Britta Pester

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.

Time-variant coherence between heart rate variability and EEG activity in epileptic patients: an advanced coupling analysis between physiological networks

Time-variant coherence analysis between the heart rate variability (HRV) and the channel-related envelopes of adaptively selected EEG components was used as an indicator for the occurrence of (correlative) couplings between the central autonomic network (CAN) and the epileptic network before, during and after epileptic seizures. Two groups of patients were investigated, a group with left and a group with right hemispheric temporal lobe epilepsy. The individual EEG components were extracted by a signal-adaptive approach, the multivariate empirical mode decomposition, and the envelopes of each resulting intrinsic mode function (IMF) were computed by using Hilbert transform. Two IMFs, whose envelopes were strongly correlated with the HRV’s low-frequency oscillation (HRV-LF; ≈0.1Hz) before and after the seizure were identified. The frequency ranges of these IMFs correspond to the EEG delta-band. The timevariant coherence was statistically quantified and tensor decomposition of the time-frequency coherence maps was applied to explore the topography-timefrequency characteristics of the coherence analysis. Results allow the hypothesis

A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity.

Detecting changes of spatially high-resolution functional connectivity patterns in the brain is crucial for improving the fundamental understanding of brain function in both health and disease, yet still poses one of the biggest challenges in computational neuroscience. Currently, classical multivariate Granger Causality analyses of directed interactions between single process components in coupled systems are commonly restricted to spatially low- dimensional data, which requires a pre-selection or aggregation of time series as a preprocessing step. In this paper we propose a new fully multivariate Granger Causality approach with embedded dimension reduction that makes it possible to obtain a representation of functional connectivity for spatially high-dimensional data. The resulting functional connectivity networks may consist of several thousand vertices and thus contain more detailed information compared to connectivity networks obtained from approaches based on particular regions of interest. Our large scale Granger Causality approach is applied to synthetic and resting state fMRI data with a focus on how well network community structure, which represents a functional segmentation of the network, is preserved. It is demonstrated that a number of different community detection algorithms, which utilize a variety of algorithmic strategies and exploit topological features differently, reveal meaningful information on the underlying network module structure.

Nonlinear Directed Interactions Between HRV and EEG Activity in Children With TLE

Objective: Epileptic seizure activity influences the autonomic nervous system (ANS) in different ways. Heart rate variability (HRV) is used as indicator for alterations of the ANS. It was shown that linear, nondirected interactions between HRV and EEG activity before, during, and after epileptic seizure occur. Accordingly, investigations of directed nonlinear interactions are logical steps to provide, e.g., deeper insight into the development of seizure onsets. Methods: Convergent cross mapping (CCM) investigates nonlinear, directed interactions between time series by using nonlinear state space reconstruction. CCM is applied to simulated and clinically relevant data, i.e., interactions between HRV and specific EEG components of children with temporal lobe epilepsy (TLE). In addition, time-variant multivariate Autoregressive model (AR)-based estimation of partial directed coherence (PDC) was performed for the same data. Results: Influence of estimation parameters and time-varying behavior of CCM estimation could be demonstrated by means of simulated data. AR-based estimation of PDC failed for the investigation of our clinical data. Time-varying interval-based application of CCM on these data revealed directed interactions between HRV and delta-related EEG activity. Interactions between HRV and alpha-related EEG activity were visible but less pronounced. EEG components mainly drive HRV. The interaction pattern and directionality clearly changed with onset of seizure. Statistical relevant interactions were quantified by bootstrapping and surrogate data approach. Conclusion and Significance: In contrast to AR-based estimation of PDC CCM was able to reveal time-courses and frequency-selective views of nonlinear interactions for the further understanding of complex interactions between the epileptic network and the ANS in children with TLE.

Synchronization analysis between heart rate variability and EEG activity before, during, and after epileptic seizure

Abstract An innovative concept for synchronization analysis between heart rate (HR) components and rhythms in EEG envelopes is represented; it applies time-variant analyses to heart rate variability (HRV) and EEG, and it was tested in children with temporal lobe epilepsy (TLE). After a removal of ocular and movement-related artifacts, EEG band activity was computed by means of the frequency-selective Hilbert transform providing envelopes of frequency bands. Synchronization between HRV and EEG envelopes was quantified by Morlet wavelet coherence. A surrogate data approach was adapted to test for statistical significance of time-variant coherences. Using this processing scheme, significant coherence values between a HRV low-frequency sub-band (0.08–0.12 Hz) and the EEG δ envelope (1.5–4 Hz) occurring both in the preictal and early postictal periods of a seizure can be shown. Investigations were performed for all electrodes at 20-s intervals and for selected electrode pairs (T3÷C3, T4÷C4) in a time-variant mode. Synchronization was more pronounced in the group of right hemispheric TLE patients than in the left hemispheric group. Such a group-specific augmentation of synchronization confirms the hypothesis of a right hemispheric lateralization of sympathetic cardiac control of the low-frequency HRV components.

