Abstract
BackgroundTransfer entropy (TE) is a measure for the detection of directed interactions. Transfer entropy is an information theoretic implementation of Wiener's principle of observational causality. It offers an approach to the detection of neuronal interactions that is free of an explicit model of the interactions. Hence, it offers the power to analyze linear and nonlinear interactions alike. This allows for example the comprehensive analysis of directed interactions in neural networks at various levels of description. Here we present the open-source MATLAB toolbox TRENTOOL that allows the user to handle the considerable complexity of this measure and to validate the obtained results using non-parametrical statistical testing. We demonstrate the use of the toolbox and the performance of the algorithm on simulated data with nonlinear (quadratic) coupling and on local field potentials (LFP) recorded from the retina and the optic tectum of the turtle (Pseudemys scripta elegans) where a neuronal one-way connection is likely present.ResultsIn simulated data TE detected information flow in the simulated direction reliably with false positives not exceeding the rates expected under the null hypothesis. In the LFP data we found directed interactions from the retina to the tectum, despite the complicated signal transformations between these stages. No false positive interactions in the reverse directions were detected.ConclusionsTRENTOOL is an implementation of transfer entropy and mutual information analysis that aims to support the user in the application of this information theoretic measure. TRENTOOL is implemented as a MATLAB toolbox and available under an open source license (GPL v3). For the use with neural data TRENTOOL seamlessly integrates with the popular FieldTrip toolbox.
Highlights
Transfer entropy (TE) is a measure for the detection of directed interactions
Validation for simulated data We tested our implementation of Transfer Entropy with a representative set of simulated data which mimic electrophysiological recordings and where we have control over all parameters such as coupling direction, delay and strength6
Sensitivity analysis - impact of embedding parameters The sensitivity of the TE metric mostly depends on two parameters - the prediction time u that quantifies the expected interaction delay between the two systems and which has to be set by the user and the combination of embedding dimension d and delay τ, which is estimated by either the Cao or the Ragwitz criterion (d and τ)
Summary
In the first case (A) of two independent Gaussian white noise processes the detection rate of directed interactions and of volume conduction was at chance level (Figure 6 A). In the second case (B) of only one Gaussian white noise process mixed onto two noisy sensors, no directed interactions were present. In this case, coupling was detected at rates at or below chance level for all ε (Figure 6 B). For ε > 0, the shift test did robustly detect the instantaneous mixing in 100% of simulated cases. The shift test was not significant in the direction of coupling X ® Y, but did robustly detect instantaneous mixing for the opposite direction Y ® X if 50 Hz was present and at a rate of 68% when the signal had been filtered, indicating that filtering does not remove all effects of the common noise.
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