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PubMed2005

Deterministic and stochastic features of rhythmic human movement.

The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method's merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.

Forearm↗
PubMed2004

Scalar modeling and analysis of a 3D biochemical reaction model.

For many systems it is advantageous if analysis and modeling can be accomplished from a scalar time series because this greatly facilitates the experimental setup. Moreover, in real-life systems it is hardly true that all the state variables are available for analysis and modeling. Since the late 1980s, techniques have been put forward for building mathematical models from a scalar time series. One of the objectives of this paper is to verify if it is possible to obtain global non-linear models (non-linear differential equations) from scalar time series. Such data are obtained using a model of biochemical reaction with aperiodic (chaotic) oscillations as recently observed in the case of a glycolytic reaction (Nielsen, K., Sorensen, P.G., Hynne, F., 1997. Chaos in glycolysis. J Theor. Biol. 186, 303-306.). The main objective, however, is to investigate which state variable is more convenient for the task in practice. It is shown that observability indices seem to quantify quite well which variable should be preferred as the observable. The validity of the results are established performing rigorous topological analysis on the original system and the obtained models. The influence of noise, always present in experimental time series, on the dynamics underlying such a system is also investigated.

Catalysis↗
PubMed2004

Food chain chaos with canard explosion.

The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contains a canard singularity. Singular return maps are constructed for which some subdynamics are shown to be equivalent to chaotic shift maps. Parameter regions in which the described chaotic dynamics exist are explicitly given.

Adaptation, Physiological↗
PubMed1996

Containers, mental space and psychodynamics.

The concept of the container has a place within cognitive science as well as within psychodynamic theories. Cognitive semantics has shown that many metaphors giving meaning to daily life-events use the container as a basic reference point. Psychoanalytic theory, most notably, Freud's psychosexual developmental model, illustrates how the container of the body results in meaning. Object relations theory in psychoanalysis has shown how patients with borderline personality disorder behave according to the dynamics of container and containment. Both the cognitive and the psychodynamic conceptions of containers are clinically relevant. The fundamental notion of the container leads to an exploration of 'container dynamics' both in cognitive semantics and in psychodynamic work. A model of the cusp may be of help in the description of the dynamics at the border of the container. Furthermore, the descriptions of the patient's communication of emotion and thoughts may involve three interacting dimensions: an effective-perceptual dimension, a phantasy dimension and a socio-interactive dimension. The interaction between these dimensions has implications for dealing with container dynamics and the process of containment.

Borderline Personality Disorder↗
PubMed2002

Complex dynamics and the structure of small neural networks.

The discrete-time dynamics of small neural networks is studied empirically, with emphasis laid on non-trivial bifurcation scenarios. For particular two- and three-neuron networks interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them co-existing for one and the same set of parameters. An appropriate equivalence class of networks is defined, describing them as parametrized dynamical systems with identical dynamical capacities. Combined symmetries in phase space and parameter space are shown to generate different representatives of such a class. Moreover, conditions on the connectivity structure are suggested, which guarantee the existence of complex dynamics for a considered equivalence class of network configurations.

Algorithms↗
PubMed1990

Receptor interactions in modulating ventilatory activity.

