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Results for “Nonlinear Dynamics”

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At least 739 records · Page 41Linked to original sources

PubMed2002

Automatic stride interval extraction from long, highly variable and noisy gait timing signals.

This paper presents a probabilistic algorithm for automatically extracting the stride interval time series from long, highly variable and noisy two-state timing signals. Long interstride temporal records are of particular interest in nonlinear dynamical analysis of gait. The proposed method consists of probabilistic estimation and extraction followed by post-extraction filtering. With noisy timing signals from 10 children with Spastic Diplegia, no statistical differences in the numbers of extracted strides (p=0.94), the mean stride intervals (p=0.55) and the scaling exponents (p=0.94) (a measure of temporal heterogeneity) were found between series extracted by hand and by the probabilistic algorithm. The method is robust to noise and violations of normality. Results support the use of probabilistic extraction as an alternative to laborious manual extraction.

Algorithms↗

PubMed1997

Development and evaluation of totally implantable ventricular assist system using a vibrating flow pump and transcutaneous energy transmission system with amorphous fibers.

We have developed a vibrating flow pump (VFP) that can generate oscillated blood flow with a relatively high frequency (10-50 Hz) for a totally implantable ventricular assist system (VAS). To evaluate the newly developed VAS, left heart bypasses, using the VFP, were performed in chronic animal experiments. Hemodynamic parameters were recorded in a data recorder in healthy adult goats during an awake condition and analyzed in a personal computer system through an alternating-direct current converter. Basic performance of the total system with a transcutaneous energy transmission system were satisfactory. During left ventricular assistance with the VFP, Mayer wave fluctuations of hemodynamics were decreased in the power spectrum, the fractal dimensions of the hemodynamics were significantly decreased, and peripheral vascular resistance was significantly decreased. These results suggest that cardiovascular regulatory nonlinear dynamics, which mediate the hemodynamics, may be affected by left ventricular bypass with oscillated flow. The decreased power of the Mayer wave in the spectrum caused the limit cycle attractor of the hemodynamics and decreased peripheral resistance. These results suggest that this newly developed VAS is useful for the totally implantable system with unique characteristics that can control hemodynamic properties.

Animals↗

PubMed2006

Bifurcation analysis of Jansen's neural mass model.

We present a mathematical model of a neural mass developed by a number of people, including Lopes da Silva and Jansen. This model features three interacting populations of cortical neurons and is described by a six-dimensional nonlinear dynamical system. We address some aspects of its behavior through a bifurcation analysis with respect to the input parameter of the system. This leads to a compact description of the oscillatory behaviors observed in Jansen and Rit (1995) (alpha activity) and Wendling, Bellanger, Bartolomei, and Chauvel (2000) (spike-like epileptic activity). In the case of small or slow variation of the input, the model can even be described as a binary unit. Again using the bifurcation framework, we discuss the influence of other parameters of the system on the behavior of the neural mass model.

Action Potentials↗

PubMed2006

From pulsus to pulseless: the saga of cardiac alternans.

Computer simulations and nonlinear dynamics have provided invaluable tools for illuminating the underlying mechanisms of cardiac arrhythmias. Here, we review how this approach has led to major insights into the mechanisms of spatially discordant alternans, a key arrhythmogenic factor predisposing the heart to re-entry and lethal arrhythmias. During spatially discordant alternans, the action potential duration (APD) alternates out of phase in different regions of the heart, markedly enhancing dispersion of refractoriness so that ectopic beats have a high probability of inducing reentry. We show how, at the cellular level, instabilities in membrane voltage (ie, steep APD restitution slope) and intracellular Ca (Cai) cycling dynamics cause APD and the Cai transient to alternate and how the characteristics of alternans are affected by different "modes" of the bidirectional coupling between voltage and Cai. We illustrate how, at the tissue level, additional factors, such as conduction velocity restitution and ectopic beats, promote spatially discordant alternans. These insights have illuminated the mechanistic basis underlying the clinical association of cardiac alternans (eg, T wave alternans) with arrhythmia risk, which may lead to novel therapeutic approaches to avert sudden cardiac death.

