Wolters Carsten H, Anwander Alfred, Berti Guntram, Hartmann Ulrich
Institute for Biomagnetism and Biosignalanalysis, Westfälische Wilhelms-Universität Münster, Malmedyweg 15, 48149 Münster, Germany.
IEEE Trans Biomed Eng. 2007 Aug;54(8):1446-53. doi: 10.1109/TBME.2007.890736.
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.
在基于有限元（FE）方法的脑电图（EEG）源分析中，网格生成通常对结果的准确性有很大影响。因此，确定一种能同时实现可接受的电位分布精度、合理的计算时间和内存使用的网格划分策略非常重要。在本文中，我们建议通过使用节点移动方法在材料界面处平滑规则六面体有限元来实现这一目标。我们首先介绍了在有限元体积导体中对电流偶极子进行建模的两种不同技术的基础理论，即减法和直接电位法。然后，我们针对这两种电位方法在四层球体模型中评估规则和平滑单元，并比较它们的精度。最后，我们使用减法和直接电位法在人体头部的规则和几何适配的三室六面体有限元体积导体模型中，计算并可视化体感皮层中切向和径向源的电位分布。平均而言，对于两种电位方法，节点移动可将切向源的地形和幅度误差降低2倍以上，将径向源的误差降低1.5倍。然而，对于位于不规则六面体内或靠近不规则六面体的源，必须谨慎进行节点移动，因为特别是对于减法方法，极端变形可能会导致更大的整体误差。关于实际的体积导体建模，因此应将节点移动的六面体用于皮肤和颅骨部分，而我们不建议在灰质和白质表面使单元变形。
