Electric lead field for a piecewise homogeneous volume conductor model of the head

A new method is presented for computing the electric lead field of a realistic head shape model which has piecewise homogeneous conductivity. The basic formulae are derived using the well-known reciprocity theorem. Previously described methods are also based upon this theorem, but these first calculate the electric potential inside the head by a scalar boundary element method (BEM), and then approximate the ohmic current density by some sort of gradient. In contrast, this paper proposes the direct evaluation of the ohmic current density by discretizing the vector Green's second identity which leads to a vector version of BEM. This approach also allows the derivation of the same equations for the three concentric spheres model as obtained by Rush and Driscoll [8]. The results of simulations on a spherical head model indicate that the use of a vector BEM leads to an improvement of accuracy in the computation of the ohmic current density with respect to those reported previously, in term of different measures of error.