and determine the utility of CRC index in HF phenotypes and its utility as a potential biomarker of response with neuromodulation.

Separation of ventilation and perfusion of electrical impedance tomography image streams using multi-dimensional ensemble empirical mode decomposition

Objective.In the future, thoracic electrical impedance tomography (EIT) monitoring may include continuous and simultaneous tracking of both breathing and heart activity. However, an effective way to decompose an EIT image stream into physiological processes as ventilation-related and cardiac-related signals is missing.Approach.This study analyses the potential ofMulti-dimensional Ensemble Empirical Mode Decompositionby application of theComplete Ensemble Empirical Mode Decomposition with Adaptive Noiseand a novel frequency-based combination criterion for detrending, denoising and source separation of EIT image streams, collected from nine healthy male test subjects with similar age and constitution.Main results.In this paper, a novel approach to estimate the lung, the heart and the perfused regions of an EIT image is proposed, which is based on theRoot Mean Square Errorbetween the index of maximal respiratory and cardiac variation to their surroundings. The summation of the indexes of the respective regions reveals physiologically meaningful time signals, separated into the physiological bandwidths of ventilation and heart activity at rest. Moreover, the respective regions were compared with the relative thorax movement and photoplethysmogram (PPG) signal. In linear regression analysis and in the Bland-Altman plot, the beat-to-beat time course of both the ventilation-related signal and the cardiac-related signal showed a high similarity with the respective reference signal.Significance.Analysis of the data reveals a fair separation of ventilatory and cardiac activity realizing the aimed source separation, with optional detrending and denoising. For all performed analyses, a feasible correlation of 0.587 to 0.905 was found between the cardiac-related signal and the PPG signal.

Exploring Cardiopulmonary Interactions: A Novel Phase-Amplitude Coupling Method

The cardiopulmonary coupling (CPC) involves complex interactions between the autonomic nervous system and respiratory control, affecting heart and respiratory rates. This study introduces a novel phase-amplitude coupling (PAC) method using the direct modulation index (dMI) for analyzing the bidirectional interactions between the heart rate variability and respiration of participants listening to classical music. The Empirical Mode Decomposition (EMD) was employed to decompose the RR intervals and the respiration signals, and the dMI-based PAC is then applied to the decomposed IMFs. The results demonstrate a notable enhancement in RESP-RR interactions during music exposure, indicating a stronger influence of respiratory patterns on heart rate during this relaxed state. Additionally, a pronounced cardiopulmonary coupling was observed in the low-frequency bands under conditions of listening to music. These findings highlight the complex, bidirectional interactions between breathing and heart rate. The dMI method emerges as a robust, noise-resistant analytical tool with promising implications for cardiovascular research and potential clinical applications.

Two Operational Modes of Cardio-Respiratory Coupling Revealed by Pulse-Respiration Quotient

Due to the fact that respiratory breath-to-breath and cardiac intervals between two successive R peaks (BBI and RRI, respectively) are not temporally concurrent, in a previous paper, we proposed a method to calculate both the integer and non-integer parts of the pulse respiration quotient (PRQ = BBI/RRI = PRQ_int + b1 + b2), b1 and b2 being parts of the border RRIs for each BBI. In this work, we study the correlations between BBI and PRQ, as well as those between BBI and mean RRI within each BBI (mRRI), on a group of twenty subjects in four conditions: in supine and standing positions, in combination with spontaneous and slow breathing. Results show that the BBI vs. PRQ correlations are positive; whereas the breathing regime had little or no effect on the linear regression slopes, body posture did. Two types of scatter plots were obtained with the BBI vs. mRRI correlations: one showed points aggregated around the concurrent PRQ_int lines, while the other showed randomly distributed points. Five out of six of the proposed aggregation measures confirmed the existence of these two cardio-respiratory coupling regimes. We also used b1 to study the positions of R pulses relative to the respiration onsets and showed that they were more synchronous with sympathetic activation. Overall, this method should be used in different pathological states.

Age-dependent cardiorespiratory directional coupling in wake-resting state

Objective.Cooperation in the cardiorespiratory system helps maintain internal stability. Various types of system interactions have been investigated; however, the characteristics of the interactions have mostly been studied using data collected in well-defined physiological states, such as sleep. Furthermore, most analyses provided general information about the interaction, making it difficult to quantify how the systems influenced one another.Approach.Cardiorespiratory directional coupling was investigated in different age groups (20 young and 19 elderly subjects) in a wake-resting state. The directionality index (DI) was calculated using instantaneous phases from the heartbeat interval and respiratory signal to provide information about the strength and direction of interaction between the systems. Statistical analysis was performed between the groups on the DI and independent measures of directionality (nc_r: influence from cardiac system to respiratory system, and nc_c: influence from the respiratory system to the cardiac system).Main results.The values of DI were -0.52 and -0.17 in the young and elderly groups, respectively (p< 0.001). Furthermore, the values of nc_rand nc_cwere found to be significantly different between the groups (p< 0.001), respectively.Significance.Changes in both directions between the systems influence different aspects of cardiorespiratory coupling between the groups. This observation could be linked to different levels of autonomic modulation associated with ageing. Our approach could aid in quantitatively tracking and comprehending how systems interact in response to physiological and environmental changes. It could also be used to understand how abnormal interaction characteristics influence physiological system dysfunctions and disorders.

