A Comparative Study of the Robustness of Frequency-Domain Connectivity Measures to Finite Data Length

Abstract

In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time-series. We assume that the neural sources follow a stable MultiVariate AutoRegressive model, and consider three connectivity metrics: imaginary part of coherency (IC), generalized partial directed coherence (gPDC) and frequency-domain granger causality (fGC). In order to assess the statistical significance of the estimated values, we use the surrogate data test by generating phase-randomized and autoregressive surrogate data. We first consider the ideal case where we know the source time courses exactly. Here we show how, expectedly, even exact knowledge of the source time courses is not sufficient to provide reliable estimates of the connectivity when the number of samples gets small; however, while gPDC and fGC tend to provide a larger number of false positives, the IC becomes less sensitive to the presence of connectivity. Then we proceed with more realistic simulations, where the source time courses are estimated using eLORETA, and the EEG signal is affected by biological noise of increasing intensity. Using the ideal case as a reference, we show that the impact of biological noise on IC estimates is qualitatively different from the impact on gPDC and fGC.

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Notes

  1. 1.

    In literature, this type of surrogate data is also known as Fourier transform surrogate data (Faes et al. 2004).

  2. 2.

    In order to simulate \(\{ {\varvec{x}}(t_p)\}_{p=1}^P\) we modified the Matlab code available at http://neuroinformation.incf.org.

  3. 3.

    We observe that either the frontal yellow dipole or the ten sources just described are not connected with anyone of the other dipoles of the networks. However, while the latter are used to simulate biological noise the former contributes to the scalp potential of interest and is used to evaluate the sensitivity of each connectivity measure to false positive.

  4. 4.

    We show only the results obtained when the statistical test is performed using AR surrogate data. The results with PR surrogate data are almost equal.

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Acknowledgements

The authors thank the anonymous reviewers for their valuable comments and suggestions. L.M. and V.P. have been supported in part by the grant Functional connectivity and neuroplasticity in physiological and pathological aging, PRIN 20102011 n. 2010SH7H3F_006, and by the grant Breaking the Nonuniqueness Barrier in Electromagnetic Neuroimaging (BREAKBEN), H2020-FETOPEN-2014-2015/H2020-FETOPEN-2014-2015-RIA, Project reference: 686865.

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Correspondence to Sara Sommariva.

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This is one of several papers published together in Brain Topography on the “Special Issue: Controversies in EEG Source Analysis”.

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Sommariva, S., Sorrentino, A., Piana, M. et al. A Comparative Study of the Robustness of Frequency-Domain Connectivity Measures to Finite Data Length. Brain Topogr 32, 675–695 (2019). https://doi.org/10.1007/s10548-017-0609-4

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Keywords

  • Dynamic functional connectivity
  • Imaginary part of coherency
  • Generalized partial directed coherence
  • Frequency-domain granger causality
  • Surrogate data
  • EEG