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PubMed2001

Nonlinear behavior of human respiratory movement during different sleep stages.

To investigate the nonlinear properties of respiratory movement during different sleep stages, we applied an algorithm proposed by Grassberger and Procaccia to calculate the correlation dimension in rapid eye movement and non-rapid eye movement sleep. We also tested for nonlinearity in respiratory movement by comparing the correlation dimension for the original data with that for surrogate data. The study population included eight healthy volunteers. We recorded respiratory movement and the sleep electroencephalogram for 8 h. The correlation dimension for respiratory movement was 3.28+/-0.19 (mean +/- SD) during rapid eye movement sleep, 2.31+/-0.21 during light sleep (stage I) and 1.64+/-0.25 during deep slow-wave sleep (stage IV). Thus, the correlation dimension differed significantly by sleep stage (p < 0.001): it was least during stage IV sleep and greatest during REM. The correlation dimension for the original data also differed from that for surrogate data, confirming nonlinearity in original data. The results suggest that the nonlinear dynamics of respiratory movement in sleep changes with sleep stage, presumably due to the information processing by the cerebral cortex. The increased correlation dimension for respiratory movement in REM sleep may be related to increased cortical information processing associated with dreaming.

Adult↗

PubMed2003

[Analysis of variability in physiologic parameters using sequence plots].

The assessment of cardiovascular (and respiratory) parameters changes provides an information about the control systems involved and about their complex regulation. Methods based on nonlinear dynamics are able to quantify characteristics of the biosignal, that cannot be detected by conventional analysis methods. The sequence plot analysis is one of them. The aim of this paper is to provide basic information about this simple method and its application in the physiological research and in the clinical practice.

Analysis of Variance↗

PubMed2003

Prognostic value of nonlinear heart rate dynamics in hemodialysis patients with coronary artery disease.

BACKGROUND: Although altered nonlinear heart rate dynamics predicts death in patients with coronary artery disease (CAD), its prognostic value in chronic hemodialysis patients with CAD is unknown. METHODS: We analyzed 24-hour electrocardiogram for nonlinear heart rate dynamics and heart rate variability in a retrospective cohort of 81 chronic hemodialysis patients with CAD. RESULTS: During a follow-up period of 31 +/- 20 months, 19 cardiac and 8 noncardiac deaths were observed. Cox hazards model, including diabetes, left ventricular ejection fraction, and the number of diseased coronary arteries, revealed that abnormal alpha2 (defined as both increase and decrease in alpha2 because of its J curve relationship with cardiac mortality), decreased approximate entropy and decreased heart rate variability (triangular index and ultra-low frequency power) were significant and independent predictors of cardiac death. No significant and independent predictive power for noncardiac death was observed in either the heart rate dynamics or the heart rate variability measures. The predictive power of alpha2 and approximate entropy was independent of that of triangular index and ultra-low frequency power. Combinations of two categories of measures improved the predictive accuracy; overall accuracy of approximate entropy + ultra-low frequency power for cardiac death was 87%. CONCLUSION: Altered nonlinear heart rate dynamics are independent predictors of cardiac death in chronic hemodialysis patients with CAD and their combinations with decreased heart rate variability provide clinically useful markers for risk stratification.

Aged↗

PubMed1997

Description of the ventriculoarterial interaction dynamics using recurrence plot strategies.

