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.
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.
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.
Different regions of the brain must communicate with each other to provide the basis for the integration of sensory information, sensory-motor coordination and many other functions that are critical ...for learning, memory, information processing, perception and the behaviour of organisms. Hebb suggested that this is accomplished by the formation of assemblies of cells whose synaptic linkages are strengthened whenever the cells are activated or 'ignited' synchronously. Hebb's seminal concept has intrigued investigators since its formulation, but the technology to demonstrate its existence had been lacking until the past decade. Previous studies have shown that very fast electroencephalographic activity in the gamma band (20-70 Hz) increases during, and may be involved in, the formation of percepts and memory, linguistic processing, and other behavioural and preceptual functions. We show here that increased gamma-band activity is also involved in associative learning. In addition, we find that another measure, gamma-band coherence, increases between regions of the brain that receive the two classes of stimuli involved in an associative-learning procedure in humans. An increase in coherence could fulfil the criteria required for the formation of hebbian cell assemblies, binding together parts of the brain that must communicate with one another in order for associative learning to take place. In this way, coherence may be a signature for this and other types of learning.
An advanced graph theoretical approach is introduced that enables a higher level of functional interpretation of samples of directed networks with identical fixed pairwise different vertex labels ...that are drawn from a particular population. Compared to the analysis of single networks, their investigation promises to yield more detailed information about the represented system. Often patterns of directed edges in sample element networks are too intractable for a direct evaluation and interpretation. The new approach addresses the problem of simplifying topological information and characterizes such a sample of networks by finding its locatable characteristic topological patterns. These patterns, essentially sample-specific network motifs with vertex labeling, might represent the essence of the intricate topological information contained in all sample element networks and provides as well a means of differentiating network samples. Central to the accurateness of this approach is the null model and its properties, which is needed to assign significance to topological patterns. As a proof of principle the proposed approach has been applied to the analysis of networks that represent brain connectivity before and during painful stimulation in patients with major depression and in healthy subjects. The accomplished reduction of topological information enables a cautious functional interpretation of the altered neuronal processing of pain in both groups.
This study investigated electroencephalographic correlates in chronically depressed patients compared to healthy controls using intracutaneously applied electrical pain stimulus, to better understand ...the interaction between pain processing and depression. A close interaction between pain and depression is generally recognized although the precise mechanisms are not yet fully understood. The present study focuses on the hypothesis that effective brain connectivity in major depression patients is altered. Multifunctional interactions between brain regions represent a robust index of effective interactions within the brain, and can be quantified by network redundancy. Thus, structural network differences between 18 normal controls and 18 major depression patients before as well as during the processing of moderately painful intracutaneous electrical stimuli were investigated on the basis of network redundancy differences. In our sample, both patients and control subjects exhibit comparable network redundancies before stimulus application. Caused by the stimulus, there is a global increase of network redundancy in both groups. This increase is diminished in the group of major depression patients. We found clear differences between patients and controls during the stimulus processing, where the network redundancy in normal controls is larger in comparison to patients. The differences might be explained by the fact that major depression patients are more restricted to the affective component of the processing. The well-established biasing to affective processing might suppress the somatosensory processing resulting in a lower number of connections within the considered network. This might then lead to a reduction in network redundancy during stimulus processing.
Low-frequency (0.5–2.5 Hz) and individually defined high-frequency (7–11 or 8–12 Hz; 11–15 or 14–18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from ...thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17–26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude–frequency dependencies (envelope–envelope, envelope–frequency, and frequency–frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude–frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope–envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5–2.5 and 7–11 or 8–12 Hz); (3) the rise characteristics of all individually averaged envelope–frequency courses (IE–IF) are strongly correlated; (4) for the 7–11 or 8–12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude–frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7–11 or 8–12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5–2.5 and 7–11 or 8–12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude–frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.
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.
Evoked and induced activities are two typical components in the EEG and MEG time series after a stimulation. While evoked activity is phase-locked to the stimulus, induced activity is not. Present ...analysis methods are able to detect non-phase-locked parts of the signal, however, they do not improve the signal-to-noise ratio (SNR) of these signal components.
We present a new method for estimating induced activation in EEG multi-trial data sets. It is based on the multiple correlation of single trials. Our method not only detects induced components within the EEG signal, it also improves their SNR. The method is successfully tested with artificial data sets. Application to real data is exemplified using EEG data recorded in a photic driving experiment.
We show that the SNR of the induced activity is enhanced by our method, and the method found longer lasting induced activity after the end of stimulation compared with a conventional method.
•EEG missing values.•Handling of imputation methods.•Imputation for neuronal networks.
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.
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