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At least 685 records · Page 38Linked to original sources
PubMed2003

Temporal integration by calcium dynamics in a model neuron.

The calculation and memory of position variables by temporal integration of velocity signals is essential for posture, the vestibulo-ocular reflex (VOR) and navigation. Integrator neurons exhibit persistent firing at multiple rates, which represent the values of memorized position variables. A widespread hypothesis is that temporal integration is the outcome of reverberating feedback loops within recurrent networks, but this hypothesis has not been proven experimentally. Here we present a single-cell model of a neural integrator. The nonlinear dynamics of calcium gives rise to propagating calcium wave-fronts along dendritic processes. The wave-front velocity is modulated by synaptic inputs such that the front location covaries with the temporal sum of its previous inputs. Calcium-dependent currents convert this information into concomitant persistent firing. Calcium dynamics in single neurons could thus be the physiological basis of the graded persistent activity and temporal integration observed in neurons during analog memory tasks.

Action Potentials↗
PubMed2001

Estimating Lyapunov exponents in biomedical time series.

Among nonlinear dynamical invariants, determination of the largest Lyapunov exponent is well suited to positive identification of chaos in observed time series. When analyzing the dynamics of biomedical series, such as an electro-encephalogram (EEG), model-based methods should be used. Moreover, in the absence of any well founded theoretical model, and because of unexplained variability in the data, candidate models must provide for a stochastic component. Here we use nonlinear autoregressive stochastic modeling to estimate the dominant Lyapunov exponent in an EEG series and compute confidence intervals from surrogate data. The results are found to differ from those of approaches which aim at deleting noise prior to analysis.

Algorithms↗
PubMed2004

Three-dimensional chaotic flows with discrete symmetries.

There are a number of well-known three-dimensional flows with quadratic nonlinearities, which demonstrate a chaotic behavior. The most popular among them are Lorenz and Rössler systems. Using an exhaustive computer search, J. Sprott found 19 examples of chaotic flows with either five terms and two quadratic nonlinearities or six terms and one nonlinearity [Phys. Rev. E 50, R647 (1994)]. In contrast to this approach, we use symmetry-related considerations to construct types of chaotic flows with an arbitrary dimension. The discussion is based on our previous work devoted to nonlinear dynamics of the physical systems with discrete symmetries [see Physica D 117, 43 (1998), etc.]. Here, we present all possible chaotic flows with quadratic nonlinearities which are invariant under the action of 32 point groups of crystallographic symmetry. These systems demonstrate a typical chaotic behavior as well as general dynamical properties of nonlinear systems with discrete symmetries. In particular, we found a dynamical system with the point symmetry group D2 which seems to be more simple and more elegant than those by Lorenz and Rössler.

Journal Article↗
PubMed1999

Dynamic characteristics of laser-Doppler flux in normal individuals and patients with Raynaud's phenomenon before and after treatment with nifedipine under different thermal conditions.

The study was aimed at choosing an appropriate characteristic of laser-Doppler flux (LDF) data for (1) distinguishing patients with Raynaud's disease from normal controls and (2) evaluating the effect of nifedipine under different thermal conditions. We checked the reliability of three characteristics of nonlinear dynamics as statistical dimension Ds, correlation dimension D2 and power-law index PLI. Their values depended heavily on the thermal condition. The most reliable characteristics that enabled us to distinguish the patients from normal controls and the effect of nifedipine under definite thermal condition proved to be Ds and PLI. The latter is simple for computation and is thus recommendable for clinical practice. Ds and PLI were higher in patients with Raynaud's compared to normal controls and diminished during the transitions from low to high temperature. However, the characteristics used were unable to distinguish significantly Raynaud's I from Raynaud's II patients.

Algorithms↗
PubMed2005

Fractals analysis of cardiac arrhythmias.

Heart rhythms are generated by complex self-regulating systems governed by the laws of chaos. Consequently, heart rhythms have fractal organization, characterized by self-similar dynamics with long-range order operating over multiple time scales. This allows for the self-organization and adaptability of heart rhythms under stress. Breakdown of this fractal organization into excessive order or uncorrelated randomness leads to a less-adaptable system, characteristic of aging and disease. With the tools of nonlinear dynamics, this fractal breakdown can be quantified with potential applications to diagnostic and prognostic clinical assessment. In this paper, I review the methodologies for fractal analysis of cardiac rhythms and the current literature on their applications in the clinical context. A brief overview of the basic mathematics of fractals is also included. Furthermore, I illustrate the usefulness of these powerful tools to clinical medicine by describing a novel noninvasive technique to monitor drug therapy in atrial fibrillation.

