An explicit reconstruction method for magnetic resonance electrical property tomography based on the generalized Cauchy formula

Nara, Takaaki; Tetsuya, Furuichi; Fushimi, Motofumi

doi:10.1088/1361-6420/aa8414

Cited by 14 publications

(23 citation statements)

References 16 publications

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“…The Dirichlet-type integral formula reconstructs EPs correctly outside of the region where |∂H + | and |E z | are low when the true boundary condition is given. As mentioned in Section 2.1, this spot-like artifact occurs in regions where |∂H + | and |E z | become zero and most state-of-the-art methods using single channel birdcage coils have the same problem [19], [20], [29], [31], [32]. The method of displacing this spot-like artifact by inserting a dielectric pad was proposed in [29] and is applicable to both our previous and proposed methods.…”

Section: Resultsmentioning

confidence: 97%

“…This is due to the assumption that ∂ z H + 0. In [32], we have already proposed an iterative method to correct the error in this assumption. We confirmed that a single iteration significantly suppressed the error in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The conventional approaches in [29], [31], [32] assume that κ on the boundary of the ROI is given a priori, resulting in the Dirichlet boundary condition E z = −4∂H + /ωκ. In Section 2.2, our previous method assuming the Dirichlet boundary condition is summarized.…”

Section: Complex Representation Of the Governing Equationsmentioning

confidence: 99%

“…We previously proposed an explicit pointwise reconstruction formula for MREPT [32], which is classified as the third approach. In this method, a complex linear PDE, known as the D-bar equation, of the electric field E z is derived and solved in an explicit pointwise manner by the generalized Cauchy integral formula with the Dirichlet boundary condition.…”

Section: Introductionmentioning

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: 97%

Section: Resultsmentioning

confidence: 99%

Section: Complex Representation Of the Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…In Ammari et al, the forward problem of MREPT is also modeled as a PDE and an inverse problem approach is used to iteratively find the EPs by minimizing the norm of the difference between the measured and calculated

B_{1}^{+}

. More recently, in Fushimi and Nara and Nara et al, a 2‐stage algorithm is developed whereby the axial electric field is also estimated together with the EPs.…”

Section: Introductionmentioning

confidence: 99%

Use of dielectric padding to eliminate low convective field artifact in cr‐MREPT conductivity images

Yildiz

Ider

2019

Magnetic Resonance in Med

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Purpose Convection–reaction equation‐based magnetic resonance electrical properties tomography (cr‐MREPT) provides conductivity images that are boundary artifact‐free and robust against noise. However, these images suffer from the low convective field (LCF) artifact. We propose to use dielectric pads to alter the transmit magnetic field (B1+), shift the LCF region, and eliminate the LCF artifact. Methods Computer simulations were conducted to analyze the effects of pad electrical properties, pad thickness, pad height, arc angle, and thickness of the pad–object gap. In 3T MR experiments, water pads and BaTiO3 pads were used with agar–saline phantoms. Two data sets (e.g., with the pad located on the left or on the right of the object [phantom]) were acquired, and the corresponding linear systems were simultaneously solved to get LCF artifact‐free conductivity images. Results A pad needed to have 180° arc angle and the same height with the phantom for maximum benefit. Increasing the pad thickness and/or the relative permittivity of the pad increased the LCF shift, whereas excessive amounts of these parameters caused errors in conductivity reconstructions because the effect of neglected Bz terms became noticeable. Conductivity of the pad, on the other hand, had minimal effect on elimination of the LCF artifact. Combining 2 data sets (i.e., with 2 different dielectric pad positions) resulted in more accurate conductivity maps (low L2‐errors) as opposed to no pad or single pad cases in experiments and simulations. Conclusions Using the proposed technique, LCF artifact is significantly removed, and the reconstructed conductivity values are improved.

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Magnetic resonance-based imaging of human electric properties with phaseless contrast source inversion

et al. 2018

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Magnetic resonance imaging scanners can provide, by B1-mapping techniques, measurements of the transmit sensitivity magnitude, whereas the transmit sensitivity phase can only be approximated under symmetry assumptions of the coil and the sample. Nonetheless, up to now many techniques have been proposed to retrieve electric properties maps at radiofrequency by elaborating the complex transmit sensitivity. These techniques are usually referred to as magnetic resonance-based electric properties tomography. In order to perform imaging of the elecric properties also in cases which do not fulfill the assumptions for transmit sensitivity phase estimation, a variation of the phaseless contrast source inversion technique is proposed in this paper to retrieve the electric properties by elaborating only the magnitude of the transmit sensitivity. The novel technique is described in a generalised framework based on a functional viewpoint and it is specialised to deal with two-dimensional boundaryfree problems. Moreover, a phaseless back propagation solution is proposed as initial guess. The proposed technique and initial guess have been tested on realistic twodimensional model problems, which show that the numerical minimisation converges towards the global minimum when multiple linearly independent measurements are provided and that it is quite robust with respect to noisy inputs.

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An explicit reconstruction method for magnetic resonance electrical property tomography based on the generalized Cauchy formula

Cited by 14 publications

References 16 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

Use of dielectric padding to eliminate low convective field artifact in cr‐MREPT conductivity images

Magnetic resonance-based imaging of human electric properties with phaseless contrast source inversion

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