PROBABILITY-BASED CURRENT DIPOLE LOCALIZATION FROM BIOMAGNETIC FIELDS

Focal biomagnetic sources are described as pointlike current dipoles. The dipole parameters, position, and moment coordinates are commonly d etermined from biomagnetic data using iterative nonlinear optimization algorithms such as the Levenberg-Marquardt algorithm. However, even f or single dipole sources, mislocalizations can occur due to side minim a of the cost function or due to a wrong choice of the start vector. T his can be shown by introducing a cost function where the independent variables are only the position coordinates instead of position and mo ment coordinates. This dimensional reduction-which is also possible fo r multiple dipole sources-is achieved by calculating the cost function at each position with the position and data-dependent, optimum dipole moments. We call these dipoles with-in a least squares sense-optimum moments, locally optimal dipoles. The visualization of such a single-d ipole cost function and of the iteration steps of the Levenberg-Marqua rdt algorithm show why mislocalizations cannot be avoided. Therefore, we propose an alternative noniterative localization algorithm for sing le-dipole sources without this drawback. It uses localization probabil ities calculated by means of the locally optimal dipoles. Besides the determination of the dipole parameters, the proposed algorithm furnish es a reliable error for each localization. Its effectiveness is shown with simulated and real patient data.