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1.
Self-organized neuronal dynamics revealed by cortical α-rhythms occur as episodes, which are rarely observed without extraction
of the α-band from the other spectral components. Three episodes of an unusually long duration of 10 s, two with no signal
processing after data recording at the clinic, are described and show evidence of low-dimensional α-dynamics. The evidence
is gained from an analysis of scaled structures appearing in families of slope curves of the correlation integrals and is
checked against time reparametrization. The data for the two unprocessed 10-s episodes are used for a test of the methodology,
as well as a re-examination of the adequacy of the model of an autonomous dynamic system in steady state and of the concept
of an attractor in brain dynamics investigations. Striking evidence for the model’s inadequacy is provided by the episode
of subject S1. In this example five consecutive overlapping 6-s sections do show evidence for low-dimensional dynamics, whereas the 10-s
section containing those sections does not. The episode of subject 1 provides an example of α-activity which may involve self-organized
dynamics extending down to low frequencies. The system (the neuronal network) showing episodes of attractor-ruled dynamics,
under conditions of blurred and smoothly fading out evidence that it stays on an attractor, is designated as being ruled by
a ‘shadow-attractor’. This concept is compared with that of a ‘quasi-attractor’ introduced by H. Haken in studies of physiological
systems. One possible mechanism for the observed episodes is proposed, based on a time-dependent number of enslaved sub-systems.
Received: 28 June 1996 / Accepted in revised form: 27 May 1995 相似文献
2.
Periodic complexes (PC), occurring lateralised or diffuse, are relatively rare EEG phenomena which reflect acute severe brain
disease. The pathophysiology is still incompletely understood. One hypothesis suggested by the alpha rhythm model of Lopes
da Silva is that periodic complexes reflect limit cycle dynamics of cortical networks caused by excessive excitatory feedback.
We examined this hypothesis by applying a recently developed technique to EEGs displaying periodic complexes and to periodic
complexes generated by the model. The technique, non-linear cross prediction, characterises how well a time series can be
predicted, and how much amplitude and time asymmetry is present. Amplitude and time asymmetry are indications of non-linearity.
In accordance with the model, most EEG channels with PC showed clear evidence of amplitude and time asymmetry, pointing to
non-linear dynamics. However, the non-linear predictability of true PC was substantially lower than that of PC generated by
the model. Furthermore, no finite value for the correlation dimension could be obtained for the real EEG data, whereas the
model time series had a dimension slighter higher than one, consistent with a limit cycle attractor. Thus we can conclude
that PC reflect non-linear dynamics, but a limit cycle attractor is too simple an explanation. The possibility of more complex
(high dimensional and spatio-temporal) non-linear dynamics should be investigated.
Received: 26 February 1998 / Accepted in revised form: 24 August 1998 相似文献
3.
J. G. Taylor 《Biological cybernetics》1999,80(6):393-409
An extension to two dimensions of recent results in continuum neural field theory (CNFT) in one dimension is presented here.
Focus is placed on the treatment of receptive fields and of learning on afferent synapses to obtain topographic maps.
Received: 26 March 1997 / Accepted in revised form: 16 December 1998 相似文献
4.
Mark Shelhamer 《Biological cybernetics》1997,76(4):237-250
We discuss the estimation of the correlation dimension of optokinetic nystagmus (OKN), a type of reflexive eye movement.
Parameters of the time-delay reconstruction of the attractor are investigated, including the number of data points, the time
delay, the window duration, and the duration of the signal being analyzed. Adequate values are recommended. Digital low-pass
filtering causes the dimension to increase as the filter cutoff frequency decreases, in accord with a previously published
prediction. The stationarity of the correlation dimension is examined; the dimension appears to decrease over the course of
120 s of continuous stimulation. Implications for the reliable estimation of the dimension are considered. Several surrogate
data sets are constructed, based on both early (0–30 s) and late (100–130 s) OKN segments. Most of the surrogate data sets
randomize some aspect of the original OKN, while maintaining other aspects. Dimensions are found for all surrogates and for
the original OKN. Evidence is found that is consistent with some amount of deterministic and nonlinear dynamics in OKN. When
this structure is randomized in the surrogate, the dimension changes or the dimension algorithm ceases to converge to a finite
value. Implications for further analysis and modeling of OKN are discussed.
Received: 30 August 1996/Accepted in revised form: 13 November 1996 相似文献
5.