Directional couplings between the respiration and parasympathetic control of the heart rate during sleep and wakefulness in healthy subjects at different ages

Cardiorespiratory interactions are important, both for understanding the fundamental processes of functioning of the human body and for development of methods for diagnostics of various pathologies. The properties of cardiorespiratory interaction are determined by the processes of autonomic control of blood circulation, which are modulated by the higher nervous activity. We study the directional couplings between the respiration and the process of parasympathetic control of the heart rate in the awake state and different stages of sleep in 96 healthy subjects from different age groups. The detection of directional couplings is carried out using the method of phase dynamics modeling applied to experimental RR-intervals and the signal of respiration. We reveal the presence of bidirectional couplings between the studied processes in all age groups. Our results show that the coupling from respiration to the process of parasympathetic control of the heart rate is stronger than the coupling in the opposite direction. The difference in the strength of bidirectional couplings between the considered processes is most pronounced in deep sleep.

Decrease of coherence between the respiration and parasympathetic control of the heart rate with aging

The study of coordinated behavior between different systems of the human body provides useful information on the functioning of the body. The peculiarities of interaction and coordinated dynamics of the heart rate and respiration are of particular interest. We investigated the coherence of the processes of respiration and autonomic control of the heart rate for people of different ages in the awake state, in sleep with rapid eye movement, and in deep sleep. Our analysis revealed a monotonic decrease in the coherence of these processes with increasing age. This can be explained by age-related changes in the system of autonomic control of circulation. For all age groups, we found a qualitatively similar dynamics of the coherence between the studied processes during a transition from the awake state to sleep.

Phase-dynamic causalities within dynamical effects framework

This work investigates numerics of several widely known phase-dynamic quantifiers of directional (causal) couplings between oscillatory systems: transfer entropy (TE), differential quantifier, and squared-coefficients quantifier based on an evolution map. The study is performed on the system of two stochastic Kuramoto oscillators within the framework of dynamical causal effects. The quantifiers are related to each other and to an asymptotic effect of the coupling on phase diffusion. Several novel findings are listed as follows: (i) for a non-synchronous regime and high enough noise levels, the TE rate multiplied by a certain characteristic time (called here reduced TE) equals twice an asymptotic effect of a directional coupling on phase diffusion; (ii) "information flow" expressed by the TE rate unboundedly rises with the coupling coefficient even in the domain of effective synchronization; (iii) in any effective synchronization regime, the reduced TE is equal to 1/8 n.u. in each direction for equal coupling coefficients and equal noise intensities, and it is in general a simple function of the ratio of noise intensities and the ratio of coupling coefficients.

The Link Between Spinal Cord Stimulation and the Parasympathetic Nervous System in Patients With Failed Back Surgery Syndrome

OBJECTIVES

In patients with chronic pain, a relative lower parasympathetic activity is suggested based on heart rate variability measurements. It is hypothesized that spinal cord stimulation (SCS) is able to influence the autonomic nervous system. The aim of this study is to further explore the influence of SCS on the autonomic nervous system by evaluating whether SCS is able to influence skin conductance, blood volume pulse, heart rate, and respiration rate.

MATERIALS AND METHODS

Twenty-eight patients with Failed Back Surgery Syndrome (FBSS), who are treated with SCS, took part in this multicenter study. Skin conductance and cardiorespiratory parameters (blood volume pulse, heart rate, and respiration rate) were measured during on and off states of SCS. Paired statistics were performed on a 5-min recording segment for all parameters.

RESULTS

SCS significantly decreased back and leg pain intensity scores in patients with FBSS. Skin conductance level and blood volume pulse were not altered between on and off states of SCS. Heart rate and respiration rate significantly decreased when SCS was activated.

CONCLUSIONS

Parameters that are regulated by the sympathetic nervous system were not significantly different between SCS on and off states, leading to the hypothesis that SCS is capable of restoring the dysregulation of the autonomic nervous system by primarily increasing the activity of the parasympathetic system, in patients with FBSS.

Grip force anticipation of nonlinear, underactuated load force

Feedforward internal model-based control enabled by efference copies of motor commands is the prevailing theoretical account of motor anticipation. Grip force control during object manipulation-a paradigmatic example of motor anticipation-is a key line of evidence for that account. However, the internal model approach has not addressed the computational challenges faced by the act of manipulating mechanically complex objects with nonlinear, underactuated degrees of freedom. These objects exhibit complex and unpredictable load force dynamics which cannot be encoded by efference copies of underlying motor commands, leading to the prediction from the perspective of an efference copy-enabled feedforward control scheme that grip force should either lag or fail to coordinate with changes in load force. In contrast to that prediction, we found evidence for strong, precise, anticipatory grip force control during manipulations of a complex object. The results are therefore inconsistent with the internal forward model approach and suggest that efference copies of motor commands are not necessary to enable anticipatory control during active object manipulation.NEW & NOTEWORTHY From the perspective of feedforward internal model-based control, precise, anticipatory grip force (GF) control when manipulating a complex object should not be possible as the object's changing load forces (LFs) cannot be encoded by efference copies of the underlying movements. However, we observed that GF exhibited strong, precise, anticipatory coupling with LF during extended manipulations of a complex object. These findings suggest that an alternative theoretical framework is needed to account for anticipatory GF control.

Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p < 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.

Transfer Entropy Modeling of Newborn Cardiorespiratory Regulation

This study investigates the complex interplay between the cardiac and respiratory systems in 268 healthy neonates born between 35 and 40 weeks of gestation. The aim is to provide a comprehensive description of the developing cardiorespiratory information transfer mechanisms as a function of gestational age (GA). This report proposes an extension of the traditional Transfer Entropy measure (TE), which employs multiple lagged versions of the time series of the intervals between two successive R waves of the QRS signal on the electrocardiogram (RR series) and respiration time series (RESP). The method aims to quantify the instantaneous and delayed effects between the two processes within a fine-grained time scale. Firstly, lagged TE was validated on a simulated dataset. Subsequently, lagged TE was employed on newborn cardiorespiratory data. Results indicate a progressive increase in information transfer as a function of gestational age, as well as significant differences in terms of instantaneous and delayed interactions between the cardiac and the respiratory system when comparing the two TE directionalities (RR→RESP vs. RESP→RR). The proposed investigation addresses the role of the different autonomic nervous system (ANS) branches involved in the cardiorespiratory system, since the sympathetic and parasympathetic branches operate at different time scales. Our results allow to infer that the two TE directionalities are uniquely and differently modulated by both branches of the ANS. TE adds an original quantitative tool to understanding cardiorespiratory imbalance in early infancy.

A perinatal stress calculator for the neonatal intensive care unit: an unobtrusive approach

OBJECTIVE

Early experience of pain and stress in the neonatal intensive care unit is known to have an effect on the neurodevelopment of the infant. However, an automated method to quantify the procedural pain or perinatal stress in premature patients does not exist.

APPROACH

In the current study, EEG and ECG data were collected for more than 3 hours from 136 patients in order to quantify stress exposure. Specifically, features extracted from the EEG and heart-rate variability in both quiet and non-quiet sleep segments were used to develop a subspace linear-discriminant analysis stress classifier.

MAIN RESULTS

The main novelty of the study lies in the absence of intrusive methods or pain elicitation protocols to develop the stress classifier. Three main findings can be reported. First, we developed different stress classifiers for the different age groups and stress intensities, obtaining an area under the curve in the range [0.78-0.93] for non-quiet sleep and [0.77-0.96] for quiet sleep. Second, a dysmature EEG was found in patients under stress. Third, an enhanced cortical connectivity and increased brain-heart communication was correlated with a higher stress load, while the autonomic activity did not seem to be associated to stress exposure.

SIGNIFICANCE

The results shed a light on the pain and stress processing in preterm neonates, suggesting that software tools to investigate dysmature EEG might be helpful to assess stress load in premature patients. These results could be the foundation to assess the impact of stress on infants' development and to tune preventive care.

Sleep-Dependent Directional Interactions of the Central Nervous System-Cardiorespiratory Network

OBJECTIVE

We investigated the nature of interactions between the central nervous system (CNS) and the cardiorespiratory system during sleep.

METHODS

Overnight polysomnography recordings were obtained from 33 healthy individuals. The relative spectral powers of five frequency bands, three ECG morphological features and respiratory rate were obtained from six EEG channels, ECG, and oronasal airflow, respectively. The synchronous feature series were interpolated to 1 Hz to retain the high time-resolution required to detect rapid physiological variations. CNS-cardiorespiratory interaction networks were built for each EEG channel and a directionality analysis was conducted using multivariate transfer entropy. Finally, the difference in interaction between Deep, Light, and REM sleep (DS, LS, and REM) was studied.

RESULTS

Bidirectional interactions existed in central-cardiorespiratory networks, and the dominant direction was from the cardiorespiratory system to the brain during all sleep stages. Sleep stages had evident influence on these interactions, with the strength of information transfer from heart rate and respiration rate to the brain gradually increasing with the sequence of REM, LS, and DS. Furthermore, the occipital lobe appeared to receive the most input from the cardiorespiratory system during LS. Finally, different ECG morphological features were found to be involved with various central-cardiac and cardiac-respiratory interactions.

CONCLUSION

These findings reveal detailed information regarding CNS-cardiorespiratory interactions during sleep and provide new insights into understanding of sleep control mechanisms.

SIGNIFICANCE

Our approach may facilitate the investigation of the pathological cardiorespiratory complications of sleep disorders.

Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction

Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered-measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems.

Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Human Heart Rhythms Synchronize While Co-sleeping

Human physiological systems have a major role in maintenance of internal stability. Previous studies have found that these systems are regulated by various types of interactions associated with physiological homeostasis. However, whether there is any interaction between these systems in different individuals is not well-understood. The aim of this research was to determine whether or not there is any interaction between the physiological systems of independent individuals in an environment where they are connected with one another. We investigated the heart rhythms of co-sleeping individuals and found evidence that in co-sleepers, not only do independent heart rhythms appear in the same relative phase for prolonged periods, but also that their occurrence has a bidirectional causal relationship. Under controlled experimental conditions, this finding may be attributed to weak cardiac vibration delivered from one individual to the other via a mechanical bed connection. Our experimental approach could help in understanding how sharing behaviors or social relationships between individuals are associated with interactions of physiological systems.

A Novel Framework for Estimating Time-Varying Multivariate Autoregressive Models and Application to Cardiovascular Responses to Acute Exercise

OBJECTIVE

We present a novel modeling framework for identifying time-varying (TV) couplings between time-series of biomedical relevance.

METHODS

The proposed methodology is based on multivariate autoregressive (MVAR) models, which have been extensively used to study couplings between biosignals. Contrary to the standard estimation methods that assume time-invariant relationships, we propose a modified recursive Kalman filter (KF) to track changes in the model parameters. We perform model order selection and hyperparameter optimization simultaneously using Genetic Algorithms, greatly improving accuracy and computation time. In addition, we address the effect of residual heteroscedasticity, possibly associated with event-related changes or phase transitions during a given experimental protocol, on the TV-MVAR coupling measures by using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to fit the TV-MVAR residuals.

RESULTS

Using simulated data, we show that the proposed framework yields more accurate parameter estimates compared to the conventional KF, particularly when the true system parameters exhibit different rate of variations over time. Furthermore, by accounting for heteroskedasticity, we obtain more accurate estimates of the strength and directionality of the underlying couplings. We also use our approach to investigate TV hemodynamic interactions during exercise in young and old healthy adults, as well as individuals with chronic stroke. We extract TV coupling patterns that reflect well known exercise-induced effects on the underlying regulatory mechanisms with excellent time resolution.

CONCLUSION AND SIGNIFICANCE

The proposed modeling framework can be used to efficiently quantify TV couplings between biosignals. It is fully automated and does not require prior knowledge of the system TV characteristics.

Nonlinear Interaction Analysis of Cardiovascular-Respiratory Data by Means of Convergent Cross Mapping

Appropriate analyses of directed complex interactions within the cardiovascular-respiratory system are of growing interest for a better understanding of physiological regulatory mechanisms in healthy subjects and diseased persons. There are various concepts to analyze such interactions. Convergent Cross Mapping (CCM) provides the possibility to define directed interactions in terms of nonlinear stability. A proof-of-principle approach is introduced to apply CCM to cardiovascular-respiratory data of healthy subjects during resting state period. Showing group results of time-invariant as well as single subject results of interval-based CCM, the introduced approach was able to quantify correct directionality and strength of interactions within the cardiovascular-respiratory system and to provide statistical thresholds for significant interactions. These results may serve as a methodological base to compare healthy subjects and diseased persons.

Detecting causality using symmetry transformations

Detecting causality between variables in a time series is a challenge, particularly when the relationship is nonlinear and the dataset is noisy. Here, we present a novel tool for detecting causality that leverages the properties of symmetry transformations. The aim is to develop an algorithm with the potential to detect both unidirectional and bidirectional coupling for nonlinear systems in the presence of significant sampling noise. Most of the existing tools for detecting causality can make determinations of directionality, but those determinations are relatively fragile in the presence of noise. The novel algorithm developed in the present study is robust and very conservative in that it reliably detects causal structure with a very low rate of error even in the presence of high sampling noise. We demonstrate the performance of our algorithm and compare it with two popular model-free methods, namely transfer entropy and convergent cross map. This first implementation of the method of symmetry transformations is limited in that it applies only to first-order autonomous systems.

Characterization of cardiorespiratory phase synchronization and directionality in late premature and full term infants

OBJECTIVE

Though the mutual influence of cardiovascular and respiratory rhythms in healthy newborns has been documented, its full characterization is still pending. In general, the activity of many physiological subsystems has a well-expressed rhythmic character, and often an interdependency between physiological rhythms emerges early in development. Traditional methods of data analysis only address the quantification of the strength of subsystem interactions. In this work, we will investigate system interrelationships in terms of the possible presence of causal or directional interplays.

APPROACH

In this paper, we propose a methodological application that quantifies phase coupling and its directionality in a population of newborn infants born between 35 and 40 weeks of gestational age (GA). The aim is to assess whether GA at birth significantly influences the development of phase synchronization and the directionality of the coupling between the cardiovascular and respiratory system activity. Several studies indicating irregular cardiorespiratory coupling as a leading cause of several pathologies underscore the need to investigate this phenomenon in this at-risk population.

