Mathematical modeling of EEG-dynamics

Electroencephalogram (EEG) registered on the scalp surface characterizes the distribution of electric potential during brain activity. It is widely used for the investigation of brain functioning and for diagnostics of different diseases. Event related potential (ERP) is used to characterize visual, motor, and other activities through cross-trial average. However, spatiotemporal dynamics in EEG data are difficult to interpret, they are subject-specific and highly variable, especially at the level of individual trials. These dynamics are conventionally associated with oscillating brain sources, but it is not yet clear how these oscillations emanate dynamical regimes observed on the brain surface. In this work we model spatiotemporal dynamics in EEG data with the Poisson equation where the right-hand side corresponds to the oscillating brain sources. We identify the main dynamical regimes depending on the number of sources, their frequencies and phases. Standing waves, rotating and symmetric regimes observed in 2D and 3D numerical simulations are also found in the EEG data registered during picture naming experiments. Furthermore, moving waves determined as spatial displacement of the potential distribution appear in the vicinity of brain sources, both in the simulations and in the experimental data. Overall, we conclude that the brain source model is appropriate for the description of spatiotemporal dynamics in the EEG data.