Magnetic flux density reconstruction using interleaved partial Fourier acquisitions in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) has been introduced as a non-invasive modality to visualize the internal conductivity and/or current density of an electrically conductive object by the injection of current. In order to measure a magnetic flux density signal in MREIT, the phase difference approach in an interleaved encoding scheme cancels the systematic artifacts accumulated in phase signals and also reduces the random noise effect. However, it is important to reduce scan duration maintaining spatial resolution and sufficient contrast, in order to allow for practical in vivo implementation of MREIT. The purpose of this paper is to develop a coupled partial Fourier strategy in the interleaved sampling in order to reduce the total imaging time for an MREIT acquisition, whilst maintaining an SNR of the measured magnetic flux density comparable to what is achieved with complete k-space data. The proposed method uses two key steps: one is to update the magnetic flux density by updating the complex densities using the partially interleaved k-space data and the other is to fill in the missing k-space data iteratively using the updated background field inhomogeneity and magnetic flux density data. Results from numerical simulations and animal experiments demonstrate that the proposed method reduces considerably the scanning time and provides resolution of the recovered B(z) comparable to what is obtained from complete k-space data.

Reconstruction of conductivity using the dual-loop method with one injection current in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity of an electrically conductive object. Injecting current through surface electrodes, we measure one component of the induced internal magnetic flux density using an MRI scanner. In order to reconstruct the conductivity distribution inside the imaging object, most algorithms in MREIT have required multiple magnetic flux density data by injecting at least two independent currents. In this paper, we propose a direct method to reconstruct the internal isotropic conductivity with one component of magnetic flux density data by injecting one current into the imaging object through a single pair of surface electrodes. Firstly, the proposed method reconstructs a projected current density which is a uniquely determined current from the measured one-component magnetic flux density. Using a relation between voltage potential and current, based on Kirchhoff's voltage law, the proposed method is designed to use a combination of two loops around each pixel from which to derive an implicit matrix system for determination of the internal conductivity. Results from numerical simulations demonstrate that the proposed algorithm stably determines the conductivity distribution in an imaging slice. We compare the reconstructed internal conductivity distribution using the proposed method with that using a conventional method with agarose gel phantom experiments.

Optimization of multiply acquired magnetic flux density B(z) using ICNE-Multiecho train in MREIT.

The aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the electrical properties, conductivity or current density of an object by injection of current. Recently, the prolonged data acquisition time when using the injected current nonlinear encoding (ICNE) method has been advantageous for measurement of magnetic flux density data, Bz, for MREIT in the signal-to-noise ratio (SNR). However, the ICNE method results in undesirable side artifacts, such as blurring, chemical shift and phase artifacts, due to the long data acquisition under an inhomogeneous static field. In this paper, we apply the ICNE method to a gradient and spin echo (GRASE) multi-echo train pulse sequence in order to provide the multiple k-space lines during a single RF pulse period. We analyze the SNR of the measured multiple B(z) data using the proposed ICNE-Multiecho MR pulse sequence. By determining a weighting factor for B(z) data in each of the echoes, an optimized inversion formula for the magnetic flux density data is proposed for the ICNE-Multiecho MR sequence. Using the ICNE-Multiecho method, the quality of the measured magnetic flux density is considerably increased by the injection of a long current through the echo train length and by optimization of the voxel-by-voxel noise level of the B(z) value. Agarose-gel phantom experiments have demonstrated fewer artifacts and a better SNR using the ICNE-Multiecho method. Experimenting with the brain of an anesthetized dog, we collected valuable echoes by taking into account the noise level of each of the echoes and determined B(z) data by determining optimized weighting factors for the multiply acquired magnetic flux density data.

Axial anisotropic conductivity imaging based on projected current density in MREIT.

An aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and/or the conductivity of an imaging object. In MREIT, it is desirable to use just one component of the internal magnetic flux density vector B=(B(x),B(y),B(z)) caused by the injected current, measured without rotating the object. We present a method of visualizing the axial anisotropic conductivity tensor by use of the measured magnetic flux density B(z) data. The method involves the use of a projected current density, which is a uniquely and stably determined component of the internal current generated by the injected current, derived from the measured B(z) data. Each component of the axial anisotropic conductivity is recovered by matching the measured B(z) data with a determined intermediate isotropic conductivity and the projected currents. Results from numerical simulations demonstrate that the proposed algorithm is robust to noise and stably determines the anisotropic conductivity tensor on the imaging slice. For a practical implementation, we studied a postmortem canine brain case to visualize each component of the anisotropic conductivity. We observed that the reconstructed anisotropic conductivity images clearly reflects the anisotropic property of the white matter in the direction parallel to its fibers.

