197,053 research outputs found
Il metodo delle soluzioni fondamentali per la soluzione del problema diretto M/EEG
No full textThe research already started on the mesh-free solution of the M / EEG direct problem has led to the development of a solver based on the method of fundamental solutions (MFS, method of fundamental solutions) able to manage the physical-geometric complexity of realistic models of the head more efficiently than traditional
The method of fundamental solutions in solving coupled boundary value problems for M/EEG
No full textThe estimation of neuronal activity in the human brain from electroencephalography (EEG) and magnetoencephalography (MEG) signals is a typical inverse problem whose solution pro- cess requires an accurate and fast forward solver. In this paper the method of fundamental solutions is, for the first time, proposed as a meshfree, boundary-type, and easy-to-implement alternative to the boundary element method (BEM) for solving the M/EEG forward problem. The solution of the forward problem is obtained by numerically solving a set of coupled boundary value problems for the three-dimensional Laplace equation. Numerical accuracy, convergence, and computational load are investigated. The proposed method is shown to be a competitive alternative to the state-of-the-art BEM for M/EEG forward solving
An Improved Solver for the M/EEG Forward Problem
No full textNoninvasive investigation of the brain activity via
electroencephalography (EEG) and magnetoencephalography
(MEG) involves a typical inverse problem whose solution process
requires an accurate and fast forward solver. We propose the
Method of Fundamental Solutions (MFS) as a truly meshfree
alternative to the Boundary Element Method (BEM) for solving
the M/EEG forward problem. The solution of the forward
problem is obtained, via the Method of Particular Solutions
(MPS), by numerically solving a set of coupled boundary value
problems for the 3D Laplace equation. Numerical accuracy and
computational load are investigated for spherical geometries and
comparisons with a state-of-the-art BEM solver shows that the
proposed method is competitive
An augmented MFS approach for brain activity reconstruction
No full textWeak 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 magnetoencephalog- raphy (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 prob- lem 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
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