Summary
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.
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This research was supported by a National Research Service Award (NRSA) from National Institutes of Mental Health (NIMH # 1-F32-MH11004-01), a grant from the National Institutes of Health (NIH # 1R01NS243314), NIMH grants MH42129 and MH42669, by NIMH Small Business Innovation and Research (SBIR) grants R44 50409 and R44 51069 to Electrical Geodesics, Inc., and by a grant from the Pew Memorial Trusts and the James S. McDonnell Foundation to support the Center for the Cognitive Neuroscience of Attention. The authors also wish to thank Michael Murias for assistance with the data collection and Lynn McDougal for help with the illustrations.
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Srinivasan, R., Nunez, P.L., Tucker, D.M. et al. Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials. Brain Topogr 8, 355–366 (1996). https://doi.org/10.1007/BF01186911
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DOI: https://doi.org/10.1007/BF01186911