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Results for “Nonlinear Dynamics”

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PubMed2004

Verification of implantable cardioverter defibrillator (ICD) interventions by nonlinear analysis of heart rate variability -- preliminary results.

AIMS: Conventional ICD algorithms yield approximately 10-30% of spurious interventions. Our aim was to check whether nonlinear dynamics methods might be useful in the verification of ICD interventions. METHODS AND RESULTS: We extracted 190 consecutive RR files (approximately 2000-9000 RR intervals long) from the ICDs of 70 patients (36 with coronary artery disease, 8 with hypertrophic cardiomyopathy, 19 with dilated cardiomyopathy and 7 with other diseases). The 3D phase space trajectories in delay coordinates, window pattern entropy, and algorithmic complexity of the RR intervals were examined within a 50 beat sliding window. Data were not filtered for arrhythmia and artefacts. Of the 83 recordings with appropriate interventions 79 were correctly recognised in a blind test. Two interventions were not identified in patients with fast atrial fibrillation and two in cases of complex and frequent forms of arrhythmia. There were nine spurious interventions. In all except one case (atrial fibrillation with a fast ventricular response) the analysis by nonlinear methods showed that the intervention was not necessary. All of the 98 control recordings were correctly identified in the blind test. CONCLUSIONS: The results show that nonlinear dynamics methods may be used to supplement the existing ICD detection algorithms to enhance the detection success rate.

Adult↗

PubMed2002

Nonlinear analysis of EEG after repetitive transcranial magnetic stimulation.

The purpose of this study was to investigate whether repetitive transcranial magnetic stimulation (rTMS) can change nonlinear dynamic properties of the cerebral cortex. Two rTMS trains (10 Hz, 3 seconds, 100% of motor threshold) were administered to the left frontal area in healthy subjects. EEG signals were collected at 14 electrode sites before and after stimulation, and were filtered digitally into delta, theta, alpha, beta, and gamma bands. Basing on an improved algorithm introduced in the authors' recent study, dimension estimates were calculated on these signals as well as on the corresponding surrogate data. Sham treatment was designed into this study. The data showed that EEG signals obviously exhibited lower dimension estimates than the surrogate data, whereas the theta and alpha rhythms presented the lowest values among the frequency components. rTMS increased the dimension estimates of EEG signals during the first 2 minutes. Similar findings were also obtained on the delta and beta components. This study revealed that EEG signals in the normal state can be described by a nonlinear dynamic process. This process can be affected temporarily by rTMS. Neuronal networks revealed by EEG signals show more complicated properties after stimulation.

Adult↗

PubMed2006

Transient dynamics and nonlinear stability of spatially extended systems.

As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is often found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find, however, that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition.

Journal Article↗

PubMedDate not supplied

Stability of heartbeat interval distributions in chronic high altitude hypoxia.

Recent studies of nonlinear dynamics of the long-term variability of heart rate have identified nontrivial long-range correlations and scale-invariant power-law characteristics (l/f noise) that were remarkably consistent between individuals and were unrelated to external or environmental stimuli (Meyer et al., 1998a). The present analysis of complex nonstationary heartbeat patterns is based on the sequential application of the wavelet transform for elimination of local polynomial nonstationary behavior and an analytic signal approach by use of the Hilbert transform (Cumulative Variation Amplitude Analysis). The effects of chronic high altitude hypoxia on the distributions and scaling functions of cardiac intervals over 24 hr epochs and 4 hr day/nighttime subepochs were determined from serial heartbeat interval time series of digitized 24 hr ambulatory ECGs recorded in 9 healthy subjects (mean age 34 yrs) at sea level and during a sojourn at high altitude (5,050 m) for 34 days (Ev-K2-CNR Pyramid Laboratory, Sagarmatha National Park, Nepal). The results suggest that there exists a hidden, potentially universal, common structure in the heterogeneous time series. A common scaling function with a stable Gamma distribution defines the probability density of the amplitudes of the fluctuations in the heartbeat interval time series of individual subjects. The appropriately rescaled distributions of normal subjects at sea level demonstrated stable Gamma scaling consistent with a single scaled plot (data collapse). Longitudinal assessment of the rescaled distributions of the 24 hr recordings of individual subjects showed that the stability of the distributions was unaffected by the subject's exposure to a hypobaric (hypoxic) environment. The rescaled distributions of 4 hr subepochs showed similar scaling behavior with a stable Gamma distribution indicating that the common structure was unequivocally applicable to both day and night phases and, furthermore, did not undergo systematic changes in response to high altitude. In contrast, a single function stable over a wide range of time scales was not observed in patients with congestive heart failure or patients after cardiac transplantation. The functional form of the scaling in normal subjects would seem to be attributable to the underlying nonlinear dynamics of cardiac control. The results suggest that the observed Gamma scaling of the distributions in healthy subjects constitutes an intrinsic dynamical property of normal heart function that would not undergo early readjustment or late acclimatization to extrinsic environmental physiological stress, e.g., chronic hypoxia.

