Regions of cardiorespiratory synchronization in humans under paced respiration

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.

Abnormal synchronization patterns in the electrical stimulation-contractile response coupling decrease with noise

Synchronization theory predicts that if an oscillator interacts with a rhythmical external force, then it should react to a rhythmical force by adjusting its frequency. Furthermore, noise is present in nature, and it affects the nervous and cardiovascular systems. In this paper, we analyze the heart as an oscillator, where noisy periodic electrical stimulation can be regarded as an external forcing. This study aimed to investigate, from an experimental point of view, whether noise can induce synchronization of higher order in the mechanical heart response. A Langendorff heart preparation was used to obtain two variables of the mechanical response, intensity of contractile force and heart rate. The experiments show frequency locking in the electrical stimulation-contractile response coupling with and without noise induced. The role of noise in the response of effector organs invites further investigation.

Efficient determination of synchronization domains from observations of asynchronous dynamics

We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized.

Mechanical ventilatory modes and cardioventilatory phase synchronization in acute respiratory failure patients

Cardioventilatory phase synchronization was studied in ten critically ill patients admitted in intensive care unit (ICU) for acute respiratory failure under two mechanical ventilatory modes: (i) pressure controlled ventilation (PCV); (ii) pressure support ventilation (PSV). The two modalities were administered to the same patient in different times in a random order. Cardioventilatory phase interactions were typified by plotting the relative position of a heartbeat, detected from the electrocardiogram and collected in n groups, within m ventilatory cycles as a function of the progressive cardiac beat number via the synchrogram. n:m phase synchronized patterns were detected by computing the variability of each phase group. The percent duration of the recording featuring phase synchronization was assessed as a measure of the strength of phase synchrony and tested against situations of full phase desynchronization between cardiac and ventilatory rhythms. Indexes quantifying the variability of the cardiac and ventilatory activities were computed as well. Findings proved that: (i) a significant presence of n:m phase synchronized patterns was detected in PCV; (ii) the strength of n:m phase synchronization was stronger during PCV than PSV; (iii) different strengths of cardioventilatory phase synchronization detected during PCV and PSV were found in presence of similar heart and ventilatory rates and alike variability. We conclude that mechanical ventilation can induce a significant presence of cardioventilatory phase synchronized patterns and this amount depends on the mode of mechanical ventilation. Future studies should test the eventual link of the level of phase coordination between heart and mechanical ventilation to a clinical outcome to understand whether featuring a certain degree of cardioventilatory phase synchronization is beneficial for the critical patient in ICU.

Intermittency of intermittencies

A phenomenon of intermittency of intermittencies is discovered in the temporal behavior of two coupled complex systems. We observe for the first time the coexistence of two types of intermittent behavior taking place simultaneously near the boundary of the synchronization regime of coupled chaotic oscillators. This phenomenon is found both in the numerical and physiological experiments. The laws for both the distribution and mean length of laminar phases versus the control parameter values are analytically deduced. A very good agreement between the theoretical results and simulation is shown.

HRV strongly depends on breathing. Are we questioning the right suspect?

The fact that the heart rate variability (HRV) depends on breathing is well known. The HRV is an important phenomenon which reflects the functional state of the autonomous nervous system (ANS), although there are some doubts concerning the actual interpretation of spectral components of HRV and their postulated balance. The assessment of the functional state of the ANS is the task of paramount importance in risk stratification of cardiological patients. HRV is considered to depend mainly on the properties of the sinus node (SN), which achieves neurohumoral input from the ANS. Interestingly, there is growing evidence that the relation between the heart rate (HR) and breathing rate (BR) is really strong. The variety of breathing-related effects that are present in HRV is very rich, including respiratory sinus arrhythmia (RSA), cardiorespiratory synchronization and vivid heart rate response to breathing disorders. If the mean frequency of any of rhythms is changed, the other rhythm adjusts itself. This provokes the question on the actual source of the dynamics observed in the HRV. Is it possible that we observe mainly the dynamics of the respiratory rhythm which is just transduced by the heart effector? What might be the role of the intrinsic dynamics of this effector? Is the RSA a product of neural regulation or rather a by-product: what is its teleological role? In consequence: if we concentrate on the sinus node and its properties in order to understand the nature of the HRV - are we questioning the right suspect? The reasoning is supplied by suitable choice of literature and by the analysis of the computational model. Various consequences are discussed.

Impact of movement on cardiorespiratory coordination in conscious rats

In this study we assessed the impact of movement on the interaction between the heart rhythm and respiration in rats while they were conscious and freely moving. In eight male adult Sprague-Dawley (SD, n=4) and Hooded Wistar (HW, n=4) rats, we recorded respiratory rate using whole-body plethysmography with a piezoelectric sensor attached to simultaneously monitor body movement. Heart rate was recorded using a radio-telemetry transmitter. For the assessment of cardiorespiratory coordination, we analysed the phase-locking between heart rate and respiration, estimating the instantaneous phases using Hilbert transform. For statistical analysis, the piezoelectric signal was dichotomized into low-intensity (LIm) and high-intensity (HIm) movement. The R-R intervals, respiratory intervals and cardiorespiratory coordination between LIm and HIm of each rat were assessed with Student's t-test. A significant decrease in the mean values for respiratory interval (0.34 ± 0.1 vs. 0.23 ± 0.1 s, p < 0.01 in HW rats) and R-R interval (0.19 ± 0.01 vs. 0.17 ± 0.01 s, p < 0.001 in SD rats) was observed during HIm. The phase-locking between the cardiac and respiratory signals also decreased significantly during HIm (overall coordination during LIm vs. HIm: 89.3 ± 3.3% vs. 8.7 ± 1.7%, p < 0.001). In conclusion the interaction between the cardiac and respiratory oscillators is affected by voluntary movements in rats.

