An augmented MFS approach for brain activity reconstruction

Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving rise to electric and magnetic fields, which can be modeled by the quasi-stationary approximation of Maxwell’s equations. Electroencephalography (EEG) and magnetoencephalography (MEG) techniques allow for reconstructing the cerebral electrical currents and thus investigating the neuronal activity in the human brain in a non-invasive way. This is a typical electromagnetic inverse problem which can be addressed in two stages. In the first one a physical and geometrical representation of the head is used to find the relation between a given source model and the electromagnetic fields generated by the sources. Then the inverse problem is solved: the sources of measured electric scalar potentials or magnetic fields are estimated by using the forward solution. Thus, an accurate and efficient solution of the forward problem is an essential prerequisite for the solution of the inverse one. The authors have proposed the method of fundamental solutions (MFS) as an accurate, efficient, meshfree, boundary-type and easy-to-implement alternative to traditional mesh-based methods, such as the boundary element method and the finite element method, for computing the solution of the M/EEG forward problem. In this paper, further investigations about the accuracy of the MFS approximation are reported. In particular, the open question of how to efficiently design a good solution basis is approached with an algorithm inspired by the Leave-One-Out Cross Validation (LOOCV) strategy. Numerical results are presented with the aim of validating the augmented MFS with the state-of-the-art BEM approach. Promising results have been obtained.