OBJECTIVE: The classical description of ventriculoarterial coupling by calculating the ratio between the effective arterial elastance Ea to the end-systolic elastance Ees does not give insight into the underlying dynamics of the interaction between left-ventricular pressure (LVP) and aortic pressure (AOP) and flow (AOF). The aim of this study was to introduce a state space representation for the ventriculoarterial coupling and to quantify changes of the coupling state. METHODS: A ventriculoarterial state space orbit VAO was defined to be dependent on three variables: VAO = [LVP(t), AOP(t + delta t), AOF(t + delta t)]. Changes in the coupling effect directly or indirectly on the time series of these parameters. They reflect the actual state of the cardiovascular system. The time delay delta t between the LVP and the aortic signals takes respect to the short delay between the heart action and the resulting waves in the arterial tree. The recurrence map of the VAO(i) (i = 1 .. N, N = number of points) is constructed by plotting the index i of every single point on the orbit (x-axis) against the indices of his 10 nearest neighbors (y-axis) in distance. The data were recorded in 9 anaesthetized pigs with a sample frequency of 512 Hz over a period of 6 seconds using piezoelectric pressure sensors and a Doppler flowmeter. A control condition was compared to a total occlusion of the descending aorta as a strong artificial disturbance of ventriculoarterial interaction. The nonlinear parameters percent recurrence, percent determinism and the entropy were calculated from the plot. RESULTS: Periodic crossing points and forbidden zones in all plots identify the nonlinear character of the chosen variables. The recurrent patterns are less rigid for control conditions than for total occlusion. Entropy (2.3% rise) and determinism (24% rise) are significantly (p < 0.003) increased. Total aortic occlusion leads to more complex time correlation patterns. CONCLUSIONS: These results may reflect the loss of an ideal coupling state leading to a more complex deterministic behavior of the overall regulatory system. Because recurrence plots do not impose rigid constraints on data set size, stationarity, or statistical distribution, we hypothesize that this technique might be useful to describe the nonlinear dynamics between left ventricle and arterial system.

Animals↗

PubMed2001

Chaos in the brain: a short review alluding to epilepsy, depression, exercise and lateralization.

Electroencephalograms (EEGs) reflect the electrical activity of the brain. Even when they are analyzed from healthy individuals, they manifest chaos in the nervous system. EEGs are likely to be produced by a nonlinear system, since a nonlinear system with at least 3 degrees of freedom (or state variables) may exhibit chaotic behavior. Furthermore, such systems can have multiple stable states governed by "chaotic" ("strange") attractors. A key feature of chaotic systems is the presence of an infinite number of unstable periodic fixed points, which are found in spontaneously active neuronal networks (e.g., epilepsy). The brain has chemicals called neurotransmitters that convey the information through the 10(16) synapses residing there. However, each of these neurotransmitters acts through various receptors and their numerous subtypes, thereby exhibiting complex interactions. Albeit in epilepsy the role of chaos and EEG findings are well proven, in another condition, i.e., depression, the role of chaos is slowly gaining ground. The multifarious roles of exercise, neurotransmitters and (cerebral) hemispheric lateralization, in the case of depression, are also being established. The common point of reference could be nonlinear dynamics. The purpose of this review is to study those nonlinear/chaotic interactions and point towards new theoretical models incorporating the oscillation caused by the same neurotransmitter acting on its different receptor subtypes. This may lead to a better understanding of brain neurodynamics in health and disease.

Brain↗

PubMed1995

Nonlinear analysis of sleep EEG data in schizophrenia: calculation of the principal Lyapunov exponent.

The generating mechanism of the electroencephalogram (EEG) points to the hypothesis that EEG signals derive from a nonlinear dynamic system. Hence, the unpredictability of the EEG might be considered as a phenomenon exhibiting its chaotic character. The essential property of chaotic dynamics is the so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's first positive Lyapunov exponent, L1. We calculated L1 for sleep EEG segments of 13 schizophrenic patients and 13 control subjects that corresponded to sleep stages I, II, III, IV and REM (rapid eye movement), as defined by Rechtschaffen and Kales, for the lead positions Cz and Pz. During REM sleep, for both electrode positions, the principal Lyapunov exponent L1 was significantly increased in schizophrenic patients compared with control subjects. This finding points to altered nonlinear brain dynamics during REM sleep in schizophrenia.

Adult↗

PubMed2006

Recurrence plot analyses suggest a novel reference system involved in newborn spontaneous movements.

The movements of newborns have been thoroughly studied in terms of reflexes, muscle synergies, leg coordination, and target-directed arm/hand movements. Since these approaches have concentrated mainly on separate accomplishments, there has remained a clear need for more integrated investigations. Here, we report an inquiry in which we explicitly concentrated on taking such a perspective and, additionally, were guided by the methodological concept of home base behavior, which Ilan Golani developed for studies of exploratory behavior in animals. Methods from nonlinear dynamics, such as symbolic dynamics and recurrence plot analyses of kinematic data received from audiovisual newborn recordings, yielded new insights into the spatial and temporal organization of limb movements. In the framework of home base behavior, our approach uncovered a novel reference system of spontaneous newborn movements.

