Forward and Inverse Modeling via Finite Elements in EEG/MEG Source Localization: Application to Event Related Responses

This thesis aims at advancing the development of forward and inverse modeling techniques to solve the electromagnetic inverse problems arising in electro and magnetoencephalography (EEG and MEG) of the human brain. A finite element method (FEM)-based and divergence conforming H(div) forward modeling approach is applied to obtain the electric and magnetic field of the neural activity in a thin, heavily folded and multicompartment head model. This accurate H(div) approach enables inversion techniques to localize the primary current distribution of the brain robustly. Furthermore, this thesis introduces the Zeffiro Interface (ZI) code package which provides a platform for integrating forward and inverse solvers for a realistic head model. ZI uses graphics processing unit (GPU) acceleration and can, therefore, flexibly utilize finite element (FE) models with a high 1 mm accuracy. Herein, ZI is applied in method development and experimental studies.

In this thesis, a source localization approach is built upon conditionally Gaussian hierarchical Bayesian modeling (HBM), the iterative alternating sequential (IAS) reconstruction technique, a variable resolution of the source space, and random sampling. These different aspects are combined in the randomized multiresolution scanning (RAMUS) method, which is introduced as a strategy to marginalize the effect of discretization and optimization errors and thereby, minimize the depth-bias of the reconstructed activity. A prior-over-measurement signal-to-noise ratio (PM-SNR) is introduced as a way to choose hyperprior parameters for a given mesh resolution and noise level. The proposed methods are investigated using simulated and experimental somatosensory evoked potentials and fields (SEPs and SEFs). RAMUS was found to be a promising technique to distinguish the subcortical activity of the brain, which might occur simultaneously with cortical components. The non-invasive detection of subcortical activity is a scientifically important and timely topic which can have remarkable implications for the treatment of Alzheimer’s or Parkinson’s disease and, in particular, for localizing refractory epilepsy.