Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization

Date
2012-07-27
Authors
Oran, O. F.
Ider, Y. Z.
Advisor
Instructor
Source Title
Physics in Medicine and Biology
Print ISSN
0031-9155
Electronic ISSN
Publisher
Institute of Physics Publishing
Volume
57
Issue
16
Pages
5113 - 5140
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇ 2B z) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇ 2B z-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convectiondiffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.

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Book Title
Keywords
Artificial diffusion, Conductivity distributions, Convection-diffusion equations, Current distribution, Experimental data, Field variables, Finite element method FEM, Galerkin, Laplacians, Magnetic resonance electrical impedance tomographies, Petrov-Galerkin, Pure convection, Stabilization methods, Stabilization techniques, Weighted residuals, Algorithms, Electric impedance, Electric impedance tomography, Finite element method, Galerkin methods, Magnetic flux, Magnetic resonance, Stabilization, Article, Diffusion, Finite element analysis, Image quality, Impedance, Instrumentation, Methodology, Nuclear magnetic resonance imaging, Temperature, Tomography, Diffusion, Electric impedance, Finite element analysis, Magnetic resonance imaging, Phantoms, Temperature, Tomography
Citation
Published Version (Please cite this version)