Shear modulus decomposition algorithm in magnetic resonance elastography.

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the elastic properties of an object using magnetic resonance imaging (MRI) measurements of transverse acoustic strain waves induced in the object by a harmonically oscillating mechanical vibration. Various algorithms have been designed to determine the mechanical properties of the object under the assumptions of linear elasticity, isotropic and local homogeneity. One of the challenging problems in MRE is to reduce the noise effects and to maintain contrast in the reconstructed shear modulus images. In this paper, we propose a new algorithm designed to reduce the degree of noise amplification in the reconstructed shear modulus images without the assumption of local homogeneity. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based on a decomposition of the stress wave vector. Numerical simulation experiments and real experiments with agarose gel phantoms and human liver data demonstrate that the proposed algorithm is more robust to noise compared to standard inversion algorithms and stably determines the shear modulus.

Non-iterative conductivity reconstruction algorithm using projected current density in MREIT.

Magnetic resonance electrical impedance tomography (MREIT) is to visualize the current density and the conductivity distribution in an electrical object Omega using the measured magnetic flux data by an MRI scanner. MREIT uses only one component B(z) of the magnetic flux density B = (B(x), B(y), B(z)) generated by an injected electrical current into the object. In this paper, we propose a fast and direct non-iterative algorithm to reconstruct the internal conductivity distribution in Omega with the measured B(z) data. To develop the algorithm, we investigate the relation between the projected current density J(P), a uniquely determined component of J by the map from current J to measured B(z) data and the isotropic conductivity. Three-dimensional numerical simulations and phantom experiments are studied to show the feasibility of the proposed method by comparing with those using the conventional iterative harmonic B(z) algorithm.

Conductivity imaging with low level current injection using transversal J-substitution algorithm in MREIT.

An aim of magnetic resonance electrical impedance tomography (MREIT) is to visualize the internal current density and conductivity of the electrically imaged object by injecting current through electrodes attached to it. Due to a limited amount of injection current, one of the most important factors in MREIT is how to control the noise contained in the measured magnetic flux density data. This paper describes a new iterative algorithm called the transversal J-substitution algorithm which is robust to measured noise. As a result, the proposed transversal J-substitution algorithm considerably improves the quality of the reconstructed conductivity image under a low injection current. The relation between the reconstructed contrast of conductivity and the measured noise in the magnetic flux density is analyzed. We show that the contrast of first update of the conductivity with a homogeneous initial guess using the proposed algorithm has sufficient distinguishability to detect the anomaly. Results from numerical simulations demonstrate that the transversal J-substitution algorithm is robust to the noise. For practical implementations of MREIT, we tested real experiments in an agarose gel phantom using low current injection with amplitudes 1 mA and 5 mA to reconstruct the interior conductivity distribution.

Noise analysis and MR pulse sequence optimization in MREIT using an injected current nonlinear encoding (ICNE) method.

Magnetic resonance current density imaging (MRCDI) and magnetic resonance electrical impedance tomography (MREIT) visualize an internal distribution of current density and/or conductivity by injecting current into an electrically conductive object such as the human body using an MRI scanner. MREIT measures the induced magnetic flux density which appears in the phase part of the acquired MR image data. Recently, the injected current nonlinear encoding (ICNE) method in MREIT extended the duration of the current injection until the end of a reading gradient to maximize the signal intensity of the magnetic flux density. In this paper, we investigate the signal-to-noise ratio (SNR) of the magnetic flux density measured by the ICNE method in the presence of a zero-mean Gaussian random noise in measured k-space MR data. Based on the analysis of the noise standard deviation s(B(z)) of the magnetic flux density, we determine an optimal combination between the current injection pulse width T(c) and data acquisition time T(s) which minimize the noise level of the measured magnetic flux density for a given echo time T(E). On one hand, theoretically, the proposed ICNE MR pulse sequence using the optimal data acquisition time T(s)* reduces the noise level of the measured magnetic flux density by about 42.3% compared with the optimal data acquisition time of the conventional MREIT pulse sequence. On the other hand, practically, the prolonged T(s)* may result in undesirable artifacts including blurring, chemical shift and phase error along the phase encoding direction. We observe that the noise level is a function of the data acquisition time T(s) and the rate of change in the noise level is slow near T(s)=T(s)*. Numerical phantom experiments show that a compromised T(s) between the ordinary data acquisition time and the optimal T(s)* reduces a relatively large amount of undesirable artifacts and almost maintains the optimized noise level of the measured magnetic flux density.