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

N. K. Soni; K. D. Paulsen; H. Dehghani; A. Hartov

doi:10.1109/TMI.2005.861001

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

N. K. Soni^*, K. D. Paulsen, H. Dehghani, A. Hartov

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	55-61
Number of pages	7
Journal	IEEE Transactions on Medical Imaging
Volume	25
Issue number	1
DOIs	https://doi.org/10.1109/TMI.2005.861001
Publication status	Published - Jan 2006

Bibliographical note

Funding Information:
Manuscript received January 10, 2005; revised October 4, 2005. This work was supported in part by the National Institutes of Health (NIH) National Cancer Institute under Grant P01-CA80139. The Associate Editor responsible for coordinating the review of this paper an recommending its publication was C. McLeod. Asterisk indicates corresponding author. *N. K. Soni is with the Philips Medical Systems, Cleveland, OH 44143 USA (e-mail: nksoni@yahoo.com).

Keywords

Aphilipp
Electrical impedance tomography
Finite element implementation
Image reconstruction
Laplace equations
Maxwell equations

ASJC Scopus subject areas

Software
Radiological and Ultrasound Technology
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TMI.2005.861001

Cite this

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title = "Finite element implementation of Maxwell's equations for image reconstruction in electrical impedance tomography",

abstract = "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.",

keywords = "Aphilipp, Electrical impedance tomography, Finite element implementation, Image reconstruction, Laplace equations, Maxwell equations",

author = "Soni, {N. K.} and Paulsen, {K. D.} and H. Dehghani and A. Hartov",

note = "Funding Information: Manuscript received January 10, 2005; revised October 4, 2005. This work was supported in part by the National Institutes of Health (NIH) National Cancer Institute under Grant P01-CA80139. The Associate Editor responsible for coordinating the review of this paper an recommending its publication was C. McLeod. Asterisk indicates corresponding author. *N. K. Soni is with the Philips Medical Systems, Cleveland, OH 44143 USA (e-mail: nksoni@yahoo.com).",

year = "2006",

month = jan,

doi = "10.1109/TMI.2005.861001",

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AU - Soni, N. K.

AU - Paulsen, K. D.

AU - Dehghani, H.

AU - Hartov, A.

N1 - Funding Information: Manuscript received January 10, 2005; revised October 4, 2005. This work was supported in part by the National Institutes of Health (NIH) National Cancer Institute under Grant P01-CA80139. The Associate Editor responsible for coordinating the review of this paper an recommending its publication was C. McLeod. Asterisk indicates corresponding author. *N. K. Soni is with the Philips Medical Systems, Cleveland, OH 44143 USA (e-mail: nksoni@yahoo.com).

PY - 2006/1

Y1 - 2006/1

N2 - 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.

AB - 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.

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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