High-definition MEG source estimation using the reciprocal boundary element fast multipole method

Magnetoencephalographic (MEG) source estimation relies on the computation of the gain (lead-field) matrix, which embodies the linear relationship between the amplitudes of the sources and the recorded signals. However, with a realistic forward model, the calculation of the gain matrix in a "direct" fashion is a computationally expensive task, forcing the number of dipolar sources in standard MEG pipelines to be typically limited to 10,000. We propose a fast computational approach to calculate the gain matrix, which is based on the reciprocal relationship between MEG and transcranial magnetic stimulation (TMS), and which we couple with the charge-based boundary element fast multipole method (BEM-FMM). Our method allows us to efficiently generate gain matrices for high-resolution multi-layer non-nested meshes involving source spaces of up to 1 million dipoles. We employed the gain matrices generated with our approach to perform minimum norm estimate (MNE) source localization against simulated data (at varying noise levels) and experimental MEG data of evoked somatosensory fields elicited by right-hand median nerve stimulation on 5 healthy participants. Additionally, we compare our experimental source estimates against the standard 1- and 3-layer BEM models of the MNE-Python source estimation pipeline, and against a 3-layer isotropic FEM model.