Animals↗

PubMed2002

Grazing instabilities and post-bifurcation behavior in an impacting string.

A theoretical and experimental investigation of the nonlinear dynamic response of a periodically excited string subject to a knife-edge amplitude restraint is presented. The amplitude restraint creates an impact condition as the amplitude of the response grows. The focus of this work is on the influence of a grazing instability; this zero-velocity impact event leads to complicated, post-bifurcation behavior ranging from multifrequency, periodic motion to chaos. In addition to looking at the response numerically, parameter combinations leading to an incidence of grazing are clearly identified in the excitation force excitation frequency parameter space using a multiple scales perturbation analysis. Modeling issues, numerical difficulties, and experimental limitations are also discussed.

Motion↗

PubMed2006

Delay-coordinates embeddings as a data mining tool for denoising speech signals.

In this paper, we utilize techniques from the theory of nonlinear dynamical systems to define a notion of embedding estimators. More specifically, we use delay-coordinates embeddings of sets of coefficients of the measured signal (in some chosen frame) as a data mining tool to separate structures that are likely to be generated by signals belonging to some predetermined data set. We implement the embedding estimator in a windowed Fourier frame, and we apply it to speech signals heavily corrupted by white noise. Our experimental work suggests that, after training on the data sets of interest, these estimators perform well for a variety of white noise processes and noise intensity levels.

Algorithms↗

PubMed2003

Controlling system dimension: a class of real systems that obey the Kaplan-Yorke conjecture.

The Kaplan-Yorke conjecture suggests a simple relationship between the fractal dimension of a system and its Lyapunov spectrum. This relationship has important consequences in the broad field of nonlinear dynamics where dimension and Lyapunov exponents are frequently used descriptors of system dynamics. We develop an experimental system with controllable dimension by making use of the Kaplan-Yorke conjecture. A rectangular steel plate is driven with the output of a chaotic oscillator. We controlled the Lyapunov exponents of the driving and then computed the fractal dimension of the plate's response. The Kaplan-Yorke relationship predicted the system's dimension extremely well. This finding strongly suggests that other driven linear systems will behave similarly. The ability to control the dimension of a structure's vibrational response is important in the field of vibration-based structural health monitoring for the robust extraction of damage-sensitive features.

Models, Theoretical↗

PubMed2005

[Analysis of the EEG information of rats epileptic model using unstable periodic orbits].

In order to further research into the EEG information of rats epileptic model, we applied different nonlinear dynamic methods. After having analyzed the EEG signal of rat falling sickness by means of approximate entropy and correlation dimension, we adopted a the new method, unstable periodic orbits, which was used to analyze complex activity of neurons system to look for the change regularity of change in the EEG signal in the whole course of rat's falling sickness. We found period 1 orbits and period 2 orbits to be statistically significant in the data of ictal time of epilepsy. At the same time, we found period 1 orbits to be statistically significant in the data of preictal time of epilepsy.

Animals↗

PubMed1998

Measures of complexity for cancellous bone.

The problem of quantifying the structure of cancellous bone has been addressed in the past by histomorphometry and more recently by imaging techniques using X-ray attenuation. The current approaches compute and describe parts of the construction of the trabecular net. We developed a new technique which quantifies cancellous bone of human lumbar vertebrae as a whole. The interactions, transactions, and interrelationships of all parts of the structural composition of the trabeculae are accounted for and quantified. The method is based on the concept of structural complexity within the framework of nonlinear dynamics. The methodology was developed by using axial high resolution computed tomography images. The technique was transferred to quantitative computed tomography images and is based on the non-invasive assessment of 50 human L3 specimens. The value of Houndsfield units per pixel representing trabecular bone of the vertebrae was transformed into color-encoded and alphabet-encoded symbols. The procedure of transformation of the X-ray attenuation pixels into symbols was necessary as a basis on which measures of complexity were introduced to assess the composition of symbols within the images. The development of a generalization of symbolic dynamics, a mathematical method, to work with two-dimensional images was a prerequisite. The results of this study demonstrate that the structural composition of cancellous bone declines more rapidly than bone mineral density during the loss of bone. This outcome strongly suggests an exponential relationship between bone mineral density and the architectural composition of cancellous bone. Normal trabecular bone has a complex ordered structure. The structural composition during the osteopenic phase of bone loss is characterized by lower structural complexity and a significantly higher level of architectural disorder. A high grade of osteoporosis leads again to an ordered structure, although its structural complexity is minimal.

