Understanding the human brain requires the incorporation of functional interaction patterns that depend on a variety of features like experimental setup, strength of directed connectedness or variability between several individuals or groups. In addition to these external factors, there are internal properties of the brain network as for example temporal propagation of connections, or connectivity patterns that only occur in a distinct frequency range of the signal. The visualization of detected networks covering all necessary information poses a substantial problem which is mainly due to the high number of features that have to be integrated within the same view in a natural spatial context.

In neuroscience, the investigation of connectivity between different brain regions suffers from the lack of adequate solutions for visualizing detected networks. One reason is the high number of dimensions that have to be combined within the same view: neuroscientists examine brain connectivity in its natural spatial context across the additional dimensions time and frequency. To combine all these dimensions without prior merging or filtering steps, we propose a visualization in virtual reality to realize multiple coordinated views of the networks in a virtual visual analysis lab. We implemented a prototype of the new idea. In a first qualitative user study we included experts in the field of computer science, psychology as well as neuroscience. Time series of electroencephalography recordings evoked by visual stimuli were used to provide a first proof of concept trial.The positive user feedback shows that our application successfully fills a gap in the visualization of high-dimensional brain networks.

The detection of directed interactions within networks derived from spatially highly resolved data, such as functional magnetic resonance imaging (fMRI) has been a challenging task for the last years. Commonly this is solved by restricting the analysis to a small number of representative network nodes (e.g. fMRI voxels), to regions of interest (e.g. brain areas) or by using dimension reduction methods like principal or independent component analysis. Recently, these problems have successfully been encountered by combining multivariate autoregressive models and parallel factor analysis. This approach involves a cascade of analysis steps, entailing a number of parameters that have to be chosen carefully. Yet, the question of an appropriate choice of analysis parameters has not been clarified so far-in particular for temporally varying models. In this work we fill this gap. Synthetic data with known underlying ground truth structure are generated to evaluate the correctness of results in dependence on the parameter choice. Resting state fMRI data are used to assess the influence of the involved parameters in the clinical application. We found that model residuals offer a good means for determining appropriate filter algorithm parameters; the model order should be chosen according to two aspects: the well-established information criteria and the fit between Fourier and estimated spectra.

Analysis of electroencephalographic (EEG) data requires cautious consideration of interfering artefacts such as ocular, muscular or cardiac noise. Independent component analysis (ICA) has proven to be a powerful tool for the detection and separation out of these contaminating components from brain activity. Yet thus far thorough investigation is lacking into how this pre-processing step might affect or even distort the information on brain connectivity inherent in the raw signals. The aim of this work is to address this question by systematically investigating and comparing three different strategies: first, analysis of all network nodes without eliminating contamination; second, removing the node which is contaminated by artefacts; third, using the ICA artefact removal method as an initial step prior to the analysis. Multivariate, time-variant autoregressive models are used to approximate the recorded data; the assessment of information flow within the modelled networks is carried out by means partial directed coherence, offering a frequency-selective estimation of connectivity.

Appropriate analyses of directed complex interactions within the cardiovascular-respiratory system are of growing interest for a better understanding of physiological regulatory mechanisms in healthy subjects and diseased persons. There are various concepts to analyze such interactions. Convergent Cross Mapping (CCM) provides the possibility to define directed interactions in terms of nonlinear stability. A proof-of-principle approach is introduced to apply CCM to cardiovascular-respiratory data of healthy subjects during resting state period. Showing group results of time-invariant as well as single subject results of interval-based CCM, the introduced approach was able to quantify correct directionality and strength of interactions within the cardiovascular-respiratory system and to provide statistical thresholds for significant interactions. These results may serve as a methodological base to compare healthy subjects and diseased persons.

