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Results for “Nonlinear Dynamics”

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At least 1,315 records · Page 73Linked to original sources

PubMed2003

Effect of ribavirin on hepatitis C viral kinetics in patients treated with pegylated interferon.

A dynamic equilibrium between viral production and clearance characterizes untreated chronic hepatitis C viral infection. After initiating antiviral treatment, a typical multiphasic decay of viremia can be observed and analyzed using mathematical models. To elucidate the antiviral mechanism of ribavirin when used in combination with (pegylated) interferon alfa, we investigated kinetic parameters in patients with chronic hepatitis C treated with either peginterferon alpha-2a with or without ribavirin and standard interferon alpha-2b plus ribavirin for 48 weeks. Serum HCV RNA was measured frequently before, during, and at the end-of-treatment and the follow-up period. By using an appropriate model for viral dynamics, kinetic parameters were derived from nonlinear, least square fitting of serum HCV RNA quantifications. The first phase of viral decay (day 1) and the second phase of viral decay (days 2 to 21) were similar for all treatment groups. After about 7 to 28 days, a third phase of viral decay was seen in several patients, and this phase of decay was significantly faster in patients treated with peginterferon alpha-2a plus ribavirin compared with those treated with peginterferon alpha-2a alone. The decay of this third phase was associated with the virologic end-of-treatment response and sustained virologic response. In conclusion, the third-phase decay of initial viral kinetics, which may represent a treatment-enhanced degradation of infected cells, was more pronounced in patients treated with peginterferon alpha-2a plus ribavirin. This finding suggests that combination treatment leads to a better restoration of the patient's immune response.

Adult↗

PubMed2004

Flow field topology of transient mixing driven by buoyancy.

Transient mixing driven by buoyancy occurs through the birth of a symmetric Rayleigh-Taylor morphology (RTM) structure for large length scales. Beyond its critical bifurcation the RTM structure exhibits self-similarity and occurs on smaller and smaller length scales. The dynamics of the RTM structure, its nonlinear growth and internal collision, show that its genesis occurs from an explosive bifurcation which leads to the overlap of resonance regions in phase space. This event shows the coexistence of regular and chaotic regions in phase space which is corroborated with the existence of horseshoe maps. A measure of local chaos given by the topological entropy indicates that as the system evolves there is growth of uncertainty. Breakdown of the dissipative RTM structure occurs during the transition from explosive to catastrophic bifurcation; this event gives rise to annihilation of the separatrices which drives overlap of resonance regions. The global bifurcation of explosive and catastrophic events in phase space for the large length scale of the RTM structure serves as a template for which mixing occurs on smaller and smaller length scales.

Diffusion↗

PubMed2006

Statics and dynamics of an inhomogeneously nonlinear lattice.

We introduce an inhomogeneously nonlinear Schrödinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior in the vicinity of the interface than the one expected in their homogeneous counterparts. We analyze the relevant stationary states, as well as their stability, by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anticontinuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.

Journal Article↗

PubMed2004

Bubble dynamics and size distributions during focused ultrasound insonation.

The deposition of ultrasonic energy in tissue can cause tissue damage due to local heating. For pressures above a critical threshold, cavitation will occur, inducing a much larger thermal energy deposition in a local region. The present work develops a nonlinear bubble dynamics model to numerically investigate bubble oscillations and bubble-enhanced heating during focused ultrasound (HIFU) insonation. The model is applied to calculate two threshold-dependent phenomena occurring for nonlinearly oscillating bubbles: Shape instability and growth by rectified diffusion. These instabilities in turn are shown to place physical boundaries on the time-dependent bubble size distribution, and thus the thermal energy deposition.

Biomechanical Phenomena↗

PubMed2001

Investigation of the nonlinearity in the heart rate dynamics.

This paper presents the application of a neural network to predict human heart rate. Electrocardiograms were measured from 5 healthy adult human subjects and 5 data sets were constructed calculating instantaneous heart rate from the measured signal. The nonlinear radial basis function neural network was applied to have a one step ahead prediction of the 1000 point heart rate. The results of the prediction are compared to that obtained by a linear autoregressive model. The results show that the neural network performs better than the autoregressive model in predicting heart rate for 2 data sets while for the other 3 data sets the performance of the two models is statistically similar. This indicates that the heart rate may be controlled nonlinearly by the autonomic nervous system.

Adult↗

PubMed1998

Constrained optimization for neural map formation: a unifying framework for weight growth and normalization.

