Srinivasan R, Nunez P L, Tucker D M, Silberstein R B, Cadusch P J
Department of Psychology, University of Oregon, Eugene 97403-1227, USA.
Brain Topogr. 1996 Summer;8(4):355-66. doi: 10.1007/BF01186911.
The electroencephalogram (EEG) is recorded by sensors physically separated from the cortex by resistive skull tissue that smooths the potential field recorded at the scalp. This smoothing acts as a low-pass spatial filter that determines the spatial bandwidth, and thus the required spatial sampling density, of the scalp EEG. Although it is better appreciated in the time domain, the Nyquist frequency for adequate discrete sampling is evident in the spatial domain as well. A mathematical model of the low-pass spatial filtering of scalp potentials is developed, using a four concentric spheres (brain, CSF, skull, and scalp) model of the head and plausible estimates of the conductivity of each tissue layer. The surface Laplacian estimate of radial skull current density or cortical surface potential counteracts the low-pass filtering of scalp potentials by shifting the spatial spectrum of the EEG, producing a band-passed spatial signal that emphasizes local current sources. Simulations with the four spheres model and dense sensor arrays demonstrate that progressively more detail about cortical potential distribution is obtained as sampling is increased beyond 128 channels.
脑电图（EEG）是通过与皮质物理隔离的传感器记录的，中间隔着具有电阻性的颅骨组织，该组织会平滑头皮记录的电位场。这种平滑作用相当于一个低通空间滤波器，它决定了头皮脑电图的空间带宽，进而决定了所需的空间采样密度。虽然在时域中更容易理解，但足够离散采样的奈奎斯特频率在空间域中也很明显。利用头部的四个同心球体（大脑、脑脊液、颅骨和头皮）模型以及每个组织层电导率的合理估计值，建立了头皮电位低通空间滤波的数学模型。通过移动脑电图的空间频谱，表面拉普拉斯估计的颅骨径向电流密度或皮质表面电位抵消了头皮电位的低通滤波，产生了一个强调局部电流源的带通空间信号。使用四个球体模型和密集传感器阵列进行的模拟表明，当采样增加到超过128个通道时，可以获得关于皮质电位分布的越来越多的细节。