In recent years evidence has accumulated that ECG signals are of a nonlinear nature. It has been recognized that strictly
periodic cardiac rhythms are not accompanied by healthy conditions but, on the contrary, by pathological states. Therefore,
the application of methods from nonlinear system theory for the analysis of ECG signals has gained increasing interest. Crucial
for the application of nonlinear methods is the reconstruction (embedding) of the time series in a phase space with appropriate
dimension. In this study continuous ECG signals of 12 healthy subjects recorded during different sleep stages were analysed.
Proper embedding dimension was determined by application of two techniques – the false nearest neighbours method and the saturation
of the correlation dimension. Results for the ECG signals were compared with findings for simulated data (quasiperiodic dynamics,
Lorenz data, white noise) and for phase randomized surrogates. Findings obtained with the two approaches suggest that embedding
dimensions from 6 to 8 may be regarded as suitable for the topologically proper reconstruction of ECG signals.
Received: 7 June 1999 / Accepted in revised form: 10 December 1999 相似文献
6.
While learning and development are well characterized in feedforward networks, these features are more difficult to analyze
in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states
and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that
consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization.
Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through
Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally,
weight normalization may be better than constant weight decay for the development of multiple attractor states that allow
a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent
networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs.
Received: 27 April 1998 / Accepted in revised form: 16 March 1999 相似文献
7.
The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing
the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend
a novel model reduction method, based on “scales of dominance,” to multi-compartment models. We use this method to systematically
reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits
distinct modes of oscillation—tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals
dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two
and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model
over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single,
globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and
the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could
be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze
the interactions between different modes of activity. 相似文献
8.
B. Gasser M. Toussaint R. Luthringer J. P. Macher R. Cerf 《Journal of biological physics》1996,22(4):209-225
Attempts to demonstrate low-dimensional attractor behaviour in the analysis of electroencephalographic (EEG) signals meet with difficulties that in part stem from a departure from single-system dynamics. In order to address this problem, the -waves can be extracted by digital filtering or by wave separation; these two techniques are compared in order to specify the conditions in which finite impulse response (FIR) bandpass filters can be used. The comparison was made using 18 EEG records of 3 min duration under resting conditions (6 subjects, 3 records per subject: prior to apomorphine administration, then 90 min and 150 min post-treatment). No presence of low-dimensional dynamic episodes in -signals was observed without digital processing. Sixty 5 s sections showing attractor behaviour were found after filtering and twenty five 5 s sections after wave separation. The mean correlation dimension was calculated for each experimental condition and for 4 subjects, in order to observe the temporal profile of the drug. When attractors were found after wave separation, bandpass filtering then also showed attractor behaviour, with the same temporal profile. However, the reverse is not true: attractors were found after bandpass filtering that were not present after wave separation; in this case the results deserve confirmation, although the temporal profiles for all cases in which attractors were found after filtering remained comparable. 相似文献
9.
The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual
EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model.
The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter.
On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The
analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha
rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of
a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al.
(1978) is present in actual brain dynamics.
Received: 11 August 1997 / Accepted in revised form: 20 April 1999 相似文献
10.
Topographic analysis of dimension estimates of EEG and filtered rhythms in epileptic patients with complex partial seizures 总被引:2,自引:0,他引:2
Nonlinear dynamic properties were analyzed on the EEG and filtered rhythms recorded from healthy subjects and epileptic patients
with complex partial seizures. Estimates of correlation dimensions of control EEG, interictal EEG and ictal EEG were calculated.
The values were demonstrated on topograms. The delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz) and gamma
(30–40 Hz) components were obtained and considered as signals from the cortex. Corresponding surrogate data was produced.
Firstly, the influence of sampling parameters on the calculation was tested. The dimension estimates of the signals from the
frontal, temporal, parietal and occipital regions were computed and compared with the results of surrogate data. In the control
subjects, the estimates between the EEG and surrogate data did not differ (P > 0.05). The interictal EEG from the frontal region and occipital region, as well as its theta component from the frontal
region, and temporal region, showed obviously low dimensions (P < 0.01). The ictal EEG exhibited significantly low-dimension estimates across the scalp. All filtered rhythms from the temporal
region yielded lower results than those of the surrogate data (P < 0.01). The dimension estimates of the EEG and filtered components markedly changed when the neurological state varied.
For each neurological state, the dimension estimates were not uniform among the EEG and frequency components. The signal with
a different frequency range and in a different neurological state showed a different dimension estimate. Furthermore, the
theta and alpha components demonstrated the same estimates not only within each neurological state, but also among the different
states. These results indicate that the theta and alpha components may be caused by similar dynamic processes. We conclude
that the brain function underlying the ictal EEG has a simple mechanism. Several heterogeneous dynamic systems play important
roles in the generation of EEG.
