Nonlinear EEG analysis based on a neural mass model

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     

Topographic analysis of dimension estimates of EEG and filtered rhythms in epileptic patients with complex partial seizures

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     

The prediction of EEG signals using a feedback-structured adaptive rational function filter

 In this article, we present a feedback-structured adaptive rational function filter based on a recursive modified Gram-Schmidt algorithm and apply it to the prediction of an EEG signal that has nonlinear and nonstationary characteristics. For the evaluation of the prediction performance, the proposed filter is compared with other methods, where a single-step prediction and a multi-step prediction are considered for a short-term prediction, and the prediction performance is assessed in normalized mean square error. The experimental results show that the proposed filter shows better performance than other methods considered for the short-term prediction of EEG signals. Received: 22 September 1998 / Accepted in revised form: 29 February 2000     

Frequency sensitivity in Hodgkin–Huxley systems

 The frequency sensitivity of weak periodic signal detection has been studied via numerical simulations for both a single neuron and a neuronal network. The dependence of the critical amplitude of the signal upon its frequency and a resonance between the intrinsic oscillations of a neuron and the signal could account for the frequency sensitivity. In the presence of both a subthreshold periodic signal and noise, the signal-to-noise ratio (SNR) of the output of either a single neuron or a neuronal network present the typical characteristics of stochastic resonance. In particular, there exists a frequency-sensitive range of 30–100 Hz, and for signals with frequencies within this range the SNRs have large values. This implies that the system under consideration (a single neuron or a neuronal network) is more sensitive to the detection of periodic signals, and the frequency sensitivity may be of a functional significance to signal processing. Received: 26 October 1999 / Accepted in revised form: 25 July 2000     

Investigation of the dynamics underlying periodic complexes in the EEG

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     

Synergetic analysis of spatio-temporal EEG patterns: Alzheimer's disease

 A spatio-temporal analysis has been employed on EEG signals recorded in groups of patients with Alzheimer's disease (AD). The so-called Karhunen–Loeve analysis method was applied to four groups of subjects: 12 patients who were diagnosed as having severe AD, 8 mild AD patients, 10 vascular dementia patients, and 10 normal aged controls, to obtain the spatio-temporal eigenpatterns. The local difference of the global EEG pattern in mild AD patients from that of normal controls was expanded to the frontal regions in the case of severe AD. The analysis showed significant bilateral temporal functioning differences and inter-hemispheric connection difficulty, along with remarkable intra-hemispheric correlation in severe AD patients. Compared to the normal controls, severe AD patients' brains exhibit only weak local connections and correlations, resulting into limited harmonious inter-hemispheric information processing. The results from the spatio-temporal EEG study of AD patients can be considered to be due to a change in the relative activity of the brain corresponding to the pathologic variation in AD, and the results are in accordance with reported clinical studies. Received: 3 March 2000 / Accepted in revised form: 8 January 2001     

The NAD-linked soluble hydrogenase from Alcaligenes eutrophus H16: detection and characterization of EPR signals deriving from nickel and flavin

 In this study we confirmed the previous observation that the cytoplasmic NAD-linked hydrogenase of Alcaligenes eutrophus H16 is EPR-silent in the oxidized state. We also demonstrated the presence of significant Ni-EPR signals when the enzyme was either reduced with the natural electron carrier NADH (5–10 mM) or carefully titrated with sodium dithionite to an intermediate, narrow redox potential range (–280 to –350 mV). Reduction with NADH under argon atmosphere led to a complex EPR spectrum at 80 K with g values at 2.28, 2.20, 2.14, 2.10, 2.05, 2.01 and 2.00. This spectrum could be differentiated by special light/dark treatments into three distinct signals: (1) the "classical" Ni-C signal with g values at 2.20, 2.14 and 2.01, observed with many hydrogenases in the reduced, active state; (2) the light-induced signal (Ni-L) with g values at 2.28, 2.10 and 2.05 and (3) a flavin radical (FMN semiquinone) signal at g = 2.00. The assignment of the Ni-EPR signal was clearly confirmed by EPR spectra of hydrogenase labeled with ⁶¹Ni (nuclear spin I = 3/2) yielding a broadening of the Ni spectra at all g values and a resolved ⁶¹Ni hyperfine splitting into four lines of the low field edge in the case of the light-induced Ni-EPR signal. The redox potentials determined at pH 7.0 for the described redox components were: for FMN –170 mV (midpoint potential, E_m, for appearance), –200 mV (EPR signal intensity maximum) and –230 mV (E_m for disappearance); for the Ni centre (Ni-C), –290 mV (E_m for appearance), –305 mV (signal intensity maximum) and –325 mV (E_m for disappearance). Exposure of the NADH-reduced hydrogenase to carbon monoxide led to an apparent Ni-CO species indicated by a novel rhombic EPR signal with g values at 2.35, 2.08 and 2.01. Received: 19 July 1995 / Accepted: 10 September 1995     

