Herbert Witte

Coherence of gamma-band EEG activity as a basis for associative learning.

Different regions of the brain must communicate with each other to provide the basis for the integration of sensory information, sensory-motor coordination and many other functions that are critical for learning, memory, information processing, perception and the behaviour of organisms. Hebb suggested that this is accomplished by the formation of assemblies of cells whose synaptic linkages are strengthened whenever the cells are activated or ‘ignited’ synchronously. Hebbs seminal concept has intrigued investigators since its formulation, but the technology to demonstrate its existence had been lacking until the past decade. Previous studies have shown that very fast electroencephalographic activity in the gamma band (20–70 Hz) increases during, and may be involved in, the formation of percepts and memory, linguistic processing, and other behavioural and preceptual functions. We show here that increased gamma-band activity is also involved in associative learning. In addition, we find that another measure, gamma-band coherence, increases between regions of the brain that receive the two classes of stimuli involved in an associative-learning procedure in humans. An increase in coherence could fulfil the criteria required for the formation of hebbian cell assemblies, binding together parts of the brain that must communicate with one another in order for associative learning to take place. In this way, coherence may be a signature for this and other types of learning.

Adaptive AR modeling of nonstationary time series by means of Kalman filtering

An adaptive on-line procedure is presented for autoregressive (AR) modeling of nonstationary multivariate time series by means of Kalman filtering. The parameters of the estimated time-varying model can be used to calculate instantaneous measures of linear dependence. The usefulness of the procedures in the analysis of physiological signals is discussed in two examples: first, in the analysis of respiratory movement, heart rate fluctuation, and blood pressure, and second, in the analysis of multichannel electroencephalogram (EEG) signals. It was shown for the first time that in intact animals the transition from a normoxic to a hypoxic state requires tremendous short-term readjustment of the autonomic cardiac-respiratory control. An application with experimental EEG data supported observations that the development of coherences among cell assemblies of the brain is a basic element of associative learning or conditioning.

Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems

Over the last decades several techniques have been developed to analyze interactions in multivariate dynamic systems. These analysis techniques have been applied to empirical data recorded in various branches of research, ranging from economics to biomedical sciences. Investigations of interactions between different brain structures are of strong interest in neuroscience. The information contained in electromagnetic signals may be used to quantify the information transfer between those structures. When investigating such interactions, one has to face an inverse problem. Usually the distinct features and different conceptual properties of the underlying processes generating the empirical data and therefore the appropriate analysis technique are not known in advance. The performance of these methods has mainly been assessed on the basis of those model systems they have been developed for. To draw reliable conclusions upon application to empirical time series, understanding the properties and performances of the time series analysis techniques is essential. To this aim, the performances of four representative multivariate linear signal processing techniques in the time and frequency domain have been investigated in this study. The partial cross-spectral analysis and three different quantities measuring Granger causality, i.e. a Granger causality index, partial directed coherence, and the directed transfer function are compared on the basis of different model systems. To capture distinct properties in the dynamics of brain neural networks, we have investigated multivariate linear, multivariate nonlinear as well as multivariate non-stationary model systems. In an application to neural data recorded by electrothalamography and electrocorticography from juvenile pigs under sedation, directed as well as time-varying interactions have been studied between thalamic and cortical brain structures. The time-dependent alterations in local activity and changes in the interactions have been analyzed by the Granger causality index and the partial directed coherence. Both methods have been shown to be most suitable for this application to brain neural networks based on our model systems investigated. The results of this investigation contribute to the long-term goal to understand the relationships in neural structures in an abnormal state of deep sedation.

Tracking the Time-Varying Cortical Connectivity Patterns by Adaptive Multivariate Estimators

The directed transfer function (DTF) and the partial directed coherence (PDC) are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods is based on the multivariate autoregressive modelling (MVAR) of time series, which requires the stationarity of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR) and to apply it to a set of real high resolution EEG data. This approach will allow the observation of rapidly changing influences between the cortical areas during the execution of a task. The simulation results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of signal-to-noise ratio (SNR) ad number of trials. An SNR of Ave and a number of trials of at least 20 provide a good accuracy in the estimation. After testing the method by the simulation study, we provide an application to the cortical estimations obtained from high resolution EEG data recorded from a group of healthy subject during a combined foot-lips movement and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected with the proposed methods, one constant across the task and the other evolving during the preparation of the joint movement.

Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models

This study presents an efficient algorithm for the fitting of multivariate autoregressive models (MVAR) with time-dependent parameters to multidimensional signals. Thereby, the dimension of the model may be chosen to equal the number of signal channels. The autoregressive (AR) parameter matrices are estimated by an extension of the recursive least squares (RLS) algorithm with forgetting factor. The estimation procedure includes a single trial as well as an ensemble mean approach. The latter approach allows the simultaneous fit of one mean MVAR model to a set of single trials, each of them representing the measurement of the same task. A particular advantage of this ensemble mean approach is that it requires only a low computation effort in comparison to well known procedures applied to single trials. Furthermore, the ensemble mean approach is linked with a high adaptation capability. The properties of the estimator are investigated using simulated time series. It can be demonstrated that the adaptation capability of the estimation (measured by its adaptation speed and variance) does not depend on the model dimension. The mean MVAR fit is applied to 19-dimensional EEG data, recorded during an elementary comparison procedure. The calculation of ordinary and multiple coherence is discussed. The sensitivity of the multiple instantaneous EEG coherence will be demonstrated.