Adult↗
PubMed1993

Bifurcations of the respiratory pattern produced with phasic vagal stimulation in the rat.

Geometric methods from nonlinear dynamics are employed to evaluate dynamic processing of vagal afferent information by the respiratory central pattern generator (RCPG). While measuring airflow and diaphragm EMG, we applied brief electrical stimuli (40- to 130-ms duration) to one afferent vagus of bilaterally vagotomized urethan-anesthetized rats during every breath at various phases of the respiratory cycle. Stimuli applied during early or late inspiration of every breath evoke highly predictable one-dimensional responses: reversible (graded inhibition) or irreversible (off-switching) inhibition of inspiratory activity, respectively. Stimulation during midinspiration produces higher-dimensional oscillations that wander unpredictably over a continuum of graded inhibition and off-switching; "spiral" attractors and "horseshoe" return maps at this phase are characteristic of Silnikov's bifurcation. Stimuli applied during early expiration always prolonged expiratory duration, but those delivered during midexpiration evoked unpredictable wandering between prolongations and shortening of expiratory duration. A narrow time window surrounds the expiratory-inspiratory (E-I) transition, where stimuli elicit either breaths of short duration and low amplitude (irreversible E-I transition, decreased total respiratory cycle duration) or transient bursts of inspiratory activity at the E-I transition followed by a prolonged breath (reversible E-I transition, increased total respiratory cycle duration). We conclude that RCPG "gating" of and adaptation to vagal feedback combine to produce complex breath-to-breath dynamics in the rat that are consistent with low-dimensional chaos.

Anesthesia↗
PubMed2005

The cingulate as a catalyst region for global dysfunction: a dynamical modelling paradigm.

The anterior cingulate (AC) often exhibits both structural and functional abnormalities in affective disorders. Neither the cause for this vulnerability nor its effect on behaviour is known. Due to its extensive connectivity, minor output changes from the AC may exert widespread consequences. A causal model describing coupling coefficients (effective connectivity) among several brain regions in healthy subjects performing a memory task inspired our work. This stationary causal analysis provides a theoretical framework for our nonlinear dynamical models. We tested the effects of global and local perturbations upon stability of a systems-level neural network of interconnected brain regions. Interactions between regions, represented by path coefficients, were modelled using connectivity matrices. We found that both characteristic behaviour and response to perturbation differed in networks representing perceptual matching and long-delay conditions. Owing to the highly interconnected character of the networks, activation of a few areas was sufficient to trigger characteristic patterns of behaviour. However, only perturbation of key regions resulted in global dysfunction. Likewise, recovery of function was possible by increasing output from some, but not all, regions. We suggest for this recovery to be context specific, conditional on the task, integrity of other regions and global properties such as neuronal excitability.

Biological Clocks↗
PubMed2004

Control of the pathogenic conformational change of the prion protein by an attractor of low order.

The molecular vibrations of the infectious part of the prion protein has been studied by the methods of nonlinear dynamics using NMR-data of the protein in solution to test a new hypothesis for the nature of the pathogenic isomerization. The result was that the conformational change accompanying the conversion of the physiological form (PrP(c)) to the pathological (PrP(Sc)) one displays the characteristic properties of an attractor of the dimension 2.7+/-0.2, whereas the dimensions of the C-terminal, potentially infectious half of the physiological and the pathological forms are 5.3+/-0.3 and 3.9+/-0.3, resp. A plot of the average RMS of the vibrations per atom of the amino acids along the peptide chain suggests a pivotal role of E(167) and D(196). The vibrations of these residues are strongly dampened by the pathogenic conformational change suggesting that the neutralization to the hydrophobic form facilitates the isomerisation. This observation lends credence to the hypothesis that the pathological conformational change is released by the charge neutralization of the abundant, basic side chains lining the cleft in PrP(c) by a pK-shift caused by a transient ion flux from an action potential or by an RNA ligand. The attractor ensures that only the two conformers PrP(c) and PrP(Sc)-monomer, which are switching the polyadenylation of mRNA for synaptic proteins on and off, prevail. Some xenogenic PrP(Sc) seem to have a tendency to polymerize irreversibly, which is likely to inhibit the translation, thus killing neurons. The autocorrelation function is dampened (long correlation length for the 3 cases), the Poincaré plot seems to show the cross-section of a dense attractor for PrP(Sc) and a loose one for PrP(c), the Lyapunov exponent is positive and the power spectrum is broad. The Hurst plots of PrP(Sc) and PcP(c) show monofractality. The attractor hypothesis offers a supplement, or an alternative, to the current, inconclusive ideas of the nature of the PrP isomerization. The identification of the control factors may permit the reversal of the fatal conformational change. The dynamic parameters were checked by the interpoint distance method of Judd and by an analysis of the Fourier-transformed data.

