Simulation of nonstationary phenomena in atmospheric-pressure glow discharge

Nonstationary processes in atmospheric-pressure glow discharge manifest themselves in spontaneous transitions from the normal glow discharge into a spark. In the experiments, both so-called completed transitions in which a highly conductive constricted channel arises and incomplete transitions accompanied by the formation of a diffuse channel are observed. A model of the positive column of a discharge in air is elaborated that allows one to interpret specific features of the discharge both in the stationary stage and during its transition into a spark and makes it possible to calculate the characteristic oscillatory current waveforms for completed transitions into a spark and aperiodic ones for incomplete transitions. The calculated parameters of the positive column in the glow discharge mode agree well with experiment. Data on the densities of the most abundant species generated in the discharge (such as atomic oxygen, metastable nitrogen molecules, ozone, nitrogen oxides, and negative oxygen ions) are presented.     

Simulation of chaotic EEG patterns with a dynamic model of the olfactory system

The main parts of the central olfactory system are the bulb (OB), anterior nucleus (AON), and prepyriform cortex (PC). Each part consists of a mass of excitatory or inhibitory neurons that is modelled in its noninteractive state by a 2nd order ordinary differential equation (ODE) having a static nonlinearity. The model is called a KO_e or a KO_t set respectively; it is evaluated in the open loop state under deep anesthesia. Interactions in waking states are represented by coupled KO sets, respectivelyKI _e (mutual excitation) andKI _i (mutual inhibition). The coupledKI _e andKI _i sets form aKII set, which suffices to represent the dynamics of theOB, AON, andPC separately. The coupling of these three structures by both excitatory and inhibitory feedback loops forms aKIII set. The solutions to this high-dimensional system ofODEs suffice to simulate the chaotic patterns of the EEG, including the normal low-level background activity, the high-level relatively coherent bursts of oscillation that accompany reception of input to the bulb, and a degenerate state of an epileptic seizure determined by a toroidal chaotic attractor. An example is given of the Ruelle-Takens-Newhouse route to chaos in the olfactory system. Due to the simplicity and generality of the elements of the model and their interconnections, the model can serve as the starting point for other neural systems that generate deterministic chaotic activity.Supported by a grant MH06686 from the National Institute of Mental Health     

Identification of nonstationary dynamics in physiological recordings

We present a novel framework for the analysis of time series from dynamical systems that alternate between different operating modes. The method simultaneously segments and identifies the dynamical modes by using predictive models. In extension to previous approaches, it allows an identification of smooth transition between successive modes. The method can be used for analysis, diagnosis, prediction, and control. In an application to EEG and respiratory data recorded from humans during afternoon naps, the obtained segmentations of the data agree with the sleep stage segmentation of a medical expert to a large extent. However, in contrast to the manual segmentation, our method does not require a priori knowledge about physiology. Moreover, it has a high temporal resolution and reveals previously unclassified details of the transitions. In particular, a parameter is found that is potentially helpful for vigilance monitoring. We expect that the method will generally be useful for the analysis of nonstationary dynamical systems, which are abundant in medicine, chemistry, biology and engineering. Received: 5 May 1999 / Accepted in revised form: 28 December 1999     

A Pharmacokinetics-Neural Mass Model (PK-NMM) for the Simulation of EEG Activity during Propofol Anesthesia

Modeling the effects of anesthetic drugs on brain activity is very helpful in understanding anesthesia mechanisms. The aim of this study was to set up a combined model to relate actual drug levels to EEG dynamics and behavioral states during propofol-induced anesthesia. We proposed a new combined theoretical model based on a pharmacokinetics (PK) model and a neural mass model (NMM), which we termed PK-NMM—with the aim of simulating electroencephalogram (EEG) activity during propofol-induced general anesthesia. The PK model was used to derive propofol effect-site drug concentrations (C_eff) based on the actual drug infusion regimen. The NMM model took C_eff as the control parameter to produce simulated EEG-like (sEEG) data. For comparison, we used real prefrontal EEG (rEEG) data of nine volunteers undergoing propofol anesthesia from a previous experiment. To see how well the sEEG could describe the dynamic changes of neural activity during anesthesia, the rEEG data and the sEEG data were compared with respect to: power-frequency plots; nonlinear exponent (permutation entropy (PE)); and bispectral SynchFastSlow (SFS) parameters. We found that the PK-NMM model was able to reproduce anesthesia EEG-like signals based on the estimated drug concentration and patients’ condition. The frequency spectrum indicated that the frequency power peak of the sEEG moved towards the low frequency band as anesthesia deepened. Different anesthetic states could be differentiated by the PE index. The correlation coefficient of PE was 0.80±0.13 (mean±standard deviation) between rEEG and sEEG for all subjects. Additionally, SFS could track the depth of anesthesia and the SFS of rEEG and sEEG were highly correlated with a correlation coefficient of 0.77±0.13. The PK-NMM model could simulate EEG activity and might be a useful tool for understanding the action of propofol on brain activity.     

The flux ratio equation under nonstationary conditions

Summary The time dependent (i.e., nonstationary) unidirectional fluxes through a multilayered system consisting of sandwiched layers of arbitrary composition and exhibiting arbitrary potential and resistance profiles have been calculated, assuming that the flux is governed by the Smoluchowski equation (i.e., a flux resulting from a diffusion process superimposed upon a migration and/or a convection process, where part of the latter may arise from an active transport process). It is shown that during the building up of the concentration profile of the isotope inside the system towards the stationary value the ratio between the two oppositely directed, time-dependent unidirectional fluxes is, from the very first appearance of the isotope in the surrounding solutions, equal to the value of the stationary flux ratio. The practical implications of this result are discussed.     

