Vol.:(0123456789) 1 3Brain Topography https://doi.org/10.1007/s10548-017-0609-4ORIGINAL PAPERA Comparative Study of the Robustness of Frequency?Domain Connectivity Measures to Finite Data LengthSara Sommariva 1 · Alberto Sorrentino 1 · Michele Piana 1 · Vittorio Pizzella 2,3 · Laura Marzetti 2,3Received: 4 March 2016 / Accepted: 13 November 2017 © Springer Science+Business Media, LLC, part of Springer Nature 2017AbstractIn this work we use numerical simulation to investigate how the temporal length of the data af f ects 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 signif i cance of the estimated values, we use the surrogate data test by generating phase-randomized and autoregressive surrogate data. We fi rst 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 suf f i cient 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 af f ected 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 dif f erent from the impact on gPDC and fGC.Keywords Dynamic functional connectivity · Imaginary part of coherency · Generalized partial directed coherence · Frequency-domain granger causality · Surrogate data · EEGIntroductionThe idea that the synergic cooperation of several regions is required for the brain to be able to instantiate specif i c functions and behaviors has, in the recent years, become central to neuroscience. Largely interconnected brain net-works have indeed been reported to act as building blocks for the dynamic segregation and integration of brain areas during task execution or at rest in a wide range of spatial and temporal scales (Engel et al. 2013). Understanding brain connectivity, both at structural and functional level, is thus a prerequisite for understanding brain functioning as well as its alterations (Stam 2010). In this framework, magnetoencephalography (MEG) and electroencephalog-raphy (EEG) have signif i cantly contributed to unravel the functional wiring of the brain by putting emphasis on its temporal aspects, and looking for mechanisms of oscillatory coupling (in the range of about 1–100 Hz) as well as for cou-pled slower aperiodic fl uctuations of brain activity (Engel et al. 2013). To robustly measure functional coupling in task related or ongoing brain activity, a lot of ef f ort has thus been made in the recent years in the development of methods for MEG and EEG connectivity with the aim of capturing one aspect or the other (Marzetti et al. 2008; Stam and Straaten 2012; Hillebrand et al. 2012; Ewald et al. 2012; Marzetti et al. 2013; Chella et al. 2014; Brookes et al. 2011a, b, 2012; de Pasquale et al. 2010, 2012). Several time-domain or frequency-domain metrics have thus been designed to cap-ture the statistical dependencies or the causal relationships This is one of several papers published together in Brain Topography on the “Special Issue: Controversies in EEG Source Analysis”. * Sara Sommariva sommariva@dima.unige.it1 Dipartimento di Matematica, Università di Genova, Genoa, Italy2 Department of Neuroscience, Imaging and Clinical Sciences, G. d’Annunzio University of Chieti-Pescara, Chieti, Italy3 Institute for Advanced Biomedical Technologies, G. d’Annunzio University of Chieti-Pescara, Chieti, Italy