The ventilatory control system utilizes a variety of sensory receptor groups, including chemoreceptors and mechanoreceptors, to provide feedback concerning the status of controlled variables. Most ventilatory responses to altered receptor inputs generally involve a complex interaction between several receptor groups, central integrative mechanisms, and other modulatory inputs (e.g., "state," hormonal, or neurotransmitter status). Because the control system is complex, nonlinear, and dynamic, the ultimate ventilatory response elicited by a given stimulus is not easy to predict based on the reflex effects of individual receptor groups studied in isolation. A full understanding of the role that sensory receptors play in ventilatory control requires information concerning interactions among receptor groups and with other elements of the control system. The complexity of the problem and the lack of a uniform definition of the term "interaction" has hindered research in this area. An interaction is defined as a nonadditive relationship between independent inputs to the system. Within this definition, five domains of interaction are described. 1) Algebraic interactions occur in ventilation and/or its components because of their multiplicative and nonlinear relationship. 2) Closed-loop interactions occur because of the prevalence of feedback loops within the respiratory control system. 3) Neural interactions reflect central nervous system integration of simultaneous receptor inputs and are demonstrated when feedback loops are opened. Three subdomains of neural interactions are defined: modulatory, dynamic, and range-specific neural interactions. 4) Mechanical interactions result from nonlinear transformations of motoneuron output into mechanical actions. 5) Adaptive interactions occur when paired receptor or modulatory inputs alter future responses. To understand the role of any sensory receptor group in ventilatory control, it is necessary to define its interactions with other control system elements in each of these domains. Understanding the mechanisms of these interactions requires detailed information about the physical system subserving ventilatory control (mechanics and gas exchange) and the relevant properties of the neural network coordinating their actions.

Adaptation, Physiological↗
PubMed2002

Characterizing instantaneous phase relationships in whole-brain fMRI activation data.

Typically, fMRI data is processed in the time domain with linear methods such as regression and correlation analysis. We propose that the theory of phase synchronization may be used to more completely understand the dynamics of interacting systems, and can be applied to fMRI data as a novel method of detecting activation. Generalized synchronization is a phenomenon that occurs when there is a nonlinear functional relationship present between two or more coupled, oscillatory systems, whereas phase synchronization is defined as the locking of the phases while the amplitudes may vary. In this study, we developed an application of phase synchronization analysis that is appropriate for fMRI data, in which the phase locking condition is investigated between a voxel time series and the reference function of the task performed. A synchronization index is calculated to quantify the level of phase locking, and a nonparametric permutation test is used to determine the statistical significance of the results. We performed the phase synchronization analysis on the data from five volunteers for an event-related finger-tapping task. Functional maps were created that provide information on the interrelations between the instantaneous phases of the reference function and the voxel time series in a whole-brain fMRI activation data set. We conclude that this method of analysis is useful for revealing additional information on the complex nature of the fMRI time series.

Adult↗
PubMed1993

Use of chaos theory and complex systems modeling to study alcohol effects on fetal condition.

A systems dynamics computer model to predict birth complications for individual pregnant woman was developed from prospectively conducted data on a database of 125 pregnant women. The model is based upon nonlinear mathematics derived from the study of chaos and complex systems. The model was then tested prospectively on 27 additional pregnant women, making predictions on their level of obstetrical risk. The model was refined until it correctly predicted the outcomes of all 125 cases in the development database. Prediction was made with an accuracy of 25/27 cases for the prospective test cases. Predictions were made for fetal condition at birth, presence or absence of operative delivery, and presence or absence of uterine dysfunction. Then the model was used to explore alcohol use during pregnancy. A reasonable spread of alcohol use existed among subjects, allowing consideration of alcohol effects. Alcohol was found to have differential effects on fetal condition at birth depending upon the presence or absence of high levels of psychosocial stress and the use of other substances. In all cases, the effect of alcohol was only evident after the 10 drinks per week level was reached. For the high-stress/one other substance group, there could be an 18-fold effect on fetal condition at birth. For the low-stress/one other substance group, the effect was only 3-fold, and for the alcohol alone group, the effect was negligible.

Alcohol Drinking↗
PubMed2003

[Method of heart rate variability analysis and its application in the field of space medicine].

The analysis of Heart Rate Variability (HRV), as a noninvasive method in detecting function hearts has been applied widely and is a hot spot for ECG signal processing for its capability to assess function of autonomic nervous system and intrinsic dynamic mechanism of heart quantitatively, and to explain and predict the heart movements. In the present, the method of analysis of HRV signal mainly lies in linear analysis and nonlinear analysis. Research progress of several methods of HRV analysis is presented. And expectation is presented to the analysis of HRV signal and its application in the field of space medicine in the future.

