Lutz Leistritz

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.

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.

Light paths in retinal vessel oximetry

The oxygen utilization and, therefore, the metabolic state, of a distinctive area of the retina may be calculated from the diameter of the supplying artery and vein, the haemoglobin oxygenation, and the velocity of the blood. The first two parameters can be determined by imaging spectrometry at the patients ocular fundus. However the reflected light emerging from a vessel followed different pathways through the ocular fundus layers and the vessel embedded in the retina. The contribution of the single pathways to the vessel reflection profile is investigated by a Monte Carlo simulation. Considering retinal vessels with diameters of 25-200 /spl mu/m we found the reflection from a thin vessel to be determined by the single and double transmission of light at 560 nm. The backscattering from the blood column determines the reflectance in the case of a thick vessel. However, both components are in the same order of magnitude. This has to be considered in the calculation of the oxygen saturation of blood in retinal vessels from their reflection spectra.

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.

New Approaches for the Detection and Analysis of Electroencephalographic Burst-Suppression Patterns in Patients under Sedation

An automatic EEG pattern detection unit was developed and tested for the recognition of burst-suppression periods and for the separation of burst from suppression patterns. The median, standard deviation and the 95% edge frequency were computed from single channels of the EEG within a moving window and completed by the continuous computation of frequency band power via an adapted Hilbert resonance filter. These parameters were given to the inputs of two hierarchically arranged artificial neural networks (NNs). The output signals of NNs indicate the suppression and burst phases. The burst recognition was focused on the precise recognition of the burst onset. In subsequent processing steps the time course of percentages of burst patterns within their corresponding burst-suppression-phases was calculated and the time locations of burst onsets can be used to trigger an averaging for a burst-related analysis. The data for our investigations were derived from the routine EEG derivations of 12 patients with various neurosurgical diseases. A group-related training of the NNs was realized. For the group-related trained NNs EEG data for 6 patients were used for training and the data of 6 other patients for testing the classification performance of the pattern recognition units. Additionally, the reliability of the detection algorithm was tested with data of two patients with convulsive state, resistant to treatment, and burst-suppression like pattern EEG.

Imaging spectroscopy of the human ocular fundus in vivo

Spectroscopic measurement of light that is reflected from biological tissue in vivo is being investigated for various clinical applications. One special object of investigation using optical methods is the human ocular fundus. A fundus reflectometer that enables the simultaneous acquisition of up to 192 spectra arranged in a horizontal line across the fundus is described. The underlying optical principle of the device is the confocal imaging of an illuminated narrow, slitlike field at the fundus to the entrance slit of a spectrograph. This is imaged by the grating of the spectrograph onto a two-dimensional CCD chip that records the local distribution of ocular fundus reflectance spectra within a wavelength range of 400 up to 710 nm with a resolution better than 2 nm and a local resolution of 23 mm in a field dimension of 1.5 mm. The performance of the device was investigated, the effects of confocal and nonconfocal imaging are discussed, and some representative measurements are presented.

Time-variant partial directed coherence for analysing connectivity: A methodological study

For the past decade, the detection and quantification of interactions within and between physiological networks has become a priority-in-common between the fields of biomedicine and computer science. Prominent examples are the interaction analysis of brain networks and of the cardiovascular–respiratory system. The aim of the study is to show how and to what extent results from time-variant partial directed coherence analysis are influenced by some basic estimator and data parameters. The impacts of the Kalman filter settings, the order of the autoregressive (AR) model, signal-to-noise ratios, filter procedures and volume conduction were investigated. These systematic investigations are based on data derived from simulated connectivity networks and were performed using a Kalman filter approach for the estimation of the time-variant multivariate AR model. Additionally, the influence of electrooculogram artefact rejection on the significance and dynamics of interactions in 29 channel electroencephalography recordings, derived from a photic driving experiment, is demonstrated. For artefact rejection, independent component analysis was used. The study provides rules to correctly apply particular methods that will aid users to achieve more reliable interpretations of the results.

How Do Brain Areas Communicate During the Processing of Noxious Stimuli? An Analysis of Laser-Evoked Event-Related Potentials Using the Granger Causality Index

Several imaging techniques have identified different brain areas involved in the processing of noxious stimulation and thus in the constitution of pain. However, only little is known how these brain areas communicate with one another after activation by stimulus processing and which areas directionally affect or modulate the activity of succeeding areas. One measure for the analysis of such interactions is represented by the Granger Causality Index (GCI). In applying time-varying bivariate and partial variants of this concept (tvGCI), the aim of the present study was to investigate the interaction of neural activities between a set of scalp electrodes that best represent the brain electrical neural activity of major cortical areas involved in the processing of noxious laser-heat stimuli and their variation in time. Bivariate and partial tvGCIs were calculated within four different intervals of laser-evoked event-related potentials (LEPs) including a baseline period prior to stimulus application and three intervals immediately following stimulus application, i.e., between 170 and 200 ms (at the N2 component), between 260 and 320 ms (P2 component), and between 320 and 400 ms (P3 component of LEPs). Results show some similarities, but also some striking differences between bivariate and partial tvGCIs. These differences might be explained by the nature of bivariate and partial tvGCIs. However, both tvGCI approaches revealed a directed interaction between medial and lateral electrodes of the centroparietal region. This result was interpreted as a directed interaction between the anterior cingulate cortex and the secondary somatosensory cortex and the insula, structures that are significantly involved in the constitution of pain.

Training trajectories by continuous recurrent multilayer networks

This paper addresses the problem of training trajectories by means of continuous recurrent neural networks whose feedforward parts are multilayer perceptrons. Such networks can approximate a general nonlinear dynamic system with arbitrary accuracy. The learning process is transformed into an optimal control framework where the weights are the controls to be determined. A training algorithm based upon a variational formulation of Pontryagins maximum principle is proposed for such networks. Computer examples demonstrating the efficiency of the given approach are also presented.

Detection of directed information flow in biosignals

Abstract Several analysis techniques have been developed for time series to detect interactions in multidimensional dynamic systems. When analyzing biosignals generated by unknown dynamic systems, awareness of the different concepts upon which these analysis techniques are based, as well as the particular aspects the methods focus on, is a basic requirement for drawing reliable conclusions. For this purpose, we compare four different techniques for linear time series analysis. In general, these techniques detect the presence of interactions, as well as the directions of information flow, in a multidimensional system. We review the different conceptual properties of partial coherence, a Granger causality index, directed transfer function, and partial directed coherence. The performance of these tools is demonstrated by application to linear dynamic systems.