Received: 10 December 1999 / Accepted in revised form: 8 May 2000 相似文献
11.
Moira L. Steyn-Ross D. Alistair Steyn-Ross Jamie W. Sleigh 《Cognitive neurodynamics》2012,6(3):215-225
During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are
characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state
might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure
event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap
junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing
gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report
theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition
from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits
both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (≲8 Hz) oscillatory
states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay
between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show
that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that
weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity
for seizure and simultaneously an increased sensitivity to GABAergic anesthesia. 相似文献
12.
We report on the nonlinear analysis of electroencephalogram (EEG) recordings in the rabbit visual cortex. Epileptic seizures
were induced by local penicillin application and triggered by visual stimulation. The analysis procedures for nonlinear signals
have been developed over the past few years and applied primarily to physical systems. This is an early application to biological
systems and the first to EEG data. We find that during epileptic activity, both global and local embedding dimensions are
reduced with respect to nonepileptic activity. Interestingly, these values are very low () and do not change between preictal and tonic stages of epileptic activity, also the Lyapunov dimension remains constant.
However, between these two stages the manifestations of the local dynamics change quite drastically, as can be seen, e.g.,
from the shape of the attractors. Furthermore, the largest Lyapunov exponent is reduced by a factor of about two in the second
stage and characterizes the difference in dynamics. Thus, the occurrence of clinical symptoms associated with the tonic seizure
activity seems to be mainly related to the local dynamics of the nonlinear system. These results thus seem to give a strong
indication that the dynamics remains much the same in these stages of behavior, and changes are due to alterations in model
parameters and consequent bifurcations of the observed orbits.
Received: 5 February 1997 / Accepted in revised form: 18 September 1997 相似文献
13.
The generalized dimension defined by [Mandelbrot (1995) J Fourier Anal Appl special J.P. Kahane issue: 409–432] was applied
to studying the interrelationship between various parts of human cerebral cortex in different functional conditions. Taking
EEG signals from different brain areas as different sets, the generalized dimensions of their intersections were calculated
to describe the interrelationship between them. The results showed that the generalized dimensions of intersections in different
brain states decreased according to the following order: rest with eyes open, closed, light sleep, and deep sleep. The generalized
dimensions of intersections related to the left or right temporal lobe were higher than the others when the subjects was doing
mental arithmetic, and there was a decrease when the subjects listened to soft classical music. In addition, it was found
that there was a noticeable difference in singular spectra between epileptic patients and normal subjects, irrespective of
whether the epileptic patient was experiencing a seizure or not.
Received: 3 July 2000 / Accepted in revised form: 30 October 2000 相似文献
14.
To uncover the underlying control structure of three-ball cascade juggling, we studied its spatiotemporal properties in detail.
Juggling patterns, performed at fast and preferred speeds, were recorded in the frontal plane and subsequently analyzed using
principal component analysis and serial correlation techniques. As was expected on theoretical grounds, the principal component
analysis revealed that maximally four instead of the original six dimensions (3 balls × 2 planar coordinates) are sufficient
for describing the juggling dynamics. Juggling speed was shown to affect the number of dimensions (four for the fast condition,
two for the preferred condition) as well as the smoothness of the time evolution of the eigenvectors of the principal component
analysis, particularly around the catches. Contrary to the throws and the zeniths, and regardless of juggling speed, consecutive
catches of the same hand showed a markedly negative lag-one serial correlation, suggesting that the catches are timed so as
to preserve the temporal integrity of the juggling act.
Received: 1 April 1999 / Accepted in revised form: 9 August 1999 相似文献
15.
The hypothesis that cardiac rhythms are associated with chaotic dynamics implicating a healthy flexibility has motivated
the investigation of continuous ECG with methods of nonlinear system theory. Sleep is known to be associated with modulations
of the sympathetic and parasympathetic control of cardiac dynamics. Thus, the differentiation of ECG signals recorded during
different sleep stages can serve to determine the usefulness of nonlinear measures in discriminating ECG states in general.