MAIN RESULTS

Results from our investigation show a different directionality profile as a function of GA and sleep state.

SIGNIFICANCE

These findings are a contribution to the understanding of higher risk for the documented negative outcomes in the late preterm population. Moreover, these parameters could provide a tool for the development of early markers of cardiorespiratory dysregulation in infants.

Assessment of Quadratic Nonlinear Cardiorespiratory Couplings During Tilt-Table Test by Means of Real Wavelet Biphase

OBJECTIVE

In this paper, a method for assessment of quadratic phase coupling (QPC) between respiration and heart rate variability (HRV) is presented.

METHODS

First, a method for QPC detection is proposed named real wavelet biphase (RWB). Then, a method for QPC quantification is proposed based on the normalized wavelet biamplitude (NWB). A simulation study has been conducted to test the reliability of RWB to identify QPC, even in the presence of constant delays between interacting oscillations, and to discriminate it from quadratic phase uncoupling. Significant QPC was assessed based on surrogate data analysis. Then, quadratic cardiorespiratory couplings were studied during a tilt-table test protocol of 17 young healthy subjects.

RESULTS

Simulation study showed that RWB is able to detect even weak QPC with delays in the range of [Formula: see text] s, which are usual in the autonomic nervous system (ANS) control of heart rate. Results from the database revealed a significant reduction ([Formula: see text]) of NWB between respiration and both low and high frequencies of HRV in head-up tilt position compared to early supine.

CONCLUSION

The proposed technique detects and quantifies robustly QPC and is able to track the coupling between respiration and various HRV components during ANS changes.

SIGNIFICANCE

The proposed method can help to assess alternations of nonlinear cardiorespiratory interactions related to ANS dysfunction and physiological regulation of HRV in cardiovascular diseases.

Bidirectional Cardio-Respiratory Interactions in Heart Failure

We investigated cardio-respiratory coupling in patients with heart failure by quantification of bidirectional interactions between cardiac (RR intervals) and respiratory signals with complementary measures of time series analysis. Heart failure patients were divided into three groups of twenty, age and gender matched, subjects: with sinus rhythm (HF-Sin), with sinus rhythm and ventricular extrasystoles (HF-VES), and with permanent atrial fibrillation (HF-AF). We included patients with indication for implantation of implantable cardioverter defibrillator or cardiac resynchronization therapy device. ECG and respiratory signals were simultaneously acquired during 20 min in supine position at spontaneous breathing frequency in 20 healthy control subjects and in patients before device implantation. We used coherence, Granger causality and cross-sample entropy analysis as complementary measures of bidirectional interactions between RR intervals and respiratory rhythm. In heart failure patients with arrhythmias (HF-VES and HF-AF) there is no coherence between signals (p < 0.01), while in HF-Sin it is reduced (p < 0.05), compared with control subjects. In all heart failure groups causality between signals is diminished, but with significantly stronger causality of RR signal in respiratory signal in HF-VES. Cross-sample entropy analysis revealed the strongest synchrony between respiratory and RR signal in HF-VES group. Beside respiratory sinus arrhythmia there is another type of cardio-respiratory interaction based on the synchrony between cardiac and respiratory rhythm. Both of them are altered in heart failure patients. Respiratory sinus arrhythmia is reduced in HF-Sin patients and vanished in heart failure patients with arrhythmias. Contrary, in HF-Sin and HF-VES groups, synchrony increased, probably as consequence of some dominant neural compensatory mechanisms. The coupling of cardiac and respiratory rhythm in heart failure patients varies depending on the presence of atrial/ventricular arrhythmias and it could be revealed by complementary methods of time series analysis.

Cardiorespiratory coupling in young healthy subjects

OBJECTIVE

To quantify the presence of cardiorespiratory interaction in a group of 41 healthy subjects performing a subset of the Ewing test battery.

APPROACH

We measure the empirical distribution of the cardiorespiratory coupling time (RI), defined as the time from inspiration onset to R peaks in the ECG. The study protocol is a subset of the Ewing test battery. The respiratory function was measured with a thoracic belt and heart rate was obtained from a two channel ECG measurement. Both series of fiducial points were determined using custom software. Additionally, we determine the presence of cardiorespiratory coupling (CRC) and cardiorespiratory interaction (CRI) using Shannon entropy, synchrograms and coordigrams.

MAIN RESULTS

We observe that the RI distribution is asymmetric and nonuniform. These features are a manifestation of the causal relation between heart action and respiration. The preceding R peak strongly affects a position of inspiration onset. From the asymmetry of the RI distribution we conclude that this relation is stronger than the relation between inspiration onset and the following R peak. We use a suitable choice of surrogate data to prove that the result cannot be falsified. We observe a dual structure of the RI histograms, which may be related to the respiratory rhythmogenesis. We compare the sensitivity of RI histograms with other measures of CRI and CRC. In 46% of subjects, CRC appears in at least one stage of the examination, most often in resting states. In states of increased stress-orthostasis or physical (exercise)-the strength of coupling is visibly diminished. The nonuniform structure of the RI histogram is more sensitive to the presence of CRI than synchrograms or coordigrams are, as is well visible in the group averages. We also refer to the question of the most proper mathematical description of cardiorespiratory dynamics (phase domain or time domain). Finally, we formulate the hypothesis that the arterial blood pressure is a common driver of cardiac and respiratory rhythms.