Acclimatization↗

PubMed2006

A stability boundary based method for finding saddle points on potential energy surfaces.

The task of finding saddle points on potential energy surfaces plays a crucial role in understanding the dynamics of a micromolecule as well as in studying the folding pathways of macromolecules like proteins. The problem of finding the saddle points on a high dimensional potential energy surface is transformed into the problem of finding decomposition points of its corresponding nonlinear dynamical system. This paper introduces a new method based on TRUST-TECH (TRansformation Under STability reTained Equilibria CHaracterization) to compute saddle points on potential energy surfaces using stability boundaries. Our method explores the dynamic and geometric characteristics of stability boundaries of a nonlinear dynamical system. A novel trajectory adjustment procedure is used to trace the stability boundary. Our method was successful in finding the saddle points on different potential energy surfaces of various dimensions. A simplified version of the algorithm has also been used to find the saddle points of symmetric systems with the help of some analytical knowledge. The main advantages and effectiveness of the method are clearly illustrated with some examples. Promising results of our method are shown on various problems with varied degrees of freedom.

Algorithms↗

PubMedDate not supplied

Fuzzy methods in tremor assessment, prediction, and rehabilitation.

Tremor is a disabling condition for a large segment of population, mainly elderly. To the present date, there are no adequate tools to diagnose and help rehabilitation of subjects with tremor, but recently there is a tremendous surge of interest in the research in the field. We report on the use of fuzzy methods in applications for rehabilitation, namely in tremor diagnosing and control. We synthesize our results regarding the characterization of the tremor by means of nonlinear dynamics techniques and fuzzy logic, and the prediction of tremor movements in view of rehabilitation purposes. Based on linear and nonlinear analysis of tremor, and using fuzzy aggregation, the fusing of tremor parameters in global functional disabling factors is proposed. Nonlinear dynamic parameters, namely correlation dimension and Lyapunov exponent is used in order to improve the assessment of tremor. The benefits of the fuzzy fused tremor parameters rely on more complete and accurate assessment of the functional impairment and on improved feedback for rehabilitation, based on the fused parameters of the tremor. Further steps in rehabilitation may require external muscular control. In turn, the control of tremor by electrical stimulation requires movement prediction. Several neural and neuro-fuzzy predictors are compared and a neuro-fuzzy predictor is presented, allowing us five-step ahead prediction, with an RMS error of the order of 10%. The benefits of the neuro-fuzzy predictor are good prediction capability, versatility, and apparently a high robustness to individual variations of the tremor. The reported research, which extended over several years and included development of sensors, equipment, and software, has been aimed to development of products. The results may also open new ways in tremor rehabilitation.

Aged↗

PubMed1988

System analysis of Phycomyces light-growth response with Gaussian white noise and sum-of-sinusoids test stimuli.

The sporangiophore (fruiting body) of the fungus Phycomyces modulates its elongation rate in response to changes in blue light intensity. This light-growth response of wild-type and behavioral mutant strains has been studied extensively by two methods of nonlinear system identification employing Gaussian white noise and sum-of-sinusoids test stimuli. Both methods are in the framework of the Wiener theory of nonlinear systems. The light-growth response is well described by the first-order Wiener G-functional; addition of the second-order functional improves the precision. The Wiener kernel of first-order resembles the light-growth response to a nonsaturating pulse stimulus. The second-order kernel indicates the nonlinear property of rectification. The kernels have been interpreted by system analysis methods in the frequency domain. A nonlinear dynamic model of the light-growth response has been developed from the kernels obtained by both methods. The model includes a nonlinear dynamic subsystem, including a squarer, followed by a linear dynamic subsystem (which, by itself, accounts for the first-order kernel). This parametric model has been used to evaluate light-growth response kernels under various conditions (viz. wavelength, temperature, and genetic strain). The kernels of single and double mutants have been analyzed jointly with a nonparametric model to reveal interactions among the products of eight genes that influence the light-growth response. The extent of interactions found suggests that these gene products function together in a molecular complex.

