International Journal of Bioelectromagnetism Vol. 4, No. 2, pp. 7-8, 2002. |
www.ijbem.org |
NONLINEAR ANALYSIS OF EEG/MEG: Fernando H. Lopes da Silva The brain is a highly complex dynamical system that consists of neuronal networks formed by neurons with nonlinear properties. These networks can display distinct types of oscillatory patterns. The different oscillatory modes are reflected in the properties of local field potentials or, at the macroscopic scale, of the EEG or MEG. Transitions (bifurcations) between such oscillatory modes may occur, occasionally dramatically as in epilepsy, and commonly depend on subtle changes of control parameters and/or initial conditions. This exquisite dependency of the collective behavior of neuronal networks on such subtle changes of parameters is a typical property of nonlinear dynamical systems. The theory of nonlinear dynamics provides a useful framework to obtain insight into the processes responsible for the generation and modulation of brain rhythms both under normal and pathological conditions. In general we may state that a dynamical system is characterized by properties that change or evolve in time. The system’s behavior can be graphically described by sketching the time evolution of a system’s variable, constructing the so-called phase-space portrait of the system. An important notion in dynamics is the fact that systems are characterized by the presence of attracting sets, or attractors, in the phase space: i.e. the point or sets of points representing the various possible steady-state conditions of the system. The attractors represent an equilibrium state or group of states to which a dynamical system converges. Changes in one or more parameters may produce an abrupt change in the qualitative form of an attractor that is reflected in the system’s steady state behavior (bifurcation). The critical parameter value at which the system’s trajectory divides into 2 (or more) branches is known as a bifurcation point. In order to understand how pathophysiological processes such as epileptic seizures may occur, concepts derived from the theory of nonlinear dynamics can be useful, since epileptic seizures may be considered as expressions of abnormal dynamics of neuronal networks. Indeed a seizure is a sudden qualitative change in the temporal behavior of a neuronal network, that may be assumed to result from a bifurcation in the system’s dynamics. Thus epilepsies may be seen as diseases of brain dynamics. Accordingly we may consider the epileptic brain as one which possesses abnormal dynamics such that some neuronal networks are prone to enter an epileptic “ictal” state characterized by a specific sort of oscillations (the “seizure”) that disturb the normal function of motor or sensory functions and/or the flow of consciousness. Although these oscillations may be complex, it is remarkable that they may recur in the same subject with a very similar pattern, suggesting that the underlying process is deterministic albeit it may appear random. Thus, the epileptic brain can relatively easily enter in this abnormal oscillatory state, even after only very subtle changes in control parameters. The latter sometimes may even be provoked by random fluctuations. Thus we consider that neuronal networks involved in epilepsy, possess bi(multi)-stable dynamics, i.e. they may display two (at least) dynamical states, one characterized by a normal (apparently stochastic) steady-state (non-ictal state) and the other by the paroxysmal occurrence of a widespread synchronous oscillatory or seizure (ictal state). Understanding how neural dynamical processes may evolve into seizures is not only a fundamental scientific question but it is also of practical interest with respect to the possible use of methods derived from the theory of nonlinear dynamics in order to analyze EEG/MEG signals for prediction or anticipation of epileptic seizures. From the analysis of epileptic seizures in man and in experimental animals and of the behavior of computational models of neuronal networks, we propose 3 main scenarios that can account for the transition between the “non-ictal” and the “ictal” states. (i) In some epileptic brains the distance, in phase space, between the “non-ictal” and the “ictal” state is very small in contrast to that of a normal brain (possibly due to genetic and/or developmental factors, for example in the case of typical absence seizures). Therefore, discrete random fluctuations of some parameters can be sufficient for the occurrence of a transition to the “ictal” state. This may be called the bifurcation scenario. These changes can lead to closing the distance, in a topological sense, between the interictal and an already existing ictal attractor. The actual transition to seizure is then due to a random fluctuation (generated e.g. by noisy or random processes). In this dynamic scenario, there is no clear way to find EEG/MEG signals that may be precursors of an impending seizure, since the bifurcation is in itself caused by a random fluctuation. (ii) In another kind of epileptic brains (e.g. limbic cortex epilepsies) the distance between “non-ictal” and “ictal” attractors is, in general, rather large such that random fluctuations are commonly not capable of triggering the transition to a seizure. However, in these brains there are neuronal networks that have abnormal features characterized by unstable parameters that are very vulnerable to the influence of endogenous and/or exogenous factors. This means that the changes of the system’s parameters affect directly the current attractor, which can deform either gradually or suddenly into a low-dimensional “ictal” attractor. When this deformation becomes substantial a clinically manifest seizure may take place. This scenario may be called a deformation scenario. Therefore, the changes of the system’s dynamics preceding a seizure in these cases may either be detectable in the EEG and thus the route to the seizure may be predictable, or it may be unobservable using only EEG/MEG measurements. It is thinkable that in some cases changes in the excitability state of the underlying networks may be uncovered using appropriate stimuli configurations before changes in the dynamics of the on-going EEG activity become evident. (iii) In addition reflex epilepsies form a special case since in these forms of seizures these can be induced by a known and specific external stimulus, albeit not in a perfectly deterministic way. This is the case of photosensitive epilepsy characterized by visual sensitivity to Intermittent Photic Stimulation or IPS. Thus in these cases the external stimulus causes a change in some parameters of the underlying neuronal networks such that a transition in the system’s attractor can take place. The problem of “predicting” the outcome of the IPS itself is reduced to the question of whether it is possible to identify properties of the measured EEG/MEG signals recorded under the influence of IPS that differ between the sessions where the external driving of the system leads to paroxysmal discharges and those where such discharges do not occur. We may call the dynamics of such a system as of the deformation type triggered by a specific external factor. In this lecture we consider, first, the dynamics of the neuronal systems responsible for absence type of seizures characterized by Spike-and-Wave Discharges (SWDs) on the basis of a computer model based on neurophysiological data. In this way we can put in evidence which neuronal parameters are most critical to transform a normal brain into a brain prone to absence epilepsy, with especial emphasis on the properties of calcium channels, GABA-A and –B receptors and cholinergic modulation. Second we analyse, using nonlinear analysis methods, in an experimental genetic animal model of absence epilepsy the question of whether the origin of SWDs is cortical or centrencephalic. This allowed us to conclude that the initiation of SWDs in this experimental model is situated in a specific cortical area, but in the course of the oscillations the thalamo-cortical networks behave as a closed loop. Third, in a human “model” of absence epilepsy, the photosensitive epilepsy, we use nonlinear analysis to search for EEG/MEG changes preceding the transition between normal activity to SWDs. In this respect we studied ten patients with idiopathic Photosensitive Epilepsy (PSE) using magnetoencephalography. An enhancement of phase synchrony in the gamma-band (30-120 Hz), harmonically related to the frequency of stimulation, preceded the stimulation trials that evolved into Paroxysmal Photosensitive Responses (PPR), and which differed significantly from that encountered in trials not followed by PPR or in control subjects. We postulate, on the basis of these experimental results and of model studies, that a pathological deviation of normally occurring synchronization of gamma oscillations of the cortex, that normally underlie perceptional and voluntary motor processes, might mediate the transition to epileptic seizures in PSE. This pathologic deviation of the parameters that control gamma cortical oscillations may reflect the deformation of the system’s attractor that leads to the “ictal” state in Photosensitive Epilepsy (PSE).
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