Conventional and Reciprocal Approaches to the Inverse Dipole Localization Problem for N₂₀–P₂₀ Somatosensory Evoked Potentials

The non-invasive localization of the primary sensory hand area can be achieved by solving the inverse problem of electroencephalography (EEG) for N₂₀–P₂₀ somatosensory evoked potentials (SEPs). This study compares two different mathematical approaches for the computation of transfer matrices used to solve the EEG inverse problem. Forward transfer matrices relating dipole sources to scalp potentials are determined via conventional and reciprocal approaches using individual, realistically shaped head models. The reciprocal approach entails calculating the electric field at the dipole position when scalp electrodes are reciprocally energized with unit current—scalp potentials are obtained from the scalar product of this electric field and the dipole moment. Median nerve stimulation is performed on three healthy subjects and single-dipole inverse solutions for the N₂₀–P₂₀ SEPs are then obtained by simplex minimization and validated against the primary sensory hand area identified on magnetic resonance images. Solutions are presented for different time points, filtering strategies, boundary-element method discretizations, and skull conductivity values. Both approaches produce similarly small position errors for the N₂₀–P₂₀ SEP. Position error for single-dipole inverse solutions is inherently robust to inaccuracies in forward transfer matrices but dependent on the overlapping activity of other neural sources. Significantly smaller time and storage requirements are the principal advantages of the reciprocal approach. Reduced computational requirements and similar dipole position accuracy support the use of reciprocal approaches over conventional approaches for N₂₀–P₂₀ SEP source localization.