Synchronization in the human cardiorespiratory system

Model for cardiorespiratory synchronization in humans

Recent experimental studies suggest that there is evidence for a synchronization between human heartbeat and respiration. We develop a physiologically plausible model for this cardiorespiratory synchronization, and numerically show that the model can exhibit stable synchronization against given perturbations. In our model, in addition to the well-known influence of respiration on heartbeat, the influence of heartbeat (and hence blood pressure) on respiration is also important for cardiorespiratory synchronization.

Identification of coupling direction: application to cardiorespiratory interaction

We consider the problem of experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. We further develop the method introduced by Rosenblum and Pikovsky [Phys. Rev. E 64, 045202 (2001)], suggesting an alternative approach. Next, we consider another framework for identification of directionality, based on the idea of mutual predictability. Our algorithms provide directionality index that shows whether the coupling between the oscillators is unidirectional or bidirectional, and quantifies the asymmetry of bidirectional coupling. We demonstrate the efficiency of three different algorithms in determination of directionality index from short and noisy data. These techniques are then applied to analysis of cardiorespiratory interaction in healthy infants. The results reveal that the direction of coupling between cardiovascular and respiratory systems varies with the age within the first 6 months of life. We find a tendency to change from nearly symmetric bidirectional interaction to nearly unidirectional one (from respiration to the cardiovascular system).

Amplitude envelope synchronization in coupled chaotic oscillators

A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.

Characterizing instantaneous phase relationships in whole-brain fMRI activation data

Typically, fMRI data is processed in the time domain with linear methods such as regression and correlation analysis. We propose that the theory of phase synchronization may be used to more completely understand the dynamics of interacting systems, and can be applied to fMRI data as a novel method of detecting activation. Generalized synchronization is a phenomenon that occurs when there is a nonlinear functional relationship present between two or more coupled, oscillatory systems, whereas phase synchronization is defined as the locking of the phases while the amplitudes may vary. In this study, we developed an application of phase synchronization analysis that is appropriate for fMRI data, in which the phase locking condition is investigated between a voxel time series and the reference function of the task performed. A synchronization index is calculated to quantify the level of phase locking, and a nonparametric permutation test is used to determine the statistical significance of the results. We performed the phase synchronization analysis on the data from five volunteers for an event-related finger-tapping task. Functional maps were created that provide information on the interrelations between the instantaneous phases of the reference function and the voxel time series in a whole-brain fMRI activation data set. We conclude that this method of analysis is useful for revealing additional information on the complex nature of the fMRI time series.

Does synchronization reflect a true interaction in the cardiorespiratory system?

Cardiorespiratory synchronization, studied within the framework of phase synchronization, has recently raised interest as one of the interactions in the cardiorespiratory system. In this work, we present a quantitative approach to the analysis of this nonlinear phenomenon. Our primary aim is to determine whether synchronization between HR and respiration rate is a real phenomenon or a random one. First, we developed an algorithm, which detects epochs of synchronization automatically and objectively. The algorithm was applied to recordings of respiration and HR obtained from 13 normal subjects and 13 heart transplant patients. Surrogate data sets were constructed from the original recordings, specifically lacking the coupling between HR and respiration. The statistical properties of synchronization in the two data sets and in their surrogates were compared. Synchronization was observed in all groups: in normal subjects, in the heart transplant patients and in the surrogates. Interestingly, synchronization was less abundant in normal subjects than in the transplant patients, indicating that the unique physiological condition of the latter promote cardiorespiratory synchronization. The duration of synchronization epochs was significantly shorter in the surrogate data of both data sets, suggesting that at least some of the synchronization epochs are real. In view of those results, cardiorespiratory synchronization, although not a major feature of cardiorespiratory interaction, seems to be a real phenomenon rather than an artifact.

Synchronization of hyperexcitable systems with phase-repulsive coupling

We study two-dimensional arrays of FitzHugh-Nagumo elements with nearest-neighbor coupling from the viewpoint of synchronization. The elements are diffusively coupled. By varying the diffusion coefficient from positive to negative values, interesting synchronization patterns are observed. The results of the simulations resemble the intracellular oscillation patterns observed in cultured human epileptic astrocytes. Three measures are proposed to determine the degree of synchronization (or coupling) in both the simulated and the experimental system.

Modelling couplings among the oscillators of the cardiovascular system

A mathematical model of the cardiovascular system is simulated numerically. The basic unit in the model is an oscillator that possesses a structural stability and robustness motivated by physiological understanding and by the analysis of measured time series. Oscillators with linear couplings are found to reproduce the main characteristic features of the experimentally obtained spectra. To explain the variability of cardiac and respiratory frequencies, however, it is essential to take into account the rest of the system, i.e. to consider the effect of noise. It is found that the addition of noise also results in epochs of synchronization, as observed experimentally. Preliminary analysis suggests that there is a mixture of linear and parametric couplings, but that the linear coupling seems to dominate.

Reversible transitions between synchronization states of the cardiorespiratory system

Phase synchronization between cardiac and respiratory oscillations is investigated during anesthesia in rats. Synchrograms and time evolution of synchronization indices are used to show that the system passes reversibly through a sequence of different phase-synchronized states as the anesthesia level changes, indicating that it can undergo phase transitionlike phenomena. It appears that the synchronization state may be used to characterize the depth of anesthesia.

Phase synchronization in the forced Lorenz system

We demonstrate that the dynamics of phase synchronization in a chaotic system under weak periodic forcing depends crucially on the distribution of intrinsic characteristic times of this system. Under the external periodic action, the frequency of every unstable periodic orbit is locked to the frequency of the force. In systems which in the autonomous case displays nearly isochronous chaotic rotations, the locking ratio is the same for all periodic orbits; since a typical chaotic orbit wanders between the periodic ones, its phase follows the phase of the force. For the Lorenz attractor with its unbounded times of return onto a Poincaré surface, such state of perfect phase synchronization is inaccessible. Analysis with the help of unstable periodic orbits shows that this state is replaced by another one, which we call "imperfect phase synchronization," and in which we observe alternation of temporal segments, corresponding to different rational values of frequency lockings.