Forward volumetric modeling framework for realistic head models towards accurate EEG source localization (2018)
Synergetic effects connecting spatial and functional neuroimaging techniques allows reduction of the weakness for single method analysis. Specifically, Electroencephalographic (EEG) Source Imaging (ESI) relating structural head models and distributed source localization techniques improves the time and spatial resolution of single MRI or EEG analysis. The construction of more accurate forward models for ESI solutions, holding better precision and less computational burden is an important task for investigative purposes, but also for surgery planning and disorder treatments. In this regard, we present a novel finite-difference EEG forward problem solution that we called ghost-filling finite difference anisotropic reciprocity method (GFDARM). First, we introduce a finite difference numerical solution for the conservative form of the Poisson equation, using an asymmetric volumetric stencil, together with the transition layer technique to formulate finite differences that properly deal with the considered Newman and Dirichlet boundary conditions. Later, we formulate a solution for an irregular free-form boundary domain, based on a second-order accuracy ghost-filling approximation for the homogeneous Newman flux condition, allowing us to solve the discretized finite differences volume only for the significant potential unknowns. Then we analyze the linear equation system solution and the considerations for a reciprocity solution over the electrodes space. Further, we test our method using a multilayer spherical head model that can include anisotropy and can admit an analytical solution of the Poisson equation. Finally, we analyze a noisy linear equation system to study the numerical stability of the technique in the presence of perturbations. Our results show stability and super-linear convergence. Moreover, validation against an analytical solution shows high correspondence in the potential distribution for a wide range of dipole positions and orientations. As a final stage, we introduce a realistic patient-specific EEG forward modeling pipeline, including anisotropy in the skull and the white matter; MRI segmentation; electrode co-register; voxelwise conductivity definitions; reciprocity space solution; and GFDARM numeric EEG forward solver. Our results using Bayesian model selection for group studies in a random fixed effect analysis show strong evidence in favor of more complex head models, including anisotropic skull and white matter modeling