Graichen Uwe, Klee Sascha, Fiedler Patrique, Hofmann Lydia, Haueisen Jens
Division Biostatistics and Data Science, Karl Landsteiner University of Health Sciences, Dr.-Karl-Dorrek-Str. 30, 3500 Krems an der Donau, Austria.
Institute of Biomedical Engineering and Informatics (BMTI), Faculty of Computer Science and Automation, Technische Universität Ilmenau, Gustav-Kirchhoff-Str. 2, 98693 Ilmenau, Germany.
Biosensors (Basel). 2025 Sep 6;15(9):585. doi: 10.3390/bios15090585.
Electroencephalography (EEG) is a non-invasive biosensing platform with a spatial-frequency content that is of significant relevance for a multitude of aspects in the neurosciences, ranging from optimal spatial sampling of the EEG to the design of spatial filters and source reconstruction. In the past, simplified spherical head models had to be used for this analysis. We propose a method for spatial frequency analysis in EEG for realistically shaped volume conductors, and we exemplify our method with a five-compartment Boundary Element Method (BEM) model of the head. We employ the recently developed technique for spatial harmonic analysis (Sphara), which allows for spatial Fourier analysis on arbitrarily shaped surfaces in space. We first validate and compare Sphara with the established method for spatial Fourier analysis on spherical surfaces, discrete spherical harmonics, using a spherical volume conductor. We provide uncertainty limits for Sphara. We derive relationships between the signal-to-noise ratio (SNR) and the required spatial sampling of the EEG. Our results demonstrate that conventional 10-20 sampling might misestimate EEG power by up to 50%, and even 64 electrodes might misestimate EEG power by up to 15%. Our results also provide insights into the targeting problem of transcranial electric stimulation.
脑电图（EEG）是一种非侵入性生物传感平台，其空间频率内容与神经科学的多个方面密切相关，从脑电图的最佳空间采样到空间滤波器的设计和源重建。过去，这种分析必须使用简化的球形头部模型。我们提出了一种针对实际形状的体积导体进行脑电图空间频率分析的方法，并以头部的五室边界元法（BEM）模型为例来说明我们的方法。我们采用了最近开发的空间谐波分析技术（Sphara），该技术允许在空间中任意形状的表面上进行空间傅里叶分析。我们首先使用球形体积导体，将Sphara与用于球形表面空间傅里叶分析的既定方法——离散球谐函数进行验证和比较。我们提供了Sphara的不确定性限制。我们推导了信噪比（SNR）与脑电图所需空间采样之间的关系。我们的结果表明，传统的10-20采样可能会使脑电图功率估计误差高达50%，甚至64个电极也可能使脑电图功率估计误差高达15%。我们的结果还为经颅电刺激的靶向问题提供了见解。
