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

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      Author
      Oran, O. F.
      Ider, Y. Z.
      Date
      2012-07-27
      Source 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
      Article
      Item Usage Stats
      142
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      90
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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 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
      Permalink
      http://hdl.handle.net/11693/21361
      Published Version (Please cite this version)
      http://dx.doi.org/10.1088/0031-9155/57/16/5113
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      • Department of Electrical and Electronics Engineering 3524
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