Biomechanical Phenomena↗

PubMed2004

Chaotic vibrations of a vocal fold model with a unilateral polyp.

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass.

Humans↗

PubMed2002

Clinical implications of present physiological understanding of HRV components.

Time and frequency domain analysis of heart rate variability (HRV) is a non invasive technique capable of providing information on autonomic modulation of the sinus node and of stratifying risk after myocardial infarction and in heart failure. One of the basic assumptions used to explain the negative predictive value of reduced HRV was the concept that overall HRV was largely dependent on vagal mechanisms and that a reduction in HRV could reflect an increased sympathetic and a reduced vagal modulation of sinus node; i.e., an autonomic imbalance favouring cardiac electrical instability. This initial interpretation was challenged by several findings indicating a greater complexity of the relationship between neural input and sinus node responsiveness as well as the possible interference with non neural mechanisms.Nevertheless, the prognostic value of time and geometric parameters of HRV has been consistently confirmed. More complex is the interpretation of spectral parameters particularly when they are computed on 24-hour recordings. Under controlled conditions, instead, the computation of low and high frequency components and of their ratio seems to provide information on sympatho-vagal balance in normal subjects as well as in most patients with preserved left ventricular function, thus providing an unique tool to investigate neural control mechanisms. More recently, analysis on nonlinear dynamics of HRV has been utilized to describe the fractal-like characteristics of the variability signal and has been shown to identify patients at risk for sudden cardiac death. In conclusion, in spite of an incomplete understanding of the physiological significance of HRV parameters, this non invasive methodology is of substantial utility to evaluate autonomic control mechanisms and to identify patients with an increased cardiac mortality.

Autonomic Nervous System↗

PubMed2002

A new framework for investigating both normal and abnormal eye movements.

Any comprehensive framework for understanding eye movements has to include both normal and abnormal eye movement behaviour. One approach which is applicable to the entire range of oculomotor behaviour is provided by the techniques of nonlinear dynamics. The stability of models of the oculomotor system can be analysed in terms of the characteristics of their fixed points and periodic orbits, and the method of delays can be used to recover such parameters from measurements of eye position. Within this framework, quantitative comparisons can be made between the predictions of different models, and both normal and clinical eye movement recordings.

Algorithms↗

PubMedDate not supplied

[Ventricular fibrillation: the current methods for analysing the degree of irregularity of the process].

Ventricular fibrillation has traditionally been described as "chaotic" and in recent years there has been discussions that fibrillation may be an instance of deterministic chaos in the context of nonlinear dynamical systems theory. The current paper summarizes modern methods of mathematical analysis of the degree of electrical irregularities of the heart during VF. The traditional methods of Fourier analysis of electrocardiographic data as well as concepts of chaos theory--fractal dimension, entropy, reconstruction of attractors and some new methods such as spatial coherence have been considered. The results are discussed in context of mathematical models and hypothesis of mechanisms of VF.

Animals↗

PubMed2006

Application of wavelet-based similarity analysis to epileptic seizures prediction.

Epileptic seizures prediction is an interesting issue in epileptology, since it can promise a novel approach to control seizures and understand the mechanism of epileptic seizures. In this paper, we describe a new method, called wavelet-based nonlinear similarity index (WNSI), to predict epileptic seizures using EEG recordings in real time. This method combines wavelet techniques and nonlinear dynamics. The test results of EEG recordings of rats and humans show that WNSI can track the hidden dynamical changes of brain electrical activity. Particularly, we found that it can obtain the best performance of seizure prediction at the beta (10-30 Hz) frequency band of EEG signals. A possible reason is suggested from the functional connectivity of the brain. In terms of this study, it is recommended that wavelet technique is very useful to improve the performance of epileptic seizures prediction.

