Transfer entropy—a model-free measure of effective connectivity for the neurosciences

Max Planck Institute for Brain Research, Frankfurt, Germany.
Journal of Computational Neuroscience (Impact Factor: 1.74). 02/2011; 30(1):45-67. DOI: 10.1007/s10827-010-0262-3
Source: PubMed


Understanding causal relationships, or effective connectivity, between parts of the brain is of utmost importance because a large part of the brain's activity is thought to be internally generated and, hence, quantifying stimulus response relationships alone does not fully describe brain dynamics. Past efforts to determine effective connectivity mostly relied on model based approaches such as Granger causality or dynamic causal modeling. Transfer entropy (TE) is an alternative measure of effective connectivity based on information theory. TE does not require a model of the interaction and is inherently non-linear. We investigated the applicability of TE as a metric in a test for effective connectivity to electrophysiological data based on simulations and magnetoencephalography (MEG) recordings in a simple motor task. In particular, we demonstrate that TE improved the detectability of effective connectivity for non-linear interactions, and for sensor level MEG signals where linear methods are hampered by signal-cross-talk due to volume conduction.

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    • "TE has been applied to MEG and EEG studies on auditory speech (Park et al., 2015), simple motor tasks (Vicente et al., 2011), auditory working memory tasks (Wibral et al., 2011), and an epileptic patient (Chávez et al., 2003). Early fMRI, EEG, and MEG studies (Hinrichs et al., 2006Hinrichs et al., , 2008) used a very similar measure, called directed information transfer (DIT), on the basis of directed transinformation (Saito and Harashima, 1981;Kamitake et al., 1984); however, this computation appears to limit the detection of directed interactions to linear ones (Vicente et al., 2011). In addition, a multivariate extension of transfer entropy and MI (Lizier et al., 2011) and a phase version of TE have been proposed (Lobier et al., 2014). "
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    ABSTRACT: Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain.
    Full-text · Article · Jan 2016 · Frontiers in Human Neuroscience
    • "In the present study, transfer entropy is estimated via the nearest neighbours statistics[36]1 . For those who are interested about the technical details, please refer to[34],[37],[38]. "

    No preview · Article · Jan 2016 · IEEE Transactions on Neural Systems and Rehabilitation Engineering
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    • "In the present study, transfer entropy is estimated via the nearest neighbours statistics [36] 1 . For those who are interested about the technical details, please refer to [34], [37], [38]. "
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    ABSTRACT: Working memory (WM) is a distributed cognitive process that employs communication between prefrontal cortex and posterior brain regions in the form of cross-frequency coupling between theta (�) and high-alpha (�2) brain waves. A novel method for deriving causal interactions between brain waves of different frequencies is essential for a better understanding of the neural dynamics of such complex cognitive process. Here, we proposed a novel method to estimate transfer entropy (TE) through a symbolization scheme, which is based on neural-gas algorithm (NG) and encodes a bivariate time series in the form of two symbolic sequences. Given the symbolic sequences, the delay symbolic transfer entropy (dSTENG) is defined. Our approach is akin to standard symbolic transfer entropy (STE) that incorporates the ordinal pattern (OP) symbolization technique. We assessed the proposed method in a WM-invoked paradigm that included a mental arithmetic task at various levels of difficulty. Effective interactions between Frontal� (F�) and Parieto-Occipital�2 (PO�2) brain waves were detected in multichannel EEG recordings from 16 subjects. Compared with conventional methods, our technique was less sensitive to noise and demonstrated improved computational efficiency in quantifying the dominating direction of effective connectivity between brain waves of different spectral content. Moreover, we discovered an efferent F� connectivity pattern and an afferent PO�2 one, in all the levels of the task. Further statistical analysis revealed an increasing dSTENG strength following the task’s difficulty.
    Full-text · Article · Dec 2015 · IEEE Transactions on Neural Systems and Rehabilitation Engineering
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