CompanyName: University of Technology Graz
Abstract: Numeric solution of the general 3D eddy current problem for magnetic induction tomography
Merwa R., Hollaus K., Brandstätter B., Scharfetter H.
Magnetic induction tomography (MIT)
aims at the reconstruction of the electrical conductivity of biological tissue
from measurements of the perturbation of an alternating magnetic field. This
contactless technique appears especially attractive for the monitoring of pathologies
in the brain, which are correlated with local fluid shifts, e. g. edema, hemorrhages
or epileptic events. Due to the inappropriateness of backprojection as a general
method for the image reconstruction  the inverse problem of MIT must be solved
in a more generic manner.
In order to tackle this problem we developed a modeling and simulation environment for the complete 3D eddy current problem. Modeling of the geometry is carried out with the commercial mesh-generator HyperMesh (Altair Inc.) and a MATLAB interface for importation and pre-processing of the anatomical information (MR images). Fast variations of the geometry, e. g. for analyzing the sensitivity to geometry changes, are possible with an additional fully automatic code generator written in MATLAB.
The eddy current problem is solved with the finite element (FE) method by applying the Ar ,V - Ar formulation . The reduced magnetic vector potential Ar is used in the whole space whereas the electric scalar potential V appears only in the conducting region. Isoparametric tetrahedral nodal FEs with fourteen nodes and quadratic shape functions are used for the description of V, while the vector potential is approximated by means of edge elements . The solution is done by the Incomplete Cholesky Conjugate Gradient technique.
A realistic model of the human brain consisting of white matter, gray matter, ventricle system and liquor around the brain has been generated. The whole model consists of approximately 20000 elements of first order and 3000 nodes. In order to consider the far boundary the surrounding air has been modeled by a sphere of additional 30000 elements and 6000 nodes.
The developed simulation package renders possible the analysis of different anatomically constrained eddy current problems and for the generation of sensitivity maps. Moreover the 3-D-solver forms the basis for the solution of the inverse problem.
 Bíró O. Edge element formulations of eddy current problems. Computer methods in applied mechanics and engineering 160: 391-405, 1999
 Kameari A. Symmetric Second Order Edge Elements for Triangles and Tetrahedra. IEEE Transactions on Magnetics 35, 1394-1396, 1999
 Scharfetter H, Riu P, Populo M, Rosell J. Sensitivity maps for low-contrast-perturbations within conducting background in magnetic induction tomography (MIT). Physiol Meas, 23: 195-202, 2002