A new approach to uncover dynamic phase coordination and synchronization

Increased cardiorespiratory synchronization evoked by a breath controller based on heartbeat detection

BACKGROUND

The cardiovascular and respiratory systems are functionally related to each other, but the underlying physiologic mechanism of cardiorespiratory coupling (CRC) is unclear. Cardiopulmonary phase synchronization is a form of cardiorespiratory coupling. However, it is difficult to study in experimental data which are very often inherently nonstationary and thus contain only quasiperiodic oscillations. So how to enhance cardiopulmonary synchronization and quantify cardiopulmonary synchronization, the changes in cardiac function under the conditions of cardiopulmonary synchronization, and the physiological mechanisms behind them are the main issues to be discussed in this paper.

RESULTS

The results showed that the cardiorespiratory synchronization significantly increased when breathing was controlled by heartbeat detection (p < 0.001). And the respiratory sinus arrhythmia (RSA) obviously decreased (p < 0.01) in the 2/2 mode and increased (p < 0.001) in the 4/4 mode. During the 2/2 breathing pattern compared with spontaneous breathing, systolic blood pressure (SBP) decreased (p < 0.05), and diastolic blood pressure (DBP), mean arterial blood pressure (MBP), and SV decreased significantly (p < 0.01). During the 4/4 breathing pattern compared to 2/2 breathing patterns, DBP, MBP, and cardiac output (CO) increased (p < 0.05), and stroke volume (SV) increased significantly (p < 0.01). When analyzing the relationships among these parameters, the RSA was found to be associated with the respiration rate in all respiratory patterns.

CONCLUSIONS

We demonstrated that voluntary cardiorespiratory synchronization (VCRS) can effectively enhance cardiopulmonary phase synchronization, but cardiopulmonary phase synchronization and RSA represent different aspects of the cardiorespiratory interaction. It is found that cardiac function parameters such as the blood pressure and output per stroke could be affected by the number of heartbeats contained in the exhalation and inspiratory phase regulated through VCRS. So we can study cardiopulmonary phase synchronization by VCRS. It can be used to study in experimental data for the physiological mechanism of cardiopulmonary coupling.

Inferring functional neural connectivity with phase synchronization analysis: a review of methodology

Functional neural connectivity is drawing increasing attention in neuroscience research. To infer functional connectivity from observed neural signals, various methods have been proposed. Among them, phase synchronization analysis is an important and effective one which examines the relationship of instantaneous phase between neural signals but neglecting the influence of their amplitudes. In this paper, we review the advances in methodologies of phase synchronization analysis. In particular, we discuss the definitions of instantaneous phase, the indexes of phase synchronization and their significance test, the issues that may affect the detection of phase synchronization and the extensions of phase synchronization analysis. In practice, phase synchronization analysis may be affected by observational noise, insufficient samples of the signals, volume conduction, and reference in recording neural signals. We make comments and suggestions on these issues so as to better apply phase synchronization analysis to inferring functional connectivity from neural signals.

A quantitative comparison of different methods to detect cardiorespiratory coordination during night-time sleep

Background

The univariate approaches used to analyze heart rate variability have recently been extended by several bivariate approaches with respect to cardiorespiratory coordination. Some approaches are explicitly based on mathematical models which investigate the synchronization between weakly coupled complex systems. Others use an heuristic approach, i.e. characteristic features of both time series, to develop appropriate bivariate methods.

Objective

In this study six different methods used to analyze cardiorespiratory coordination have been quantitatively compared with respect to their performance (no. of sequences with cardiorespiratory coordination, no. of heart beats coordinated with respiration). Five of these approaches have been suggested in the recent literature whereas one method originates from older studies.

Results

The methods were applied to the simultaneous recordings of an electrocardiogram and a respiratory trace of 20 healthy subjects during night-time sleep from 0:00 to 6:00. The best temporal resolution and the highest number of coordinated heart beats were obtained with the analysis of 'Phase Recurrences'. Apart from the oldest method, all methods showed similar qualitative results although the quantities varied between the different approaches. In contrast, the oldest method detected considerably fewer coordinated heart beats since it only used part of the maximum amount of information available in each recording.

Conclusions

The method of 'Phase Recurrences' should be the method of choice for the detection of cardiorespiratory coordination since it offers the best temporal resolution and the highest number of coordinated sequences and heart beats. Excluding the oldest method, the results of the heuristic approaches may also be interpreted in terms of the mathematical models.

Comparison of two different approaches in the detection of intermittent cardiorespiratory coordination during night sleep

BACKGROUND

The objective was to evaluate and to compare two completely different detection algorithms of intermittent (short-term) cardiorespiratory coordination during night sleep. The first method is based on a combination of respiratory flow and electrocardiogram recordings and determines the relative phases of R waves between successive onsets of inspiration. Intermittent phase coordination is defined as phase recurrence with accuracy alpha over at least k heartbeats. The second, recently introduced method utilizes only binary coded variations of heart rate (acceleration = 1, deceleration = 0) and identifies binary pattern classes which can be assigned to respiratory sinus arrhythmia (RSA). It is hypothesized that RSA pattern class recurrence over at least k heartbeats is strongly related with the intermittent phase coordination defined above.

RESULTS

Both methods were applied to night time recordings of 20 healthy subjects. In subjects <45 yrs and setting k = 3 and alpha = 0.03, the phase and RSA pattern recurrence were highly correlated. Furthermore, in most subjects the pattern predominance (PP) showed a pronounced oscillation which is most likely linked with the dynamics of sleep stages. However, the analysis of bivariate variation and the use of surrogate data suggest that short-term phase coordination mainly resulted from central adjustment of heart rate and respiratory rate rather than from real phase synchronization due to physiological interaction.

CONCLUSION

Binary pattern analysis provides essential information on short-term phase recurrence and reflects nighttime sleep architecture, but is only weakly linked with true phase synchronization which is rare in physiological processes of man.

n:m phase synchronization with mutual coupling phase signals

We generalize the n:m phase synchronization between two chaotic oscillators by mutual coupling phase signals. To characterize this phenomenon, we use two coupled oscillators to demonstrate their phase synchronization with amplitudes practically noncorrelated. We take the 1:1 phase synchronization as an example to show the properties of mean frequencies, mean phase difference, and Lyapunov exponents at various values of coupling strength. The phase difference increases with 2pi phase slips below the transition. The scaling rules of the slip near and away from the transition are studied. Furthermore, we demonstrate the transition to a variety of n:m phase synchronizations and analyze the corresponding coupling dynamics. (c) 2002 American Institute of Physics.

Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction

The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.

Phase signal coupling induced n:m phase synchronization in drive-response oscillators

We have studied phase synchronization between two identical Rössler oscillators connected in the drive-response configuration by a single phase signal. Before the transition to phase synchronization, the distribution of the time interval between consecutive 2pi jumps shows several sharp peaks. With a strong phase signal coupling, the n:m phase synchronization between the oscillators can be achieved. For the n (not equal) m phase synchronizing state, some values of coupling strength result in a phenomenon characterized by a reduction in the mean amplitude of the response termed amplitude reduction. In these regions, the mean rotation speed of the response remains approximately constant while the locking ratio n:m varies.