Bioelectric Field Simulation and Visualization

The reconstruction of the bioelectric field in the human brain from non-invasive measurements like electroencephalographic recordings (EEG) has the potential to become a powerful tool in neurology. From a mathematical point of view, the reconstruction can be considered as an inverse problem, which can be solved by repeated numerical simulations of the potential distribution for assumed dipolar current sources in the brain. An accurate reconstruction of the electrical brain activity, however, involves the consideration of a realistic head model, which is ideally obtained from registered Computer Tomography (CT) and Magnetic Resonance (MR) images. Furthermore, with the advent of Diffusion Tensor Magnetic Resonance Imaging (DT-MRI), an estimation of the anisotropic conductivities within the brain has been made available, which allows a further, patient specific, refinement of the realistic head model. This thesis gives an overview of two discretization methods, finite differences and finite elements, which allow to incorporate anisotropic conductivities in the numerical simulations. The discretization methods are evaluated by studying their convergence rates with respect to selected problems. For this purpose, the numerical results are compared to analytical results obtained from a four-layer anisotropic concentric spherical volume conductor. Furthermore, the influence of anisotropic conductivities is studied with respect to the solution of the inverse problem. Chapter