Conductivity and Permittivity Image Reconstruction at the Larmor Frequency Using MRI

Song, Yizhuang; Seo, Jin Keun

doi:10.1137/130906842

Cited by 15 publications

(17 citation statements)

References 26 publications

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“…We confirmed that the result of the proposed method improves when we obtained H − in addition to H + from the simulation and used both to give the normal derivative of E z based on Eq. (18). The method to obtain both H + and H − by multichannel surface coils in addition to the quadrature birdcage coil is referred to in [14].…”

Section: Resultsmentioning

confidence: 99%

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A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

Fushimi

Nara

2017

SICE Journal of Control, Measurement, and System Integration

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: The electrical properties (EPs) of biological tissue, consisting of conductivity and permittivity, provide useful information for the diagnosis of malignant tissues and the evaluation of heat absorption rates. Recently, magnetic resonance electrical properties tomography (MREPT), by which EPs are reconstructed from internal magnetic field data measured by using magnetic resonance imaging (MRI), has been actively studied. We previously proposed an explicit pointwise reconstruction method for MREPT based on a complex partial differential equation (PDE), known as the D-bar equation, of the electric field and its explicit solution given by an integral formula. In this method, as in some other conventional methods, EP values on the boundary of the region of interest must be given as a Dirichlet boundary condition of the PDE. However, it is difficult to know these values precisely in practical situations. Therefore, in this paper, we propose a novel method for reconstructing EPs in a circular region without any knowledge of boundary EP values. Starting from the integral solution to solve the D-bar equation in a circular region with the Neumann boundary condition, we show that the contour integral term of the integral formula is eliminated by using Faraday's law and solve the PDE based only on magnetic field data measured by using MRI. Numerical simulations show that the proposed method yields a good reconstruction results without any knowledge of boundary EP values.

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Section: Resultsmentioning

confidence: 99%

“…The first approach is to solve the PDE using an iterative optimization calculation [18]- [21]. In these iterative methods, it is important to give the optimal initial value, without which a local minimum solution can be obtained.…”

Section: Introductionmentioning

confidence: 99%

A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

Fushimi

Nara

2017

SICE Journal of Control, Measurement, and System Integration

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“…In Serralles et al, the above‐mentioned LMT was converted to a forward problem, now called ‘global Maxwell tomography’. Based on Song and Seo, Ammari iteratively minimized the mismatch between the forward model and observed data starting with an initial guess by solving Equation for the complex H + . This method was further developed by Palamodov …”

Section: Advanced Reconstruction Techniquesmentioning

confidence: 99%

Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications

2017

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Electric properties tomography (EPT) derives the patient's electric properties, i.e. conductivity and permittivity, using standard magnetic resonance (MR) systems and standard MR sequences. Thus, EPT does not apply externally mounted electrodes, currents or radiofrequency (RF) probes, as is the case in competing techniques. EPT is quantitative MR, i.e. it yields absolute values of conductivity and permittivity. This review summarizes the physical equations underlying EPT, the corresponding basic and advanced reconstruction techniques and practical numerical aspects to realize these reconstruction techniques. MR sequences which map the field information required for EPT are outlined, and experiments to validate EPT in phantom and in vivo studies are described. Furthermore, the review describes the clinical findings which have been obtained with EPT so far, and attempts to understand the physiologic background of these findings.

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“…Another MREPT method ( 22 ) was proposed on the basis of the fact that the magnetic field

near the center of a birdcage or a transverse electromagnetic coil is homogeneous along its central axis ( 23 , 24 ), and it is assumed that the contribution of the along-axis component of the magnetic field is negligible when the region of interest is close to the center of the coil. A first-order PDE including a gradient term of the unknown EP was formulated via properly manipulating Maxwell equations, and the gradient term describes the inhomogeneity of the object under investigation.…”

Section: Introductionmentioning

confidence: 99%

An MR-Based Viscosity-Type Regularization Method for Electrical Property Tomography

Wang

Huang

2017

Tomography

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Here, a method based on viscosity-type regularization is proposed for magnetic resonance electrical property tomography (MREPT) to mitigate persistent artifacts when it is used to reconstruct a map of electrical properties based on data from a magnetic resonance imaging scanner. The challenges for solving the corresponding partial differential equation (PDE) are discussed in detail. The existing artifacts in the numerical results are pointed out and classified. The methods in the literature for MREPT are mainly based on an assumption of local homogeneity, which makes the approach simple but leads to artifacts in the transition region where electrical properties vary rapidly. Recent work has focused on eliminating the assumption of local homogeneity, and one of the solutions is convection–reaction MREPT that is based on a first-order PDE. Numerical solutions of the PDE have persistent artifacts in certain regions and global spurious oscillations. Here, a method based on viscosity-type regularization is proposed to effectively mitigate the aforementioned problems. Finite difference method is used for discretizing the governing PDE. Numerical experiments are presented to analyze the problem in detail. Electrical properties of different phantoms are successfully retrieved. The efficiency, accuracy, and noise tolerance of the proposed method are illustrated with numerical results.

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Conductivity and Permittivity Image Reconstruction at the Larmor Frequency Using MRI

Abstract: • Magnetic Resonance Electrical Property Tomography (MREPT) aims to visualize both conductivity σ and permittivity ǫ distributions at the Larmor frequency (≈ 128 MHz for a 3 T MRI).

Cited by 15 publications

References 26 publications

A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications

An MR-Based Viscosity-Type Regularization Method for Electrical Property Tomography

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