Light↗

PubMed2005

Stabilization and relative phase effects in a dichromatically driven diatomic Morse molecule: interpretation based on nonlinear classical dynamics.

The dissociation dynamics of a dichromatically laser-driven diatomic Morse molecule vibrating in the ground state is investigated by applying tools of the nonlinear theory of classical Hamiltonian systems. Emphasis is placed on the role of the relative phase of the two fields, phi. First, it is found that, just like in quantum mechanics, there is dependence of the dissociation probability on phi. Then, it is demonstrated that addition of the second laser leads to suppression of probability (stabilization), when the intensity of the first laser is kept constant just above or below the single laser dissociation threshold. This "chemical bond hardening" diminishes as phi increases. These effects are investigated and interpreted in terms of modifications in phase space topology. Variations of phi as well as of the intensity of the second laser may cause (i) appearance/disappearance of the stability island corresponding to the common resonance with the lowest energy and (ii) deformation and movement of the region of Kolmogorov-Arnold-Moser tori that survive from the undriven system. The latter is the main origin in phase space of stabilization and phi dependence. Finally, it is shown that the use of short laser pulses enhances both effects.

Journal Article↗

PubMed2003

Parameter estimation in biochemical pathways: a comparison of global optimization methods.

Here we address the problem of parameter estimation (inverse problem) of nonlinear dynamic biochemical pathways. This problem is stated as a nonlinear programming (NLP) problem subject to nonlinear differential-algebraic constraints. These problems are known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based) local optimization methods fail to arrive at satisfactory solutions. To surmount this limitation, the use of several state-of-the-art deterministic and stochastic global optimization methods is explored. A case study considering the estimation of 36 parameters of a nonlinear biochemical dynamic model is taken as a benchmark. Only a certain type of stochastic algorithm, evolution strategies (ES), is able to solve this problem successfully. Although these stochastic methods cannot guarantee global optimality with certainty, their robustness, plus the fact that in inverse problems they have a known lower bound for the cost function, make them the best available candidates.

Algorithms↗

PubMed1978

Accommodation dynamics I. Range nonlinearity.

We show the presence of a new nonlinearity in accommodation dynamics. Positive accommodation is slower when the eye is operating in the near range; conversely, relaxation of accommodation is apparently slower during work in the far range. Latency of accommodation is unaffected by working range. This new dynamic range nonlinearity has been defined in connection with a continuing research study of accommodation responses in normal subjects and in clinic patients. Instrumentation and analysis procedures are described.

Accommodation, Ocular↗

PubMed2004

Evolutionary optimization with data collocation for reverse engineering of biological networks.

MOTIVATION: Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. RESULTS: We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Algorithms↗

PubMed1998

Global asymptotic stability of bone remodeling theories: a new approach based on non-linear dynamical systems analysis.

Mathematical tools for the analysis of nonlinear dynamical systems are applied to the study of stability of bone remodeling theories. As a practical application, the same problem studied by Harrigan and Hamilton (1992) and Cowin et al. (1994b) is analysed using these tools, and their findings on the necessary and sufficient conditions to ensure local asymptotic stability are easily confirmed. Using a general approach based on Lyapunov's method the same condition has been found to be necessary and sufficient also for the global asymptotic stability, thus confirming a result obtained by Harrigan and Hamilton (1994) by variational methods applied to finite-element models. The proof is based on the discretization of the spatial domain but the results for the continuum can be easily extrapolated.

Animals↗

PubMed1994

Solitary wave dynamics as a mechanism for explaining the internal motion during microtubule growth.

Microtubules, which play many diverse and important roles in biological systems, are usually made up of 13 nearly axial protofilaments formed from individual tubulin molecules. In this paper, a nonlinear dynamic model has been developed to elucidate the mechanism of the internal motion occurring during the assembly of microtubules. The results derived from the model indicate that such internal motion is associated with a solitary wave, or kink, excited by the energy released from the hydrolysis of GTP-->GDP in microtubular solutions. As the kink moves forward, the individual tubulin molecules involved in the kink undergo motions that can be likened to the dislocation of atoms within the crystal lattice. Thus, the dynamic instability of microtubules may be characterized by a series of dislocation motions of the tubulin molecules. An energy estimate shows that a kink in the system possesses about 0.36-0.44 eV, which is quite close to but smaller than the 0.49 eV of energy released from the hydrolysis of GTP. Therefore, the relevant energy derived from our model is fully consistent with experimental observations; this finding also suggests that the hydrolysis energy may be responsible for exciting the solitary wave, or kink, leading to tubulin dislocation in microtubules. Our model, and its intrinsic properties, i.e., dynamic nonlinearity, thermodynamic irreversibility, as well as an energy input from a sustained source, implies that the growth of microtubules is a typical dissipative process and that their structure in vivo is typical of dissipative structures.

