A meshfree approach for brain activity source modeling

Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving raise to electric and magnetic fields, which are representable by means of quasi-stationary approximation of the Maxwell’s equations. Measurements of electric scalar potential differences at the scalp and magnetic fields near the head constitute the input data for, respectively, electroencephalography (EEG) and magnetoencepharography (MEG), which 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 erectromagnetic inverse problem, since measurements of electric scalar potentials ali magnetic fields provide no direct information on the position of the source, of electrical activity in the brain. The problem of reconstructing the neural activity is addressed in two stages. The first stage concerns the forward problem m, physical and geometrical representation of the head and the electromagnetic field theory are both used to find the relation between a given source model and the electromagnetic fields that the sources generate. In the second stage, the inverse problem is solved: the sources of measured electric scalar potential or magnetic fields are estimated by using the forward solution obtained in the first stage. Errors in the forward model do affect the accuracy of source estimation, so an accurate solution of the forward problem is an essential prerequisite for the solution of the inverse problem. Moreover, the process of solution of the inverse problem requires several forward problems to be solved. Therefore, the efficiency of the forward solver is another crucial aspect to take into account. The method of fundamental solutions (MFS) [3] has been proposed as an accurate, efficient, meshfree, boundary-type and easy-to-implement-arternative to traditional mesh-based methods, such as the boundary element method (BEM) for computing the solution of the M/EEG forward problem. In this work, we discuss applications of the MFS in the fielad of brain activity source modeling. Numerical results will be presented with the aim of composing the meshfree approach with the state-of-the-art BEM approach in solving M/EEG inverse problem.