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.

We address the correspondence problem which arises when applying empirical mode decomposition (EMD) to multi-trial and multi-subject data. EMD decomposes a signal into a set of narrow-band components named intrinsic mode functions (IMFs). The number of IMFs and their signal properties can be different between trials, channels and subjects. In order to assign IMFs with similar characteristics to each other, we compare two assignment methods, unbalanced assignment and k-cardinality assignment and two clustering algorithms, namely hierarchical clustering and density-based spatial clustering of applications with noise based on heart rate variability data of children with temporal lobe epilepsy.

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.

Clinical electroencephalographic (EEG) data are often contaminated by muscle and eye movement artefacts that can strongly influence the following analysis. Two existing methods (Independent Component Analysis and Robust Artefact Removal) used for the rejection of artefacts are applied to EEG data from epileptic patients. A comparison between the methods and a discussion on the results are made.

Summary Objectives: Empirical mode decomposition (EMD) is a frequently used signal processing approach which adaptively decomposes a signal into a set of narrow-band components known as intrinsic mode functions (IMFs). For multi-trial, multivariate (multiple simultaneous recordings), and multi-subject analyses the number and signal properties of the IMFs can deviate from each other between trials, channels and subjects. A further processing of IMFs, e.g. a simple ensemble averaging, should determine which IMFs of one signal correspond to IMFs from another signal. When the signal properties have similar characteristics, the IMFs are assigned to each other. This problem is known as correspondence problem. Methods: From the mathematical point of view, in some cases the correspondence problem can be transformed into an assignment problem which can be solved e.g. by the Kuhn-Munkres algorithm (KMA) by which a minimal cost matching can be found. We use the KMA for solving classic assignment problems, i.e. the pairwise correspondence between two sets of IMFs of equal cardinalities, and for pairwise correspondences between two sets of IMFs with different cardinalities representing an unbalanced assignment problem which is a special case of the k-cardinality assignment problem. Results: A KMA-based approach to solve the correspondence problem was tested by using simulated, heart rate variability (HRV), and EEG data. The KMA-based results of HRV decomposition are compared with those obtained from a hierarchical cluster analysis (state-of-the-art). The major difference between the two approaches is that there is a more consistent assignment pattern using KMA. Integrating KMA into complex analysis concepts enables a comprehensive exploitation of the key advantages of the EMD. This can be demonstrated by non-linear analysis of HRV-related IMFs and by an EMD-based cross-frequency coupling analysis of the EEG data. Conclusions: The successful application to HRV and EEG analysis demonstrates that our solutions can be used for automated EMD-based processing concepts for biomedical signals.

Aim of this study is to investigate advantages and disadvantages of empirical mode decomposition (EMD) approaches for the investigation of heart rate variability (HRV). Signal-adaptive approaches like EMD can be used to separate components of HRV which are associated with cardiovascular regulatory mechanisms. Two EMD approaches, standard EMD and complete empirical mode decomposition (CEMD) are used to decompose the HRV of children during temporal lobe epilepsy (TLE; 10 min recordings of 18 children). As nonlinear properties are preserved by EMD, analysis of nonlinear predictability of HRV components is applied resulting in a nonlinear, time-variant, frequency-selective examination of HRV. Especially mode mixing problems are investigated. Complementary analysis steps are suggested to detect their occurrence. CEMD is able to better separate defined HRV components and to reduce, but not completely solve, mode mixing. Nonlinear analysis of CEMD based HRV components results in more distinct differences between specific seizure-related states.

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.

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.

The major aim of our study is to demonstrate that a concerted combination of time-variant, frequency-selective, linear and nonlinear analysis approaches can be beneficially used for the analysis of heart rate variability (HRV) in epileptic patients to reveal premonitory information regarding an imminent seizure and to provide more information on the mechanisms leading to changes of the autonomic nervous system. The quest is to demonstrate that the combined approach gains new insights into specific short-term patterns in HRV during preictal, ictal, and postictal periods in epileptic children. The continuous Morlet-wavelet transform was used to explore the time-frequency characteristics of the HRV using spectrogram, phase-locking, band-power and quadratic phase coupling analyses. These results are completed by time-variant characteristics derived from a signal-adaptive approach. Advanced empirical mode decomposition was utilized to separate out certain HRV components, in particular blood-pressure-related Mayer waves (≈0.1 Hz) and respiratory sinus arrhythmia (≈0.3 Hz). Their time-variant nonlinear predictability was analyzed using local estimations of the largest Lyapunov exponent (point prediction error). Approximately 80-100 s before the seizure onset timing and coordination of both HRV components can be observed. A higher degree of synchronization is found and with it a higher predictability of the HRV. All investigated linear and nonlinear analyses contribute with a specific importance to these results.

Time-variant coherence between the heart rate variability and the channel-related envelopes of the EEG delta activity was used as an indicator for interactions between the autonomic nervous system and cortical processes before, during and after epileptic seizures. The tensor decomposition was applied to explore the topography-time-frequency characteristics of these correlative interactions for each patient and for two sub-groups (left and right hemispheric seizure). It can be demonstrated that tensor decomposition strongly supports the interaction analysis and its interpretation.

This study investigates the connectivity between EEG signals (cortical connectivity - CC) as well as between EEG-envelopes and heart rate variability (cortical-neurovegetative connectivity - CNC) by using time-variant Partial Directed Coherence analysis (for CC) and Wavelet Coherence (for CNC). Data from 18 patients suffering from temporal lobe epilepsy has been used to test our methodological approaches. The analysis intervals contain 5 min before and 5 min after seizure onset. Accordingly, the dynamics of the CC and CNC connectivity networks can be studied before, during and after the seizure. Our results concerning CC (1.5 - 4 Hz) demonstrate that the same lateralization of interaction networks exists before and during seizure, i.e. the interaction networks are clearly on the side of the epileptic focus. Additionally, the number of interactions is increased during the seizure. All results with regard to CNC support our hypothesis of interrelations between the neurovegetative system and cortical brain structures.

The analysis of the fetal heart rate (fHR) is important in detecting the fetal distress related with hypoxic episodes, noticed sometimes during the uterine activity, which can severely affect the fetus. Occasional synchrony between the fHR and the maternal heart rate (mHR) was reported and the mHR shows some variations during pregnancy and labor, especially when the contractions are very strong. The current study proposes a new strategy to investigate the relations between the fHR, the mHR and the uterine activity, by applying the time-variant Partial Directed Coherence (tvPDC).