Energy Metabolism↗

PubMed2004

Nonlinear and nonequilibrium dynamics in geomaterials.

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.

Journal Article↗

PubMed1992

Psychophysiological processes during insight-oriented therapy. Further investigations into nonlinear psychodynamics.

Experimental evidence shows that many physiological processes abide by nonlinear dynamics and evidence chaos. Novel conceptual models postulate chaotic phenomena in psychological processes as well. The challenge in empirically testing these models is to develop measures that are sufficiently precise to permit nonlinear dynamical analyses and that also say something meaningful about psychological phenomena. Toward this end, we examined the spontaneously occurring autonomic activity of a patient during psychotherapy. Phase portraits were constructed of the patient's heart rate data for each of several therapy sessions. The flows within these phase spaces were visually segmented and assigned to one of four previously defined trajectory classifications. These trajectories were quantitatively analyzed, and the corresponding clinical material was assessed qualitatively. The trajectories in the physiological phase space were recognizable, recurrent, and robust; they appeared coupled to ongoing psychological processes. Possible refinements in this typology are discussed and suggestions are made for potentially using such analyses to track and navigate among psychophysiological states.

Adult↗

PubMed2002

Cyclic dynamics in simulated plant populations.

Despite the general interest in nonlinear dynamics in animal populations, plant populations are supposed to show a stable equilibrium that is attributed to fundamental differences compared with animals. Some studies find more complex dynamics, but empirical studies usually are too short and most modelling studies ignore important spatial aspects of local competition and establishment. Therefore, we used a spatially explicit individual-based model of a hypothetical, non-clonal perennial to explore which mechanisms might generate complex dynamics, i.e. cycles. The model is based on the field-of-neighbourhood approach that describes local competition and establishment in a phenomenological manner. We found cyclic population dynamics for a wide spectrum of model variants, provided that mortality is determined by local competition and recruitment is virtually completely suppressed within the zone of influence of established plants. This destabilizing effect of local processes within plant populations might have wide-ranging implications for the understanding of plant community dynamics and coexistence.

Ecosystem↗

PubMed2006

Early dynamic changes in pulse oximetry signals in preterm newborns with histologic chorioamnionitis.

OBJECTIVE: No reliable clinical markers of histologic chorioamnionitis (HCA), a major and often subclinical cause of prematurity leading to high neonatal morbidity and mortality, are available to date. Increasing evidence indicates myocardial dysfunctions in affected fetuses and newborns. We sought to assess the value of nonlinear dynamics from pulse oximetry signals in identifying affected newborns. DESIGN: Prospective case-control study. SETTING: Tertiary level neonatal intensive care unit, Brindisi Hospital. PATIENTS AND INTERVENTION: Pulse oximetry-derived signals (pulse rate, oxygen saturation, and perfusion index), recorded within the first 1.5 hrs of life, were analyzed for 110 very low-birth-weight infants, of whom 54 had histopathological evidence of HCA. MEASUREMENTS AND MAIN RESULTS: Four different time series parameters were determined for nonlinear dynamical (NLD) analysis. Significantly decreased Lempel-Ziv, Lyapunov largest exponent, and correlation dimension, with significantly increased Hurst values for heart rate and perfusion index (p < .00001), were observed in newborns with HCA. Heart rate Lempel-Ziv </=0.218 showed 100% sensitivity (95% confidence interval, 98.8-100) and 100% specificity (95% confidence interval, 98.6-100) in distinguishing cases from controls, with positive and negative predictive values of 100% and 95.7%, respectively. CONCLUSIONS: Our findings indicate that early autonomic tone balance abnormalities are present in newborns with HCA and suggest that early dynamic analysis of pulse oximetry signals could be useful in identifying affected infants.

Case-Control Studies↗

PubMedDate not supplied

Continuum models in neurobiology and information processing.

Continuum models have been used with considerable success for single neurons but have been neglected in the study of neuronal populations. In more popular discrete neuronal network models, the geometric details of the neuronal centers are usually neglected. We here give a continuum nonlinear dynamical model and an approximate model which admits the possibility of ascertaining the roles of the various connectivity patterns from center to center in the central nervous system. Frequency transfer characteristics are used to incorporate the nonlinear dynamics of single neurons. Simple examples are evaluated both analytically and numerically and the results presented graphically.

Models, Neurological↗