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.

Evaluation of Granger Causality Measures for Constructing Networks from Multivariate Time Series

“…Recent comparative studies have assessed causal effects with various causality measures, using also significance tests for each causal effect [ 14 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 ]. Some studies concentrated on the comparison of direct and indirect causality measures [ 46 , 52 ], whereas other studies focused on specific types of causality measures, e.g., frequency domain measures [ 53 , 54 , 55 , 56 ], or different significance tests for a causality measure [ 57 , 58 , 59 ]. These studies are done on specific real data types, mostly from brain, which limits the generalization of the conclusions.…”

Controversies in EEG Source Imaging and Connectivity: Modeling, Validation, Benchmarking

“…A similar modelling framework was adopted in (Sommariva et al 2017) to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity in frequency domain from EEG time-series. Also in this study it was shown that 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.…”

Brain Functional Connectivity Through Phase Coupling of Neuronal Oscillations: A Perspective From Magnetoencephalography

“…In practice, data length is always finite, and the reliability of these methods is impacted by the overall number of available data time points. This issue has been discussed in simulated data for linear coupling methods (e.g., Sommariva et al, 2017), while for cross-frequency coupling methods this is still to be explicitly investigated. Moreover, to date several evidences have been provided concerning the changes of functional connectivity patterns across different time-scales (Breakspears et al, 2004).…”