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PubMed1997

Influence of forced respiration on nonlinear dynamics in heart rate variability.

Although it is doubtful whether the normal sinus rhythm can be described as low-dimensional chaos, there is evidence for inherent nonlinear dynamics and determinism in time series of consecutive R-R intervals. However, the physiological origin for these nonlinearities is unknown. The aim of this study was to test whether the known nonlinear input from spontaneous respiration is a source for the nonlinearities in heart rate variability. Twelve healthy subjects were examined in supine position with 3-h electrocardiogram recordings during both spontaneous and forced respiration in accordance with a metronome set to 12 min(-1). Nonlinear dynamics were measured as the correlation dimension and the nonlinear prediction error. Complexity expressed as correlation dimension was unchanged from normal respiration, 9.1 +/- 0.5, compared with forced respiration, 9.3 +/- 0.6. Also, nonlinear determinism expressed as the nonlinear prediction error did not differ between spontaneous respiration, 32.3 +/- 3.4 ms, and forced respiration, 31.9 +/- 5.7. It is concluded that the origin of the nonlinear dynamics in heart rate variability is not a nonlinear input from the respiration into the cardiovascular oscillator. Additional studies are needed to elucidate the mechanisms behind the nonlinear dynamics in heart rate variability.

Adolescent↗
PubMed1999

[Primary study on HRV analysis of nonlinear dynamics in animal experiment].

The purpose of this study was to address the relationship between the parameters of nonlinear dynamics and functions of heart. We adopted the methods of nonlinear dynamics in observing the changes of the parameters of nonlinear dynamics under the conditions that sympathetic or parasympathetic nerve of heart exists singly as well as the coronary artery is narrowed. The results showed that in case the sympathetic or parasympathetic nerve was cut off the correlation dimension and entropy were lower than the normals, and in case the coronary artery was seriously narrowed the correlation dimension, entropy and laypunav exponent were also lower than the normals. The conclusion is that the parameters of nolinear dynamics can indicate the changes of the functions of autonomic nerve under the above conditions.

Animals↗
PubMedDate not supplied

[Connection of the tangents of the regression slope of the heart rate graph with linear and nonlinear dynamics in stationary short-time series].

The connection of the regression slope of heart rate graph (b1) with linear and nonlinear dynamics in stationary short-time series (256 points) was studied. A new index for the estimation of nonlinear dynamics in stationary short-time series was used, which is based on the correlation dimension. The results of the study indicated that the dynamics of heart rate in stationary short-time series can be represented as the sum of linear (periodic) and nonlinear (stochastic) processes. A relation of b1 with both linear and nonlinear dynamics of heart rate was found. The formulas for the calculation of absolute and relative (to the amplitude of periodic fluctuations) noise levels in heart rate dynamics were derived. A comparative analysis of nonlinear dynamics of heart rate in stationary short-time series for different functional states of humans was performed. The increase in the relative noise level in heart rate dynamics with increasing breathing frequency is related not only to a decrease in control breathing amplitude but also to an increase in the noise amplitude. The decrease in the absolute noise level for nervous excitation, fatigue, and mental stress were found. The predominance of nonlinear (stochastic) processes over linear (periodic) processes in the relaxed state was established.

Heart↗
PubMed2004

Dynamical resetting of the human brain at epileptic seizures: application of nonlinear dynamics and global optimization techniques.

Epileptic seizures occur intermittently as a result of complex dynamical interactions among many regions of the brain. By applying signal processing techniques from the theory of nonlinear dynamics and global optimization to the analysis of long-term (3.6 to 12 days) continuous multichannel electroencephalographic recordings from four epileptic patients, we present evidence that epileptic seizures appear to serve as dynamical resetting mechanisms of the brain, that is the dynamically entrained brain areas before seizures disentrain faster and more frequently (p < 0.05) at epileptic seizures than any other periods. We expect these results to shed light into the mechanisms of epileptogenesis, seizure intervention and control, as well as into investigations of intermittent spatiotemporal state transitions in other complex biological and physical systems.

