Fast multipole acceleration of the MEG/EEG boundary element method

The accurate solution of the forward electrostatic problem is an essential first step before solving the inverse problem of magneto- and electroencephalography (MEG/EEG). The symmetric Galerkin boundary element method is accurate but cannot be used for very large problems because of its computational complexity and memory requirements. We describe a fast multipole-based acceleration for the symmetric boundary element method (BEM). It creates a hierarchical structure of the elements and approximates far interactions using spherical harmonics expansions. The accelerated method is shown to be as accurate as the direct method, yet for large problems it is both faster and more economical in terms of memory consumption.

[1]  Jussi Rahola,et al.  Experiments On Iterative Methods And The Fast Multipole Method In Electromagnetic Scattering Calcula , 1998 .

[2]  Symmetric BEM and Multiscale Fast Multipole Method for the E/MEG Problem , .

[3]  W. Hackbusch,et al.  Introduction to Hierarchical Matrices with Applications , 2003 .

[4]  A fast multipole boundary element method for the symmetric boundary integral formulation , 2002 .

[5]  A. S. Ferguson,et al.  Factors affecting the accuracy of the boundary element method in the forward problem. I. Calculating surface potentials , 1997, IEEE Transactions on Biomedical Engineering.

[6]  Olivier D. Faugeras,et al.  A common formalism for the Integral formulations of the forward EEG problem , 2005, IEEE Transactions on Medical Imaging.

[7]  R. Beatson,et al.  A short course on fast multipole methods , 1997 .

[8]  Olivier D. Faugeras,et al.  The fast multipole method for the direct E/MEG problem , 2002, Proceedings IEEE International Symposium on Biomedical Imaging.

[9]  R M Leahy,et al.  Imaging neural activity using MEG and EEG. , 1997, IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society.

[10]  Junichiro Makino.  Yet Another Fast Multipole Method without Multipoles-Pseudoparticle Multipole Method , 1999 .

[11]  Michael A. Epton,et al.  Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations , 1995, SIAM J. Sci. Comput..

[12]  S. Tissari,et al.  A precorrected-fFT method to accelerate the solution of the forward problem in magnetoencephalography. , 2003, Physics in medicine and biology.

[13]  O. Faugeras,et al.  COMPARISON OF BEM AND FEM METHODS FOR THE E/MEG PROBLEM , 2004 .

[14]  R. Ilmoniemi,et al.  Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain , 1993 .

[15]  Satu Tissari,et al.  Iterative solution of dense linear systems arising from the electrostatic integral equation in MEG. , 2002, Physics in medicine and biology.

[16]  J. Rahola.  Iterative Solution of Dense Linear Systems , 2007 .

[17]  B. Dembart,et al.  The accuracy of fast multipole methods for Maxwell's equations , 1998 .

[18]  L. Greengard,et al.  Regular Article: A Fast Adaptive Multipole Algorithm in Three Dimensions , 1999 .

[19]  D. Apalkov,et al.  Fast multipole method for micromagnetic simulation of periodic systems , 2003 .