Animals↗
PubMed2003

Signatures of deterministic chaos in dyslipidemic erythrocytes under shear stress.

The erythrocytes deformation under shear stress, the viscoelastic properties and the effects observed on healthy donors and on dyslipidemic patients are investigated from the point of view of nonlinear dynamics. Finally it is suggested that the different results obtained could be useful with regard to pathophysiological disturbances and their treatment.

Biophysical Phenomena↗
PubMed1994

Decrease of complexity in EEG as a symptom of depression.

Nonlinear dynamic analysis provides new methods for the processing of the electroencephalogram (EEG). We demonstrate here that the EEG dynamics of major depressive subjects is more predictable, that is less complex, than that of control subjects. Moreover, the consequence of treatment upon the EEG dynamics seems to be dependent on the appearance of the illness. Although the specificity of this dynamic signature for different stages of depression is to be confirmed, the assumption of a strong link between a healthy system and a high level of complexity in dynamics is further supported.

Adult↗
PubMed2006

Separation of heart rate variability components of the autonomic nervous system by utilizing principal dynamic modes.

This work introduces a modified Principal Dynamic Modes (PDM) methodology using eigenvalue/eigenvector analysis to separate individual components of the sympathetic and parasympathetic nervous contributions to heart rate variability. We have modified the PDM technique to be used with even a single output signal of heart rate variability data, whereas the original PDMs required both input and output data. This method specifically accounts for the inherent nonlinear dynamics of heart rate control, which the current method of power spectrum density (PSD) is unable to do. Propranolol and atropine were administered to normal human volunteers intravenously to inhibit the sympathetic and parasympathetic activities, respectively. With separate applications of the respective drugs, we found a significant decrease in the amplitude of the waveforms that correspond to each nervous activity. Furthermore, we observed near complete elimination of these dynamics when both drugs were given to the subjects. Comparison of our method to the conventional low/high frequency ratio of PSD shows that PDM methodology provides much more accurate assessment of the autonomic nervous balance by separation of individual components of the autonomic nervous activities. The PDM methodology is expected to have an added benefit that diagnosis and prognostication of a patient's health can be determined simply via a non-invasive electrocardiogram.

Adult↗
PubMed1994

Chaos, self-organization, and psychology.

A variety of investigators in recent years have proposed models of psychological systems based on the concepts of chaos, nonlinear dynamics, and self-organization. Unfortunately, psychologists in general have little understanding of these important ideas. These terms are defined, and their relationships are discussed. The value of applying these concepts to psychological systems is demonstrated by exploring their utility in areas ranging from neuroscience to clinical psychology. Some of the difficulties in using nonlinear concepts and methodologies in empirical investigations are also discussed.

Animals↗
PubMed2003

Catastrophe and nursing turnover: nonlinear models.

Creating a culture of retention is one antidote to high costs of nurse turnover. However, nurse turnover behavior has proven to be largely uncertain and unpredictable. A new approach to analyzing nurse turnover attitudes and behavior is discussed. A cusp catastrophe nonlinear model of nurse turnover is presented as having usefulness for the prediction of turnover for managerial decision making in nursing care delivery systems. Viewing nursing from the perspective of nonlinear dynamics can create new strategies for effective and efficient nursing services.

Affect↗
PubMed1996

Dynamical entropy is conserved during cocaine-induced changes in fetal rat motor patterns.

