In symbolic terms, the EEG forward problem is that of finding, in a reasonable time, the potential g(r, r dip , d) at an electrode positioned on the scalp at a point having position vector r due to a single dipole with dipole moment d = de d (with magnitude d and orientation e d ), positioned at r dip (see Figure 1). This amounts to solving Poisson's equation to find the potentials V on the scalp for different configurations of r dip and d. For multiple dipole sources, the electrode potential would be m(r)=∑ig(r,rdipi,di). Assuming the principle of superposition, this can be rewritten as ∑ig(r,rdipi)(dix,diy,diz)T=∑ig(r,rdipi)diei, where g(r, rdipi) now has three components corresponding to the Cartesian x, y, z directions, d i = (d ix , d iy , d iz ) is a vector consisting of the three dipole magnitude components, ' T ' denotes the transpose of a vector, d i = ||d i || is the dipole magnitude and ei=di‖di‖ is the dipole orientation. In practice, one calculates a potential between an electrode and a reference (which can be another electrode or an average reference).
