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A new boundary element method formulation for the forward problem solution of electro-magnetic source imaging

Numerical solution of the potential and magnetic fields far a given electrical source distribution in the human brain is the essential part of electro-magnetic source imaging. In this study, the performance of Boundary Element Method (BEM) with different surface element types is explored. A new BEM formulation is derived that makes use of isoparametric linear and quadratic elements. It is shown that, quadratic elements provides superior performance over linear elements in terms of computation time and accuracy. For example, a maximum error of 1.8% is obtained using 2048 quadratic elements for a selected dipole location. Whereas, in order to obtain such an accuracy with linear elements, this number should be in the order of ten thousands. The developed surface integration tools and selected isoparametric quadratic element type can also be used to salve the magnetic held of the neural ectivity in the cerebral cortex.