Cortical Imaging Based on an Analytic High Resolution EEG

It is well known that the EEG is a blurred and spatially low-pass filtered representation of the cortical activity. Since additional recording electrodes will not necessarily lead to an improved spatial resolution, further steps have to be taken. We derived the analytic downward continuation of the scalp potential field to an arbitrary inner surface for a spherical volume conductor model with piecewise constant conductivities. The basic idea of the Analytic High Resolution BEG (AHREEG) is the fact that a function defined on a sphere can be expressed as a weighted sum of spherical harmonics. Considering the spatial transfer function between the cortex and the scalp surface, the potential distribution on the cortex is theoretically computed by the application of the inverse transfer function to the scalp potential field. Compared to source localization procedures, the AHREEG is not based on any source distribution or on the nature of the sources. Furthermore the proposed method is unique, though ill-posed. Due to this fact and the fact that real world data are always contaminated by noise, a regularization based on general cross validation is performed to stabilize the inverse solution. Simulation results as well as the application of the AHREEG to EEG recorded during median nerve stimulation will be presented and critically discussed.