Eccentric spheres models of the head

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Abstract
Equations are derived for electric potentials (electroencephalograms) and magnetic fields (magnetoencephalograms) produced by dipolar sources in three eccentric spheres models of the head. In these models, I) the thickness of the layer representing the skull varies around the model, II) the thickness of the scalp layer varies, and III) the electrical conductivity of an eccentric spherical "bubble" in the brain region varies. Using these equations, it was found that variations in these features of the models have at most only small effects on the general spatial patterns of the electric potentials and the radial component of the magnetic fields. However, some significant effects on the amplitudes were found. The effects of the variations in the skull and scalp layer thicknesses on the field amplitudes were found to be significantly smaller than on the potential amplitudes. The effects on the field amplitudes of the variations in the bubble conductivity were found to be only somewhat smaller than on the potential amplitudes. It was also found that the effects of variations in these features of the models on source localization accuracy were significantly smaller for inverse solutions using fields than for solutions using potentials.