Electroencephalographic Signal Source Estimation Using Power Dissipation and Interface Surface Charge

The inverse problem in electroencephalography (EEG) is the determination of form and location of neural activity associated to EEG recordings. This determination is of interest in evoked potential experiments where the activity is elicited by an external stimulus. This work investigates three aspects of this problem: the use of forward methods in its solution, the elimination of artifacts that complicate the accurate determination of sources, and the construction of physical models that capture the electrical properties of the human head.

Results from this work aim to increase the accuracy and performance of the inverse solution process.

The inverse problem can be approached by constructing forward solutions where, for a know source, the scalp potentials are determined. This work demonstrates that the use of two variables, the dissipated power and the accumulated charge at interfaces, leads to a new solution method for the forward problem. The accumulated charge satisfies a boundary integral equation. Consideration of dissipated power determines bounds on the range of eigenvalues of the integral operators that appear in this formulation. The new method uses the eigenvalue structure to regularize singular integral operators thus allowing unambiguous solutions to the forward problem.

A major problem in the estimation of properties of neural sources is the presence of artifacts that corrupt EEG recordings. A method is proposed for the determination of inverse solutions that integrates sequential Bayesian estimation with probabilistic data association in order to suppress artifacts before estimating neural activity. This method improves the tracking of neural activity in a dynamic setting in the presence of artifacts.

Solution of the inverse problem requires the use of models of the human head. The electrical properties of biological tissues are best described by frequency dependent complex conductivities. Head models in EEG analysis, however, usually consider head regions as having only constant real conductivities. This work presents a model for tissues as composed of confined electrolytes that predicts complex conductivities for macroscopic measurements. These results indicate ways in which EEG models can be improved.