Conductivity and permittivity image reconstruction at the larmor frequency using MRI

Yizhuang Song, Jin Keun Seo

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper presents a new method of providing both conductivity (θ) and permittivity (-) images at the MR Larmor frequency in magnetic resonance electrical property tomography (MREPT), a relatively new MR-based electrical tissue property imaging modality. In MREPT, the RF coil of the MR scanner is used to feed a sinusoidal current at the Larmor frequency, ε/2π (approximately 128 MHz for a 3 Tesla MRI machine), to an imaging object within the MR scanner. Inside the object, this injection current induces a time-harmonic magnetic field, H = (Hx,Hy,Hz), that is influenced by the body's admittivity distribution, δ = θ + iε, via Maxwell's equations. Currently, the positive rotating field, H + = (Hx + iHy)/2, is the only measurable quantity which can be obtained from B1 mapping techniques. The inverse problem of MREPT is to reconstruct δ from the H+ data. Existing MREPT reconstruction methods use the local homogeneity assumption (δ = 0) to simplify the relation between δ and H+, so that the admittivity is proportional to the ratio of the Laplacian 2H+ to H+. However, the conventional reconstruction method based on this local homogeneity assumption gives rise to serious reconstruction errors at large |δ||δ|. Hence, the major issue in MREPT is to find a reconstruction formula without assuming the local homogeneity condition. The proposed method removes the assumption of ( θ θx δ, θ θy δ) = 0 (but still requires θ θz δ ? 0). We have found an exact relation between δ and H+, so that δ is a solution of a semilinear elliptic PDE with coefficients depending only upon H+. Numerical simulations show that the proposed method successfully reconstructs discontinuous admittivities.

Original languageEnglish
Pages (from-to)2262-2280
Number of pages19
JournalSIAM Journal on Applied Mathematics
Volume73
Issue number6
DOIs
Publication statusPublished - 2013 Dec 1

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Magnetic Resonance
Electrical Properties
Permittivity
Image Reconstruction
Magnetic resonance
Tomography
Image reconstruction
Magnetic resonance imaging
Conductivity
Electric properties
Homogeneity
Scanner
Imaging
Imaging techniques
Elliptic PDE
Maxwell equations
Coil
Inverse problems
Maxwell's equations
Semilinear

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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abstract = "This paper presents a new method of providing both conductivity (θ) and permittivity (-) images at the MR Larmor frequency in magnetic resonance electrical property tomography (MREPT), a relatively new MR-based electrical tissue property imaging modality. In MREPT, the RF coil of the MR scanner is used to feed a sinusoidal current at the Larmor frequency, ε/2π (approximately 128 MHz for a 3 Tesla MRI machine), to an imaging object within the MR scanner. Inside the object, this injection current induces a time-harmonic magnetic field, H = (Hx,Hy,Hz), that is influenced by the body's admittivity distribution, δ = θ + iε, via Maxwell's equations. Currently, the positive rotating field, H + = (Hx + iHy)/2, is the only measurable quantity which can be obtained from B1 mapping techniques. The inverse problem of MREPT is to reconstruct δ from the H+ data. Existing MREPT reconstruction methods use the local homogeneity assumption (δ = 0) to simplify the relation between δ and H+, so that the admittivity is proportional to the ratio of the Laplacian 2H+ to H+. However, the conventional reconstruction method based on this local homogeneity assumption gives rise to serious reconstruction errors at large |δ||δ|. Hence, the major issue in MREPT is to find a reconstruction formula without assuming the local homogeneity condition. The proposed method removes the assumption of ( θ θx δ, θ θy δ) = 0 (but still requires θ θz δ ? 0). We have found an exact relation between δ and H+, so that δ is a solution of a semilinear elliptic PDE with coefficients depending only upon H+. Numerical simulations show that the proposed method successfully reconstructs discontinuous admittivities.",
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Conductivity and permittivity image reconstruction at the larmor frequency using MRI. / Song, Yizhuang; Seo, Jin Keun.

In: SIAM Journal on Applied Mathematics, Vol. 73, No. 6, 01.12.2013, p. 2262-2280.

Research output: Contribution to journalArticle

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