Geometry-Adapted Hexahedral Meshes Improve Accuracy of Finite-Element-Method-Based EEG Source Analysis

Mesh generation in finite-element- (FE) method-based electroencephalography (EEG) source analysis generally influences greatly the accuracy of the results. It is thus important to determine a meshing strategy well adopted to achieve both acceptable accuracy for potential distributions and reasonable computation times and memory usage. In this paper, we propose to achieve this goal by smoothing regular hexahedral finite elements at material interfaces using a node-shift approach. We first present the underlying theory for two different techniques for modeling a current dipole in FE volume conductors, a subtraction and a direct potential method. We then evaluate regular and smoothed elements in a four-layer sphere model for both potential approaches and compare their accuracy. We finally compute and visualize potential distributions for a tangentially and a radially oriented source in the somatosensory cortex in regular and geometry-adapted three-compartment hexahedra FE volume conductor models of the human head using both the subtraction and the direct potential method. On the average, node-shifting reduces both topography and magnitude errors by more than a factor of 2 for tangential and 1.5 for radial sources for both potential approaches. Nevertheless, node-shifting has to be carried out with caution for sources located within or close to irregular hexahedra, because especially for the subtraction method extreme deformations might lead to larger overall errors. With regard to realistic volume conductor modeling, node-shifted hexahedra should thus be used for the skin and skull compartments while we would not recommend deforming elements at the grey and white matter surfaces.