Modelling EEG Dynamics with Brain Sources

An electroencephalogram (EEG), recorded on the surface of the scalp, serves to characterize the distribution of electric potential during brain activity. This method finds extensive application in investigating brain functioning and diagnosing various diseases. Event-related potential (ERP) is employed to delineate visual, motor, and other activities through cross-trial averages. Despite its utility, interpreting the spatiotemporal dynamics in EEG data poses challenges, as they are inherently subject-specific and highly variable, particularly at the level of individual trials. Conventionally associated with oscillating brain sources, these dynamics raise questions regarding how these oscillations give rise to the observed dynamical regimes on the brain surface. In this study, we propose a model for spatiotemporal dynamics in EEG data using the Poisson equation, with the right-hand side corresponding to the oscillating brain sources. Through our analysis, we identify primary dynamical regimes based on factors such as the number of sources, their frequencies, and phases. Our numerical simulations, conducted in both 2D and 3D, revealed the presence of standing waves, rotating patterns, and symmetric regimes, mirroring observations in EEG data recorded during picture naming experiments. Notably, moving waves, indicative of spatial displacement in the potential distribution, manifested in the vicinity of brain sources, as was evident in both the simulations and experimental data. In summary, our findings support the conclusion that the brain source model aptly describes the spatiotemporal dynamics observed in EEG data.