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Absence seizures are the most pure form of generalized epilepsy. They are characterized in the electroencephalogram by widespread bilaterally synchronous spike-wave discharges (SWDs), which are the reflections of highly synchronized oscillations in thalamocortical networks. To reveal network mechanisms responsible for the initiation and generalization of the discharges, we studied the interrelationships between multisite cortical and thalamic field potentials recorded during spontaneous SWDs in the freely moving WAG/Rij rat, a genetic model of absence epilepsy. Nonlinear association analysis revealed a consistent cortical "focus" within the peri-oral region of the somatosensory cortex. The SWDs recorded at other cortical sites consistently lagged this focal site, with time delays that increased with electrode distance (corresponding to a mean propagation velocity of 1.4 m/sec). Intra-thalamic relationships were more complex and could not account for the observed cortical propagation pattern. Cortical and thalamic sites interacted bi-directionally, whereas the direction of this coupling could vary throughout one seizure. However, during the first 500 msec, the cortical focus was consistently found to lead the thalamus. These findings argue against the existence of one common subcortical pacemaker for the generation of generalized spike-wave discharges characteristic for absence seizures in the rat. Instead, the results suggest that a cortical focus is the dominant factor in initiating the paroxysmal oscillation within the corticothalamic loops, and that the large-scale synchronization is mediated by ways of an extremely fast intracortical spread of seizure activity. Analogous mechanisms may underlie the pathophysiology of human absence epilepsy.

Object: For a better understanding of the physiological mechanisms responsible for alpha rhythms it is important to know whether non-linear processes play a role in their generation. We used non-linear forecasting in combination with surrogate data testing to investigate the prevalence and nature of alpha rhythm non-linearity, based on EEG recordings from humans. We interpreted these findings using computer simulations of the alpha rhythm model of Lopes da Silva et al. (1974)., Methods: EEGs were recorded at 02 and O1 in 60 healthy subjects (30 males; 30 females; age: 49.28 years; range 11-84) during a resting eyes-closed state. Four artefact-free epochs (2.5 s; sample frequency 200 Hz) from each subject were tested for non-linearity using a non-linear prediction statistic and phase-randomized surrogate data. A similar type of analysis was done on the output of the alpha model for different values of input., Results: In the 480 (60 subjects, 2 derivations, 4 blocks) epochs studied, the null hypothesis that the alpha rhythms can result from linearly filtered noise, could be rejected in 6 cases (1.25%). The alpha model showed a bifurcation from a point attractor to a limit cycle at an input pulse density of 615 pps. Non-linearity could only be detected in the model output close to and beyond this bifurcation point. The sources of the non-linearity are the sigmoidal relationships between average membrane potential and output pulse density of the various cells of the neuronal populations., Conclusion: The alpha rhythm is a heterogeneous entity dynamically: 98.75% of the epochs (type I alpha) cannot be distinguished from filtered noise. Apparently, during these epochs the activity of the brain has such a high complexity that it cannot be distinguished from a random process. In 1.25% of the epochs (type II alpha) non-linearity was found which may be explained by dynamics in the vicinity of a bifurcation to a limit cycle. There is thus experimental evidence from the point of view of dynamics for the existence of the two types of alpha rhythm and the bifurcation predicted by the model.

Objective: Intracranial EEG recordings from patients suffering from medically intractable temporal lobe epilepsy were analyzed with the aim of characterizing the dynamics of EEG epochs recorded before and during a seizure and comparing the classification of the EEG epochs on the basis of visual inspection to the results of the numerical analysis., Methods: The stationarity of the selected EEGs was assessed qualitatively. The coarse-grained correlation dimension and coarse-grained correlation entropy were used for the non-linear characterization of the EEG epochs., Results: High-pass filtering was necessary in order to make the majority of the epochs appear stationarity beyond a time scale of about 2 s. It was found that the dimension of the ictal EEGs decreased with respect to the epochs containing ongoing (interictal) activity. The entropy of the ictal recordings however increased. A scaling of the entropy was applied and it was found that the scaled entropy of the ictal EEG decreased, consistent with the increased regularity of the ictal EEG. The coarse-grained quantities discriminated well between EEG epochs recorded prior to and during seizures at locations displaying ictal activity and classification improved by including the linear autocorrelation time in the analysis., Conclusions: It is concluded that ictal and non-ictal EEG can be well distinguished on the basis of non-linear analysis. The results are in good agreement with the visual analysis.

Purpose: An understanding of the principles governing the behavior of complex neuronal networks, in particular their capability of generating epileptic seizures implies the characterization of the conditions under which a transition from the interictal to the ictal state takes place. Signal analysis methods derived from the theory of nonlinear dynamics provide new tools to characterize the behavior of such networks, and are particularly relevant for the analysis of epileptiform activity., Methods: We calculated the correlation dimension, tested for irreversibility, and made recurrence plots of EEG signals recorded intracranially both during interictal and ictal states in temporal lobe epilepsy patients who were surgical candidates., Results: Epileptic seizure activity often, but not always, emerges as a low-dimensional oscillation. In general, the seizure behaves as a nonstationary phenomenon during which both phases of low and high complexity may occur. Nevertheless a low dimension may be found mainly in the zone of ictal onset and nearby structures. Both the zone of ictal onset and the pattern of propagation of seizure activity in the brain could be identified using this type of analysis. Furthermore, the results obtained were in close agreement with visual inspection of the EEG records., Conclusions: Application of these mathematical tools provides novel insights into the spatio-temporal dynamics of "epileptic brain states". In this way it may be of practical use in the localization of an epileptogenic region in the brain, and thus be of assistance in the presurgical evaluation of patients with localization-related epilepsy.

Alpha rhythms appear as sinusoidal-like oscillations in the electroencephalogram (EEG) within the frequency range 8-12 Hz that waxe and wane in a more or less irregular way. The irregularity may have various origins. It may be due to noise or the oscillations may have an intrinsic irregular character, e.g. they may be generated by chaotic processes [Jansen (1991) Quantitative analysis of electroencephalograms: is there chaos in the future? Int. J. Biomed. Comput., 27: 95-123; Pradham, N. and Dutt, D.N. (1993) A nonlinear perspective in understanding the neurodynamics of EEG. Comput. Biol. Med., 23: 425-442; Pritchard et al. (1995) Dimensional analysis of resting human EEG II: Surrogate-data testing indicates nonlinearily but not low-dimensional chaos. Psychophysiology. 32: 486]. The term noise is often used in neurophysiology with different connotations as pointed out by Bullock (1990), either meaning an unwanted signal from the point of view of the receiver of a message, or a signal with intrinsic random fluctuations, i.e. with a stochastic character. Here we consider noise in this sense, as random or quasi-random neural activity. In this overview, we concentrate on the question of whether alpha rhythms should be considered generated in neuronal networks (1) as forms of filtered noise, (2) as deterministic oscillations influenced by noise or (3) as the result of chaotic dynamics. A clear answer to this question can have theoretical value because it may lead to a general model of the generation of this important EEG signal. Such a model, of course, would be a macroscopic one, since it would primarily account for the properties of the alpha rhythms at the neuronal network level. A translation of these properties to the microscopic, i.e. neuronal, level will not be easy to achieve without more direct knowledge of the membrane and synaptic basic properties of the neurons involved. Here we consider the question formulated above by presenting some relevant experimental evidence and theoretical arguments. The consideration whether alpha rhythms may have noise or chaotic sources implies examining how and where such sources can occur in the neuronal networks of the brain. Therefore we present, first, some basic data regarding the possible origin of noise and of chaos in neuronal networks. Second, the signal analysis methods that have to be applied in order to discriminate between filtered noise activities and chaotic oscillations are introduced. Third, the implications of these signal analyses regarding the possible answer to the initial question are discussed.

The aim of this overview is to present evidence that local neuronal networks (LNNs) are functionally organized in such a way that they behave as dynamic non-linear systems that can exhibit multiple types of attractor and can present bifurcations between different attractors, depending on control parameters. To begin with, some of the theoretical concepts of non-linear dynamics and chaos are briefly presented. As a case study, we described the CA1 area of the hippocampus and the changes that the corresponding LNNs undergo during kindling epileptogenesis. During epileptic seizures, evidence exists for the presence of low-dimensional chaos, since the correlation dimension estimated from the corresponding EEG signals decreases dramatically from a large value, characteristic of the resting state, to a low value typical of deterministic chaos. We propose that, among other things, an important control parameter of the dynamics of this brain area is the balance between excitatory (E) and inhibitory (I) processes. We assume that this balance can be experimentally estimated by using a paired-pulse paradigm. Accordingly, we demonstrate that the paired-pulse response changes during kindling epileptogenesis in the sense that the E/I ratio increases in the course of the establishment of a kindled epileptogenic focus. This change in E/I leads to a shift in the operating point of the LNN moving it close to a bifurcation where a rapid state change takes place. In this way, the LNN dynamics can change more readily to the basin of attraction of a chaotic attractor than under normal conditions. This is in essence what makes the behavior of the LNN more sensitive to tetanus, and predicts the facilitated occurrence of epileptic seizures during kindling.

The relationship between ipsi- and contralateral epileptiform electroencephalographic (EEG) activity was investigated in rats that were kindled daily in the amygdala. Two types of relationships--linear and non-linear associations--were studied and used to estimate time delays of EEG activity between homotopic amygdalar sites during consecutive tetanizations. The progressive development of epileptiform EEG and convulsive behaviour was accompanied by an increase in association. Maximal association values of the non-linear function were significantly higher than linear association values. The gradual development of motor seizure severity was correlated with increased non-linearity. Time delays between the two amygdalae were estimated comparably with the linear and non-linear function: 30.0 +/- 3.3 and 24.6 +/- 1.7 ms (ipsilateral leading contralateral), respectively. However, in rats displaying exclusively bilaterally generalized motor convulsions, maximal values of both functions decreased but were still significantly higher than control values of phase-randomized EEG. Corresponding positive as well as negative interhemispheric time delays were recorded during the afterdischarge. These results demonstrated a strengthened association between the ipsi- and contralateral amygdala during primary epileptogenesis induced by amygdala kindling. In contrast, development of a secondary focus in the contralateral homotopic region resulted in a weakened interhemispheric association. Secondary bilateral synchrony between the ipsi- and contralateral amygdala occurred during the evoked epileptiform EEG activity.

EEG signals have been considered to result either from random processes or to be generated by non-linear dynamic systems exhibiting chaotic behaviour. In the latter case, the system may behave as a deterministic chaotic attractor. The complexity of the attractor can be characterized by the correlation dimension that can be computed from one signal generated by the system. A new procedure was developed and applied in order to test whether the correlation dimension, calculated from an EEG epoch, may correspond to a chaotic attractor or to a random process. This procedure was applied to EEG signals recorded from different sites of the limbic cortex of the rat during different states: wakeful rest, locomotion and in the course of an epileptic seizure induced by kindling. The signals recorded during the first two states had high dimensions and could not be distinguished from random noise. However, during an epileptic seizure the correlation dimension became low (between 2 and 4) indicating that in this state the networks behave as chaotic systems. A low correlation dimension appeared at different times and brain sites during an epileptic seizure. These results show that the computation of the correlation dimension may be useful in order to obtain insight into the dynamics of the propagation of an epileptic seizure in the brain.

The role of the forebrain commissures and the septal area in the interhemispheric transfer of hippocampal afterdischarges (ADs) was investigated in the rat under halothane anesthesia. Electrical seizures were elicited from the dorsal hippocampus before and after commissurotomy. The degree of relatedness between EEG signals recorded from homologous sites of both hippocampi was quantified using two approaches: (i) a time domain analysis considering an AD as a succession of discrete bursts; the onset times of such bursts were measured and used to estimate interhemispheric onset delays; (ii) using signal analysis the linear (r2) and non-linear (h2) regression coefficients between pairs of EEG signals were computed as a function of time shift between the two signals. In this way the values of association (linear and non-linear) and the corresponding time delays were measured. In general a tetanus applied unilaterally to the dorsal CA3 field resulted in bilaterally synchronous ADs. The estimated interhemispheric time delay was in most cases zero. This bilateral synchrony disappeared after section of a specific part of the ventral hippocampal commissure (VHC), the dorso-caudal third, but was not affected by section of other commissural fibers or by a lesion of the septal area. This study also allowed evaluation of different methods of quantification of the association between EEG signals, namely the linear (r2) and the non-linear (h2) regression coefficients. The latter was shown to be a more robust measure than the former and to yield values of association even in cases in which r2 was at noise level. The experimental findings allow the conclusion that ADs elicited from an epileptogenic focus spread to homologous sites in the contralateral hemisphere following commissural systems that may be strong enough to ensure the forming of one bilateral oscillating system.

