6533b81ffe1ef96bd1277d13

RESEARCH PRODUCT

The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG

Michael MccourtElisa FrancomanoGregory E. FasshauerGuido AlaSalvatore Ganci

subject

Laplace's equationQuantitative Biology::Neurons and Cognitionmedicine.diagnostic_testApplied MathematicsPhysics::Medical PhysicsMathematical analysisMagnetoencephalographyInverse problemElectroencephalographySettore MAT/08 - Analisi NumericaSettore ING-IND/31 - ElettrotecnicaComputational MathematicsConvergence (routing)medicineMethod of fundamental solutionsBoundary value problemkernel-based methods method of fundamental solutions EEG MEGBoundary element methodMathematics

description

The 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.

yearjournalcountryeditionlanguage
2015-01-01SIAM Journal on Scientific Computing
https://doi.org/10.1137/13094921x