For this purpose the following six nonlinear measures were implemented: correlation dimension D2, Lyapunov exponent L1. Kolmogorov
entropy K2, as well as three measures derived from the analysis of unstable periodic orbits. Results of this study show that
continuous ECG signals can be differentiated from linear stochastic surrogates by each of the nonlinear measures. The most
significant finding with respect to the sleep-related differentiation of ECG signals is an increase in dominant chaoticity
assessed by L1 and a reduction in the degrees of freedom estimated by D2 during REM sleep compared to slow wave sleep. Our
findings suggest that the increase in dominant chaoticity during REM sleep with regard to time-continuous nonlinear analysis
is comparable to an increased heart rate variability. The reduction in the correlation dimension may be interpreted as an
expression of the withdrawal of respiratory influences during REM sleep.
Received: 7 June 1999 / Accepted in revised form: 10 December 1999 相似文献
16.
In a previous study, nonlinear autoregressive (NLAR) models applied to ictal electroencephalogram (EEG) recordings in six
patients revealed nonlinear signal interactions that correlated with seizure type and clinical diagnosis. Here we interpret
these models from a theoretical viewpoint. Extended models with multiple nonlinear terms are employed to demonstrate the independence
of nonlinear dynamical interactions identified in the ‘NLAR fingerprint’ of patients with 3/s seizure discharges. Analysis
of the role of periodicity in the EEG signal reveals that the fingerprints reflect the dynamics not only of the periodic discharge
itself, but also of the fluctuations of each cycle about an average waveform. A stability analysis is used to make qualitative
inferences concerning the network properties of the ictal generators. Finally, the NLAR fingerprint is analyzed in the context
of Volterra-Weiner theory.
Received: 6 April 1994/Accepted in revised form: 18 November 1994 相似文献
17.
Peter Neal Taylor Marc Goodfellow Yujiang Wang Gerold Baier 《Biological cybernetics》2013,107(1):83-94
Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time. 相似文献
18.
《IRBM》2008,29(4):239-244
ObjectivesThe electroencephalogram (EEG) signal contains information about the state and condition of the brain. The aim of the study is to conduct a nonlinear analysis of the EEG signals and to compare the differences in the nonlinear characteristics of the EEG during normal state and the epileptic state.DataThe EEG data used for this study – which consisted of epileptic EEG and normal EEG – were obtained from the EEG database available with the Bonn University, Germany.ResultsThe attractors seen in normal and epileptic human brain dynamics were studied and compared. Surrogate data analyses were conducted on two nonlinear measures, namely the largest Lyapunov exponent and the correlation dimension, to test the hypothesis whether EEG signals were in accordance with linear stochastic models.DiscussionsThe existence of deterministic chaos in brain activity is confirmed by the existence of a chaotic attractor; also, saturation of the correlation dimension towards a definite value is the manifestation of a deterministic dynamics. Also a reduction is observed between the dimensionalities of the brain attractors from normal state to the epileptic state. The evaluation of the largest Lyapunov exponent also confirms the lowering of complexity during an episode of seizure.ConclusionIn case of Lyapunov exponent of EEG data, the change due to surrogating is small suggesting that it is not representing the system complexity properly but there is a marked change in the case of correlation dimension value due to surrogating. 相似文献
19.
Further developments are presented in the technique for analysing attractor behaviour from small data sets, based on the
observation of scaled structures in families of slope curves of correlation integrals. Scaled doublet structures are investigated
systematically for short time series obeying the Mackey and Glass delay differential equation. At an attractor correlation
dimension close to 5, ranges of values of T (the length of the time sequence) and of f (the recording frequency) are described in which the scaled doublet structures are unambiguously identified and distinguished
from structures that can occasionally be found with randomized time sequences. Implications for the characterization of low-dimension
attractors, notably from electroencephalographic recordings, are discussed, including in particular the advantage to be gained
from moderately oversampling the data.
Received: 11 July 1994/Accepted: 4 August 1994 相似文献
20.
Non-linear time sequence analysis has been performed on infant sleep measurement data in order to obtain more information
about the respiratory processes. As a first step, respiration data during REM sleep were analysed with methods from non-linear
dynamics, especially, the correlation integral and the slope of its log-log plot, representing the correlation dimension.
Before calculation of the correlation integral, a special kind of filtering has to be applied to the data. This filtering
algorithm is a state space and singular value decomposition-based noise reduction method, and it is used to separate the noise
and signal subspaces. The dynamics of a signal (in our case data from the respiratory process) and its degrees of freedom
can be characterised by the correlation integral and by the correlation dimension, respectively. The main result of this study
is that the highly irregular-looking breathing patterns during REM sleep could be described by a deterministic system, and
finally the physiological significance of this finding is discussed.
Received: 17 June 1994/Accepted in revised form: 18 November 1994 相似文献