Adaptation, Physiological↗
PubMed1997

Automated ventricular tachyarrhythmia recognition: a combination of cycle length and nonlinear dynamics measurements.

INTRODUCTION: Cardiac monitoring devices such as external cardioverter defibrillators and ICU computerized ECG monitoring systems sense individual QRS complexes to detect and subclassify ventricular tachyarrhythmias. Many algorithms that evaluate ECG morphology mark individual QRS complexes so that specific waveform characteristics can be measured. QRS sensors miss a percentage of electrogram events, especially during fibrillatory rhythms; thus, a morphology algorithm that helps subclassify arrhythmias without marking individual electrogram events may be more robust and improve arrhythmia detection accuracy. METHODS AND RESULTS: Four nonlinear dynamics calculations were evaluated for detecting ventricular tachyarrhythmias and for subclassifying monomorphic ventricular tachycardia (MVT) and polymorphic ventricular tachycardia (PVT). Five-second epochs of normal (NML, n = 48), MVT (n = 58), and PVT (n = 75) rhythms were presented to a statistical discriminant function based on cycle length (CL), and its performance was compared to two other discriminant functions, one consisting of the nonlinear dynamics calculations and one consisting of a combination of all variables. The discriminant function based on nonlinear dynamics calculations and CL detected 100% of the ventricular tachyarrhythmias, and subclassified more (P < 0.001) MVT and PVT arrhythmias (90%) than that based on CL alone (71%). CONCLUSIONS: The nonlinear dynamics measurements used in this study significantly increased the subclassification accuracy of the CL-based discriminant function, and they were calculated from ECG signals without marking individual QRS complexes. Therefore, arrhythmia detectors that use nonlinear dynamics measurements may commit fewer classification errors due to QRS undersensing and aid therapy decisions when circumstances suggest that QRS sensing is inaccurate.

Electrocardiography↗
PubMed2001

Nonlinear dynamics of human postural sway during upright stance.

We present a procedure for characterizing the postural sway during quiet upright stance using methods of nonlinear dynamics. The displacements of the centre of foot pressure in anterior-posterior and lateral directions were measured using a force platform. We examined the changes of the postural control mechanisms when visual or proprioceptive information are reduced. We applied four analytic procedures to test the nature of posturographic time series: Kolmogorov-Smirnov test for amplitude distribution; shapes of autocorelation functions; structure functions and log-log plots of power spectra. Nongaussian distribution and nonlinear dynamics were established by all tests. The power spectra (PS) exhibited an exponential decreasing shape, which is commonly referred to as "1/f noise". The fractal structure of the process was characterised by fractal dimension (Df) and shape of structure functions. Our results show that the maintenance of postural stability in upright stance and reduced sensory inputs is nonlinear dynamic process with fractal structure.

Adult↗
PubMed2006

Viscoelastic and dynamic nonlinear properties of airway smooth muscle tissue: roles of mechanical force and the cytoskeleton.

The viscoelastic and dynamic nonlinear properties of guinea pig tracheal smooth muscle tissues were investigated by measuring the storage (G') and loss (G") moduli using pseudorandom small-amplitude length oscillations between 0.12 and 3.5 Hz superimposed on static strains of either 10 or 20% of initial length. The G" and G' spectra were interpreted using a linear viscoelastic model incorporating damping (G) and stiffness (H), respectively. Both G and H were elevated following an increase in strain from 10 to 20%. There was no change in harmonic distortion (K(d)), an index of dynamic nonlinearity, between 10 and 20% strains. Application of methacholine at 10% strain significantly increased G and H while it decreased K(d). Cytochalasin D, isoproterenol, and HA-1077, a Rho-kinase inhibitor, significantly decreased both G and H but increased K(d). Following cytochalasin D, G, H, and K(d) were all elevated when mean strain increased from 10 to 20%. There were no changes in hysteresivity, G/H, under any condition. We conclude that not all aspects of the viscoelastic properties of tracheal smooth muscle strips are similar to those previously observed in cultured cells. We attribute these differences to the contribution of the extracellular matrix. Additionally, using a network model, we show that the dynamic nonlinear behavior, which has not been observed in cell culture, is associated with the state of the contractile stress and may derive from active polymerization within the cytoskeleton.

