Abstract

The Laplacian of the potential field on the scalp ${\nabla }^2\text{V=}\frac{{\partial }^{\text{2}}\text{V}}{\partial {\text{x}}^{\text{2}}}\text{+}\frac{{\partial }^{\text{2}}\text{V}}{\partial {\text{y}}^{\text{2}}}$, where V(x,y,t) is the time-varying potential field in x,y scalp dimensions, can be conveniently estimated using 5 electrodes arranged as a cross to measure the sum of orthogonal second differences (Laplacian derivation). The three concentric sphere model of the human head was used to assess some important properties. The Laplacian derivation may be represented by a spatial filter through which brain activity is "seen". The point spread function has a "Mexican hat" shape, or equivalently, brain activity is seen through a spatial bandpass filter different from that of a conventional, "monopolar", electrode derivation which approximates a lowpass filter. As the distance between the individual electrodes of the Laplacian derivation is made smaller, the peak spatial frequency increases, the bandpass narrows, sidelobes become increasingly prominent, and overall signal-to-noise decreases. At a distance of 2.5 cm between individual electrodes, the ratio of spatial resolution (approximately 2.0 cm, bandpass approximately .3 to 1.6 cycles per cm on the surface of the cortex) to signal-to-noise is nearly optimal. The Laplacian derivation is about ten times more sensitive to radially oriented than to tangentially oriented source-sink configurations. Thus, the Laplacian derivation has several useful attributes for localization studies, i.e. it is reference free, sensitive mostly to activity in the cortical mantle, has a resolution of 2 cm or better, and is insensitive to alpha activity. Because the passive properties of the head are nearly linear, no inversion of scalp potential field to yield a unique configuration of the underlying brain activity is in general possible without initial highly restrictive assumptions. But, the initial assumption required when the Laplacian derivation is used is relaxed to one concerning the dimension of the cortical region activated.

© 1985 Optical Society of America