Solution of Poisson’s equation in a volume conductor using resistor mesh models: Application to event related potential imaging

In electroencephalography (EEG) and event related potentials (ERP), localizing the electrical sources at the origin of scalp potentials (inverse problem) imposes, in a first step, the computation of scalp potential distribution from the simulation of sources (forward problem). This article proposes an alternative method for mimicing both the electrical and geometrical properties of the head, including brain, skull, and scalp tissue with resistors. Two resistor mesh models have been designed to reproduce the three-sphere reference model (analytical model). The first one (spherical resistor mesh) closely mimics the geometrical and electrical properties of the analytical model. The second one (cubic resistor mesh) is designed to conveniently handle anatomical data from magnetic resonance imaging. Both models have been validated, in reference to the analytical solution calculated on the three-sphere model, by computing the magnification factor and the relative difference measure. Results suggest that the mesh...