Synchronization of low-frequency oscillations in the human cardiovascular system

We investigate synchronization between the low-frequency oscillations of heart rate and blood pressure having in humans a basic frequency close to 0.1 Hz. A method is proposed for quantitative estimation of synchronization between these oscillating processes based on calculation of relative time of phase synchronization of oscillations. It is shown that healthy subjects exhibit on average substantially longer epochs of internal synchronization between the low-frequency oscillations in heart rate and blood pressure than patients after acute myocardial infarction.

Time-varying surrogate data to assess nonlinearity in nonstationary time series: application to heart rate variability

We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discriminating statistic. Analysis of simulated time series showed that using TIV surrogates, linear nonstationary time series may be erroneously regarded as nonlinear and weak TV nonlinearities may remain unrevealed, while the use of TV AR surrogates markedly increases the probability of a correct interpretation. Application to short (500 beats) heart rate variability (HRV) time series recorded at rest (R), after head-up tilt (T), and during paced breathing (PB) showed: 1) modifications of the SE statistic that were well interpretable with the known cardiovascular physiology; 2) significant contribution of nonlinear dynamics to HRV in all conditions, with significant increase during PB at 0.2 Hz respiration rate; and 3) a disagreement between TV AR surrogates and TIV surrogates in about a quarter of the series, suggesting that nonstationarity may affect HRV recordings and bias the outcome of the traditional surrogate-based nonlinearity test.

The effect of low-frequency oscillations on cardio-respiratory synchronization: Observations during rest and exercise

We show that the transitions which occur between close orders of synchronization in the cardio-respiratory system are mainly due to modulation of the cardiac and respiratory processes by low-frequency components. The experimental evidence is derived from recordings on healthy subjects at rest and during exercise. Exercise acts as a perturbation of the system that alters the mean cardiac and respiratory frequencies and changes the amount of their modulation by low-frequency oscillations. The conclusion is supported by numerical evidence based on a model of phase-coupled oscillators, with white noise and low-frequency noise. Both the experimental and numerical approaches confirm that low-frequency oscillations play a significant role in the transitional behavior between close orders of synchronization.

High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing

We consider a rotator whose equation of motion for the angle theta consists of the zeroth and first Fourier modes. Numerical analysis based on the trailing of saddle-node bifurcations is used to locate the n:1 Arnold tongues where synchronization occurs. Several of them are wide enough for high-order synchronization to be seen in passive observations. By sweeping the system parameters within a certain range, we find that the stronger the dependence of theta[over ] on theta , the wider the regions of synchronization. Use of a synchronization index reveals a vast number of very narrow n:m Arnold tongues. A competition phenomenon among the tongues is observed, in that they "push" and "squeeze" one another: as some tongues widen, others narrow. Two mechanisms for transitions between different n:m synchronization states are considered: slow variation of the driving frequency, and the influence of low-frequency noise on the rotator.

Detection of synchronization from univariate data using wavelet transform

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

We propose a method for detecting the presence of a synchronization of a self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of the self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to a driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.

Leave-one-out prediction error of systolic arterial pressure time series under paced breathing

In this paper, we consider systolic arterial pressure time series from healthy subjects and chronic heart failure patients, undergoing paced respiration, and show that different physiological states and pathological conditions may be characterized in terms of predictability of time series signals from the underlying biological system. We model time series by the regularized least-squares approach and quantify predictability by the leave-one-out error. We find that the entrainment mechanism connected to paced breath, that renders the arterial blood pressure signal more regular and thus more predictable, is less effective in patients, and this effect correlates with the seriousness of the heart failure. Using a Gaussian kernel, so that all orders of nonlinearity are taken into account, the leave-one-out error separates controls from patients (probability less than 10(-7)), and alive patients from patients for whom cardiac death occurred (probability less than 0.01).

Nonlinear cardio-respiratory interactions revealed by time-phase bispectral analysis

Bispectral analysis based on high order statistics, introduced recently as a technique for revealing time-phase relationships among interacting noisy oscillators, has been used to study the nature of the coupling between cardiac and respiratory activity. Univariate blood flow signals recorded simultaneously by laser-Doppler flowmetry on both legs and arms were analysed. Coupling between cardiac and respiratory activity was also checked by use of bivariate data and computation of the cross-bispectrum between the ECG and respiratory signals. Measurements were made on six healthy males aged 25-27 years. Recordings were taken during spontaneous breathing (20 min), and during paced respiration at frequencies both lower and higher than that of spontaneous respiration (either two or three recordings with a constant frequency in the interval between 0.09 and 0.35 Hz). At each paced frequency recordings were taken for 12 min. It was confirmed that the dynamics of blood flow can usefully be considered in terms of coupled oscillators, and demonstrated that interactions between the cardiac and respiratory processes are weak and time-varying, and that they can be nonlinear. Nonlinear coupling was revealed to exist during both spontaneous and paced respiration. When present, it was detected in all four blood flow signals and in the cross-bispectrum between the ECG and respiratory signal. The episodes with nonlinear coupling were detected in 11 out of 22 recordings and lasted between 19 s in the case of high frequency (0.34 Hz) and 106 s in the case of low frequency paced respiration (0.11 Hz).

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.

Synchronization between main rhythmic processes in the human cardiovascular system

For the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency, we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans, namely, the main heart rhythm, respiration, and the process whose fundamental frequency is close to 0.1 Hz. The analysis of the experimental records reveals synchronous regimes of different orders n:m between all the three main rhythms. The influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered.