J.P. Pijn

Dynamics of the human alpha rhythm: evidence for non-linearity?

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.

Alpha rhythms: noise, dynamics and models

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.

Dynamics of local neuronal networks: control parameters and state bifurcations in epileptogenesis

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.

Non-linear analysis of intracranial human EEG in temporal lobe epilepsy

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.

Source analysis of lesional frontal-lobe epilepsy

Patients with frontal-lobe epilepsy comprise the second largest group undergoing epilepsy surgery. It has been reported that the difficulty in localizing the epileptogenic zone in these patients is due to the rapid spread of the epileptiform activity within the frontal lobe and to adjoining regions of the brain. We formulated the question of whether the functional localization of dynamic sources of interictal activity in patients with well-defined frontal lesions would yield clear evidence regarding both the topology of the primary sources in relation to the epileptogenic lesion and the pattern of spread of the epileptiform activity throughout the brain. In order to achieve this, we used high-resolution EEG recordings combined with MRI, and advanced source-reconstruction algorithms. In this article, the source-imaging procedures used will be discussed extensively, based on one exemplary patient with complex partial FLE.

Signal Processing of EEG: Evidence for Chaos or Noise. An Application to Seizure Activity in Epilepsy

The EEG is an important signal for the diagnosis of functional disturbances of the brain, and in particular, of epilepsy. The non-linear dynamical analysis of EEG signals recorded during seizure activity in comparison with on-going signals allowed us to formulate a hypothesis about the generation of epileptic activity. According to this model, epilepsy should be envisaged as a dynamical disease of neuronal networks, that may exhibit different types of attractors, i.e., may present bifurcations. One of these attractors is characterized by the generation of irregular oscillations, typical of epileptic seizures.