Algorithms↗

PubMed1995

Patterns of attractor dimensions of sleep EEG.

Low dimensional chaos is a property of many physiological oscillatory systems including the brain. Time series of sleep EEG records have been analyzed in the framework of recent developments in nonlinear dynamics. One of the characteristics of a chaotic time series is its attractor dimension. The running attractor dimension of a chaotic time series may reflect changes in states more accurately than manually scored records. In the present study the attractor dimensions of consecutive EEG segments of five sleep records were analyzed. The block of the EEG segment (window) was shifted by various lengths along the entire sleep data of each subject thus producing a running attractor dimension curve for each record. The attractor dimension values for different sleep stages were significantly different. The pattern of the running attractor dimension closely matched the scored hypnograms in these five sleep records.

Adolescent↗

PubMed1994

Chaos and antichaos in pathology.

Deterministic chaos is a pattern of fluctuations that may seem to be stochastic (caused by random external forces) but is actually produced, in a determined manner, by the action of nonlinear dynamic processes. The existence of this phenomenon has important implications for pathologists because it means that experimental data with apparently random fluctuations may be caused by a deterministic process. The patterns noted in deterministic chaos are very sensitive to variation in initial conditions, so if chaotic processes do occur in pathology then methods of predicting biological behavior (prognosis) of lesions, such as tumors, will have to be modified. This review shows the properties of deterministic chaos using a simple mathematical model of tumor growth and describes the methods that may be used to analyze experimental data for the presence of such chaos illustrating these with some clinical data. Established applications in medicine are reviewed and antichaotic mechanisms are discussed.

Humans↗

PubMed1997

A synergetic model for the verbal transformation effect.

We describe a nonlinear dynamical model based on synergetics for the auditory perceptual illusion known as the verbal transformation effect. The model is an extension of a synergetic model of perceptual oscillations of visual ambiguous figures. The main extension is connected to the number of reported alternative phonemic structures, which is typically much greater than the two or three alternatives usually reported in experiments with visual ambiguous figures. The properties of the model, which are derived using basic psychophysical principles, are presented and evaluated on the basis of the fit to earlier empirical work. It will be shown that there is very good agreement between the empirically observed properties of the verbal transformation effect and the properties detected by the model.

Attention↗

PubMed2004

BDNF boosts spike fidelity in chaotic neural oscillations.

Oscillatory activity and its nonlinear dynamics are of fundamental importance for information processing in the central nervous system. Here we show that in aperiodic oscillations, brain-derived neurotrophic factor (BDNF), a member of the neurotrophin family, enhances the accuracy of action potentials in terms of spike reliability and temporal precision. Cultured hippocampal neurons displayed irregular oscillations of membrane potential in response to sinusoidal 20-Hz somatic current injection, yielding wobbly orbits in the phase space, i.e., a strange attractor. Brief application of BDNF suppressed this unpredictable dynamics and stabilized membrane potential fluctuations, leading to rhythmical firing. Even in complex oscillations induced by external stimuli of 40 Hz (gamma) on a 5-Hz (theta) carrier, BDNF-treated neurons generated more precisely timed spikes, i.e., phase-locked firing, coupled with theta-phase precession. These phenomena were sensitive to K252a, an inhibitor of tyrosine receptor kinases and appeared attributable to BDNF-evoked Na(+) current. The data are the first indication of pharmacological control of endogenous chaos. BDNF diminishes the ambiguity of spike time jitter and thereby might assure neural encoding, such as spike timing-dependent synaptic plasticity.

Action Potentials↗

PubMed1996

Use of methods from chaos theory to quantify a fundamental dysfunction in the behavioral organization of schizophrenic patients.

