Head-Specific Spatial Spectra of Electroencephalography Explained: A Sphara and BEM Investigation

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.