Aerospace Medicine↗
PubMed2006

Numerical method for coherent electron dynamics with position-dependent effective-mass distributions in semiconductor heterostructures.

We develop a numerical scheme for solving the time-dependent Kohn-Sham equation in semiconductor heterostructures. Based on the efficient and accurate method recently proposed by Watanabe and Tsukada [Phys. Rev. E 65, 036705 (2002)], an extension is made for treating effective-mass mismatch between different semiconductor materials. A demonstrative calculation shows that the energy of the quantum-well state is accurately conserved during the time-evolution calculation with the present method. Examples under the existence of Hartree and exchange-correlation interactions are also shown as demonstrations of nonlinear electron dynamics in quantum wells. The present method is particularly useful for analyzing nonlinear coherent charge oscillations in semiconductor quantum wells, taking into account many-body effects.

Journal Article↗
PubMed2000

Single-particle tracking: Brownian dynamics of viscoelastic materials.

A unifying theoretical framework for analyzing stochastic data from single-particle tracking (SPT) in viscoelastic materials is presented. A generalization of the bead-spring model for linear polymers is developed from a molecular point of view and from the standpoint of phenomenological linear viscoelasticity. The hydrodynamic interaction in the former is identified as the dashpots in the latter. In elementary terms, the intimate correspondence between time-correlation of the fluctuation measurements and transient relaxation kinetics after perturbation is discussed, and the central role of the fluctuation-dissipation relation is emphasized. The work presented here provides a bridge between the microscopic and the macroscopic views of linear viscoelastic biological materials, and is applicable to membrane protein diffusion, linear DNA chain dynamics, and mechanics of intracellular cytoskeletal networks.

Biopolymers↗
PubMed1999

Anaerobic threshold measurement using dynamic neural network models.

This paper deals with the subject of anaerobic threshold measurements for athletes involved in aerobic or aerobic/anaerobic sports. Traditionally, anaerobic threshold has been determined using invasive tests or using a non-invasive technique using steady-state heart-rate/work rate data. Non-invasive tests have the advantage of not requiring specialised equipment, but the acquisition of steady-state information can be problematic. This paper demonstrates how dynamical data can be used to accurately determine the steady-state heart-rate/work-rate curve (SSHW curve) using neural network dynamic models.

Anaerobic Threshold↗
PubMed2001

Modeling temporal and compressive properties of the normal and impaired auditory system.

Three modifications of a psychoacoustically and physiologically motivated processing model [Dau et al., J. Acoust. Soc. Am. 102 (1997a) 2892-2905] are presented and tested. The modifications aim at simulating sensorineural hearing loss and incorporate a level-dependent peripheral compression whose properties are affected by hearing impairment. Model 1 realizes this difference by introducing for impaired listeners an instantaneous level-dependent expansion prior to the adaptation stage of the model. Model 2 and Model 3 realize a level-dependent compression with time constants of 5 and 15 ms, respectively, for normal hearing and a reduced compression for impaired hearing. In Model 2, the compression occurs after the envelope extraction stage, while in Model 3, envelope extraction follows compression. All models account to a similar extent for the recruitment phenomenon measured with narrow-band stimuli and for forward-masking data of normal-hearing and hearing-impaired subjects using a 20-ms, 2-kHz tone signal and a 1-kHz-wide bandpass noise masker centered at 2 kHz. A clear difference between the different models occurs for the processing of temporally fluctuating stimuli. A modulation-rate-independent increase in modulation-response level for simulating impaired hearing is only predicted by Model 1 while the other two models realize a modulation-rate-dependent increase. Hence, the predictions of Model 2 and Model 3 are in conflict with the results of modulation-matching experiments reported in the literature. It is concluded that key properties of sensorineural hearing loss (altered loudness perception, reduced dynamic range, normal temporal properties but prolonged forward-masking effects) can effectively be modeled by incorporating a fast-acting expansion within the current processing model prior to the nonlinear adaptation stage. Based on these findings, a model of both normal and impaired hearing is proposed which incorporates a fast-acting compressive nonlinearity, representing the cochlear nonlinearity (which is reduced in impaired listeners), followed by an instantaneous expansion and the nonlinear adaptation stage which represent aspects of the retro-cochlear information processing in the auditory system.

