  Multichannel transcranial current stimulation (tCS) systems offer the
possibility of EEG-guided optimized, non-invasive brain stimulation. In this
brief technical note I explain how it is possible to use tCS electric field
realistic 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 generate
2D cortical surface dipole fields that could produce the observed EEG electrode
voltages. The main tool is the reciprocity theorem derived by Helmholtz. The
application of reciprocity for the generation of a forward mapping matrix (lead
field 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 with
realistic head model tCS optimization. I also provide a generalization of the
reciprocity theorem [Helmholtz 1853] to the case of multiple electrode contact
points and dipole sources, and discuss its uses in non-invasive brain
stimulation based on EEG. This, as far as I know, is a novel result.
Applications are discussed.