Advanced Insights into Functional Brain Connectivity by Combining Tensor Decomposition and Partial Directed Coherence.

Quantification of functional connectivity in physiological networks is frequently performed by means of time-variant partial directed coherence (tvPDC), based on time-variant multivariate autoregressive models. The principle advantage of tvPDC lies in the combination of directionality, time variance and frequency selectivity simultaneously, offering a more differentiated view into complex brain networks. Yet the advantages specific to tvPDC also cause a large number of results, leading to serious problems in interpretability. To counter this issue, we propose the decomposition of multi-dimensional tvPDC results into a sum of rank-1 outer products. This leads to a data condensation which enables an advanced interpretation of results. Furthermore it is thereby possible to uncover inherent interaction patterns of induced neuronal subsystems by limiting the decomposition to several relevant channels, while retaining the global influence determined by the preceding multivariate AR estimation and tvPDC calculation of the entire scalp. Finally a comparison between several subjects is considerably easier, as individual tvPDC results are summarized within a comprehensive model equipped with subject-specific loading coefficients. A proof-of-principle of the approach is provided by means of simulated data; EEG data of an experiment concerning visual evoked potentials are used to demonstrate the applicability to real data.

Exploring Effective Connectivity by a Granger Causality Approach with Embedded Dimension Reduction

We propose applying the linear Granger Causality concept to very high-dimensional time series. The approach is based on integrating dimensionality reduction into a multivariate time series model. If residuals of dimensionality reduced models can be transformed back into the original space, prediction errors in the high–dimensional space may be computed, and a Granger Causality Index (GCI) is properly defined. We provide a proof–of–principle, and compare the results with the classical GCI.

Impact of multivariate Granger causality analyses with embedded dimension reduction on network modules.

High dimensional functional MRI data in combination with a low temporal resolution imposes computational limits on classical Granger Causality analyses with respect to a large-scale representations of functional interactions in the brain. To overcome these limitations and exploit information inherent in resulting brain connectivity networks at the large scale, we propose a multivariate Granger Causality approach with embedded dimension reduction. Using this approach, we computed binary connectivity networks from resting state fMRI images and analyzed them with respect to network module structure, which might be linked to distinct brain regions with an increased density of particular interaction patterns as compared to inter-module regions. As a proof of concept, we show that the modular structure of these large-scale connectivity networks can be recovered. These results are promising since further analysis of large-scale brain network partitions into modules might prove valuable for understanding and tracing changes in brain connectivity at a more detailed resolution level than before.

Cortical Correlates of Human Balance Control

Balance control is a fundamental component of human every day motor activities such as standing or walking, and its impairment is associated with an increased risk of falling. However, in humans the exact neurobiological mechanisms underlying balance control are still unclear. Specifically, although previous studies have identified a number of cortical regions that become significantly activated during real or imagined balancing, the interactions within and between the relevant cortical regions remain to be investigated. The working hypothesis of this study is that cortical networks contribute to an optimization of balance control, and that this contribution can be revealed by partial directed coherence—a time-variant, frequency-selective and directed functional connectivity analysis tool. Electroencephalographic activity was recorded in 37 subjects during single-leg balancing on a stable as well as an unstable surface. Results of this study show that in the transition from balancing on a stable surface to an unstable surface, two topographically delimitable connectivity networks (weighted directed networks) are established; one associated with the alpha and one with the theta frequency band. The theta network sequence can be described as a set of subnetworks (modules) comprising the frontal, central and parietal cortex with individual temporal and spatial developments within and between those modules. In the alpha network, the occipital electrodes O1 and O2 act as a source, and the interactions propagate predominantly in the directions from occipital to parietal and to centro-parietal areas. These important findings indicate that balance control is supported by at least two functional cortical networks.

Pair-wise clustering of large scale Granger causality index matrices for revealing communities

The analysis of large ensembles of time series is a fundamental challenge in different domains of biomedical image processing applications, specifically in the area of functional MRI data processing. An important aspect of such analysis is the ability to reconstruct community network structures based on interactive behavior between different nodes of the network which are captured in such time series. In this study, we start with a previously proposed novel approach that applies the linear Granger Causality concept to very high-dimensional time series. This approach is based on integrating dimensionality reduction into a multivariate time series model. If residuals of dimensionality reduced models can be transformed back into the original space, prediction errors in the high–dimensional space may be computed, and a large scale Granger Causality Index (lsGCI) is properly defined. The primary goal of this study was then to present an approach for recovering network structure from such lsGCI interactions through the application of pair-wise clustering. We specifically focus on a clustering approach based on topographic mapping of proximity data (TMP) for this purpose. We demonstrate our approach with a simulated network composed of five pair-wise different internal networks with varying strengths of community structure (based on the number of inter-network vertices). Our results suggest that such pair-wise clustering with TMP is capable of reconstructing the structure of the original network from lsGCI matrices that record the interactions between different nodes of the network when there is sufficient disparity between the intra- and inter-network vertices.