Animals↗
PubMed2003

Nonlinear dynamics of phonations in excised larynx experiments.

Nonlinear dynamic methods including correlation dimension and Lyapunov exponents are applied to quantitatively analyze phonations in excised larynx experiments. Irregular phonations are typically characterized by aperiodic waveforms and broadband spectra. Finite correlation dimensions and positive Lyapunov exponents of irregular phonations demonstrate the existence of chaos in excised larynx phonations. Furthermore, the correlation dimension, maximal Lyapunov exponent, jitter, shimmer, and peak prominence ratio are used to statistically distinguish irregular phonations from normal phonations. The correlation dimension and maximal Lyapunov exponent indicate a significant difference between irregular and normal phonations; however, jitter, shimmer, and peak prominence ratio do not reveal such a significant difference and thus are unsuitable to differentiate between irregular phonations and normal phonations. These findings might potentially assist investigators in understanding rough phonations and developing clinically valuable methodologies for the diagnosis of voice disorders.

Animals↗
PubMed2001

Surrogate analysis for detecting nonlinear dynamics in normal vowels.

Normal vowels are known to have irregularities in the pitch-to-pitch variation which is quite important for speech signals to be perceived as natural human sound. Such pitch-to-pitch variation of vowels is studied in the light of nonlinear dynamics. For the analysis, five normal vowels recorded from three male and two female subjects are exploited, where the vowel signals are shown to have normal levels of the pitch-to-pitch variation. First, by the false nearest-neighbor analysis, nonlinear dynamics of the vowels are shown to be well analyzed by using a relatively low-dimensional reconstructing dimension of 4 < or = d < or = 7. Then, we further studied nonlinear dynamics of the vowels by spike-and-wave surrogate analysis. The results imply that there exists nonlinear dynamical correlation between one pitch-waveform pattern to another in the vowel signals. On the basis of the analysis results, applicability of the nonlinear prediction technique to vowel synthesis is discussed.

Humans↗
PubMed2003

Nonlinear dynamics of a Bose-Einstein condensate in a magnetic waveguide.

We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Because of the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. Thereby, the condensate shows shape oscillations with an extremely large change in the aspect ratio of up to a factor of 10. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.

Journal Article↗
PubMed1999

[Research on stochastic factors of heart rhythm variability in nonlinear dynamic analysis].

In this study, the influence of external noise on heart rhythm variability (HRV) in nonlinear dynamic analysis and the internal stochastic factor of HRV were discussed in connection with their physiological significance. The sampling rate, stationary and non-uniformity time interval were analyzed. An interpolation algorithm for heart period was introduced. The experiment demonstrated that the influence was highly reduced by the mentioned procedure. The internal stochastic factors of HRV were investigated by several nonlinear dynamic methods such as surrogate data, mutual information and nonlinear forecasting. The results suggested the colligation of deterministic chaos and stochastic process should be a favorite to interpret HRV.

Electrocardiography↗
PubMed2001

Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation.