Whenever neurophysiological data, such as EEG data are recorded, occurring artifacts pose an essential problem. This study addresses this issue by using imputation methods whereby whole data sets of a trial, or distinct electrodes, are not removed from the analysis of the EEG data but are replaced. We present different imputation strategies but use only two which are optimal for this particular study; predictive mean matching and data augmentation. The study addresses the as of yet unresolved question if the quality of derived brain functional networks is improved by imputation methods compared to traditional exclusion techniques which drop data, and will finally assesses the differences between the two imputation methods themselves used here. In this study, EEG data from a study evaluating dyslexia-specific therapy on a neurophysiological level were used to investigate imputation strategies in research of cortical interaction. Several recorded values were artificially declared as 'missing'. This enables the comparison of networks based on the complete data set without any missing values (pseudo ground truth) and those derived from imputation approaches in a realistic situation of disturbed data. Functional connectivity was quantified by time-variant partial directed coherence, providing a directed, temporally varying and frequency-selective connectivity measure. Based on the comparison between pseudo ground truth and networks of data with excluded missing values and data with imputed values, we found that any imputation strategy is preferable to the entire exclusion of data. The study also showed that the choice of the applied imputation algorithm impacts the resulting networks only marginally.

Analyzing directed interactions within brain networks of high spatial resolution is always associated with a limited interpretability due to the high amount of possible connections. Here, module detection algorithms have proven to helpfully subsume the information of the resulting networks for each proband. However, the between-subject comparison of clusters is not straightforward since identified modules are not matched to each other across different subjects. Tensor decomposition has successfully been applied for the detection of group-wide connectivity patterns. Yet, a thorough investigation of the effect of the involved analysis parameters and data properties on decomposition results has still been missing. In this study we filled this gap and found that - given appropriate parameter choices - tensor decomposition of functional connectivity data reveals meaningful, group-specific insights into the brain's information processing.

Identification of module structure in brain functional networks is a promising way to obtain novel insights into neural information processing, as modules correspond to delineated brain regions in which interactions are strongly increased. Tracking of network modules in time-varying brain functional networks is not yet commonly considered in neuroscience despite its potential for gaining an understanding of the time evolution of functional interaction patterns and associated changing degrees of functional segregation and integration. We introduce a general computational framework for extracting consensus partitions from defined time windows in sequences of weighted directed edge-complete networks and show how the temporal reorganization of the module structure can be tracked and visualized. Part of the framework is a new approach for computing edge weight thresholds for individual networks based on multiobjective optimization of module structure quality criteria as well as an approach for matching modules across time steps. By testing our framework using synthetic network sequences and applying it to brain functional networks computed from electroencephalographic recordings of healthy subjects that were exposed to a major balance perturbation, we demonstrate the framework's potential for gaining meaningful insights into dynamic brain function in the form of evolving network modules. The precise chronology of the neural processing inferred with our framework and its interpretation helps to improve the currently incomplete understanding of the cortical contribution for the compensation of such balance perturbations.

Background. The quantification of directed interactions within the brain and in particular their time courses are of highest interest for the investigation of epilepsy. The underlying coordinated neuronal mass activities span functionally diverse and structurally widely distributed cortical and subcortical brain regions, i.e. dynamic, distributed epileptic network can be assumed possibly not fitting in the concept of linearity. Consequently, nonlinear, time-variant, and directed connectivity and synchronization analysis could be helpful to understand processes contributing to the seizure onset and propagation.Methods. The nonlinear convergent cross mapping (CCM) quantifies directed interactions between time series by using nonlinear state space reconstruction. CCM is applied to the EEG of 18 children with temporal lobe epilepsy (TLE), i.e. directed interactions within EEG activity and within specific components of EEG activity (delta-activity and alpha-activity) are investigated. Linear time-variant multivariate AR modeling was performed for these data to test for subsequent applications of linear AR-based connectivity measures.Results. Linear MVAR models proved to be inappropriate for our data. Time-varying application of CCM revealed that statistically significant nonlinear interactions within the EEG activity and within specific components of the EEG exist in the preictal, ictal, and postictal periods. Distinct time courses of such interactions and differences in the time pattern of interactions occurring in the different components of EEG activity that we investigated discovered the high complexity of the underlying processes. No distinct results could be found concerning the presumed directionalities of interactions. Statistical relevant interactions were quantified by bootstrapping and surrogate data approach.Conclusion. Advanced nonlinear CCM approach was able to uncover time pattern of nonlinear interactions thereby possibly contributing to the further understanding of complex behavior of the brain during TLE. Our investigation may provide deeper insight into physiological state of complex networks, e.g. during the development of an epileptic seizure or the recovery in the postictal state.

