The Method of Fundamental Solutions in Solving Coupled
Boundary Value Problems for EEG/MEG
Salvatore Ganci
University of Palermo
Viale delle Scienze, Edificio 9, Palermo, Italy
salvatore.ganci@unipa.it
Keywords. Neuroimaging; Method of Fundamental Solutions; EEG/MEG
forward problem.
Estimation of neuronal activity in the human brain from
electroencephalography (EEG) and/or magnetoencephalography (MEG) signals is
a typical inverse problem whose solution process requires an accurate and
efficient forward solver [1-2].
We introduce the Method of Fundamental Solution (MFS) [3-4] as a truly
meshless, boundary-type, integration-free and easy to implement alternative to the
state of the art Boundary Element Method (BEM) for solving the EEG/MEG
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 which has well behaved analytic
fundamental solutions.
Accuracy, convergence and computational load are investigated and
comparisons with BEM show the potentiality of the proposed method.
Acknowledgements
Joint work with Guido Ala, Gregory Fasshauer, Elisa Francomano and Mike
McCourt.
References
[1] Hallez H. et al. (2007) “Review on solving the forward problem in EEG
source analysis.” Journal of Neuroengineering and Rehabilitation, Vol. 4, p.
46.
[2] Hämäläinen M. et al. (1993) “Magnetoencephalography–theory,
instrumentation, and applications to noninvasive studies of the working human
brain." Reviews of Modern Physics, Vol. 65, p. 413.
[3] Fairweather G., Karageorghis A. (1998) “The method of fundamental solutions
for elliptic boundary value problems.” Advances in Computational
Mathematics, Vol. 9.1-2, pp. 69-95.
[4] Golberg M.A., Chen C.S. (1998) “The method of fundamental solutions for
potential, Helmholtz and diffusion problems.” Boundary Integral Methods Numerical and Mathematical Aspects, pp. 103-176.