Institute of Electrical and Biomedical Engineering, UMIT - Private University for Health Sciences, Medical Informatics and Technology, Hall in Tirol, Austria; Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany.
Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, Germany.
Neuroimage. 2019 Nov 1;201:116039. doi: 10.1016/j.neuroimage.2019.116039. Epub 2019 Jul 29.
For accurate EEG forward solutions, it is necessary to apply numerical methods that allow to take into account the realistic geometry of the subject's head. A commonly used method to solve this task is the finite element method (FEM). Different approaches have been developed to obtain EEG forward solutions for dipolar sources with the FEM. The St. Venant approach is frequently applied, since its high numerical accuracy and stability as well as its computational efficiency was demonstrated in multiple comparison studies. In this manuscript, we propose a variation of the St. Venant approach, the multipole approach, to improve the numerical accuracy of the St. Venant approach even further and to allow for the simulation of additional source scenarios, such as quadrupolar sources. Exploiting the multipole expansion of electric fields, we demonstrate that the newly proposed multipole approach achieves even higher numerical accuracies than the St. Venant approach in both multi-layer sphere and realistic head models. Additionally, we exemplarily show that the multipole approach allows to not only simulate dipolar but also quadrupolar sources.
为了获得准确的 EEG 正向解，有必要采用数值方法，以考虑到受检者头部的实际几何形状。一种常用的解决此任务的方法是有限元方法（FEM）。已经开发了不同的方法来使用 FEM 获得双极源的 EEG 正向解。圣维南方法经常被应用，因为它的高数值精度、稳定性和计算效率在多项比较研究中得到了证明。在本文中，我们提出了圣维南方法的一种变体，即多极方法，以进一步提高圣维南方法的数值精度，并允许模拟其他源场景，例如四极源。利用电场的多极展开，我们证明新提出的多极方法在多层球和实际头部模型中都比圣维南方法具有更高的数值精度。此外，我们还举例说明了多极方法不仅可以模拟双极源，还可以模拟四极源。
