The magnetic field of cortical current sources: the application of a spatial filtering model to the forward and inverse problems.

We extend our theoretical model based on spatial filtering to determine the ability of a SQUID magnetometer to resolve 2 localized current sources in the brain. We find that in order to resolve 2 separated but coaxial cortical sources, the source-to-pickup coil distance must be comparable to the distance between the 2 sources. The size of the current sources affects the resolving power of a magnetometer, but an anisotropy of 3 in the cortical tissue does not produce a significant effect. The model also provides a solution of the inverse calculation, either to reconstruct the original current source distribution from the measured magnetic field, or to continue the field at the magnetometer inward towards the sources. Both the inverse and inward calculations are limited by the fact that the inverse filter function serves as a high-pass filter, which leads to instabilities at high spatial frequencies, particularly in the presence of noise. The instabilities can be minimized by choosing an appropriate window to attenuate the noise, but this in turn reduces the spatial resolution.