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Multichannel transcranial current stimulation (tCS) systems offer thepossibility of EEG-guided optimized, non-invasive brain stimulation. In thisbrief technical note I explain how it is possible to use tCS electric fieldrealistic brain model to create a forward "lead-field" matrix and, from that,an EEG inverter for cortical mapping. Starting from EEG I show how to generate2D cortical surface dipole fields that could produce the observed EEG electrodevoltages. The main tool is the reciprocity theorem derived by Helmholtz. Theapplication of reciprocity for the generation of a forward mapping matrix (leadfield matrix as is sometimes known) is well known [Rush and Driscoll, 1969],but here we will use it in combination with the realistic head models of[Miranda et al 2013] to provide cortical mapping solutions compatible withrealistic head model tCS optimization. I also provide a generalization of thereciprocity theorem [Helmholtz 1853] to the case of multiple electrode contactpoints and dipole sources, and discuss its uses in non-invasive brainstimulation based on EEG. This, as far as I know, is a novel result.Applications are discussed.

Application of the reciprocity theorem to EEG inversion and optimization  of EEG-driven transcranial current stimulation (tCS, including tDCS, tACS,  tRNS)