Modulation of the EEG alpha-band envelope during mental tasks: A task-related index based on second-order derivatives

This study proposes an electroencephalography (EEG) analysis method using second-order derivatives of the alpha-band envelope to characterize task-related brain dynamics. An open dataset including EEG data from 60 healthy participants was analyzed during rest and three eyes-closed tasks: calculation, memory, and music. Sixty-second epochs were extracted, alpha-band activity (8-13 Hz) was filtered, and amplitude envelopes were computed via the Hilbert transform. Second-order derivatives were derived and separated into positive (Ap) and negative (An) components. Source-localized EEG signals were mapped to 68 cortical regions using the Desikan-Killiany atlas. Regional differences in Ap, An, their ratio, envelope amplitude, and peak alpha frequency were tested using corrected Wilcoxon signed-rank tests. The calculation task increased Ap, An, and amplitude in prefrontal and cingulate cortices, while reducing An in medial parietal regions. The memory task showed increased An in the left fusiform gyrus, whereas the music task showed no significant changes. Peak alpha frequency and Ap-An ratio were unchanged. These results suggest that derivative-based features capture task- and region-specific brain dynamics not detected by conventional measures, providing complementary descriptors of EEG activity in healthy individuals. Conceptual illustration of the present study. We hypothesized that the second-order derivatives of fluctuations in the alpha-band envelope, which are relatively preserved after the Fourier-based filtering process, may contain biologically relevant information. In this study, we examined whether the second-order derivatives (force, shown in red), in addition to conventional amplitude (green) and frequency (blue) measures, exhibit task-related changes in healthy individuals. By incorporating second-order derivative measures into node-wise functional descriptors of brain regions within an intracerebral network framework, the present results provide a complementary perspective for characterizing brain function. Ap and An denote the positive and negative components of the second-order derivative, respectively.