OBJECTIVE: This study aimed to quantify the complexity of behavioral sequences of patients with schizophrenia and comparison subjects by using methods from nonlinear dynamical systems theory. METHOD: A simple choice task consisting of predicting 500 random right or left appearances of a stimulus was used to obtain binary response sequences in 22 patients with schizophrenia and 16 comparison subjects. Dynamical entropy was measured and the fluctuation spectrum of local subsequence entropies calculated to quantify the degree of interdependency between consecutive responses of patients and comparison subjects. RESULTS: The response sequences generated by the schizophrenic patients exhibited a higher degree of interdependency than those of comparison subjects. Moreover, schizophrenic patients exhibited significantly less consistency in their response selection and ordering, characterized by a greater contribution of both highly perseverative and highly unpredictable subsequences of responses within a test session. CONCLUSIONS: The result of the biological abnormality underlying schizophrenia may not be a simple increase or decrease of neuropsychological or neurobiological functions. Instead, the observed abnormalities in behavioral patterns reflect a quantifiable dysregulation and disorganization of these functions.

Adult↗

PubMed1991

Vagal afferent activity increases dynamical dimension of respiration in rats.

Geometric and numerical techniques from nonlinear dynamics are employed to characterize the respiratory patterns of adult rats. In phase space constructions from volume measurements, the respiratory behavior of the vagotomized rat is seen to be unimodal and periodic, whereas that of the vagi-intact animal is bimodal and sensitive to initial conditions and displays stretching and folding of trajectories. By use of the correlation integral, the dimension and entropy were estimated for the respiratory patterns of five urethan-anesthetized rats (before and after vagotomy) and two awake animals (resting, vagi intact only). The results indicate that the central respiratory pattern of the anesthetized vagotomized rat behaves primarily as a single degree-of-freedom oscillator, which can be moved into a regime of low-order chaos in the presence of feedback from pulmonary stretch receptors, contributing significantly to the variability observed in the respiratory pattern of the vagi-intact animal. A model designed to emulate the Hering-Breuer inflation reflex demonstrates that the inspiration-inhibiting action of the reflex interacting with the oscillator at a critical phase transition is sufficient to drive the central pattern generator output into low-order chaos.

Afferent Pathways↗

PubMed2006

Nonlinear time series analysis of jerk congenital nystagmus.

Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system.This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses.

Action Potentials↗

PubMed1993

Modeling of neural systems by use of neuronal modes.

A methodology for modeling spike-output neural systems from input-output data is proposed, which makes use of "neuronal modes" (NM) and "multi-input threshold" (MT) operators. The modeling concept of NM's was introduced in a previously published paper in order to provide concise and general mathematical representations of the nonlinear dynamics involved in signal transformation and coding by a class of neural systems. This paper presents and demonstrates (with computer simulations) a method by which the NM's are determined using the 1st- and 2nd-order kernel estimates of the system, obtained from input-output data. The MT operator (i.e., a binary operator with multiple real-valued operands which are the outputs of the NM's) possesses an intrinsic refractory mechanism and generates the sequence of output spikes. The spike-generating characteristics of the MT operator are determined by the "trigger regions" defined on the basis of data. This approach is offered as a reasonable compromise between modeling complexity and prediction accuracy, which may provide a common methodological framework for modeling a certain class of neural systems.

Computer Simulation↗

PubMed2001

Perception of odors by a nonlinear model of the olfactory bulb.

The behavior of the olfactory bulb is modeled as a network of interconnected cells with nonlinear dynamics. External inputs from sensory neurons are introduced as perturbations to subsets of cells within the network. We describe the attractors of the system and show how they can be classified and ordered according to their varying degrees of symmetry. By studying networks of attractors in the system's phase space, it is shown how different perturbations may evoke specific switches between various patterns of behavior. This ensures that different odors, even if present at extremely low concentrations, are able to evoke a specific spatio-temporal behavior in the olfactory bulb, permitting their unique perception. The model incorporates many of the processes proposed to mediate perception, such as the topographic organisation of sensory systems, destabilization of cortex by sensory input and synchronisation between neurons. It is also consistent with the character of the olfactory electroencephalogram.

Electroencephalography↗