The surface Laplacian operator of the potentials on a bounded volume conductor has a unique inverse.
In the discussion on the use of the surface Laplacian (SL) of the distribution of bioelectric potentials on the body surface, the question remained open whether a complete specification of the SL of the potential over the surface bounding a volume conductor would uniquely specify the potential on that surface up to a constant. This paper reports that this is indeed the case. In addition, it is shown that the integral of the SL over a closed surface is zero, a property that may serve as a check on the accuracy of any numerical approximation of the SL.
van Oosterom
Adriaan
A
Department of Cardiology, University of Lausanne, Switzerland. adriaan.vanoosterom@epfl.ch
D000465:Algorithms; D018780:Body Surface Potential Mapping / Q000379:methods*; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D003936:Diagnosis, Computer-Assisted / Q000379:methods; D004553:Electric Conductivity; D004569:Electroencephalography / Q000379:methods*; D006329:Heart Conduction System / Q000502:physiology*; D008955:Models, Cardiovascular; D008959:Models, Neurological