Wolfram Hesse

The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies.

Understanding of brain functioning requires the investigation of activated cortical networks, in particular the detection of interactions between different cortical sites. Commonly, coherence and correlation are used to describe interrelations between EEG signals. However, on this basis, no statements on causality or the direction of their interrelations are possible. Causality between two signals may be expressed in terms of upgrading the predictability of one signal by the knowledge of the immediate past of the other signal. The best-established approach in this context is the so-called Granger causality. The classical estimation of Granger causality requires the stationarity of the signals. In this way, transient pathways of information transfer stay hidden. The study presents an adaptive estimation of Granger causality. Simulations demonstrate the usefulness of the time-variant Granger causality for detecting dynamic causal relations within time intervals of less than 100 ms. The time-variant Granger causality is applied to EEG data from the Stroop task. It was shown that conflict situations generate dense webs of interactions directed from posterior to anterior cortical sites. The web of directed interactions occurs mainly 400 ms after the stimulus onset and lasts up to the end of the task.

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.

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.

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.

Development of interaction measures based on adaptive non-linear time series analysis of biomedical signals / Entwicklung von Interaktionsmaßen auf der Grundlage adaptiver, nichtlinearer Zeitreihenanalyse von biomedizinischen Signalen

Abstract An important feature of interaction between two signal components is the direction of the interaction. Recently, different methods have been developed and applied for detecting the direction of interactions. Besides frequency-dependent methods, Granger causality is a well-known frequency-independent approach. One popular linear approach is based on autoregressive modeling of the underlying process and evaluates prediction errors under different past assumptions. In the present study, this linear concept is extended to self-exciting threshold autoregressive models, which cover a wider class of processes. An approach for the definition of a state-dependent Granger causality is given and applied to simulated data.

Coupled oscillators for modeling and analysis of EEG/MEG oscillations

Abstract This study presents three EEG/MEG applications in which the modeling of oscillatory signal components offers complementary analysis and an improved explanation of the underlying generator structures. Coupled oscillator networks were used for modeling. Parameters of the corresponding ordinary coupled differential equation (ODE) system are identified using EEG/MEG data and the resulting solution yields the modeled signals. This model-related analysis strategy provides information about the coupling quantity and quality between signal components (example 1, neonatal EEG during quiet sleep), allows identification of the possible contribution of hidden generator structures (example 2, 600-Hz MEG oscillations in somatosensory evoked magnetic fields), and can explain complex signal characteristics such as amplitude-frequency coupling and frequency entrainment (example 3, EEG burst patterns in sedated patients).

Estimation of the time-varying cortical connectivity patterns by the adaptive multivariate estimators in high resolution EEG studies

The Directed Transfer Function (DTF) and the Partial Directed Coherence (PDC) are frequency-domain estimators, based on the multivariate autoregressive modelling (MVAR) of time series, that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods requires the stationary 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). This approach will allow the observation of transient influences between the cortical areas during the execution of a task. Time-varying DTF and PDC were obtained by the adaptive recursive fit of an MVAR model with time-dependent parameters, by means of a generalized recursive least-square (RLS) algorithm, taking into consideration a set of EEG epochs. Simulations were performed under different levels of Signal to Noise Ratio (SNR), number of trials (TRIALS) and frequency bands (BAND), and of different values of the RLS adaptation factor adopted (factor C). The results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of SNR ad number of trials. Moreover, the capability of follow the rapid changes in connectivity is highly increased by the number of trials at disposal, and by the right choice of the value adopted for the adaptation factor C. The results of the simulation study indicate that DTF and PDC computed on adaptive MVAR can be effectively used to estimate time-varying patterns of functional connectivity between cortical activations, under general conditions met in practical EEG recordings

Multivariate Time Series Analysis

Nowadays, modern measurement devices are capable to deliver signals with increasing data rates and higher spatial resolutions. When analyzing these data, particular interest is focused on disentangling the network structure underlying the recorded signals. Neither univariate nor bivariate analysis techniques are expected to describe the interactions between the processes sufficiently well. Moreover, the direction of the direct interactions is particularly important to understand the underlying network structure sufficiently well. Here, we present multivariate approaches to time series analysis being able to distinguish direct and indirect, in some cases the directions of interactions in linear as well as nonlinear systems.

Time-varying cortical connectivity by adaptive multivariate estimators applied to a combined foot-lips movement

In this paper we propose the use of an adaptive multivariate approach to define time-varying multivariate estimators based on the directed transfer function (DTF) and the partial directed coherence (PDC). DTF and PDC are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. Time-varying DTF and PDC were obtained by the adaptive recursive fit of an MVAR model with time- dependent parameters, by means of a generalized recursive least-square (RLS) algorithm, taking into consideration a set of EEG epochs. Such estimators are able to follow rapid changes in the connectivity between cortical areas during an experimental task. 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, one constant across the task and the other evolving during the preparation of the joint movement.