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

Abstract

Abstract-Mesh generation in finite-element-(FE) methodbased 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.

The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem

“…As presented in [26], the CG-FEM method with hexahedral elements might suffer from skull leakage currents on coarser meshes. The most important difference might thus be that this can be alleviated by employing the DG-FEM approach [26] and especially the here presented UDG-FEM, but not by the CG-FEM geometryadaptation of [28].…”

“…Another method to improve the geometric representation of the standard CG-FEM approach on a structured hexahedral mesh has been presented in [28]. In order to reduce the effect of a staircase approximation of the different compartment surfaces, the position of the mesh nodes is geometrically adapted based on the different conductivities in the surrounding elements.…”

“…As nodes are moved solely based on the voxel segmentation, the topology of the mesh is restricted to the one given by the segmentation and no further geometric information is included. In [28], the geometry-adapted hexahedral CG-FEM method is verified in a 4-layer sphere model, parameterized like here with the only exception that skull conductivity was chosen 0.0042 S/m (note, the lower the skull conductivity, the higher the expected numerical errors). A 2 mm mesh resolution was used and sources were modeled with subtraction and Saint-Venant approaches.…”

“…Therefore, methods have been developed to reduce such geometrical errors. In [28], the structured mesh was modified to obtain a smoother interface between different tissue compartments. However, this method might still suffer from skull leakages and geometry adaptation is limited by the need for positive Jacobian determinants.…”

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

“…Regular and geometry adapted hexahedral FE approaches: While regular hexahedral FE approaches have been used in many simulation studies [10,11,7], 200 we developed an isoparametric FE approach for EEG source analysis [37] and for tCS modeling [9] that is specifically tailored to geometry-adapted hexahedral models. First, a hexahedral FE mesh was constructed out of the labeled volume of the four compartment sphere model using an edge length of 1 mm.…”