Electrostatic field analysis of anisotropic conductive media using voxel-based static method of moments with fast multipole method
Keywords:
Voxel-based analysis, static method of moments, indirect boundary element method, fast multipole method, fast Fourier transform, electrostatic field, anisotropic conductivityAbstract
A voxel-based static method of moments (MoM) is proposed to analyse electrostatic fields in biological tissues with anisotropic conductivities, such as nerve fibre. This MoM emulates a volume element by using surface elements and boundary equations; thus, it is regarded as a type of indirect boundary element method (IBEM). Therefore, the MoM can be concurrently applied with the voxel-based IBEM, and both methods can be accelerated by the fast multipole method and fast Fourier transform in the same manner. After validating the MoM, we calculate the magnetically induced electric field in a simplified human head model constructed using diffusion tensor imaging data. It is confirmed that the proposed voxelbased MoM is applicable to field analyses of voxel models composed of isotropic and anisotropic tissues. In addition, by analysing variants of the original inhomogeneous anisotropic model, we observe the variation in the electric current distributions in (i) an inhomogeneous isotropic model, (ii) a homogeneous isotropic model and (iii) an inhomogeneous anisotropic model with finer voxel size. The calculated electric currents in these models exhibit qualitatively reasonable distributions. The proposed method is applied to models with up to 188,296,465 unknowns using a personal computer.
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