Felix Siebenhühner

Measuring Information-Transfer Delays

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

Phase transfer entropy: a novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions.

We introduce here phase transfer entropy (Phase TE) as a measure of directed connectivity among neuronal oscillations. Phase TE quantifies the transfer entropy between phase time-series extracted from neuronal signals by filtering for instance. To validate the measure, we used coupled Neuronal Mass Models to both evaluate the characteristics of Phase TE and compare its performance with that of a real-valued TE implementation. We showed that Phase TE detects the strength and direction of connectivity even in the presence of such amounts of noise and linear mixing that typically characterize MEG and EEG recordings. Phase TE performed well across a wide range of analysis lags and sample sizes. Comparisons between Phase TE and real-valued TE estimates showed that Phase TE is more robust to nuisance parameters and considerably more efficient computationally. In addition, Phase TE accurately untangled bidirectional frequency band specific interaction patterns that confounded real-valued TE. Finally, we found that surrogate data can be used to construct appropriate null-hypothesis distributions and to estimate statistical significance of Phase TE. These results hence suggest that Phase TE is well suited for the estimation of directed phase-based connectivity in large-scale investigations of the human functional connectome.

Intra- and Inter-Frequency Brain Network Structure in Health and Schizophrenia

Empirical studies over the past two decades have provided support for the hypothesis that schizophrenia is characterized by altered connectivity patterns in functional brain networks. These alterations have been proposed as genetically mediated diagnostic biomarkers and are thought to underlie altered cognitive functions such as working memory. However, the nature of this dysconnectivity remains far from understood. In this study, we perform an extensive analysis of functional connectivity patterns extracted from MEG data in 14 subjects with schizophrenia and 14 healthy controls during a 2-back working memory task. We investigate uni-, bi- and multivariate properties of sensor time series by computing wavelet entropy of and correlation between time series, and by constructing binary networks of functional connectivity both within and between classical frequency bands (, , , and ). Networks are based on the mutual information between wavelet time series, and estimated for each trial window separately, enabling us to consider both network topology and network dynamics. We observed significant decreases in time series entropy and significant increases in functional connectivity in the schizophrenia group in comparison to the healthy controls and identified an inverse relationship between these measures across both subjects and sensors that varied over frequency bands and was more pronounced in controls than in patients. The topological organization of connectivity was altered in schizophrenia specifically in high frequency and band networks as well as in the - cross-frequency networks. Network topology varied over trials to a greater extent in patients than in controls, suggesting disease-associated alterations in dynamic network properties of brain function. Our results identify signatures of aberrant neurophysiological behavior in schizophrenia across uni-, bi- and multivariate scales and lay the groundwork for further clinical studies that might lead to the discovery of new intermediate phenotypes.

Cross-frequency synchronization connects networks of fast and slow oscillations during visual working memory maintenance

Neuronal activity in sensory and fronto-parietal (FP) areas underlies the representation and attentional control, respectively, of sensory information maintained in visual working memory (VWM). Within these regions, beta/gamma phase-synchronization supports the integration of sensory functions, while synchronization in theta/alpha bands supports the regulation of attentional functions. A key challenge is to understand which mechanisms integrate neuronal processing across these distinct frequencies and thereby the sensory and attentional functions. We investigated whether such integration could be achieved by cross-frequency phase synchrony (CFS). Using concurrent magneto- and electroencephalography, we found that CFS was load-dependently enhanced between theta and alpha–gamma and between alpha and beta-gamma oscillations during VWM maintenance among visual, FP, and dorsal attention (DA) systems. CFS also connected the hubs of within-frequency-synchronized networks and its strength predicted individual VWM capacity. We propose that CFS integrates processing among synchronized neuronal networks from theta to gamma frequencies to link sensory and attentional functions. DOI: http://dx.doi.org/10.7554/eLife.13451.001

Hyperedge bundling: A practical solution to spurious interactions in MEG/EEG source connectivity analyses

