The inverse problem in electroencephalography using the bidomain model of electrical activity

Acquiring information about the distribution of electrical sources in the brain from electroencephalography (EEG) data remains a significant challenge. An accurate solution would provide an understanding of the inner mechanisms of the electrical activity in the brain and information about damaged tissue.

In this paper, we present a methodology for reconstructing brain electrical activity from EEG data by using the bidomain formulation. The bidomain model considers continuous active neural tissue coupled with a nonlinear cell model. Using this technique, we aim to find the brain sources that give rise to the scalp potential recorded by EEG measurements taking into account a non-static reconstruction.

We simulate electrical sources in the brain volume and compare the reconstruction to the minimum norm estimates (MNEs) and low resolution electrical tomography (LORETA) results. Then, with the EEG dataset from the EEG Motor Movement/Imagery Database of the Physiobank, we identify the reaction to visual stimuli by calculating the time between stimulus presentation and the spike in electrical activity. Finally, we compare the activation in the brain with the registered activation using the LinkRbrain platform.

Our methodology shows an improved reconstruction of the electrical activity and source localization in comparison with MNE and LORETA. For the Motor Movement/Imagery Database, the reconstruction is consistent with the expected position and time delay generated by the stimuli. Thus, this methodology is a suitable option for continuously reconstructing brain potentials.