Katarzyna J. Blinowska

A new method of the description of the information flow in the brain structures

The paper describes the method of determining direction and frequency content of the brain activity flow. The method was formulated in the framework of the AR model. The transfer function matrix was found for multichannel EEG process. Elements of this matrix, properly normalized, appeared to be good estimators of the propagation direction and spectral properties of the investigated signals. Simulation experiments have shown that the estimator proposed by us unequivocally reveals the direction of the signal flow and is able to distinguish between direct and indirect transfer of information. The method was applied to the signals recorded in the brain structures of the experimental animals and also to the human normal and epileptic EEG. The sensitivity of the method and its usefulness in the neurological and clinical applications was demonstrated.

Determination of EEG activity propagation: pair-wise versus multichannel estimate

Performance of different estimators describing propagation of electroencephalogram (EEG) activity, namely: Granger causality, directed transfer function (DTF), direct DTF (dDTF), short-time DTF (SDTF), bivariate coherence, and partial directed coherence are compared by means of simulations and on the examples of experimental signals. In particular, the differences between pair-wise and multichannel estimates are studied. The results show unequivocally that in most cases, the pair-wise estimates are incorrect and a complete set of signals involved in a given process has to be used to obtain the correct pattern of EEG flows. Different performance of multivariate estimators of propagation depending on their normalization is discussed. Advantages of multivariate autoregressive model are pointed out.

Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method

A modification of directed transfer function-direct DTF-is proposed for the analysis of direct information transfer among brain structures on the basis of local field potentials (LFP). Comparison of results obtained by the analysis of simulated and experimental data with a new dDTF and DTF method is shown. A new measure to estimate direct causal relations between signals is defined. The present results demonstrate the effectiveness of the new dDTF method and indicate that the dDTF method can be used to obtain the reliable patterns of connections between various brain structures.

Topographic analysis of coherence and propagation of EEG activity during sleep and wakefulness

Overnight sleep EEG recorded from 21 derivations was studied in 8 healthy subjects. The vector autoregressive model was fitted to all 21 channels simultaneously. Ordinary, multiple and partial coherences and directed transfer functions were estimated for sleep stages and wakefulness. Ordinary coherences give rather trivial information that coherence decreases with distance. Partial coherences revealed specific structure that was well repeatable for the subjects studied. Differences in coherence patterns between sleep stages were found by means of statistical tests. An increase of coherence was found for sleep stages 2, 3 and 4. Directed transfer function made possible the identification of the main centers from which EEG activity is spreading during sleep and wakefulness. During sleep the influence of subcortical structures was manifested by propagation of activity from the fronto-central region. The range of this interaction was highest in sleep stages 3 and 4. An EEG analysis, based on the approach of treating time series as a realization of one process and on the simultaneous (not pair-wise) evaluation of signals offers new possibilities in the investigation of synchronization and functional relations in the brain.

Single evoked potential reconstruction by means of wavelet transform

We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach — the wavelet representation of the signal. Wavelets were introduced by Grossman and Morlet in 1984. The method is based on the multiresolution signal decomposition. Wavelets are already used for speech recognition, geophysics investigations and fractal analysis. This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal. We would like to introduce wavelet formalism for the first time to brain signal analysis. One of the most important problems in this field is the analysis of evoked potentials. This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used. This method is based on several assumptions. Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent. These assumptions have been challenged e.g. the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis. In view of the works of Sayers et al. (1974) and Başar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases. Several attempts to overcome the limitation of the averaging method have been made. Heintze and Künkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments. This was possible under two condiitons: high signal to noise ratio and clear separation of the EEG and EP spectra. These assumptions are not easy to fulfill, though. Cerutti et al. (1987) modeled background EEG activity by means of an AR process and event related brain activity by ARMA. In this way they were able to find a filter extracting single EP. Nevertheless, their method was not quite free of assumptions, since they since they used averaged EP to define their ARMA filter. In the following we shall briefly describe the method of the multiresolution decomposition and we will apply it to the analysis and reconstruction of single evoked potentials.

High resolution study of sleep spindles

OBJECTIVE Universal high-resolution time-frequency parameterization of sleep EEG structures. METHODS A new algorithm called Matching Pursuit was used for the decomposition of sleep EEG into waveforms chosen from a large and redundant set of functions. As a result all signal structures were parameterized in terms of their frequency, time occurrence, time span and energy. Slow wave activity and sleep spindles were identified according to neurophysiological criteria and various distributions describing their time evolution, topographical and frequency characteristics were constructed. RESULTS Two types of sleep spindles of different topological and spectral properties were identified. High time-frequency resolution made possible separation of superimposed spindles. Cross-correlation between high- and low-frequency components of superimposed spindles revealed a fixed time-delay between them, the high-frequency component preceding the low-frequency one. CONCLUSION The results of our study suggest that processes of generation of both types of sleep spindles are weakly coupled.

Stochastic time-frequency dictionaries for matching pursuit

Analyzing large amounts of sleep electroencephalogram (EEG) data by means of the matching pursuit (MP) algorithm, we encountered a statistical bias of the decomposition, resulting from the structure of the applied dictionary. As a solution, we propose stochastic dictionaries, where the parameters of the dictionarys waveforms are randomized before each decomposition. The MP algorithm was modified for this purpose and tuned for maximum time-frequency resolution. Examples of applications of the new method include parameterization of EEG structures and time-frequency representation of signals with changing frequency.

The application of parametric multichannel spectral estimates in the study of electrical brain activity

A parametric autoregressive model was applied to the multichannel EEG time series. Small statistical fluctuations of the spectral estimates obtained from the short data strings made possible to follow the time changes of the signals. The multiple and partial coherences were calculated for the four channel process and compared with the coherences computed between the pairs of channels. From the study it followed that the partial coherences are the proper measure of the synchronization of brain structures and their intrinsic relationships. The partial phase spectra give the information about the phase delays. The advantages of the parametric description of signals in the frequency domain in respect to the modelling of dynamic systems was pointed out.

Review of the methods of determination of directed connectivity from multichannel data

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented.

Multichannel matching pursuit and EEG inverse solutions

We present a new approach to the preprocessing of the electroencephalographic time series for EEG inverse solutions. As the first step, EEG recordings are decomposed by multichannel matching pursuit algorithm--in this study we introduce a computationally efficient, suboptimal solution. Then, based upon the parameters of the waveforms fitted to the EEG (frequency, amplitude and duration), we choose those corresponding to the the phenomena of interest, like e.g. sleep spindles. For each structure, the corresponding weights of each channel define a topographic signature, which can be subject to an inverse solution procedure, like e.g. Loreta, used in this work. As an example, we present an automatic detection and parameterization of sleep spindles, appearing in overnight polysomnographic recordings. Inverse solutions obtained for single sleep spindles are coherent with the averages obtained for 20 overnight EEG recordings analyzed in this study, as well as with the results reported previously in literature as inter-subject averages of solutions for spectral integrals, computed on visually selected spindles.