Instantaneous EEG coherence analysis during the Stroop task

OBJECTIVE In the present study the Stroop effect is analyzed by means of EEG coherence analysis in addition to traditional analysis of behavioral data (reaction time) and ERP analysis. Data from 10 normal subjects are examined. METHODS In particular, a special dynamic approach for a continuous coherence estimation is applied to investigate the procedural evolution of functional cortical relationships during the Stroop task. RESULTS The frequency band of 13-20 Hz is found to be sensitive to the discrimination between the congruent and the incongruent task conditions on the basis of instantaneous coherence analysis. The magnitude of coherence values within the time interval of late potentials and the maximal coherence values are used to assess the strength of interaction between distinct areas of the cortex. Higher coherences are observed within the left frontal and left parietal areas, as well as between them for the incongruent situation in comparison with the congruent situation. Furthermore, the time-points of maximal coherence allows a procedural discrimination between both situations. The peak synchrony described by the time-points of maximal coherence correlates strongly with the reaction times mainly within the frontal area and between fronto-parietal areas in the incongruent case, whereas this correlation is restricted to the right hemisphere in the congruent case.

A new Kalman filter approach for the estimation of high-dimensional time-variant multivariate AR models and its application in analysis of laser-evoked brain potentials

In this methodological study we present a new version of a Kalman filter technique to estimate high-dimensional time-variant (tv) multivariate autoregressive (tvMVAR) models. It is based on an extension of the state-space model for a multivariate time series to a matrix-state-space model for multi-trial multivariate time series. The result is a general linear Kalman filter (GLKF). The GLKF enables a tvMVAR model estimation which was applied for interaction analysis of simulated data and high-dimensional multi-trial laser-evoked brain potentials (LEP). The tv partial Granger causality index (tvpGCI) was used to investigate the interaction patterns between LEPs derived from an experiment with noxious laser stimulation. First, the new approach was compared with the multi-trial version of the recursive least squares (RLS) algorithm with forgetting factor (Moller et al., 2001) by using 24 distinct electrodes. The RLS failed for a channel number (dimension) higher than 24. Secondly, the analysis was repeated by using all 58 electrodes and the similarities and differences of the GCI-based interaction patterns are discussed. It can be demonstrated that the application of high-dimensional tvMVAR modelling will contribute to a better understanding of the relationship between structure and function.

Brain Network Analysis From High-Resolution EEG Recordings by the Application of Theoretical Graph Indexes

The extraction of the salient characteristics from brain connectivity patterns is an open challenging topic since often the estimated cerebral networks have a relative large size and complex structure. Since a graph is a mathematical representation of a network, which is essentially reduced to nodes and connections between them, the use of a theoretical graph approach would extract significant information from the functional brain networks estimated through different neuroimaging techniques. The present work intends to support the development of the ldquobrain network analysis:rdquo a mathematical tool consisting in a body of indexes based on the graph theory able to improve the comprehension of the complex interactions within the brain. In the present work, we applied for demonstrative purpose some graph indexes to the time-varying networks estimated from a set of high-resolution EEG data in a group of healthy subjects during the performance of a motor task. The comparison with a random benchmark allowed extracting the significant properties of the estimated networks in the representative Alpha (7-12 Hz) band. Altogether, our findings aim at proving how the brain network analysis could reveal important information about the time-frequency dynamics of the functional cortical networks.

Time-variant non-linear phase-coupling analysis of EEG burst patterns in sedated patients during electroencephalic burst suppression period

OBJECTIVES The quadratic phase-coupling (QPC) within burst patterns during electroencephalic burst suppression has been quantified. METHODS It can be shown that a QPC exists between the frequency ranges 0-2.5 and 3-7.5 Hz and between the frequency ranges 0-2.5 and 8-12 Hz. By means of time-variant bicoherence analysis, a strong phase-locking between the modulating and the modulated component can be identified. The phase-locking is demonstrable within the first 250 ms after the burst onset and comes up to the maximum between 750 and 1250 ms. RESULTS The effect is maintained over the whole first part of the burst (2 s) with a decreasing tendency after 1250 ms. All these effects cannot be found in the EEG before entering the burst suppression period (BSP). The transient coupling phenomena in the EEG bursts during BSP can be regarded as indicators for short-term interrelations between the underlying electrophysiologic processes. CONCLUSIONS It can be suggested that the method introduced for the quantification of the sedation depth should be used.

Learning continuous trajectories in recurrent neural networks with time-dependent weights

This paper is concerned with a general learning (with arbitrary criterion and state-dependent constraints) of continuous trajectories by means of recurrent neural networks with time-varying weights. The learning process is transformed into an optimal control framework, where the weights to be found are treated as controls. A new learning algorithm based on a variational formulation of Pontryagins maximum principle is proposed. This algorithm is shown to converge, under reasonable conditions, to an optimal solution. The neural networks with time-dependent weights make it possible to efficiently find an admissible solution (i.e., initial weights satisfying state constraints) which then serves as an initial guess to carry out a proper minimization of a given criterion. The proposed methodology may be directly applicable to both classification of temporal sequences and to optimal tracking of nonlinear dynamic systems. Numerical examples are also given which demonstrate the efficiency of the approach presented.