SIGNIFICANCE

Analysis of the asymmetry of RI histograms is an interesting and sensitive method to study cardiorespiratory interaction and autonomic balance, in order to assess physical and mental health. The dual structure of the RI histograms which we have observed suggests the possible presence of a twofold mechanism for respiratory rhythmogenesis, as proposed by Galletly and Larsen.

Directionality indices: Testing information transfer with surrogate correction

Directionality indices can be used as an indicator of the asymmetry in coupling between systems and have found particular application in relation to neurological systems. The directionality index between two systems is a function of measures of information transfer in both directions. Here we illustrate that before inferring the directionality of coupling it is first necessary to consider the use of appropriate tests of significance. We propose a surrogate corrected directionality index which incorporates such testing. We also highlight the differences between testing the significance of the directionality index itself versus testing the individual measures of information transfer in each direction. To validate the approach we compared two different methods of estimating coupling, both of which have previously been used to estimate directionality indices. These were the modeling-based evolution map approach and a conditional mutual information (CMI) method for calculating dynamic information rates. For the CMI-based approach we also compared two different methods for estimating the CMI, an equiquantization-based estimator and a k-nearest neighbors estimator.

Reconstructing networks of pulse-coupled oscillators from spike trains

We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections.

Coupling strength versus coupling impact in nonidentical bidirectionally coupled dynamics

The understanding of interacting dynamics is important for the characterization of real-world networks. In general, real-world networks are heterogeneous in the sense that each node of the network is a dynamics with different properties. For coupled nonidentical dynamics symmetric interactions are not straightforwardly defined from the coupling strength values. Thus, a challenging issue is whether we can define a symmetric interaction in this asymmetric setting. To address this problem we introduce the notion of the coupling impact. The coupling impact considers not only the coupling strength but also the energy of the individual dynamics, which is conveyed via the coupling. To illustrate this concept, we follow a data-driven approach by analyzing signals from pairs of coupled model dynamics using two different connectivity measures. We find that the coupling impact, but not the coupling strength, correctly detects a symmetric interaction between pairs of coupled dynamics regardless of their degree of asymmetry. Therefore, this approach allows us to reveal the real impact that one dynamics has on the other and hence to define symmetric interactions in pairs of nonidentical dynamics.

Heart Rate and Respiratory Rate Influence on Heart Rate Variability Repeatability: Effects of the Correction for the Prevailing Heart Rate

Background: Since heart rate variability (HRV) is associated with average heart rate (HR) and respiratory rate (RespRate), alterations in these parameters may impose changes in HRV. Hence the repeatability of HRV measurements may be affected by differences in HR and RespRate. The study aimed to evaluate HRV repeatability and its association with changes in HR and RespRate.

Methods: Forty healthy volunteers underwent two ECG examinations 7 days apart. Standard HRV indices were calculated from 5-min ECG recordings. The ECG-derived respiration signal was estimated to assess RespRate. To investigate HR impact on HRV, HRV parameters were corrected for prevailing HR.

Results: Differences in HRV parameters between the measurements were associated with the changes in HR and RespRate. However, in multiple regression analysis only HR alteration proved to be independent determinant of the HRV differences—every change in HR by 1 bpm changed HRV values by 16.5% on average. After overall removal of HR impact on HRV, coefficients of variation of the HRV parameters significantly dropped on average by 26.8% (p < 0.001), i.e., by the same extent HRV reproducibility improved. Additionally, the HRV correction for HR decreased association between RespRate and HRV.

Conclusions: In stable conditions, HR but not RespRate is the most powerful factor determining HRV reproducibility and even a minimal change of HR may considerably alter HRV. However, the removal of HR impact may significantly improve HRV repeatability. The association between HRV and RespRate seems to be, at least in part, HR dependent.

Respiratory Changes in Response to Cognitive Load: A Systematic Review

When people focus attention or carry out a demanding task, their breathing changes. But which parameters of respiration vary exactly and can respiration reliably be used as an index of cognitive load? These questions are addressed in the present systematic review of empirical studies investigating respiratory behavior in response to cognitive load. Most reviewed studies were restricted to time and volume parameters while less established, yet meaningful parameters such as respiratory variability have rarely been investigated. The available results show that respiratory behavior generally reflects cognitive processing and that distinct parameters differ in sensitivity: While mentally demanding episodes are clearly marked by faster breathing and higher minute ventilation, respiratory amplitude appears to remain rather stable. The present findings further indicate that total variability in respiratory rate is not systematically affected by cognitive load whereas the correlated fraction decreases. In addition, we found that cognitive load may lead to overbreathing as indicated by decreased end-tidal CO₂ but is also accompanied by elevated oxygen consumption and CO₂ release. However, additional research is needed to validate the findings on respiratory variability and gas exchange measures. We conclude by outlining recommendations for future research to increase the current understanding of respiration under cognitive load.

