RESUMO
This paper presents a novel algorithm to reconstruct parameters of a sufficient number of current dipoles that describe data (equivalent current dipoles, ECDs, hereafter) from radial/vector magnetoencephalography (MEG) with and without electroencephalography (EEG). We assume a three-compartment head model and arbitrary surfaces on which the MEG sensors and EEG electrodes are placed. Via the multipole expansion of the magnetic field, we obtain algebraic equations relating the dipole parameters to the vector MEG/EEG data. By solving them directly, without providing initial parameter guesses and computing forward solutions iteratively, the dipole positions and moments projected onto the xy-plane (equatorial plane) are reconstructed from a single time shot of the data. In addition, when the head layers and the sensor surfaces are spherically symmetric, we show that the required data reduce to radial MEG only. This clarifies the advantage of vector MEG/EEG measurements and algorithms for a generally-shaped head and sensor surfaces. In the numerical simulations, the centroids of the patch sources are well localized using vector/radial MEG measured on the upper hemisphere. By assuming the model order to be larger than the actual dipole number, the resultant spurious dipole is shown to have a much smaller strength magnetic moment (about 0.05 times smaller when the SNR = 16 dB), so that the number of ECDs is reasonably estimated. We consider that our direct method with greatly reduced computational cost can also be used to provide a good initial guess for conventional dipolar/multipolar fitting algorithms.