Brain Topography

, Volume 8, Issue 4, pp 355–366 | Cite as

Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials

  • Ramesh Srinivasan
  • Paul L. Nunez
  • Don M. Tucker
  • Richard B. Silberstein
  • Peter J. Cadusch
Article

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.

Key words

Spatial nyquist Laplacian Splines 

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Copyright information

© Human Sciences Press, Inc 1996

Authors and Affiliations

  • Ramesh Srinivasan
    • 1
    • 2
  • Paul L. Nunez
    • 3
  • Don M. Tucker
    • 1
    • 2
  • Richard B. Silberstein
    • 4
  • Peter J. Cadusch
    • 4
  1. 1.Institute of Cognitive and Decision Sciences, Department of PsychologyUniversity of OregonEugeneUSA
  2. 2.Electrical Geodesics, Inc.EugeneUSA
  3. 3.Brain Physics Group, Department of Biomedical EngineeringTulane UniversityNew OrleansUSA
  4. 4.Centre for Applied Neurosciences and Department of PhysicsSwinburne University of TechnologyMelbourneAustralia

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