The problem of nonstationary ion fluxes in excitable membranes

Time-dependent electrodiffusion through a membrane is analysed within a simple model treating the boundary-layers in a consistent manner. It is shown that time-independent reversal potentials for the ion fluxes exist only under steady-state conditions. We argue that this result holds very generally. Therefore nonstationary effects like ion storage and depletion inside the membrane should not contribute to the phenomena of excitability.Glossary of Symbols A _mv [V] functional cf. Equation (3) - C membrane capacitance - d one half the thickness of the membrane - F[V] functional cf. Equation (1) - g _i electrochemical potential inside membrane - g _i electrochemical potentials outside membrane at x ±d, respectively - i (index) refers to i-th ionic species - J electric current across membrane - j = j ^} = j ^< current density measured by external electrodes - j _i (x) current density inside membrane in x-direction - j _i ^inst(x) instantaneous current density - J _i ^stat steady-state current density - k Boltzmann constant - m (index) is used in Sec. 2 to denote the independent diffusion currents - n ^< ionic strength of electrolyte at x = - - n _i density of ions inside membrane - n _i density of ions outside membrane at x = ±, respectively - Q charge per unit area of boundary layers at x ± d, respectively - Q ₀ fixed charge per unit area of membrane - q elementary charge - q _i ionic charges - T temperature - it time - V membrane potential (= (-)-()) - V _i Nernst potential - V potential drops inside boundary layers (can be neglected, see Appendix II) - V ^± potential steps at x = ± d, cf. Equation (29) - V ₀ = V ^–-V ⁺ - w _i activation energy inside membrane - x spatial coordinate perpendicular to membrane - y, z spatial coordinates parallel to membrane - dielecric constant - ₀ dielectric constant of electrolyte solution ( 80) - _m dielectric constant of membrane ( 5) - (x) electrostatic potential - charge density of boundary layers - ⁰ fixed charge density inside membrane - spatial average, cf. Equation (12)     

Interpreting power spectra from nonstationary membrane current fluctuations

It is often desirable to characterize membrane current fluctuations from ionic channels under conditions in which the mean current and the variance of the fluctuations change with time. A simple theory is developed that relates the power spectrum to the channel characteristics under such nonstationary conditions, assuming that the mean current time-course has been removed from the fluctuation records. Strategies for removing the mean time-course are discussed, the spectra are calculated from simulated channel fluctuations for comparison with the theory.     

Autoregression models of EEG

This paper considers the properties of parameters (natural frequencies and damping coefficients) obtained from segment-by-segment autoregression analysis of ECoG of rat. The use of a reference signal as control for parameter estimate errors, and multiple regression analyses indicate that the dependencies among parameters calculated from ECoG in the alert (desynchronised) state are of a form consistent with imposition of time-invariance assumptions (implicit in autoregression) on an inherently non-stationary, multimodal, linear and near-equilibrium “thermal” process.     

脑电信息处理

脑电信息处理是脑功能研究重要组成部分。本文介绍了脑电信息处理的前沿领域,包括诱发电位、事件相关电位（ＥＲＰ）、正弦调制光（声）诱发脑电、４０ＨｚＥＲＰ和脑电非线笥动力学研究,并论及了认知活动与分形维数的关系。     

Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents

We assessed on Monte-Carlo simulated excitatory post-synaptic currents the ability of autoregressive (AR)-model fitting to evaluate their fluctuations. AR-model fitting consists of a linear filter describing the process that generates the fluctuations when driven with a white noise. Its fluctuations provide a filtered version of the signal and have a spectral density depending on the properties of the linear filter. When the spectra of the non-stationary fluctuations of excitatory post-synaptic currents were estimated by fitting AR-models to the segments of current fluctuations, assumed to be stationary and independent, the parameter and spectral estimates were scattered. The scatter was much reduced if the time-variant AR-models were fitted using stochastic adaptive estimators (Kalman, recursive least squares and least mean squares). The ability of time-variant AR-models to accurately fit the current fluctuations was monitored by comparing the fluctuations with predicted fluctuations, and by evaluating the model-learning rate. The median frequency of current fluctuations, which could be rapidly tracked and estimated from the individual quantal events (either Monte-Carlo simulated or recorded from pyramidal neurons of rat hippocampus), rose during the rise phase, before declining to a lower steady-state level during the decay phase of quantal event, whereas the variance showed a broad peak. The closing rate of AMPA channels directly affects the steady-state median frequency, whereas the transient peak can be modulated by a variety of factors—number of molecules released, ability of glutamate molecules to re-enter the synaptic cleft, diffusion constant of glutamate in the cleft and opening rate of AMPA channels. In each case, the effect on the amplitude and decay time of mEPSCs and on the current fluctuations differs. Each factor thus leaves its own kinetic fingerprint arguing that the contribution of such factors can be inferred from the combined kinetic properties of individual mEPSCs.     

Artificial neural network learning of nonstationary behavior in time series

We refine and complement a previously-proposed artificial neural network method for learning hidden signals forcing nonstationary behavior in time series. The method adds an extra input unit to the network and feeds it with the proposed profile for the unknown perturbing signal. The correct time evolution of this new input parameter is learned simultaneously with the intrinsic stationary dynamics underlying the series, which is accomplished by minimizing a suitably-defined error function for the training process. We incorporate here the use of validation data, held out from the training set, to accurately determine the optimal value of a hyperparameter required by the method. Furthermore, we evaluate this algorithm in a controlled situation and show that it outperforms other existing methods in the literature. Finally, we discuss a preliminary application to the real-world sunspot time series and link the obtained hidden perturbing signal to the secular evolution of the solar magnetic field.