On the inverse EEG problem for a 1D current distribution

Albanese and monk (2006) have shown that,it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. on the other hand,it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. in the present work,we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. the immediate representation of this problem refers to the inverse problem of electroencephalography (eeg) with a linear current distribution and the spherical model of the brain-head system. it is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. numerical tests show that this system has exactly one real solution. exact solutions are analytically obtained for a couple of special cases. © 2014 george dassios et al.