Objective Extraction of Evoked Event-related Oscillations from Time-frequency Representation of Event-related Potentials

Abstract

Evoked event-related oscillations (EROs) have been widely used to explore the mechanisms of brain activities for both normal people and neuropsychiatric disease patients. The selection of regions of evoked EROs tends to be subjectively based on the previous studies and the visual inspection of grand averaged time-frequency representations (TFRs) which causes some missing or redundant information. Meanwhile, the evoked EROs cannot be fully extracted via the conventional time-frequency analysis (TFA) method because they are sometimes overlapped with each other or with artifacts in time, frequency, and space domains to some extent. Hence, these shortcomings may pose some challenges to investigate the related neuronal processes. A data-driven approach was introduced to fill the gaps as below: extracting the temporal and spatial components of interest simultaneously by principal component analysis and Promax rotation and projecting them to the electrode field to correct their variance and polarity indeterminacy, calculating the TFRs of the back-projected components, and determining the regions of interest objectively using the edge detection algorithm. We performed this novel approach and the conventional TFA method in analyzing both a synthetic dataset and an actual ERP dataset in a two-factor simple gambling paradigm of waiting time (short/long) and feedback (loss/gain) separately. Synthetic dataset results indicated that N2-theta and P3-delta oscillations were detected using the proposed approach, but, by comparison, only one oscillation was obtained via the conventional TFA method. Furthermore, the actual ERP dataset results of P3-delta for our approach revealed that it was sensitive to the waiting time (which also was found in the previous reports) but not for that of the conventional TFA method. This study manifested that the proposed approach can objectively extract evoked EROs, which allows a better understanding of the modulations of the oscillatory responses.

Single-trial-based Temporal Principal Component Analysis on Extracting Event-related Potentials of Interest for an Individual Subject

“…In practice, the back-projection is to calculate the sums of the outer-product between temporal and spatial PCA-components for reconstructing the waveforms of desired ERPs. As shown in our recent study (Zhang et al, 2020), PCA is indeed a BSS approach when the sources are assumed to be correlated with each other and the back projection theory also works for PCA like that for ICA.…”

“…Those epochs’ datasets whose magnitudes exceeded ±80μV were discarded and the remaining epochs were baseline corrected. Finally, EEG data of all epochs were filtered by wavelet filter (Cong, Ristaniemi, & Lyytinen, 2015; Zhang et al, 2020) to improve signal-to-noise ratio (SNR). The parameters were set for wavelet filter as below: the number of decomposition level was 10; the select mother wavelet was ‘rbio6.8’; the detail coefficients at levels 5, 6, 7, 8, and 9 were used for signal reconstruction.…”

“…The application of PCA to a spatial-stacked matrix Z (the rows are time points and the channels from each condition/subject/trial (optional) are in columns) obtained from EEG dataset of either single subject or multiple subjects can be illustrated by Eq. (1) (Zhang et al, 2020). In Eq.…”

“…In Eq. (1), the number of observed signals is larger than that of sources, i.e., it is an over-determined model, and we usually change this over-determined model to determined model by some methods, for example, the accumulative explained variance (Zhang et al, 2020). where V T is the dimension reduction matrix obtained by applying some PCA algorithms to matrix Z T and H is a mixing matrix.…”

“…In this study, we take the decomposition of spatial-concatenation matrix Z as an example. The matrix Z can be mathematically expressed as below (Zhang, Li, & Cong, 2020): where, Z is generated from either trial-averaged or single-trial datasets of all subjects; s r ( t ) represents stimulus-locked, spontaneous, or noise sources; a m,r is coefficient between m th electrode and r th source. The key assumption in the above equation is that all subjects’ ERPs share the same temporal components (i.e., waveforms), that is to say, the waveforms of ERPs for different subjects are the same.…”