Auditory Pathways↗
PubMed2003

Application of partial observability for analysis and design of synchronized systems.

Synchronization in identical drive-response systems is a problem that can be cast in an observer design framework. In this paper we extend this approach by studying the analysis/design of partial synchronization by means of observer theory. In doing so, we introduce the concept of partial observer--an observer to reconstruct a part of the system state vector. It is also shown how the observability condition can be utilized to analyze the dynamics in an array of coupled identical systems.

Algorithms↗
PubMed2004

Dynamics of nonequilibrium membrane bud formation.

The dynamical response of a lipid membrane to a local perturbation of its molecular symmetry is investigated theoretically. A density asymmetry between the two membrane leaflets is predominantly released by in-plane lipid diffusion or membrane curvature, depending upon the spatial extent of the perturbation. It may result in the formation of nonequilibrium structures (buds), for which a dynamical size selection is observed. A preferred size in the microm range is predicted, as a signature of the crossover between membrane and solvent dominated dynamical membrane response.

Cell Membrane↗
PubMed1996

Brain chaos and computation.

A model cortex comprising two interconnected spatiotemporal chaotic networks is considered. The system is able to discriminate between different patterns presented as input, and also detect motion and measure its velocity. Such cognitive processes are only possible if an "attentive" state arises in one of the networks, as a result of the stabilization of a periodic orbit out of the chaotic dynamics.

Attention↗
PubMed2005

Dynamic spatiotemporal synaptic integration in cortical neurons: neuronal gain, revisited.

Gain modulation is a ubiquitous phenomenon in cortical neurons, providing flexibility to operate under changing conditions. The prevailing view is that this modulation reflects a change in the relationship between mean input and output firing rate brought about by variation in neuronal membrane characteristics. An alternative mechanism is proposed for neuronal gain modulation that takes into account the capability of cortical neurons to process spatiotemporal synaptic correlations. Through the use of numerical simulations, it is shown that voltage-gated and leak conductances, membrane potential, noise, and input firing rate modify the sensitivity of cortical neurons to the degree of temporal correlation between their synaptic inputs. These changes are expressed in a change of the temporal window for synaptic integration and the range of input correlation over which response probability is graded. The study also demonstrates that temporal integration depends on the distance between the inputs and that this interplay of space and time is modulated by voltage-gated and leak conductances. Thus, gain modulation may reflect a change in the relationship between spatiotemporal synaptic correlations and output firing probability. It is further proposed that by acting synergistically with the network, dynamic spatiotemporal synaptic integration in cortical neurons may serve a functional role in the formation of dynamic cell assemblies.

Animals↗
PubMed2004

Stability and the maintenance of balance following a perturbation from quiet stance.

We investigate stability and the maintenance of balance with the use of tools from dynamical systems. In particular we investigate the application of such tools to the study of the ground reaction forces resulting from an athlete being perturbed from quiet stance. We develop a nonlinear model consisting of a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. This model contains a basin of attraction bound by a closed curve which we call the critical curve. It is only inside this curve that perturbations can be corrected, with the orbit spiraling onto an attractor corresponding to quiet stance. We show how the critical curve and also the strength of the attractor found in the basin of attraction can be fit to model the experimental data (time series) for an individual athlete. We also discuss how our model can be used to identify nonsymmetric behavior caused by muscle imbalances and differences in the ranges of motion on either side of the body.

Adaptation, Physiological↗