Sensor fusion by neural networks using spatially represented information

 A neural network model based on a lateral-inhibition-type feedback layer is analyzed with regard to its capabilities to fuse signals from two different sensors reporting the same event (“multisensory convergence”). The model consists of two processing stages. The input stage holds spatial representations of the sensor signals and transmits them to the second stage where they are fused. If the input signals differ, the model exhibits two different processing modes: with small differences it produces a weighted average of the input signals, whereas with large differences it enters a decision mode where one of the two signals is suppressed. The dynamics of the network can be described by a series of two first-order low-pass filters, whose bandwidth depends nonlinearly on the level of concordance of the input signals. The network reduces sensor noise by means of both its averaging and filtering properties. Hence noise suppression, too, depends on the level of concordance of the inputs. When the network's neurons have internal noise, sensor noise suppression is reduced but still effective as long as the input signals do not differ strongly. The possibility of extending the scheme to three and more inputs is discussed. Received: 2 August 2000 / Accepted in revised form: 3 May 2001     

In situ localization of endogenous cytokinins during shooty tumor development on Eucalyptus globulus Labill

Our previous results demonstrated that endogenous cytokinins are involved in the shooty potential of tumors initiated on Eucalyptus globulus plantlets inoculated with Agrobacterium tumefaciens strain 82.139 [A. Azmi et al. (1997a) Plant Sci 127: 81–90]. In order to investigate whether or not these hormones are distributed homogeneously in the tumors prior to the onset of bud regeneration, decapitated hypocotyls were inoculated with the strain C58pMP90/T139 GUS-INT harboring the wild transferred DNA (T-DNA) of strain 82.139 tagged with the β-glucuronidase (gus)-reporter gene. In situ immunolocalization of zeatin, dihydrozeatin and isopentenyladenine was performed in the developing tumors and combined with the histo-enzymological β-glucuronidase assay. It was found that the expression of the T-DNA was restricted to only some small areas located deeply in the tumors. These sites were also provided with a high cytokinin signal while the untransformed parts of the tumors displayed a weaker signal, except in the early differentiating tracheary elements. The regenerated buds were untransformed and originated from superficial parts of the tumors provided with a moderate signal for cytokinins. The method of co-localization of both cytokinins and gus expression developed here might be helpful for further studies concerning the role of these hormones in controlling gene expression at cell and tissue levels. Received: 24 May 2000 / Accepted: 12 October 2000     

A computational model of action selection in the basal ganglia. I. A new functional anatomy

 We present a biologically plausible model of processing intrinsic to the basal ganglia based on the computational premise that action selection is a primary role of these central brain structures. By encoding the propensity for selecting a given action in a scalar value (the salience), it is shown that action selection may be re-cast in terms of signal selection. The generic properties of signal selection are defined and neural networks for this type of computation examined. A comparison between these networks and basal ganglia anatomy leads to a novel functional decomposition of the basal ganglia architecture into `selection' and `control' pathways. The former pathway performs the selection per se via a feedforward off-centre on-surround network. The control pathway regulates the action of the selection pathway to ensure its effective operation, and synergistically complements its dopaminergic modulation. The model contrasts with the prevailing functional segregation of basal ganglia into `direct' and `indirect' pathways. Received: 16 February 2000 / Accepted in revised form: 30 October 2000     

