Brain Connectivity Estimation Pitfall in Multiple Trials of Electroencephalography Data

Introduction: The electroencephalography signal is well suited to calculate brain connectivity due to its high temporal resolution. When the purpose is to compute connectivity from multi-trial electroencephalography (EEG) data, confusion arises about how these trials involved in calculating the connectivity. The purpose of this paper is to study this confusing issue using simulated and experimental data. Methods: To this end, Granger causality-based connectivity measures were considered. Using simulations, two signals were generated with known AR (auto-regressive) coefficients and then simple multivariate autoregressive (MVAR) models based on different numbers of trials were extracted. For accurate estimation of the MVAR model, the data samples should be sufficient. Two Granger causality-based connectivity, granger causality (GC) and Partial directed coherence (PDC) were estimated. Results: Estimating connectivity corresponding to small trial numbers (5 and 10 trials) resulted in an average value of connectivity that is significantly higher and also more variable over different estimates. By increasing the number of trials, the MVAR model has fitted more appropriately to the data and the connectivity values were converged. This procedure was implemented on real EEG data. The obtained results agreed well with the findings of simulated data. Conclusion: The results showed that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. Also, the larger the trial numbers, the MVAR model has fitted more appropriately to the data, and connectivity estimations are more reliable. Highlights The average of connectivity values on trials is considered brain connectivity. Connectivity estimations are more reliable for larger trial numbers. Estimations of connectivity for small trial numbers are not valid. Plain Language Summary Several different techniques can be utilized to evaluate brain connectivity such as functional magnetic resonance imaging (fMRI), magnetoencephalography (MEG), electroencephalography (EEG) and etc. Connectivity estimation methods are associated with computing the correspondence of neural signals over time, therefore modalities such as EEG due to their fine temporal resolution are well suited to calculate such connectivity. When the purpose is to compute connectivity from multi-trial data, confusion arises about how these trials and how many trials are involved in calculating the connectivity. During calculating brain connectivity from data with many observation epochs, the question arises whether brain connectivity is calculated for each trial and then average or for the averaged trials. The target of this paper is to study the abovementioned issue using simulated data and realistic EEG data. Our analysis indicated that the brain connectivity should calculate for each trial, and then average the connectivity values on all trials. It was also found that estimating connectivity corresponding to small trial numbers resulted in an average value of connectivity that is significantly higher and also more variable over different estimates and is not valid. These findings can help us in the correct estimation of brain connectivity.