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PubMed1999

Anticipating epileptic seizures in real time by a non-linear analysis of similarity between EEG recordings.

In a previous publication we showed that non-linear analysis can extract spatio-temporal changes of brain electrical activity prior to epileptic seizures. Here we describe a new method to analyze this long-term non-stationarity in the EEG by a measure of dynamical similarity between different parts of the time series. We apply this method to the study of a group of patients with temporal lobe epilepsy recorded intracranially during transitions to seizure. We show that the method, which can be implemented on a personal computer, can track in real time spatio-temporal changes in brain dynamics several minutes prior to seizure.

Algorithms↗
PubMed2003

Synchronization of reconstructed dynamical systems.

The problem of constructing synchronizing systems to observed signals is approached from a data driven perspective, in which it is assumed that neither the drive nor the response systems are known explicitly but have to be derived from the observations. The response systems are modeled by utilizing standard methods of nonlinear time series analysis applied to sections of the driving signals. As a result, synchronization is more robust than what might be expected, given that the reconstructed systems are only approximations of the unknown true systems. Successful synchronization also may be accomplished in cases where the driving signals result from nonlinearly transformed chaotic states. The method is readily extended and applied to limited real-time predictions of chaotic signals.

Models, Theoretical↗
PubMed1995

Influence of isometric loading on biceps EMG dynamics as assessed by linear and nonlinear tools.

The summed electrical discharges generated by a contracting skeletal muscle constitute a dynamic system conveying electromyographic (EMG) information indicative of muscle physiological status. "Steady states" of activity can be achieved with light loads, but with heavy loads the dynamic system experiences continuous status transitions that culminate in task failure. The present study was designed to assess the applicability of two mathematical tools, one linear and the other nonlinear, in addressing the time course of EMG alterations under different loading challenges. Surface EMGs of the biceps brachii muscle were recorded from 14 healthy human volunteers during light and heavy loadings, and task failure occurred at varying times among the subjects. Digitized EMG signals were analyzed by linear spectral analysis (fast Fourier transform) and nonlinear recurrence-plot analysis. With light loading, computed variables from both analyses gave "quasi-steady-state" values over time, with recurrence-plot analysis having the higher variance. With heavy loading, the nonlinear variable (%determinism) increased sooner and exhibited larger changes from control values than decreases in the linear variable (spectral center frequency). Experimental results support the conclusion that both analyses can be combined to give a fuller assessment of the biceps EMG during light or heavy loading. Implications for the detection of muscular fatigue are discussed.

Adult↗
PubMed2001

Determination of release and uptake parameters from electrically evoked dopamine dynamics measured by real-time voltammetry.

Quantifying mechanisms underlying extracellular signaling by the neurotransmitter dopamine (DA) is a difficult task, particularly in the complex extracellular microenvironment of the intact brain. In this study, two methods for evaluating release and uptake from DA dynamics monitored by real-time voltammetry are described. Both are based on a neurochemical model characterizing electrically evoked levels of DA as a balance between these opposing mechanisms. The theoretical basis of what is called here nonlinear regression and single curve analyses is given. Fitting simulated data tests the reliability of the methods. The two analyses are also compared with an experimental data set describing the effects of pharmacologically inhibiting the DA transporter in the caudate-putamen (CP) and nucleus accumbens (NAc). The results indicate that nonlinear regression and single curve analyses are suitable for quantifying release and uptake mechanisms underlying DA neurotransmission. Additionally, the most important experimental finding of this technical study was the independent confirmation of high affinity (approximately 0.2 microM) DA uptake in the intact striatum.

Action Potentials↗
PubMed1996

Low-dimensional chaotic attractors in the rat brain.

The existence of chaotic attractors for discrete time series, derived from the occurrences of spikes during electrophysiological recordings, was investigated. The time series included between 800 and 5200 points per analyzed record. The spike trains were recorded in the substantia nigra pars reticulata (n = 13) and in the auditory thalamus (n = 14). The experiments were performed on anesthetized rats during spontaneous activity and during auditory stimulation. According to standard methods of dynamical systems theory, an embedding space was constructed using delay coordinates. The embedding and correlation dimensions were computed by means of the correlation integrals. For 7 of 27 samples, a deterministic structure with a low embedding dimension (ranging between 2 and 6) and a correlation dimension between 0.14 and 3.3 could be determined. Evidence was found that the sensory stimulation may affect the chaotic behavior. Single units recorded simultaneously from the same electrode tip may display different chaotic dynamics, even with a similar time-locked response to the stimulus onset.