An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals

We propose a new measure of synchronization of multichannel ictal and interictal EEG signals. The measure is based on the residual covariance matrix of a multichannel autoregressive model. A major advantage of this measure is its ability to be interpreted both in the framework of stochastic and deterministic models. A preliminary analysis of EEG data from three patients using this measure documents the expected increased synchronization during ictal periods but also reveals that increased synchrony persists for prolonged periods (up to 2 h or more) in the postictal period. Received: 20 July 1997 / Accepted in revised form: 26 January 1999     

Partial directed coherence: a new concept in neural structure determination

 This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality. Received: 25 April 2000 / Accepted in revised form: 13 November 2000     

Molecular cloning and characterization of a gene encoding glutaminase from Aspergillus oryzae

 A glutaminase from Aspergillus oryzae was purified and its molecular weight was determined to be 82,091 by matrix-assisted laser desorption ionization time-of-flight mass spectrometry. Purified glutaminase catalysed the hydrolysis not only of l-glutamine but also of d-glutamine. Both the molecular weight and the substrate specificity of this glutaminase were different from those reported previously [Yano et al. (1998) J Ferment Technol 66: 137–143]. On the basis of its internal amino acid sequences, we have isolated and characterized the glutaminase gene (gtaA) from A. oryzae. The gtaA gene had an open reading frame coding for 690 amino acid residues, including a signal peptide of 20 amino acid residues and a mature protein of 670 amino acid residues. In the 5′-flanking region of the gene, there were three putative CreAp binding sequences and one putative AreAp binding sequence. The gtaA structural gene was introduced into A. oryzae NS4 and a marked increase in activity was detected in comparison with the control strain. The gtaA gene was also isolated from Aspergillus nidulans on the basis of the determined nucleotide sequence of the gtaA gene from A. oryzae. Received: 23 August 1999 / Received last revision: 7 January 2000 / Accepted: 14 January 2000     

Evaluation of solid substrates for enzyme production by Coriolus versicolor, for use in bioremediation of chlorophenols in aqueous effluents

In the development of a system for the removal of chlorophenols from aqueous effluents, a range of solid substrates for the growth of Coriolus versicolor were investigated. Substrates included wood chips, cereal grain, wheat husk and wheat bran. Suitability for transformation of chlorophenols depended on laccase production by the fungus. The greatest amount of laccase (<25 Units g⁻¹ substrate) was produced on wheat husk and wheat bran over 30 days colonisation. Aqueous extracts of laccase from wheat husk and wheat bran cultures removed 100% of 2,4-dichlorophenol (50 ppm) from solution within 5 h and 75–80% of pentachlorophenol (50 ppm) within 24 h. Wheat bran was formulated into pellets with biscuit flour to provide a compact substrate for fungal immobilisation. Addition of 8–12% yeast extract to the pellets increased laccase production five-fold. Colonised pellets were added to chlorophenol solutions in 200–4000-ml bioreactors, resulting in >90% removal of chlorophenols within 100 min. Received: 10 April 2000 / Received revision: 4 July 2000 / Accepted: 10 July 2000     

Interfacing a silicon chip to pairs of snail neurons connected by electrical synapses

 Future hybrid neuron-semiconductor chips will consist of complex neural networks that are directly interfaced to electronic integrated circuits. They will help us to understand the dynamics of neuronal networks and may lead to novel computational facilities. Here we report on an elementary step towards such neurochips. We designed and fabricated a silicon chip for multiple two-way interfacing, and cultured on it pairs of neurons from the pedal ganglia of the snail Lymnaea stagnalis. These neurons were joined to each other by an electrical synapse, and to the chip by a capacitive stimulator and a recording transistor. We obtained a set of neuroelectronic units with sequential and parallel signal transmission through the neuron–silicon interface and the synapse, with a bidirectionally interfaced neuron-pair and with a signal path from the chip through a synaptically connected neuron pair back to the chip. The prospects for assembling more involved hybrid networks on the basis of these neuroelectronic units are considered. Received: 13 April 2000 / Accepted in revised form: 29 September 2000     

Fluctuations of the fractal dimension of the electroencephalogram during periodic breathing in heart failure patients

