The finite-element method (FEM) is applied to solve the EEG forward problem. Two issues related to the implementation of this method are investigated. The first is the singularity due to the punctual dipole sources and the second is the numerical errors observed near the interface of different tissues. To deal with the singularity of the punctual dipole sources, three source modeling methods, namely, the direct, the subtraction and the Saint Venant's methods, are examined. To solve the problem of numerical instability near the interface of different tissues, a modification on the Saint Venant's method is introduced. The numerical results are compared with analytical solution in the case of the multilayer spherical head models. The advantages of the proposed method are highlighted.
1. Grech, R., et al., "Review on solving the inverse problem in EEG source analysis," Jnl. of Neuroengineering and Rehabilitation, Vol. 5, No. 1, 25, 2008. doi:10.1186/1743-0003-5-25
2. Hämäläinen, M., et al., "Magnetoencephalography - Theory, instrumentation, and applications to noninvasive studies of the working human brain," Reviews of Modern Physics, Vol. 65, No. 2, 413, 1993. doi:10.1103/RevModPhys.65.413
3. Tadel, F., et al., "Brainstorm: A user-friendly application for MEG/EEG analysis," Comput. Intelligence and Neuroscience, Vol. 2011, 8, 2011.
4. Hallez, H., et al., "Review on solving the forward problem in EEG analysis," Jnl. of Neuroengineering and Rehabilitation, Vol. 4, No. 1, 46, 2007. doi:10.1186/1743-0003-4-46
5. Wolters, C. H., et al., "Numerical mathematics of the subtraction method for the modeling of a current dipole in EEG source reconstruction using finite element head models," SIAM Journal on Scientific Computing, Vol. 30, No. 1, 24-45, 2007. doi:10.1137/060659053
6. Bertrand, O., M. Thevenet, and F. Perrin, "3D finite element method in brain electrical activity studies," Biomagnetic Localization and 3D Modelling, 154-171, 1991.
7. Shahid, S. and P. Wen, "Analytic and numeric evaluation of EEG forward problem using spherical volume conductor models," 2010 IEEE/ICME International Conference on IEEE Complex Medical Engineering (CME), 28-33, 2010. doi:10.1109/ICCME.2010.5558878
8. Wolters, C. H., et al., "Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: A simulation and visualization study using high-resolution finite element modeling," NeuroImage, Vol. 30, No. 3, 813-826, 2006. doi:10.1016/j.neuroimage.2005.10.014
9. Zhang, Y., Z. Ren, and D. Lautru, "Finite element modeling of current dipoles using direct and subtraction methods for EEG forward problem," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33, No. 1/2, 210, 2014.
10. Medani, T., D. Lautru, and Z. Ren, "Study of modeling of current dipoles in the finite element method for eeg forward problem," La 7ème Conférence Européenne sur les Méthodes Numériques en Electromagnétisme (NUMELEC 2012), Juillet, Marseille, France, 2012.
11. Zhang, Z., "A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres," Physics in Medicine and Biology, Vol. 40, No. 3, 335, 1995. doi:10.1088/0031-9155/40/3/001
12. Buchner, H., et al., "Inverse localization of electric dipole current sources in finite element models of the human head," Electroencephalography and Clinical Neurophysiology, Vol. 102, No. 4, 267-278, 1997. doi:10.1016/S0013-4694(96)95698-9
13. Yan, Y., P. Nunez, and R. T. Hart, "Finite-element model of the human head: Scalp potentials due to dipole sources," Medical and Biological Engineering and Computing, Vol. 29, No. 5, 475-481, 1991. doi:10.1007/BF02442317
14. Lew, S., et al., "Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis," Applied Numerical Mathematics, Vol. 59, No. 8, 1970-1988, 2009. doi:10.1016/j.apnum.2009.02.006
15. Drechsler, F., et al., "A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation," NeuroImage, Vol. 46, No. 4, 1055-1065, 2009. doi:10.1016/j.neuroimage.2009.02.024
16. Vorwerk, J., M. Clerc, M. Burger, and C. H. Wolters, "Comparison of boundary element and finite element approaches to the EEG forward problem," Biomedical Engineering, Vol. 57(Suppl. 1), 795-798, 2012.
17. Vorwerk, J., J.-H. Cho, S. Rampp, H. Hamer, T. R. Knosche, and C. H. Wolters, "A guideline for head volume conductor modeling in EEG and MEG," NeuroImage, Vol. 100, 590-607, 2014. doi:10.1016/j.neuroimage.2014.06.040
18. Fang, Q. and D. Boas, "Tetrahedral mesh generation from volumetric binary and gray-scale images," Proceedings of IEEE International Symposium on Biomedical Imaging 2009, 1142-1145, 2009.
19. Liu, A. and B. Joe, "Relationship between tetrahedron shape measures," BIT Numerical Mathematics, Vol. 34, No. 2, 268-287, 1994. doi:10.1007/BF01955874
20. Medani, T., D. Lautru, Z. Ren, D. Schwartz, and G. Sou, "Modelling of brain sources using the modified Saint Venant’s method in FEM resolution of EEG forward problem," 7th Annual International IEEE EMBS Conference on Neural Engineering, France, Apr. 2015.
21. Gramfort, A., T. Papadopoulo, E. Olivi, and M. Clerc, "OpenMEEG: Opensource software for quasistatic bioelectromagnetics," BioMedical Engin., Vol. 45, No. 9, 2010.