Inversion of simulated evoked potentials to charge distribution inside the human brain using an algebraic reconstruction technique

An analytic method is presented to estimate the evolution of electrical charge distribution inside the human brain related to the evoked potentials observed on the head surface. A three-layer concentric spherical human head model is adopted to express the relation between the observed potentials on the head surface and the spatial charge distribution inside the brain. An integral equation associated with the three-layer concentric head model Green´s function is employed. Assuming the electric potentials are measured on the head surface, the charge distributions inside the human brain are computed by solving an inverse problem. The Green´s function integral equation is inverted by using an algebraic reconstruction technique widely employed in X-ray tomography imaging. The accuracy of the proposed technique is examined by employing computer simulations and by checking the self-consistency of the algorithm