7.1 Introduction

It was demonstrated by physiologists as early as at the end of XIXth century that if two electrodes are applied to the surface of a mammalian brain a sensitive instrument can show continuous fluctuations of the electric potential difference between the two electrodes. These potentials were later proved to be the product of the superposition of the electrical activity of tens or hundreds of thousands of neuron cells (neurons) lying in the surface areas of the brain, which is called the cortex. Each such cell is an elementary electric generator. In a rest state a neuron always has a potential difference of about 70 mV between its internal content bounded by a membrane and the surrounding media. In the active state of the neuron, when it receives the information or transmits it to another neurons, the polarisation of the membrane decreases; when the cell activity is inhibited the trans-membrane potential increases. When the potential difference falls below a certain threshold it induces a quickly propagating self-excitatory process, resulting in the activation of other neurons. This is the mechanism of signal transmission in neuronal networks.

The power of a single neuron is not high enough to produce potential changes which can be registered at the brain's surface or, especially, at the surface of the skin, because the surrounding tissues and liquids are good conductors and shunt the currents produced by the neuron. But if thousands of closely located cortical neurons work in synchrony, the summed oscillations of their trans-membrane potentials can be recorded from the scalp. Thus by registering the electrical potential at the surface of the scalp one can watch the activity of the important cortical areas of the brain. This method was called electroencephalography, and the electric signal recorded by this method was called an electroencephalogram; for both the method and the signal the same abbreviation (EEG) is used. The EEG signal is derived from a number of electrodes applied to the scalp's surface at approximately equal distances. The positions and the number of electrodes depends on the specific goal of a research. In modern practice about 20 electrodes are used most often, but the number varies over a wide range, from 1--2 to 128, and even 256. The signal recorded from each EEG electrode is obtained, amplified and, usually, processed in a separate "channel"; therefore, one may speak about the EEG signal at a given electrode as well as in a given "channel".

More recently a related, but much more expensive, method, magnetoencephalography (MEG), was developed for recording the summed magnetic field of the neurons; the signal registered by this latter method is very similar to the EEG signal.

In the 1920s a German psychiatrist Hans Berger demonstrated, in a series of dramatic studies, the sensitivity of the EEG to various changes of the human brain's functional state, and therefore the high diagnostic value of the EEG. In particular, he found that such a simple action as closing the eyes gives rise to regular oscillations in the EEG, with a period about 0.1 s and almost sinusoidal in shape. These oscillations, which he called the alpha rhythm (a term generally accepted since that time), were most prominent over the occipital regions of the brain. During mental activity, in contrast, the oscillations in the EEG were faster and less regular, and their amplitude markedly decreased. High voltage slow waves were characteristic for the EEG in deep sleep and during anaesthesia.

On the basis of his analysis of EEG phenomena, Berger suggested that they are a superposition of a number of quasi-periodic components, which manifest themselves in the EEG to various extents dependent on the brain's current activity. This "polyphonic" metaphor, regardless to the "true" nature of the brain's electrical oscillations, turned out to be useful for the quantitative analysis of the EEG. Their spectral analysis therefore became one of the main tools for the estimation of the brain's state, not only in basic research but in clinical practice as well. It is useful for diagnosing traumatic brain injuries, brain tumours, epilepsy, the group of the "degenerative" diseases of the brain such as Alzheimer's disease and Huntington's Chorea, and, in some cases, even psychiatric disorders (depression, schizophrenia). A specific research area, pharmaco-electroencephalography, was established in the field of human evaluations of psychoactive drugs (Dumermuth & Molinari 1987; Fink 1984). In this area it was shown that each of the main classes of psychoactive drugs, such as anxiolytics, neuroleptics or psychostimulants, induce a specific pattern or profile of changes in the EEG frequency spectrum. Moreover, the high sensitivity of the EEG to pharmacological effects made it possible to predict the therapeutic outcome by the EEG responses to a single dose of the drug (Coppola & Herrmann 1987; Herrmann 1982). The use of the EEG was also advantageous in development of new drugs (Itil & Itil 1986; Kaplan et al. 1997d; Versavel et al. 1995), because the class to which a new drug belongs can be estimated by the pattern of EEG spectral changes.

More recently developed techniques for non-invasive studies of the human brain, such as X-ray computational tomography, positron emission tomography, and magnetic resonance imaging, give good estimates of the localization of structural and metabolic changes in the brain's tissue. These new techniques, however, can provide a temporal resolution of only seconds or even tens of seconds, whilst the elementary processes of the information processing in the brain, such as detection, recognition, memorizing of external signals and even more complex cognitive operations, short "thoughts", are of the order of hundreds of milliseconds (Lehmann et al. 1995; Poppel 1994; Weiss 1992). Since the changes of neuronal cell membrane potentials, as discussed above, underlie signal exchange between the neurons, they are absolutely synchronous with the dynamics of the brain's information processing. The fluctuations of the total potential of neurons registered at the surface of the head, therefore, follow the activity of neuronal networks without time lags. This is why the EEG remains the most efficient method for studying the basic mechanisms of homeostasis and information processing in the human brain.

The high temporal resolution and the low cost of EEG technology, as well as the feasibility of combining it with advanced tomographic techniques, ensured this method one of the leading positions for a long time in the rapidly developing assortment of instruments for brain research.

The EEG signal, nevertheless, has an important inherent feature, its high non-stationarity, which leads to severe loss of the actual temporal resolution of the method. The main methodological advantage of the EEG therefore is not realized. However, the low temporal resolution of the spectral methods, which are most extensively employed in an EEG analysis, is the result of the low temporal resolution of the methods themselves. The spectral methods used for an EEG analysis are naturally associated with averaging; the lower the stability of the EEG signal, the longer the epoch required for obtaining statistically consistent estimates. It is the fight against the high non-stationarity of an EEG signal that leads to the loss of the main advantage of the electroencephalography.

Thus, the old method of EEG needs to be enhanced by new mathematical approaches in order to provide comprehensive extraction of features from EEG recordings for the better understanding of basic mechanisms of brain activities and for better diagnostics of brain diseases.