On the realization of an analytic high-resolution EEG

The analytic solution of the harmonic downward continuation of the scalp potential field in an N-shell heterogeneous, but isotropic, spherical volume conductor model has been derived. The objective of this paper was to investigate the realization of a so-called "high-resolution electroencephalogram (EEG)": by enhancing the poor spatial resolution of EEG recordings. To this end, the forward problem for a dipolar source arbitrarily located at the source point Q=Q(r _s,φ _s,ϑ _s) has been determined in a compact matrix notation. It is possible to transfer the potential field given on the outer surface of a spherically shaped volume conductor to an arbitrary inner surface (e.g., to the cortical surface) under consideration of the electrical and geometrical properties of the model. For the application of the proposed method to real-world problems, the coefficients of the series expansion describing the cortical potential distribution are determined by minimizing the squared curvature of the scalp potential field integrated over the scalp surface. Simulation results for distributed sources show that the proposed method is superior to the surface Laplacian method for interelectrode distances below 2.5 cm.