In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural assemblies and behavioural patterns, the linkage between them, and their modifications over time, cannot be fully understood in the context of even integrative physiology, without using these new techniques. This report, which is the first of two related papers, is aimed at introducing the non expert to the fundamental aspects of nonlinear dynamics, the most spectacular aspect of which is chaos theory. After a general history and definition of chaos the principles of analysis of time series in phase space and the general properties of chaotic trajectories will be described as will be the classical measures which allow a process to be classified as chaotic in ideal systems and models. We will then proceed to show how these methods need to be adapted for handling experimental time series; the dangers and pitfalls faced when dealing with non stationary and often noisy data will be stressed, and specific criteria for suspecting determinism in neuronal cells and/or assemblies will be described. We will finally address two fundamental questions, namely i) whether and how can one distinguish, deterministic patterns from stochastic ones, and, ii) what is the advantage of chaos over randomness: we will explain why and how the former can be controlled whereas, notoriously, the latter cannot be tamed. In the second paper of the series, results obtained at the level of single cells and their membrane conductances in real neuronal networks and in the study of higher brain functions, will be critically reviewed. It will be shown that the tools of nonlinear dynamics can be irreplaceable for revealing hidden mechanisms subserving, for example, neuronal synchronization and periodic oscillations. The benefits for the brain of adopting chaotic regimes with their wide range of potential behaviours and their aptitude to quickly react to changing conditions will also be considered.

Animals↗
PubMed2005

Phonatory impairment in Parkinson's disease: evidence from nonlinear dynamic analysis and perturbation analysis.

Many persons with Parkinson's disease (PD) will eventually experience vocal impairment as their condition advances. Using standard perturbation analyses (parameters like jitter and shimmer) to measure fluctuations in phonatory signal may inhibit researchers from recognizing severely disordered patterns that seem to be present in the voices of some PD patients. Nonlinear dynamic analysis can quantify these aperiodic patterns, which indicate severe pathology that is usually characterized perceptually by hoarseness. Here, sustained vowel phonations of a heterogeneous group of PD subjects (20 women and 21 men) were compared with those of a control group (22 women and 18 men) based on results of nonlinear dynamic analyses (D(2)) and perturbation analyses. Results showed PD subjects as a whole to have significantly higher D(2) values than control subjects (P = 0.016), which indicates increased signal complexity in PD vocal pathology. Differences in the comparison of these two groups were significant in jitter (P = 0.014) but nonsignificant in shimmer (P = 0.695). Furthermore, the performance on these three measures was affected by subject sex. Nonlinear dynamic analysis showed significantly higher D(2) in the female PD group than in the female control group (P = 0.001), but jitter and shimmer did not show such a difference. The male PD group had statistically higher jitter than the male control group (P = 0.036), but these groups did not differ in D(2) or shimmer. Overall, nonlinear dynamic analysis may be a valuable method for the diagnosis of Parkinsonian laryngeal pathology.

Female↗
PubMed2000

[Nonlinear dynamics, chaos theory and wavelet analysis of the heart].

Over the past years, techniques of nonlinear dynamics have gained increasing attention in cardiology. This kind of partly interdisciplinary research is supposed to provide a better understanding of cardiac disease, especially in the field of tachyarrhythmia. This article intends to introduce the principles of diagnostic procedures in terms of nonlinear dynamics, chaos theory and stochastic processes related to cardiology. An introduction to a new technique of wavelet analysis is given, and possible applications in the quantitative classification of high-risk patients for sudden cardiac death are discussed.

Arrhythmias, Cardiac↗
PubMedDate not supplied

The nonlinear dynamical analysis of the EEG in schizophrenia with temporal and spatial embedding dimension.

We applied nonlinear dynamics theory to EEG analysis of schizophrenic patients and estimated the correlation dimension with both temporal embedding and spatial embedding. A higher D2 was found when using a time-delay embedding method. Especially at F7 and Fp1, a significant increase showed. We concluded that more complex activity occurred in certain lobes of schizophrenic patients. Using the spatial embedding method, a relative lower global correlation dimension was obtained. This shows that there might be a diffuse slow wave activity through a schizophrene's global cerebrum. Finally, we discuss the study from three angles of clinical semiology, spectrum analysis and neuropsychology and draw some conclusions about the relationship between the nonlinear analysis of schizophrenia EEG and clinical research. It seems that the theory of a nonlinear dynamics system is a powerful tool for EEG research and may prove useful in complementing visual analysis of EEG accompanied with other study means for brain electrical activity.

