Piastra Maria Carla, Nüßing Andreas, Vorwerk Johannes, Bornfleth Harald, Oostenveld Robert, Engwer Christian, Wolters Carsten H
Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany.
Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany.
Front Neurosci. 2018 Feb 2;12:30. doi: 10.3389/fnins.2018.00030. eCollection 2018.
In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves the property of and that it can, in certain situations such as the so-called , be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM%) of 1.5% and mean magnitude errors (MAG%) of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented conservative DG-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches in EEG or combined MEG/EEG source analysis scenarios, which motivates a further evaluation of DG-FEM for applications in bioelectromagnetism.
在脑电图（EEG）和脑磁图（MEG）中，源重建的一个重要要求是正向模型。在过去几十年里，连续伽辽金有限元法（CG-FEM）已成为解决正向问题的主要方法之一。最近，一种间断伽辽金有限元法（DG-FEM）EEG正向方法被提出，作为CG-FEM的替代方法（Engwer等人，2017年）。结果表明，DG-FEM保留了 的特性，并且在某些情况下，如所谓的 ，它可能优于标准的CG-FEM方法。在本文中，我们开发、实现并评估了两种用于MEG正向问题的DG-FEM方法，即一种守恒方法和一种非守恒方法。 被用作源模型。验证和评估工作在多层均匀球体模型（存在解析解）的统计研究以及六腔真实形状头部容积导体模型中进行。与理论一致，发现守恒的DG-FEM方法优于非守恒的DG-FEM实现。这种方法在六面体网格分辨率增加时也显示出收敛性。在EEG情况下，存在颅骨泄漏时，DG-FEM优于CG-FEM；而在MEG中，DG-FEM与CG-FEM方法的数值误差相似，即颅骨泄漏对MEG模式不起作用。特别是，对于距离脑-脑脊液表面1.59毫米的1毫米源的最精细网格分辨率，DG-FEM产生的磁场平均地形误差（相对差异度量，RDM%）为1.5%，平均幅度误差（MAG%）为0.1%。然而，如果目标是对EEG和MEG数据进行联合源分析，那么非常希望对EEG和MEG数据都采用相同的正向模型。基于这些结果，我们得出结论，新提出的守恒DG-FEM至少可以补充，并且在某些情况下甚至优于EEG或联合MEG/EEG源分析场景中已有的CG-FEM方法，这促使对DG-FEM在生物电磁学中的应用进行进一步评估。
