On the biomagnetic inverse problem in the case of multiple dipoles

Series of Monte Carlo simulations have been carried out which were based on the assumption that two dipoles with a distance of 0.5-2 cm are located in a homogeneous semi-infinite volume conductor (depth 3 cm), and that the magnetic field component perpendicular to the surface of the volume conductor is recorded by means of a magnetometer with infinitesimal coil diameter. Moving-dipole models (all parameters time-dependent), rotating-dipole models (dipole locations fixed, dipole orientation and amplitudes time-dependent) as well as fixed-dipole models (dipole locations and orientations fixed, amplitudes time-dependent) were considered. The algorithm used to retrieve the model parameters from the simulated field distributions (biomagnetic inverse procedure) was based on a transformation of the standard least-squares fit procedure into a minimization procedure with respect to the nonlinear parameters (dipole locations and orientations), which was solved iteratively by means of the Fletcher-Powell algorithm. It was found that the resolving power of the biomagnetic inverse procedure is highly dependent on the relative orientation of the two dipoles, the temporal overlap of the dipole moments, and the correlation of successive samples of the superimposed noise. The results obtained in this study suggest that the resolving power of the biomagnetic inverse procedure for conditions typically found in the case of auditory evoked magnetic fields is not better than 2 cm for the moving-dipole approach, and not better than 1 cm for the fixed-dipole approach, provided that no additional a priori information is available. In practice, the situation is probably even worse since the depth of the generators is usually larger than assumed in this study.