Afterdischarges (ADs) were elicited in the hippocampus of the rat under halothane anesthesia. Records were made along the septo-temporal axis of the hippocampal formation (dorsal (DHF), splenial (SP) and ventral (VHF) regions). For comparison records were also made from the contralateral DHF. The propagation of ADs was quantified using linear and non-linear regression analysis. The values of non-linear association were in general larger than those of linear association. Values of association and time delays between pairs of EEG signals recorded from different regions were estimated as function of elapsed time during the ADs. The association measures for ADs elicited by stimulation of the DHF were relatively large between the ipsi- and contralateral DHF and between the DHF and SP of the same side in contrast to those found between DHF and VHF. The threshold to elicit ADs in the VHF was considerably higher than in the DHF. We conclude that the DHF and SP form a functional entity only loosely coupled to the VHF and that simple spatial continuity is not enough for the propagation of epileptiform ADs between different areas. The estimate of time delays indicated a high degree of synchrony during ADs between homotopical sites on ipsi- and contralateral DHF whereas the degree of synchrony between DHF and SP was smaller.

Spreading of epileptiform activity in the central nervous system is one of the fundamental problems in epileptology. The patterns of spreading of after-discharges in the hippocampus and entorphinal cortex were studied in acute experiments and using the kindling model of epileptogenesis. Three methods were used to determine the time relations between EEG signals from different brain areas; visual inspections, average amount of mutual information (AAMI) and phase spectrum method. The analysis methods used are adequate for quantification of the degree of coupling between different EEG signals during an afterdischarge, but should be used jointly since different signal features are taken into consideration by different methods. During an afterdischarge only at the beginning the focal area is clearly leading the other brain areas; thereafter the pattern becomes more complex.

That the latency of the pattern evoked potential (EP) increases as the stimulus contrast decreases can be understood as the result of, first, a low-pass filtering process of the (contrast) signal followed by, second, and nonlinear 'threshold' stage. We show here that by using this simple concept it is possible to estimate the shape of the 'unit step' response of the low-pass filter with the latency vs. contrast data. We show also that the step responses calculated from several subjects are in reasonable agreement if they are normalized with using the subjects' own contrast thresholds. Within experimental error, the response of a filter consisting of four low-pass first-order stages with a 10.5 Hz cut-off frequency gives a reasonable fit to our own data and to that of one other study (Musselwhite and Jeffreys, 1982).

To investigate the degree of interdependence of EEG signals, we have to use signal analysis methods. Three of these are described and their performance is compared: the cross-correlation (coherence and phase), the average amount of mutual information (AAMI) or the normalized AAMI, also called transmission coefficient T, and the correlation ratio h2 that is a general measure of nonlinear fit between any two signals. The three methods were applied to simulated and real signals in order to put in evidence how nonlinear relationships may affect differently these three measures of association. The nature of the interdependence between EEG signals is not characterized only by the degree of association, but also by the corresponding phase relationship. A basic question is whether such a phase shift can be interpreted as a transmission delay. However, a fundamental problem is that a phase shift may be difficult to interpret in terms of a biophysical model. A procedure is described in order to solve this problem. This involves computing the phase spectrum between the pair of signals, estimating the gain of the corresponding linear transfer function and the associated minimum phase. By subtracting the minimum phase from the phase spectrum, a corrected phase function can be obtained. From the slope of this phase function, a transmission delay can be estimated. This procedure is illustrated by applications to simulated and real EEG signals. It is demonstrated that from phase shifts we may estimate transmission delays between at least certain classes of EEG signals. In this way we can asses, unambiguously, how the transmission of information between different brain sites develops.