Determination of sources using brain-evoked potential maps

Methods to localize the sources of Brain Evoked Potential Maps based on modeling of the sources as point dipoles have been widely used for more than twenty years. Such methods still lack a basic theory which can answer questions regarding the resolution and uniqueness of the results in the context of a realistic head model, with no a prior restrictions on the sources. In the first part of the paper we present simple physical models for the origin of far-field potentials associated with the auditory and somatosensory systems. An action potential travels along a straight axon can only produce a quadrupole field at far distances. We show that the far field potentials must originate when the action potential passes through a bent axon or through changes in the conductivities or in the external boundaries of the volume conductor surrounding the axon. We discuss the question of uniqueness of the solution for the 'inverse problem' of evoked potentials. This problem involved the reconstruction of the location and pattern of activity of the neuronal generators in the brain, given the map of the scalp electric potentials. We show that in a head shape with a realistic geometry spatially distinct points, line or open surface generators cannot create the same scalp potential map. The same applies to two non-overlapping generators occupying finite volumes.