F.H. Lopes da Silva

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

OBJECTnFor 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).nnnMETHODSnEEGs 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.nnnRESULTSnIn 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.nnnCONCLUSIONnThe 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.

Computational model of thalamo-cortical networks: dynamical control of alpha rhythms in relation to focal attention.

EEG/MEG rhythmic activities such as alpha rhythms, of the visual or of the somato-sensory cortex, are commonly modulated as subjects perform certain tasks or react to specific stimuli. In general, these activities change depending on extrinsic or intrinsic events. A decrease of the amplitude of alpha rhythmic activity occurring after a given event, which manifests as a decrease of a spectral peak, is called event-related desynchronization (ERD), whereas the inverse is called event-related synchronization (ERS), since it is assumed that the power of a spectral peak is related to the degree of synchrony of the underlying oscillating neuronal populations. An intriguing observation in this respect [Pfurtscheller and Neuper, Neurosci. Lett. 174 (1994) 93-96] was that ERD of alpha rhythms recorded over the central areas was accompanied by ERS, within the same frequency band, recorded over neighboring areas. In case the event was a hand movement, ERD was recorded over the scalp overlying the hand cortical area, whereas ERS was concomitantly recorded over the midline, whereas if the movement was of the foot the opposite was found. We called this phenomenon focal ERD/surround ERS. The question of how this phenomenon may be generated was approached by means of a computational model of thalamo-cortical networks, that incorporates basic properties of neurons and synaptic interactions. These simulation studies revealed that this antagonistic ERD/ERS phenomenon depends on the functional interaction between the populations of thalamo-cortical cells (TCR) and reticular nucleus cells (RE) and on how this interaction is modulated by cholinergic inputs. An essential feature of this interaction is the existence of cross-talk between different sectors of RE that correspond to distinct sensory modules (e.g. hand, foot). These observations led us to formulate the hypothesis that this basic neurophysiological mechanism can account for the general observation that enhanced attention given to a certain stimulus (the focus) is coupled to inhibition of attention to other stimuli (the surround).

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.

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

OBJECTIVEnIntracranial 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.nnnMETHODSnThe 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.nnnRESULTSnHigh-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.nnnCONCLUSIONSnIt 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.

Comparison of Combined Versus Subdural or Intracerebral Electrodes Alone in Presurgical Focus Localization

Summary: purpose: The yield of subdural versus intracerebra1 electrodes for ictal localization remains a point of controversy. We assessed the relative sensitivity of these two types of electrodes per case.

Magnetic source imaging in fixation-off sensitivity: relationship with alpha rhythm.

A patient in whom a variety of abnormal EEG findings can be elicited by elimination of central vision and fixation demonstrates fixation-off sensitivity. The underlying mechanisms of fixation-off sensitivity and its relationship with alpha rhythm remain unclear. To obtain a better understanding of this issue, we used a whole-head magnetoencephalograph to study an epileptic child with fixation-off sensitivity resulting in a 3-Hz, large-amplitude oscillation (300 microV) over the occipital regions on the EEG. Magnetic source localization revealed alpha activity around the calcarine fissure and surrounding parieto-occipital areas. Magnetic sources of abnormalities relating to fixation-off sensitivity, however, usually were located deeper in the brain, suggesting more extensively distributed sources, with involvement of the cingulate gyrus and the basomesial occipitotemporal region. Distributions of the sources of both types of activities show independent clusters but also an appreciable domain of overlap. Our findings indicate that abnormalities related to fixation-off sensitivity can emerge in thalamocortical networks, with larger and more anterior cortical distribution than those that generate alpha rhythm. Transition in the type of oscillation appears not only to depend on a change in cellular dynamics but also to be reflected in a different spatial distribution of the underlying neuronal networks.