Adult↗
PubMed2005

Eye movement instabilities and nystagmus can be predicted by a nonlinear dynamics model of the saccadic system.

The study of eye movements and oculomotor disorders has, for four decades, greatly benefitted from the application of control theoretic concepts. This paper is an example of a complementary approach based on the theory of nonlinear dynamical systems. Recently, a nonlinear dynamics model of the saccadic system was developed, comprising a symmetric piecewise-smooth system of six first-order autonomous ordinary differential equations. A preliminary numerical investigation of the model revealed that in addition to generating normal saccades, it could also simulate inaccurate saccades, and the oscillatory instability known as congenital nystagmus (CN). By varying the parameters of the model, several types of CN oscillations were produced, including jerk, bidirectional jerk and pendular nystagmus. The aim of this study was to investigate the bifurcations and attractors of the model, in order to obtain a classification of the simulated oculomotor behaviours. The application of standard stability analysis techniques, together with numerical work, revealed that the equations have a rich bifurcation structure. In addition to Hopf, homoclinic and saddlenode bifurcations organised by a Takens-Bogdanov point, the equations can undergo nonsmooth pitchfork bifurcations and nonsmooth gluing bifurcations. Evidence was also found for the existence of Hopf-initiated canards. The simulated jerk CN waveforms were found to correspond to a pair of post-canard symmetry-related limit cycles, which exist in regions of parameter space where the equations are a slow-fast system. The slow and fast phases of the simulated oscillations were attributed to the geometry of the corresponding slow manifold. The simulated bidirectional jerk and pendular waveforms were attributed to a symmetry invariant limit cycle produced by the gluing of the asymmetric cycles. In contrast to control models of the oculomotor system, the bifurcation analysis places clear restrictions on which kinds of behaviour are likely to be associated with each other in parameter space, enabling predictions to be made regarding the possible changes in the oscillation type that may be observed upon changing the model parameters. The analysis suggests that CN is one of a range of oculomotor disorders associated with a pathological saccadic braking signal, and that jerk and pendular nystagmus are the most probable oscillatory instabilities. Additionally, the transition from jerk CN to bidirectional jerk and pendular nystagmus observed experimentally when the gaze angle or attention level is changed is attributed to a gluing bifurcation. This suggests the possibility of manipulating the waveforms of subjects with jerk CN experimentally to produce waveforms with an extended foveation period, thereby improving visual resolution.

Humans↗
PubMed2003

Nonlinear dynamical model of human gait.

We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.

Biomechanical Phenomena↗
PubMed2001

Investigation of nonlinear dynamical properties by the observed complex behaviour as a basis for construction of dynamical models of atmospheric photochemical systems.

The importance of the investigation of nonlinear dynamical properties (NDPs) of the atmospheric photochemical systems (PCSs) was demonstrated in ref. 1 and 2 (A. M. Feigin and I. B. Konovalov, J. Geophys. Res., 1996, 101 (D20), 26038; 1. B. Konovalov, A. M. Feigin and A. Y. Mukhina, J. Geophys. Res., 1999, 104 (D3), 3669). The only known way to study NDPs of any natural dynamical system (including atmospheric PCSs) is to construct a mathematical model of the system. The key point here is adequacy of the NDPs of the constructed model to the system observed. We propose a new approach to construction of such an adequate model for systems manifesting nonstationary chaotic behaviour and describe an algorithm based exclusively on nonlinear dynamical analysis of the observed time series (TS) without invoking any a priori knowledge about the properties of the system observed. Potentialities of the algorithm are demonstrated with the aid of a computer model of the mesospheric PCS. The duration of the "observed" TS is limited so that the system demonstrates only one--chaotic--type of behaviour, without any bifurcations throughout the observed TS. The proposed algorithm enabled us to make a correct prognosis of bifurcation sequences and calculate probabilities to reveal, at the time instant of interest, predicted regimes of the system's behaviour for times much greater than the length of the initial TS.

Journal Article↗