Acoustic Stimulation↗
PubMed2001

Macromolecular dynamics in living cell nuclei revealed by fluorescence redistribution after photobleaching.

Regulation and structural requirements of vital nuclear processes such as DNA replication, transcription, RNA processing and DNA repair inside the eukaryote nucleus are as yet poorly understood. Although a wealth of evidence exists pointing to a considerable degree of spatial organisation of chromatin and nuclear processes, there are still questions concerning the dynamics and interaction of nuclear proteins that remain unanswered. The cloning of the gene encoding the green fluorescent protein (GFP) has revolutionised the study of proteins in living cells. The expression of recombinant cDNA fusion plasmids of GFP and proteins of interest currently enables the investigation of those proteins in living cells. Time-lapse confocal microscopy as well as quantitative fluorescence methods such as fluorescence redistribution after photobleaching (FRAP) and fluorescence resonance energy transfer are widely applied to living cells expressing GFP fusion proteins. This review gives an overview of the current state of knowledge of nuclear structure and function. In particular, the different applications of FRAP technology to study the dynamics of GFP-tagged nuclear proteins will be summarised.

Cell Nucleus↗
PubMed2003

A note on estimation of dynamics of multiple gene expression based on singular value decomposition.

Recently, data on multiple gene expression at sequential time points were analyzed, using singular value decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model we formulate a non-linear optimization problem and present how to solve it numerically using standard MATLAB procedures. We use publicly available data to test the approach. For reader's convenience, we provide a straightforward, ready-to-use, procedure in MATLAB, which employs its standard features to analyze data of this kind. Then, we investigate the sensitivity of the method to missing measurements and its possibilities to reconstruct missing data. Also, we discuss the possible consequences of data regularization, called sometimes 'polishing', on the outcome of analysis, especially when model is to be used for prediction purposes. Summarizing we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics but may also lead to unexpected difficulties, like overfitting problems.

Algorithms↗
PubMed2004

Chaotic itinerancy in the oscillator neural network without Lyapunov functions.

Chaotic itinerancy (CI), which is defined as an incessant spontaneous switching phenomenon among attractor ruins in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case of an oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S. Uchiyama and H. Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neurodynamics. It is found that CI in neural nets can be understood as the intermittent dynamics of weakly destabilized chaotic retrieval solutions.

Animals↗
PubMed2000

Origin of complexity in multicellular organisms.

Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems can exhibit complex pattern formation with spontaneous cell differentiation. Such systems employ a "cooperative" use of resources and maintain a larger growth speed than simple cell systems, which exist in a homogeneous state and behave "selfishly." The relevance of the diversity of chemicals and reaction dynamics to the growth of a multicellular organism is demonstrated. Chaotic biochemical dynamics are found to provide the multipotency of stem cells.

Cell Communication↗
PubMed2001

Excitable media in a chaotic flow.

The response to a localized perturbation of an excitable medium under stirring by chaotic advection is investigated. It is found that below a critical stirring rate a localized perturbation produces a coherent global excitation of the system. For very slow stirring, however, the coherence of the global excitation is gradually lost. We propose a simple model to describe the effect of the flow on the excitable dynamics, and explain the observed behavior as a consequence of a steady excited filament state found in the reduced problem.

Algorithms↗
PubMed2001

Dual information representation with stable firing rates and chaotic spatiotemporal spike patterns in a neural network model.

Although various means of information representation in the cortex have been considered, the fundamental mechanism for such representation is not well understood. The relation between neural network dynamics and properties of information representation needs to be examined. We examined spatial pattern properties of mean firing rates and spatiotemporal spikes in an interconnected spiking neural network model. We found that whereas the spatiotemporal spike patterns are chaotic and unstable, the spatial patterns of mean firing rates (SPMFR) are steady and stable, reflecting the internal structure of synaptic weights. Interestingly, the chaotic instability contributes to fast stabilization of the SPMFR. Findings suggest that there are two types of network dynamics behind neuronal spiking: internally-driven dynamics and externally driven dynamics. When the internally driven dynamics dominate, spikes are relatively more chaotic and independent of external inputs; the SPMFR are steady and stable. When the externally driven dynamics dominate, the spiking patterns are relatively more dependent on the spatiotemporal structure of external inputs. These emergent properties of information representation imply that the brain may adopt a dual coding system. Recent experimental data suggest that internally driven and externally driven dynamics coexist and work together in the cortex.

Action Potentials↗
PubMed2006

Stable competitive dynamics emerge from multispike interactions in a stochastic model of spike-timing-dependent plasticity.