Computational models of neural map formation can be considered on at least three different levels of abstraction: detailed models including neural activity dynamics, weight dynamics that abstract from the neural activity dynamics by an adiabatic approximation, and constrained optimization from which equations governing weight dynamics can be derived. Constrained optimization uses an objective function, from which a weight growth rule can be derived as a gradient flow, and some constraints, from which normalization rules are derived. In this article, we present an example of how an optimization problem can be derived from detailed nonlinear neural dynamics. A systematic investigation reveals how different weight dynamics introduced previously can be derived from two types of objective function terms and two types of constraints. This includes dynamic link matching as a special case of neural map formation. We focus in particular on the role of coordinate transformations to derive different weight dynamics from the same optimization problem. Several examples illustrate how the constrained optimization framework can help in understanding, generating, and comparing different models of neural map formation. The techniques used in this analysis may also be useful in investigating other types of neural dynamics.

Animals↗

PubMed2006

Dynamic output feedback stabilization for nonlinear systems based on standard neural network models.

A neural-model-based control design for some nonlinear systems is addressed. The design approach is to approximate the nonlinear systems with neural networks of which the activation functions satisfy the sector conditions. A novel neural network model termed standard neural network model (SNNM) is advanced for describing this class of approximating neural networks. Full-order dynamic output feedback control laws are then designed for the SNNMs with inputs and outputs to stabilize the closed-loop systems. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. It is shown that most neural-network-based nonlinear systems can be transformed into input-output SNNMs to be stabilization synthesized in a unified way. Finally, some application examples are presented to illustrate the control design procedures.

Algorithms↗

PubMed2001

Epileptic event forewarning from scalp EEG.

The authors present a model-independent approach to quantify changes in the dynamics underlying nonlinear time-serial data. From time-windowed datasets, the authors construct discrete distribution functions on the phase space. Condition change between base case and test case distribution functions is assessed by dissimilarity measures via L1 distance and chi2 statistic. The discriminating power of these measures is first tested on noiseless data from the Lorenz and Bondarenko models, and is then applied to detecting dynamic change in multichannel clinical scalp EEG data. The authors compare the dissimilarity measures with the traditional nonlinear measures used in the analysis of chaotic systems. They also assess the potential usefulness of the new measures for robust, accurate, and timely forewarning of epileptic events.

Adolescent↗

PubMed1991

Nonlinear effects in the dynamics of clouds of bubbles.

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.

Acoustics↗

PubMed1988

Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion.

In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t----+ infinity either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.

Aging↗

PubMed2000

Timely detection of dynamical change in scalp EEG signals.

We present a robust, model-independent technique for quantifying changes in the dynamics underlying nonlinear time-serial data. After constructing discrete density distributions of phase-space points on the attractor for time-windowed data sets, we measure the dissimilarity between density distributions via L(1)-distance and chi(2) statistics. The discriminating power of the new measures is first tested on data generated by the Bondarenko "synthetic brain" model. We also compare traditional nonlinear measures and the new dissimilarity measures to detect dynamical change in scalp EEG data. The results demonstrate a clear superiority of the new measures in comparison to traditional nonlinear measures as robust and timely discriminators of changing dynamics. (c) 2000 American Institute of Physics.

Journal Article↗

PubMed2002

Modeling of nonlinear physiological systems with fast and slow dynamics. II. Application to cerebral autoregulation.

Dynamic autoregulation of cerebral hemodynamics in healthy humans is studied using the novel methodology of the Laguerre-Volterra network for systems with fast and slow dynamics (Mitsis, G. D., and V. Z. Marmarelis, Ann. Biomed. Eng. 30:272-281, 2002). Since cerebral autoregulation is mediated by various physiological mechanisms with significantly different time constants, it is used to demonstrate the efficacy of the new method. Results are presented in the time and frequency domains and reveal that cerebral autoregulation is a nonlinear and dynamic (frequency-dependent) system with considerable nonstationarities. Quantification of the latter reveals greater variability in specific frequency bands for each subject in the low and middle frequency range (below 0.1 Hz). The nonlinear dynamics are prominent also in the low and middle frequency ranges, where the frequency response of the system exhibits reduced gain.

Adult↗

PubMed2001

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting.

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.

Algorithms↗

PubMed2004

Scaling of prediction error does not confirm chaotic dynamics underlying irregular firing using interspike intervals from midbrain dopamine neurons.

