Simplex minimization and the inverse dipole localization problem of electroencephalography

Noninvasive localization of brain electrical activity from scalp potentials often involves computing the location and moment parameters of an inverse current dipole. The correct inverse dipole parameters are those that minimize the difference between measured scalp potentials and corresponding theoretical potentials generated by the inverse dipole in a numerical head model. Performance characteristics of the simplex algorithm often used to effect this minimization were investigated in simulation studies employing the three-concentric-spheres head model. A position constraint restricting inverse solutions to the brain region was utilized with the simplex algorithm. It is shown that this algorithm is surprisingly robust even in the presence of large errors in the forward transfer matrix used to compute theoretical potentials.