A precorrected-FFT method to accelerate the solution of the forward problem in magnetoencephalography

Abstract

Accurate localization of brain activity recorded by magnetoencephalography (MEG) requires that the forward problem, i.e. the magnetic field caused by a dipolar source current in a homogeneous volume conductor, be solved precisely. We have used the Galerkin method with piecewise linear basis functions in the boundary element method to improve the solution of the forward problem. In addition, we have replaced the direct method, i.e. the LU decomposition, by a modern iterative method to solve the dense linear system of equations arising from the boundary element discretization. In this paper we describe a precorrected-FFT method which we have combined with the iterative method to accelerate the solution of the forward problem and to avoid the explicit formation of the dense coefficient matrix. For example, with a triangular mesh of 18000 triangles, the CPU time to solve the forward problem was decreased from 3.5 h to less than 5 min, and the computer memory requirements were decreased from 1.3 GB to 156 MB. The method makes it possible to solve quickly significantly larger problems with widely-used workstations.