Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization
Author
Oran, O. F.
Ider, Y. Z.
Date
2012-07-27Source Title
Physics in Medicine and Biology
Print ISSN
0031-9155
Publisher
Institute of Physics Publishing
Volume
57
Issue
16
Pages
5113 - 5140
Language
English
Type
ArticleItem Usage Stats
142
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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.
Keywords
Artificial diffusionConductivity 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
Permalink
http://hdl.handle.net/11693/21361Published Version (Please cite this version)
http://dx.doi.org/10.1088/0031-9155/57/16/5113Collections
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