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.

The connectivity analysis of spatially highly resolved data results in networks comprising an immense number of nodes and edges which makes it hard or even impossible to investigate the high-dimensional (HD) network as a whole. A solution to this problem is offered by a connectivity-based segmentation of the HD networks into subsets of functionally similar nodes (network modules) that exhibit pronounced interaction. However, an investigation of the results at group level is problematic as identified modules are not assigned to each other across different subjects. In this work, we propose a rearrangement of the subject-specific networks into an integrative tensor which is subsequently decomposed into additive factors. This reorganization provides subject-independent networks together with subject-specific loadings enabling a group-wide segmentation of the resulting networks at the large scale.

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.

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.

In neuroscience, data are typically generated from neural network activity. Complex interactions between measured time series are involved, and nothing or only little is known about the underlying dynamic system. Convergent Cross Mapping (CCM) provides the possibility to investigate nonlinear causal interactions between time series by using nonlinear state space reconstruction. Aim of this study is to investigate the general applicability, and to show potentials and limitation of CCM. Influence of estimation parameters could be demonstrated by means of simulated data, whereas interval-based application of CCM on real data could be adapted for the investigation of interactions between heart rate and specific EEG components of children with temporal lobe epilepsy.

Spatially high resolved neurophysiological data commonly pose a computational and analytical problem for the identification of functional networks in the human brain. We introduce a multivariate linear Granger Causality approach with an embedded dimension reduction that enables the computation of brain networks at the large scale. In order to grasp the information about connectivity patterns contained in the resulting high-dimensional directed networks, we furthermore propose the inclusion of module detection methods from network theory that can help to identify functionally associated brain areas. As a proof of concept, the methodology is verified by means of synthetic data with known ground truth module properties. Resting state fMRI data are used to demonstrate the applicability and benefit in the case of clinical data.

Lithium therapy has been shown to affect imaging measures of brain function and microstructure in human immunodeficiency virus (HIV)-infected subjects with cognitive impairment. The aim of this proof-of-concept study was to explore whether changes in brain microstructure also entail changes in functional connectivity. Functional MRI data of seven cognitively impaired HIV infected individuals enrolled in an open-label lithium study were included in the connectivity analysis. Seven regions of interest (ROI) were defined based on previously observed lithium induced microstructural changes measured by Diffusion Tensor Imaging. Generalized partial directed coherence (gPDC), based on time-variant multivariate autoregressive models, was used to quantify the degree of connectivity between the selected ROIs. Statistical analyses using a linear mixed model showed significant differences in the average node strength between pre and post lithium therapy conditions. Specifically, we found that lithium treatment in this population induced changes suggestive of increased strength in functional connectivity. Therefore, by exploiting the information about the strength of functional interactions provided by gPDC we can quantify the connectivity changes observed in relation to a given intervention. Furthermore, in conditions where the intervention is associated with clinical changes, we suggest that this methodology could enable an interpretation of such changes in the context of disease or treatment induced modulations in functional networks.

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.

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; approximate to 0.1 Hz) before and after the seizure were identified. The frequency ranges of these IMFs correspond to the EEG delta-band. The time-variant coherence was statistically quantified and tensor decomposition of the time-frequency coherence maps was applied to explore the topography-time-frequency characteristics of the coherence analysis. Results allow the hypothesis that couplings between the CAN, which controls the cardiovascular-cardiorespiratory system, and the 'epileptic neural network' exist. Additionally, our results confirm the hypothesis of a right hemispheric lateralization of sympathetic cardiac control of the HRV-LF.