Effects of slow and regular breathing exercise on cardiopulmonary coupling and blood pressure

Investigation of the interaction between cardiovascular variables and respiration provides a quantitative and noninvasive approach to assess the autonomic control of cardiovascular function. The aim of this paper is to investigate the changes of cardiopulmonary coupling (CPC), blood pressure (BP) and pulse transit time (PTT) during a stepwise-paced breathing (SPB) procedure (spontaneous breathing followed by paced breathing at 14, 12.5, 11, 9.5, 8 and 7 breaths per minute, 3 min each) and gain insights into the characteristics of slow breathing exercises. RR interval, respiration, BP and PTT are collected during the SPB procedure (48 healthy subjects, 27 ± 6 years). CPC is assessed through investigating both the phase and amplitude dynamics between the respiration-induced components from RR interval and respiration by the approach of ensemble empirical mode decomposition. It was found that even though the phase synchronization and amplitude oscillation of CPC were both enhanced by the SPB procedure, phase coupling does not increase monotonically along with the amplitude oscillation during the whole procedure. Meanwhile, BP was reduced significantly by the SPB procedure (SBP: from 122.0 ± 13.4 to 114.2 ± 14.9 mmHg, p < 0.001, DBP: from 82.2 ± 8.6 to 77.0 ± 9.8 mmHg, p < 0.001, PTT: from 172.8 ± 20.1 to 176.8 ± 19.2 ms, p < 0.001). Our results demonstrate that the SPB procedure can reduce BP and lengthen PTT significantly. Compared with amplitude dynamics, phase dynamics is a different marker for CPC analysis in reflecting cardiorespiratory coherence during slow breathing exercise. Our study provides a methodology to practice slow breathing exercise, including the setting of target breathing rate, change of CPC and the importance of regular breathing. The applications and usability of the study results have also been discussed.

Effects of Dopamine and Serotonin Systems on Modulating Neural Oscillations in Hippocampus-Prefrontal Cortex Pathway in Rats

Theta and gamma oscillations are believed to play an important role in cognition and memory, and their phase coupling facilitates the information transmission in hippocampal-cortex network. In a rat model of chronic stress, the phase coupling of both theta and gamma oscillations between ventral hippocampal CA1 (vCA1) and medial prefrontal cortex (mPFC) was found to be disrupted, which was associated with the impaired synaptic plasticity in the pathway. However, little was known about the mechanisms underlying the process. In order to address this issue, both dopamine and serotonin as monoaminergic neurotransmitters were involved in this study, since they were crucial factors in pathological basis of depressive disorder. Local field potentials (LFPs) were recorded simultaneously at both vCA1 and mPFC regions under anesthesia, before and after the injection of dopamine D1 receptor antagonist and 5-HT1A receptor agonist, respectively. The results showed that the blockage of D1 receptor could lead to depression-like decrement on theta phase coupling. In addition, the activation of 5-HT1A receptor enhanced vCA1-mPFC coupling on gamma oscillations, and attenuated CA1 theta-fast gamma cross frequency coupling. These data suggest that the theta phase coupling between vCA1 and mPFC may be modulated by dopamine system that is an underlying mechanism of the cognitive dysfunction in depression. Besides, the serotonergic system is probably involved in the regulation of gamma oscillations coupling in vCA1-mPFC network.

Detection of Coupling in Short Physiological Series by a Joint Distribution Entropy Method

OBJECTIVE

In this study, we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series.

METHODS

The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rössler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography data from rats and RR interval and diastolic time interval series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison.

RESULTS

Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short datasets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data.

CONCLUSION

This study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.

Two generalized algorithms measuring phase-amplitude cross-frequency coupling in neuronal oscillations network

An increasing number of studies pays attention to cross-frequency coupling in neuronal oscillations network, as it is considered to play an important role in exchanging and integrating of information. In this study, two generalized algorithms, phase-amplitude coupling-evolution map approach and phase-amplitude coupling-conditional mutual information which have been developed and applied originally in an identical rhythm, are generalized to measure cross-frequency coupling. The effectiveness of quantitatively distinguishing the changes of coupling strength from the measurement of phase-amplitude coupling (PAC) is demonstrated based on simulation data. The data suggest that the generalized algorithms are able to effectively evaluate the strength of PAC, which are consistent with those traditional approaches, such as PAC-PLV and PAC-MI. Experimental data, which are local field potentials obtained from anaesthetized SD rats, have also been analyzed by these two generalized approaches. The data show that the theta-low gamma PAC in the hippocampal CA3-CA1 network is significantly decreased in the glioma group compared to that in the control group. The results, obtained from either simulation data or real experimental signals, are consistent with that of those traditional approaches PAC-MI and PAC-PLV. It may be considered as a proper indicator for the cross frequency coupling in sub-network, such as the hippocampal CA3 and CA1.