Dopamine neurons in the substantia nigra pars compacta often fire in an irregular, single spike mode in vivo, and a similar firing pattern can be observed in vitro when small conductance calcium-activated potassium channel blockers are applied to the bath. It is not clear whether the irregular firing is due to stochastic processes or nonlinear deterministic processes. A previous study [Neuroscience 104 (2001) 829] used nonlinear forecasting methods applied to a continuous function derived from the interspike interval (ISI) data from irregularly firing dopamine neurons to show that the predictability scaled exponentially with forecast horizon and was consistent with nonlinear deterministic chaos. However, we show here that the observed exponential scaling is also consistent with a stochastic process, because it did not differ significantly from that of shuffled surrogate data. On the other hand, nonlinear forecasting directly from the ISI data using the package TISEAN provided some evidence for nonlinear deterministic structure in four of five records obtained in vitro and in two of nine records obtained in vivo. Although we cannot rule out a role for nonlinear chaotic dynamics in structuring the firing pattern, we suggest an alternate hypothesis that includes a mechanism by which the firing pattern can become more variable in the presence of a constant level of background noise.

Algorithms↗

PubMed1993

Measurement of rotational dynamics by the simultaneous nonlinear analysis of optical and EPR data.

In the preceding companion article in this issue, an optical dye and a nitroxide radical were combined in a new dual function probe, 5-SLE. In this report, it is demonstrated that time-resolved optical anisotropy and electron paramagnetic resonance (EPR) data can be combined in a single analysis to measure rotational dynamics. Rigid-limit and rotational diffusion models for simulating nitroxide EPR data have been incorporated into a general non-linear least-squares procedure based on the Marquardt-Levenberg algorithm. Simultaneous fits to simulated time-resolved fluorescence anisotropy and linear EPR data, together with simultaneous fits to experimental time-resolved phosphorescence anisotropy decays and saturation transfer EPR (ST-EPR) spectra of 5-SLE noncovalently bound to bovine serum albumin (BSA) have been performed. These results demonstrate that data from optical and EPR experiments can be combined and globally fit to a single dynamic model.

Biophysical Phenomena↗

PubMed2006

Kinetic modeling of nitric-oxide-associated reaction network.

PURPOSE: Nitric oxide and superoxide are the two important free radicals in the biological system. The coexistence of both free radicals in the physiological milieu gives rise to intricate oxidative and nitrosative reactions, which have been implicated in many physiological and/or pathophysiological conditions, such as vasodilatation and inflammation. It is difficult, if not impossible, to study the complexity of the nitric oxide/superoxide system using current experimental approaches. Computational modeling thus offers an alternative way for studying the problem. METHODS: In this present study, key reaction pathways related to the generation, reaction and scavenging of both nitric oxide and superoxide were integrated into a reaction network. The network dynamics was investigated by numerical simulations to a set of coupled differential equations and by dynamical analysis. Two specific questions pertaining to the reaction kinetics of the reactive chemical species in the nitric oxide/superoxide system were studied: (1) how does the system respond dynamically when the generation rate of nitric oxide and superoxide varies? (2) how would antioxidants such as glutathione modulate the system dynamics? RESULTS: While changing basal GSH levels does not alter the kinetics of nitric oxide, superoxide, and peroxynitrite, the kinetic profiles of N203, GSNO and GSH are sensitive to the variation of basal GSH levels. The kinetics of the potential nitrosative species, N203, is switch like, which is dependent on the level of GSH. CONCLUSIONS: The model predicts that concurrent high nitric oxide and superoxide generation--such as in the inflammatory conditions--may result in nonlinear system dynamics, and glutathione may serve as a dynamic switch of N203 mediated nitrosation reaction.

Algorithms↗

PubMed1998

Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle.

To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function. To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed.

Adult↗

PubMed2006

Improved spatial characterization of the epileptic brain by focusing on nonlinearity.

An advanced characterization of the complicated dynamical system brain is one of science's biggest challenges. Nonlinear time series analysis allows characterizing nonlinear dynamical systems in which low-dimensional nonlinearity gives rise to complex and irregular behavior. While several studies indicate that nonlinear methods can extract valuable information from neuronal dynamics, others doubt their necessity and conjecture that the same information can be obtained using classical linear techniques. To address this issue, we compared these two concepts, but included furthermore a combination of nonlinear measures with surrogates, an approach that has been designed to specifically focus on nonlinearity. As a benchmark we used the discriminative power to detect the seizure-generating hemisphere in medically intractable mesial temporal lobe epilepsy. We analyzed intracranial electroencephalographic recordings from the seizure-free interval of 29 patients. While the performance of both linear and nonlinear measures was weak, if not insignificant, a very high performance was obtained by the use of surrogate-corrected measures. Focusing on nonlinearity by using a combination of nonlinear measures with surrogates appears as the key to a successful characterization of the spatial distribution of the epileptic process.

Electroencephalography↗