EEG problems based on finite element methods

Abstract

In this thesis, we study the problem of the reconstruction of the electrical activity of the brain by using electroencephalography (EEG). The elliptic partical differential equation induced by the quasi-state Maxwell equations describes the relation of the conductivity between the primary current and the electric potential distribution of the head. The reconstruction of the primary current and the conductivity in EEG problem is known to be an inverse problem which does not have a unique solution. We will study an inverse method based on the adjoint state approach developed by Faugeras et al., suggest how to reduce the computational cost of the inverse method and observe the non-uniqueness of the inverse method through numerical experiments.