The physiological mechanisms responsible for periodic breathing (PB) in heart failure (HF) patients are still debated. A role for rhythmic shifts in the level of wakefulness has been suggested, but their existence has never been proven. In this study we investigated the existence of an oscillation in EEG activity during PB in these patients and assessed its relationship with the ventilatory oscillation. EEG activity was measured by the fractal dimension (FD) and by a spectral technique (weighted mean frequency, WMF) in 17 stable HF patients (mean age ± SD: 57±10 yrs, NYHA class: 2.6 ± 0.4, LVEF: 24 ± 6%), with sustained PB during supine rest. The relationship between minute ventilation (MV) signal and FD and WMF was assessed by coherence analysis. Most patients (10/17) showed a well defined oscillation in FD and WMF at the frequency of PB closely linked (coherence > 0.7) with the oscillation of MV. In the remaining patients, neither FD nor WMF showed a clear oscillatory pattern synchronous with MV. Overall, the two EEG-derived parameters showed the same coherence with the ventilatory oscillation (mean coherence ± SD: 0.65 ± 0.25 vs 0.66 ± 0.23, for FD and WMF respectively, p = 0.44). Our results provide evidence that during PB in HF patients, EEG activity often, but not always, fluctuates synchronously with the ventilatory oscillation. These fluctuations can be effectively detected by the fractal dimension, but classical spectral methods provide substantially the same information. Other mechanisms, particularly chemical instability in the respiratory control system, are likely to play a role in the genesis of PB.     

A gain-control mechanism for processing of chorus sounds in the afferent auditory pathway of the bushcricket Tettigonia viridissima (Orthoptera; Tettigoniidae)

The representation of alternative conspecific acoustic signals in the responses of a pair of local interneurons of the bushcricket Tettigonia viridissima was studied with variation in intensity and the direction of sound signals. The results suggest that the auditory world of the bushcricket is rather sharply divided into two azimuthal hemispheres, with signals arriving from any direction within one hemisphere being predominantly represented in the discharge of neurons of this side of the auditory pathway. In addition, each pathway also selects for the most intense of several alternative sounds. A low-intensity signal at 45 dB sound pressure level is quite effective when presented alone, but completely suppressed when given simultaneously with another signal at 60 dB sound pressure level. In a series of intracellular experiments the synaptic nature of the intensity-dependent suppression of competitive signals was investigated in a number of interneurons. The underlying synaptic mechanism is based on a membrane hyperpolarisation with a time-constant in the order of 5–10 s. The significance of this mechanism for hearing in choruses, and for the evolution of acoustic signals and signalling behaviour is discussed. Accepted: 20 November 1999     

A computational model of action selection in the basal ganglia. II. Analysis and simulation of behaviour

 In a companion paper a new functional architecture was proposed for the basal ganglia based on the premise that these brain structures play a central role in behavioural action selection. The current paper quantitatively describes the properties of the model using analysis and simulation. The decomposition of the basal ganglia into selection and control pathways is supported in several ways. First, several elegant features are exposed – capacity scaling, enhanced selectivity and synergistic dopamine modulation – which might be expected to exist in a well designed action selection mechanism. The discovery of these features also lends support to the computational premise of selection that underpins our model. Second, good matches between model globus pallidus external segment output and globus pallidus internal segment and substantia nigra reticulata area output, and neurophysiological data, have been found which are indicative of common architectural features in the model and biological basal ganglia. Third, the behaviour of the model as a signal selection mechanism has parallels with some kinds of action selection observed in animals under various levels of dopaminergic modulation. Received: 16 July 2000 / Accepted in revised form: 30 October 2000     

A nonlinear dynamics model for simulating long range correlations of cognitive bistability

Simulation results of bistable perception due to ambiguous visual stimuli are presented which are obtained with a behavioral nonlinear dynamics model using perception–attention–memory coupling. This model provides an explanation of recent experimental results of Gao et al. (Cogn Process 7:105–112, 2006a) and it supports their speculation that the fractal character of perceptual dominance time series may be understood in terms of nonlinear and reentrant dynamics of brain processing. Percept reversals are induced by attention fatigue and noise, with an attention bias which balances the relative percept duration. Dynamical coupling of the attention bias to the perception state introduces memory effects leading to significant long range correlations of perceptual duration times as quantified by the Hurst parameter H > 0.5 (Mandelbrot, The fractal geometry of nature, 1991), in agreement with Gao et al. (Cogn Process 7:105–112, 2006a).