Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography

Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms o...

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Bibliographic Details
Published in:IEEE transactions on medical imaging 2006-01, Vol.25 (1), p.55-61
Main Authors: Soni, N.K., Paulsen, K.D., Dehghani, H., Hartov, A.
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Computer Simulation
Couplings
Electric Impedance
electrical impedance tomography
Finite Element Analysis
finite element method
Finite element methods
Frequency
high-frequency EIT
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image reconstruction
Imaging, Three-Dimensional - methods
Impedance
Information Storage and Retrieval - methods
inverse problems
Laplace equations
Magnetic field measurement
Maxwell equations
Maxwell's equations
Models, Biological
Phantoms, Imaging
Tomography
Tomography - instrumentation
Tomography - methods
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Summary:Traditionally, image reconstruction in electrical impedance tomography (EIT) has been based on Laplace's equation. However, at high frequencies the coupling between electric and magnetic fields requires solution of the full Maxwell equations. In this paper, a formulation is presented in terms of the Maxwell equations expressed in scalar and vector potentials. The approach leads to boundary conditions that naturally align with the quantities measured by EIT instrumentation. A two-dimensional implementation for image reconstruction from EIT data is realized. The effect of frequency on the field distribution is illustrated using the high-frequency model and is compared with Laplace solutions. Numerical simulations and experimental results are also presented to illustrate image reconstruction over a range of frequencies using the new implementation. The results show that scalar/vector potential reconstruction produces images which are essentially indistinguishable from a Laplace algorithm for frequencies below 1 MHz but superior at frequencies reaching 10 MHz.
ISSN:0278-0062
1558-254X
DOI:10.1109/TMI.2005.861001