Uniqueness of the generators of brain evoked potential maps

Abstract
This study considers the uniqueness of neuronal generators of human brain evoked potentials measured on the scalp using the physical and mathematical properties of the volume conductor model. The results are applicable to a realistic, nonhomogeneous head shape where the potential map is known on a continuous set of points on the scalp. It is shown that sources which occupy "zero volume" in space such as point dipoles or sources distributed on an open surface or a line are uniquely defined by the potential maps. Finite volume nonoverlapping sources are also uniquely defined by their potential map. However, there are infinitely many different but overlapping sources which can create the same map. Several examples of such sources are provided. It is shown that there is a unique, minimum volume source which can be defined in this case. Results suggest that if a reconstruction of the sources starts from a continuous scalp map (obtained by interpolation of the data between electrode sites), one can obtain unique results concerning the source parameters that are not available in a search for a source whose potential map fits only at a discrete set of points.

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