Resting-state EEG coupling analysis of amnestic mild cognitive impairment with type 2 diabetes mellitus by using permutation conditional mutual information

OBJECTIVE

This study was meant to explore whether the coupling strength and direction of resting-state electroencephalogram (rsEEG) could be used as an indicator to distinguish the patients of type 2 diabetes mellitus (T2DM) with or without amnestic mild cognitive impairment (aMCI).

METHODS

Permutation conditional mutual information (PCMI) was used to calculate the coupling strength and direction of rsEEG signals between different brain areas of 19 aMCI and 20 normal control (NC) with T2DM on 7 frequency bands: Delta, Theta, Alpha1, Alpha2, Beta1, Beta2 and Gamma. The difference in coupling strength or direction of rsEEG between two groups was calculated. The correlation between coupling strength or direction of rsEEG and score of different neuropsychology scales were also calculated.

RESULTS

We have demonstrated that PCMI can calculate effectively the coupling strength and directionality of EEG signals between different brain regions. The significant difference in coupling strength and directionality of EEG signals was found between the patients of aMCI and NC with T2DM on different brain regions. There also existed significant correlation between sex or age and coupling strength or coupling directionality of EEG signals between a few different brain regions from all subjects.

CONCLUSIONS

The coupling strength or directionality of EEG signals calculated by PCMI are significantly different between aMCI and NC with T2DM.

SIGNIFICANCE

These results showed that the coupling strength or directionality of EEG signals calculated by PCMI might be used as a biomarker in distinguishing the aMCI from NC with T2DM.

Causal inference in neuronal time-series using adaptive decomposition

BACKGROUND

The assessment of directed functional connectivity from neuronal data is increasingly common in neuroscience by applying measures based in the Granger causality (GC) framework. Although initially these consisted in simple analyses based on directionality strengths, current methods aim to discriminate causal effects both in time and frequency domain.

NEW METHOD

We study the effect of adaptive data analysis on the GC framework by combining empirical mode decomposition (EMD) and causal analysis of neuronal signals. EMD decomposes data into simple amplitude and phase modulated oscillatory modes, the intrinsic mode functions (IMFs), from which it is possible to compute their instantaneous frequencies (IFs). Hence, we propose a method where causality is estimated between IMFs with comparable IFs, in a static or time-varying procedure, and then attributed to the frequencies corresponding to the IF of the driving IMF for improved frequency localization.

RESULTS

We apply a thorough simulation framework involving all possible combinations of EMD algorithms with causality metrics and realistically simulated datasets. Results show that synchrosqueezing wavelet transform and noise-assisted multivariate EMD, paired with generalized partial directed coherence or with Geweke's GC, provide the highest sensitivity and specificity results.

COMPARISON WITH EXISTING METHODS

Compared to standard causal analysis, the output of selected representative instances of this methodology result in the fulfillment of performance criteria in a well-known benchmark with real animal epicranial recordings and improved frequency resolution for simulated neural data.

CONCLUSIONS

This study presents empirical evidence that adaptive data analysis is a fruitful addition to the existing causal framework.

Quantifying the causal strength of multivariate cardiovascular couplings with momentary information transfer

This article studies a recently introduced information-theoretic approach to detect and quantify the causal couplings in a complex cardiovascular system. In the first step a causal algorithm detects the coupling delays and in the second step the causal strength of each coupling mechanism is quantified using the recently introduced momentary information transfer. As an example, the method is applied to time series of respiration, systolic and diastolic blood pressure, and heart rate of pregnant healthy women and women suffering from pre-eclampsia. A possible explanation for the influence of heart rate on systolic blood pressure is found and some differences between healthy women and patients are discussed.

Self-organized complementary joint action: Behavioral dynamics of an interpersonal collision-avoidance task

Understanding stable patterns of interpersonal movement coordination is essential to understanding successful social interaction and activity (i.e., joint action). Previous research investigating such coordination has primarily focused on the synchronization of simple rhythmic movements (e.g., finger/forearm oscillations or pendulum swinging). Very few studies, however, have explored the stable patterns of coordination that emerge during task-directed complementary coordination tasks. Thus, the aim of the current study was to investigate and model the behavioral dynamics of a complementary collision-avoidance task. Participant pairs performed a repetitive targeting task in which they moved computer stimuli back and forth between sets of target locations without colliding into each other. The results revealed that pairs quickly converged onto a stable, asymmetric pattern of movement coordination that reflected differential control across participants, with 1 participant adopting a more straight-line movement trajectory between targets, and the other participant adopting a more elliptical trajectory between targets. This asymmetric movement pattern was also characterized by a phase lag between participants and was essential to task success. Coupling directionality analysis and dynamical modeling revealed that this dynamic regime was due to participant-specific differences in the coupling functions that defined the task-dynamics of participant pairs. Collectively, the current findings provide evidence that the dynamical coordination processes previously identified to underlie simple motor synchronization can also support more complex, goal-directed, joint action behavior, and can participate the spontaneous emergence of complementary joint action roles.