Our previous studies demonstrated that the intra-cisternal (IC) administration of cocaine to fetal rats increased motor activity and decreased responsiveness to perioral stimulation. One explanation for these observations comes from the behavioral pharmacology of stimulant drugs: increased motor activity is often associated with a decrease in its variety. Previous power spectral transformation of this data suggests an alternative explanation: cocaine-induced hyperactivity fixates a new behavioral pattern with complexity equal to that of saline controls. We explore these possibilities using statistical techniques derived from studies of nonlinear dynamical systems, examining patterns of the total motor activity of the individual fetus as counts per 5 s interval on either gestational day E20 or E21 for 20 min following IC injections of saline, 2.5 or 10 mg/kg of cocaine. The results are consistent with a state in which increased spontaneous activity is associated with the emergence of a new dynamical pattern which conserves entropy and provides experimental support for a fundamental conservation-variational relation, hT approximately equal to lambda 1 x DR, that has been proven for abstract models of chaotic dynamical systems. A multivariate analysis of variance (MANOVA) followed by appropriate analyses of variance (ANOVAs) and pairwise comparisons revealed that, whereas cocaine induced increases in the total amount of motor activity, the rate of increase in the variety of new sequences in activity counts over time did not change with treatment and age conditions. This invariant is quantified by an absence of change in topological entropy, delta hT = 0. The analyses also showed that, in order to maintain hT values, compensatory changes took place in the leading Lyapounov characteristic exponent, lambda 1 (the distance between sequential values 'stretched' along the increasing amplitudes of the variations) such that delta lambda 1 > 0, and the correlation dimension, DR (the hierarchical range of possible values, 'complicated clustering') was reduced, so that delta DR < 0. Our findings are consistent with the idea that the association between cocaine-induced increases in activity and decreases in adaptive response are not due to the dynamical entropy loss of decreased behavioral variety, but are rather the result of competitive interference by a drug-induced, equally complex, new pattern of spontaneous behavior.

Animals↗
PubMed2000

Bifurcation in a simple model of the cardiovascular system.

A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the alpha-sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the beta-sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

Blood Pressure↗
PubMed2005

Scaling up population dynamics: integrating theory and data.

How to scale up from local-scale interactions to regional-scale dynamics is a critical issue in field ecology. We show how to implement a systematic approach to the problem of scaling up, using scale transition theory. Scale transition theory shows that dynamics on larger spatial scales differ from predictions based on the local dynamics alone because of an interaction between local-scale nonlinear dynamics and spatial variation in density or the environment. Based on this theory, a systematic approach to scaling up has four steps: (1) derive a model to translate the effects of local dynamics to the regional scale, and to identify key interactions between nonlinearity and spatial variation, (2) measure local-scale model parameters to determine nonlinearities at local scales, (3) measure spatial variation, and (4) combine nonlinearity and variation measures to obtain the scale transition. We illustrate the approach, with an example from benthic stream ecology of caddisflies living in riffles. By sampling from a simulated system, we show how collecting the appropriate data at local (riffle) scales to measure nonlinearities, combined with measures of spatial variation, leads to the correct inference for dynamics at the larger scale of the stream. The approach provides a way to investigate the mechanisms and consequences of changes in population dynamics with spatial scale using a relatively small amount of field data.

Animals↗
PubMed2001

A hybrid input-output approach to model metabolic systems: an application to intracellular thiamine kinetics.

Models of the dynamics of complex metabolic systems offer potential benefits to the deep comprehension of the system under study as well as for the performance of certain tasks. Unfortunately, dynamic modeling of a great deal of metabolic systems may be problematic due to the incompleteness of the available knowledge about the underlying mechanisms and to the lack of an adequate observational data set. In theory, a valid alternative to classical structural modeling through ordinary differential equations could be represented by input-output approaches. But, in practice, such methods, which learn the nonlinear dynamics of the system from input-output data, fail when the experimental data set is poor either in size or in quality. Such a situation is not rare in the case of metabolic systems. This paper deals with a hybrid approach which aims at overcoming the problems addressed above. More specifically, it allows us to solve the identification problems of the intracellular thiamine kinetics in the intestine tissue. The method, which is half way between the structural and input-output approach, uses the outcomes of the simulation of a qualitative structural model to build a good initialization of a fuzzy system identifier. Such an initialization allows us to efficiently cope with both the incompleteness of knowledge and the inadequacy of the available data set, and to derive an input-output model of the intracellular thiamine kinetics in the intestine tissue. The comparison of the predictions of the intracellular thiamine kinetics obtained by the application of such a model with those obtained by traditional approaches, namely compartmental models, neural networks, and fuzzy systems, highlighted a better performance of our model. As the structural assumptions are relaxed, we obtained a model slightly less informative than a purely structural one but robust enough to be used as a simulator. The paper also discusses the interpretative potential offered by such a model, as tested on diabetic subjects.

Animals↗