Algorithms↗

PubMed2006

Characterization of surface EMG signals using improved approximate entropy.

An improved approximate entropy (ApEn) is presented and applied to characterize surface electromyography (sEMG) signals. In most previous experiments using nonlinear dynamic analysis, this certain processing was often confronted with the problem of insufficient data points and noisy circumstances, which led to unsatisfactory results. Compared with fractal dimension as well as the standard ApEn, the improved ApEn can extract information underlying sEMG signals more efficiently and accurately. The method introduced here can also be applied to other medium-sized and noisy physiological signals.

Algorithms↗

PubMed2002

New approach for modelling ultrasound blood backscatter signal.

The ultrasound (US) scattered signal from blood has been treated as a random signal by many investigators. However, the degree of randomness of a medium is a relative term that can change considerably with the resolution of the sensor. In this study, the backscattered signal from blood has been looked at as a chaotic signal. By this treatment, according to Taken's theorem, a single variable (e.g., amplitude of the blood-backscattered signal) can be used to reconstruct the nonlinear dynamics of the blood-scattered signal. Multilayer perceptron neural network architecture, with error back-propagation, has been formulated and used as a basis for building and testing the chaotic model of the backscattered signal. This chaotic model is used successfully as a short-term predictor of the backscattered signal from blood-mimicking fluid (BMF) flowing in a vascular flow phantom under pulsatile flow. This modelling approach can be useful, for example, in detecting blood-borne emboli.

Blood↗

PubMed1996

Neuronal oscillations and stochastic limit cycles.

We investigate a model for synchronous neural activity in networks of coupled neurons. The individual systems are governed by nonlinear dynamics and can continuously vary between excitable and oscillatory behavior. Analytical calculations and computer simulations show that coupled excitable systems can undergo two different phase transitions from synchronous to asynchronous firing behavior. One of the transitions is akin to the synchronization transitions in coupled oscillator systems, while the second transition can only be found in coupled excitable systems. Using the concept of Stochastic Limit Cycles, we present an analytical derivation of the two transitions and discuss implications for synchronization transitions in biological neural networks.

Biological Clocks↗

PubMed2003

A mechanical model of vocal-fold collision with high spatial and temporal resolution.

The tissue mechanics governing vocal-fold closure and collision during phonation are modeled in order to evaluate the role of elastic forces in glottal closure and in the development of stresses that may be a risk factor for pathology development. The model is a nonlinear dynamic contact problem that incorporates a three-dimensional, linear elastic, finite-element representation of a single vocal fold, a rigid midline surface, and quasistatic air pressure boundary conditions. Qualitative behavior of the model agrees with observations of glottal closure during normal voice production. The predicted relationship between subglottal pressure and peak collision force agrees with published experimental measurements. Accurate predictions of tissue dynamics during collision suggest that elastic forces play an important role during glottal closure and are an important determinant of aerodynamic variables that are associated with voice quality. Model predictions of contact force between the vocal folds are directly proportional to compressive stress (r2 = 0.79), vertical shear stress (r2 = 0.69), and Von Mises stress (r2 = 0.83) in the tissue. These results guide the interpretation of experimental measurements by relating them to a quantity that is important in tissue damage.

Adult↗

PubMed2001

[Analysis and detection of abnormal ECG signal: ventricular tachycardia and fibrillation].

This paper, utilizing signal power spectrum and L-Z complexity measure, analyzes the abnormal ECG: ventricular tachycardia (VT) and ventricular fibrillation (VF). And on the base of linear and nonlinear dynamics, the paper forwards a new definition of information complexity rate, deduces some relative properties and applies it to complexity analysis in irregular ECG. By means of biological experiments and computer simulations, the reasonability of information complexity and complexity rate is confirmed. At last, objective analysis and explanations of the mechanism of VT and VF are reported. The results indicate: with the help of power spectrum, complexity measure and complexity rate, the recognition of VT and VF can attain 100%.

Algorithms↗

PubMed2006

Phase resetting and coupling of noisy neural oscillators.

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations.

Action Potentials↗