Karin Schiecke

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, Frequency-Selective, Linear and Nonlinear Analysis of Heart Rate Variability in Children With Temporal Lobe Epilepsy

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 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

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.

Time-Variant Modeling of Brain Processes

In science and engineering mathematical modeling serves as a tool for the understanding of processes and systems and as a testing bed for several hypotheses, e.g., concerning the testing (prediction) of functional limits by simulations. A brief overview of current modeling strategies in brain research is given, spatial scales ranging from single neuron to large scale activity of and between brain regions are considered. The models are mainly time-invariant. Three time-variant modeling strategies, which enable a model-based signal analysis, are described and applied to large scale signals. The first is derived from adaptive filter theory and covers linear system and linear as well as nonlinear process models. The second is based on modeled brain source signals, i.e., the inverse problem must be solved. The third strategy consists of a generalization of Dynamic Causal Modeling (DCM); DCM is frequently used for analysis of directed interactions between brain structures. Examples are derived from neonatal electroencephalography (EEG) monitoring of preterm and fullterm newborns. A further example is based on high-density recordings of event-related potentials (ERPs) and shows the combination of a time-variant ERP-based source model, as a part of a realistic head model, with a multivariate process model to analyze the time evolution of interactions between source processes before and during the execution of a complex motoric task. In two other examples hemodynamic signals (functional magnetic resonance imaging-fMRI) are utilized for analysis of interactions between brain regions, where nonlinear, multivariate models are used.

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.

Matching Pursuit-Based Time-Variant Bispectral Analysis and its Application to Biomedical Signals

Objective: Principle aim of this study is to investigate the performance of a matching pursuit (MP)-based bispectral analysis in the detection and quantification of quadratic phase couplings (QPC) in biomedical signals. Nonlinear approaches such as time-variant bispectral analysis are able to provide information about phase relations between oscillatory signal components. Methods: Time-variant QPC analysis is commonly performed using Gabor transform (GT) or Morlet wavelet transform (MWT), and is affected by either constant or frequency-dependent time-frequency resolution (TFR). The matched Gabor transform (MGT), which emerges from the incorporation of GT into MP, can overcome this obstacle by providing a complex time-frequency plane with an individually tailored TFR for each transient oscillatory component. QPC analysis was performed by MGT, and MWT was used as the state-of-the-art method for comparison. Results: Results were demonstrated using simulated data, which present the general case of QPC, and biomedical benchmark data with a priori knowledge about specific signal components. HRV of children during temporal lobe epilepsy and EEG during burst-interburst pattern of neonates during quiet sleep were used for the biomedical signal analysis to investigate the two main areas of biomedical signal analysis: The cardiovascular-cardiorespiratory system and neurophysiological brain activities, respectively. Simulations were able to show the applicability and reliability of the MGT for bispectral analysis. HRV and EEG analysis demonstrate the general validity of the MGT for QPC detection by quantifying statistically significant time patterns of QPC. Conclusion and Significance: Results confirm that MGT-based bispectral analysis provides significant benefits for the analysis of QPC in biomedical signals.

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.

Rod Driven Frequency Entrainment and Resonance Phenomena

A controversy exists on photic driving in the human visual cortex evoked by intermittent photic stimulation. Frequency entrainment and resonance phenomena are reported for frequencies higher than 12 Hz in some studies while missing in others. We hypothesized that this might be due to different experimental conditions, since both high and low intensity light stimulation were used. However, most studies do not report radiometric measurements, which makes it impossible to categorize the stimulation according to photopic, mesopic, and scotopic vision. Low intensity light stimulation might lead to scotopic vision, where rod perception dominates. In this study, we investigated photic driving for rod-dominated visual input under scotopic conditions. Twelve healthy volunteers were stimulated with low intensity light flashes at 20 stimulation frequencies, leading to rod activation only. The frequencies were multiples of the individual alpha frequency (α) of each volunteer in the range from 0.40 to 2.30∗α. Three hundred and six-channel whole head magnetoencephalography recordings were analyzed in time, frequency, and spatiotemporal domains with the Topographic Matching Pursuit algorithm. We found resonance phenomena and frequency entrainment for stimulations at or close to the individual alpha frequency (0.90–1.10∗α) and half of the alpha frequency (0.40–0.55∗α). No signs of resonance and frequency entrainment phenomena were revealed around 2.00∗α. Instead, on-responses at the beginning and off-responses at the end of each stimulation train were observed for the first time in a photic driving experiment at frequencies of 1.30–2.30∗α, indicating that the flicker fusion threshold was reached. All results, the resonance and entrainment as well as the fusion effects, provide evidence for rod-dominated photic driving in the visual cortex.