&NA; Inter‐areal functional connectivity (FC), neuronal synchronization in particular, is thought to constitute a key systems‐level mechanism for coordination of neuronal processing and communication between brain regions. Evidence to support this hypothesis has been gained largely using invasive electrophysiological approaches. In humans, neuronal activity can be non‐invasively recorded only with magneto‐ and electroencephalography (MEG/EEG), which have been used to assess FC networks with high temporal resolution and whole‐scalp coverage. However, even in source‐reconstructed MEG/EEG data, signal mixing, or “source leakage”, is a significant confounder for FC analyses and network localization. Signal mixing leads to two distinct kinds of false‐positive observations: artificial interactions (AI) caused directly by mixing and spurious interactions (SI) arising indirectly from the spread of signals from true interacting sources to nearby false loci. To date, several interaction metrics have been developed to solve the AI problem, but the SI problem has remained largely intractable in MEG/EEG all‐to‐all source connectivity studies. Here, we advance a novel approach for correcting SIs in FC analyses using source‐reconstructed MEG/EEG data. Our approach is to bundle observed FC connections into hyperedges by their adjacency in signal mixing. Using realistic simulations, we show here that bundling yields hyperedges with good separability of true positives and little loss in the true positive rate. Hyperedge bundling thus significantly decreases graph noise by minimizing the false‐positive to true‐positive ratio. Finally, we demonstrate the advantage of edge bundling in the visualization of large‐scale cortical networks with real MEG data. We propose that hypergraphs yielded by bundling represent well the set of true cortical interactions that are detectable and dissociable in MEG/EEG connectivity analysis.

Transfer entropy as a tool for reconstructing interaction delays in neural signals

Detecting interactions in complex networks can be very challenging, especially when using model based approaches, due to the dependency on model assumptions. To bypass this challenge, recently a model-free information-theoretic approach, transfer entropy (TE) was introduced. TE functional is capable of detecting linear as well as non-linear directed interactions. However, a full understanding of the network function also requires knowledge on interaction delays. Here we present an extension of TE which also estimates unknown interaction delays. In detail, we show that this TE functional becomes maximal if the interaction delay parameter in our TE functional equals the true interaction delay. Accordingly, in simulations of finite data the difference between estimated and true interaction delay was always within one sample. For the first time we applied this method to reconstruct intra-cerebral interaction delays from noninvasive Magnetoencephalography (MEG) recordings, and obtained biologically plausible values, suggesting a potential diagnostic use of the method.

Measuring Large-Scale Synchronization with Human MEG and EEG: Challenges and Solutions

Specific kinds of neuronal interactions, such as phase coupling of neuronal oscillations, are likely to be essential systems-level mechanisms for coordinating neuronal communication, integration, and segregation. The functional roles of these interactions during cognitive tasks in healthy humans can be investigated with magneto- and electroencephalography (MEG/EEG), the only means for noninvasive electrophysiological recordings of human cortical activity. While advances in source modeling have opened new avenues for assessing inter-areal interactions with MEG/EEG, several factors limit the accuracy and inferential value of such analyses. In this chapter, we provide an overview of common source analysis strategies for mapping inter-areal interactions with MEG/EEG. Linear mixing between sources, as caused by volume conduction and signal mixing, is the principal confounder in connectivity analysis and always leads to false positive observations. We discuss the sensitivity of different interaction metrics to directly and indirectly caused false positives and conclude with approaches to mitigate these problems. In conclusion, MEG and EEG are becoming increasingly useful for assessing inter-areal neuronal interaction in humans.

Hyperedge bundling: Data, source code, and precautions to modeling-accuracy bias to synchrony estimates

It has not been well documented that MEG/EEG functional connectivity graphs estimated with zero-lag-free interaction metrics are severely confounded by a multitude of spurious interactions (SI), i.e., the false-positive “ghosts” of true interactions [1], [2]. These SI are caused by the multivariate linear mixing between sources, and thus they pose a severe challenge to the validity of connectivity analysis. Due to the complex nature of signal mixing and the SI problem, there is a need to intuitively demonstrate how the SI are discovered and how they can be attenuated using a novel approach that we termed hyperedge bundling. Here we provide a dataset with software with which the readers can perform simulations in order to better understand the theory and the solution to SI. We include the supplementary material of [1] that is not directly relevant to the hyperedge bundling per se but reflects important properties of the MEG source model and the functional connectivity graphs. For example, the gyri of dorsal-lateral cortices are the most accurately modeled areas; the sulci of inferior temporal, frontal and the insula have the least modeling accuracy. Importantly, we found the interaction estimates are heavily biased by the modeling accuracy between regions, which means the estimates cannot be straightforwardly interpreted as the coupling between brain regions. This raise a red flag that the conventional method of thresholding graphs by estimate values is rather suboptimal: because the measured topology of the graph reflects the geometric property of source-model instead of the cortical interactions under investigation.