In earlier work we presented a stochastic model of spike-timing-dependent plasticity (STDP) in which STDP emerges only at the level of temporal or spatial synaptic ensembles. We derived the two-spike interaction function from this model and showed that it exhibits an STDP-like form. Here, we extend this work by examining the general n-spike interaction functions that may be derived from the model. A comparison between the two-spike interaction function and the higher-order interaction functions reveals profound differences. In particular, we show that the two-spike interaction function cannot support stable, competitive synaptic plasticity, such as that seen during neuronal development, without including modifications designed specifically to stabilize its behavior. In contrast, we show that all the higher-order interaction functions exhibit a fixed-point structure consistent with the presence of competitive synaptic dynamics. This difference originates in the unification of our proposed "switch" mechanism for synaptic plasticity, coupling synaptic depression and synaptic potentiation processes together. While three or more spikes are required to probe this coupling, two spikes can never do so. We conclude that this coupling is critical to the presence of competitive dynamics and that multispike interactions are therefore vital to understanding synaptic competition.

Action Potentials↗
PubMed2006

Complexity analysis of electrocardiographic signals.

Two types of electrocardiographic data series were investigated using appropriate tests based on a selection of semi-quantitative analysis algorithms. Distribution histograms, power spectra, auto-correlation functions, state-space portraits, Lyapunov exponents and wavelet transformations were applied to electrocardiograms of normal and stressed subjects. Statistical analysis using the Student's t-test revealed significant and non-significant alterations in stress-loaded cases compared to normal ones. Higher levels of adrenaline may account for a more complex dynamics (deterministic chaos) revealed in the stressed subjects.

Algorithms↗
PubMed1996

A quasi-linear constitutive relation for arterial wall materials.

In this work, considering that under physiological conditions the arteries are subjected to a large initial static deformation and additional small dynamical displacements are superimposed on this initial field, a Boltzman type of constitutive relation is presented for arterial wall materials. For its simplicity in the analysis, the material under investigation is assumed to be isotropic, incompressible and constitutionally nonlinear in Green deformation tensor but linear in the history of deformation tensor. The numerical values of elastic coefficients are obtained by comparing the analytical results with experiments by Simon et al. [Circ. Res. 30, 491-500 (1972)]. For the determination of viscoelastic coefficients we studied the propagation of torsional waves in a prestressed thin cylindrical tube and proposed a method of determining the viscoelastic coefficients.

Arteries↗
PubMed2004

Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy.

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance-based model to 2 variants of integrate-and-fire models. In the first variant (nonlinear integrate-and-fire model), parameters depend on the instantaneous membrane potential, whereas in the second variant, they depend on the time elapsed since the last spike [Spike Response Model (SRM)]. The direct reduction links features of the simple models to biophysical features of the full conductance-based model. To quantitatively test the predictive power of the SRM and of the nonlinear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70-80 percent of the spikes in the full model (with temporal precision of +/-2 ms) over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the SRM and the nonlinear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

Action Potentials↗
PubMed2005

Dynamical heterogeneity of suprachiasmatic nucleus neurons based on regularity and determinism.

The suprachiasmatic nucleus (SCN) is known to be the master biological clock in mammals. Despite the periodic mean firing rate, interspike interval (ISI) patterns of SCN neurons are quite complex and irregular. The aim of the present study was to investigate the existence of nonlinear determinism in the complex ISI patterns of SCN neurons. ISI sequences were recorded from 173 neurons in rat hypothalamic slice preparations using a cell-attached patch recording technique. Their correlation dimensions (D2) were estimated, and were then compared with those of the randomly-shuffled surrogate data. We found that only 16 neurons (16/173) exhibited deterministic ISI patterns of spikes. In addition, clustering analysis revealed that SCN neurons could be divided into two subgroups of neurons each having distinct values of coefficient of variation (CV) and skewness (SK). Interestingly, most deterministic SCN neurons (14/16) belonged to the group of irregularly spiking neurons having large CV and SK values. To see if the neuronal coupling mediated by the gamma-aminobutyric acid (GABA), the major neurotransmitter in the SCN, contributed to the deterministic nature, we examined the effect of the GABAA receptor antagonist bicuculline on D2 values of 56 SCN neurons. 8 SCN neurons which were originally stochastic became to exhibit deterministic characteristics after the bicuculline application. This result suggests that the deterministic nature of the SCN neurons arises not from GABAergic synaptic interactions, but likely from properties inherent to neurons themselves.

Action Potentials↗