Oh In Kwon

Error Analysis of Nonconstant Admittivity for MR-Based Electric Property Imaging

Magnetic resonance electrical property tomography (MREPT) is a new imaging modality to visualize a distribution of admittivity γ = σ+iωε inside the human body where σ and ε denote electrical conductivity and permittivity, respectively. Using B1 maps acquired by an magnetic resonance imaging scanner, it produces cross-sectional images of σ and ε at the Larmor frequency. Since current MREPT methods rely on an assumption of a locally homogeneous admittivity, there occurs a reconstruction error where this assumption fails. Rigorously analyzing the reconstruction error in MREPT, we showed that the error is fundamental and may cause technical difficulties in interpreting MREPT images of a general inhomogeneous object. We performed numerical simulations and phantom experiments to quantitatively support the error analysis. We compared the MREPT image reconstruction problem with that of magnetic resonance electrical impedance tomography (MREIT) to highlight distinct features of both methods to probe the same object in terms of its high- and low-frequency conductivity distributions, respectively. MREPT images showed large errors along boundaries where admittivity values changed whereas MREIT images showed no such boundary effects. Noting that MREIT makes use of the term neglected in MREPT, a novel MREPT admittivity image reconstruction method is proposed to deal with the boundary effects, which requires further investigation on the complex directional derivative in the real Euclidian space \BBR3.

Analysis of recoverable current from one component of magnetic flux density in MREIT and MRCDI

Magnetic resonance current density imaging (MRCDI) provides a current density image by measuring the induced magnetic flux density within the subject with a magnetic resonance imaging (MRI) scanner. Magnetic resonance electrical impedance tomography (MREIT) has been focused on extracting some useful information of the current density and conductivity distribution in the subject Omega using measured B(z), one component of the magnetic flux density B. In this paper, we analyze the map Tau from current density vector field J to one component of magnetic flux density B(z) without any assumption on the conductivity. The map Tau provides an orthogonal decomposition J = J(P) + J(N) of the current J where J(N) belongs to the null space of the map Tau. We explicitly describe the projected current density J(P) from measured B(z). Based on the decomposition, we prove that B(z) data due to one injection current guarantee a unique determination of the isotropic conductivity under assumptions that the current is two-dimensional and the conductivity value on the surface is known. For a two-dimensional dominating current case, the projected current density J(P) provides a good approximation of the true current J without accumulating noise effects. Numerical simulations show that J(P) from measured B(z) is quite similar to the target J. Biological tissue phantom experiments compare J(P) with the reconstructed J via the reconstructed isotropic conductivity using the harmonic B(z) algorithm.

Optimization of multiply acquired magnetic flux density Bz 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.

Electrical tissue property imaging using MRI at dc and Larmor frequency

Cross-sectional imaging of conductivity and permittivity distributions inside thehumanbodyhasbeenactivelyinvestigatedinimpedanceimagingareassuch as electrical impedance tomography (EIT) and magnetic induction tomography (MIT). Since the conductivity and permittivity values exhibit frequencydependent changes, it is worthwhile to perform spectroscopic imaging from almost dc to hundreds of MHz. To probe the human body, we may inject current using surface electrodes or induce current using external coils. In EIT and MIT, measured data are only available on the boundary or exterior of the body unless we invasively place sensors inside the body. Their image reconstruction problems are nonlinear and ill-posed to result in images with a relatively low spatial resolution. Noting that an MRI scanner can noninvasively measure magnetic fields inside the human body, electrical tissue property imaging methods using MRI have lately been proposed. Magnetic resonance EIT (MREIT) performs conductivity imaging at dc or below 1 kHz by externallyinjectingcurrentintothehumanbodyandmeasuringinducedinternal magneticfluxdensitydatausinganMRIscanner.Magneticresonanceelectrical property tomography (MREPT) produces both conductivity and permittivity images at the Larmor frequency of an MRI scanner based on B1-mapping techniques. Since internal data are only available in MREIT and MREPT, we may formulate well-posed inverse problems for image reconstructions. To develop related imaging techniques, we should clearly understand the basic principles of MREIT and MREPT, which are based on coupled physics of bioelectromagnetism and MRI as well as associated mathematical methods. In this paper, we describe the physical principles of MREIT and MREPT in a unified way and associate measurable quantities with the conductivity and permittivity. Clarifying the key relations among them, we examine existing image reconstruction algorithms to reveal their capabilities and limitations. We discuss technical issues in MREIT and MREPT and suggest future research

Feasibility of magnetic resonance electrical impedance tomography (MREIT) conductivity imaging to evaluate brain abscess lesion: in vivo canine model.

To show the feasibility of magnetic resonance electrical impedance tomography (MREIT) conductivity imaging in terms of its capability to provide new contrast information of abscess lesion and characterize time‐course variations before and after the induction of brain abscess.

Ion mobility imaging and contrast mechanism of apparent conductivity in MREIT

Magnetic resonance electrical impedance tomography (MREIT) aims to produce high-resolution cross-sectional images of conductivity distribution inside the human body. Injected current into an imaging object induces a distribution of internal magnetic flux density, which is measured by using an MRI scanner. We can reconstruct a conductivity image based on its relation with the measured magnetic flux density. In this paper, we explain the contrast mechanism in MREIT by performing and analyzing a series of numerical simulations and imaging experiments. We built a stable conductivity phantom including a hollow insulating cylinder with holes. Filling both inside and outside the hollow cylinder with the same saline, we controlled ion mobilities to create a conductivity contrast without being affected by the ion diffusion process. From numerical simulations and imaging experiments, we found that slopes of induced magnetic flux densities change with hole diameters and therefore conductivity contrasts. Associating the hole diameter with apparent conductivity of the region inside the hollow cylinder with holes, we could experimentally validate the contrast mechanism in MREIT. Interpreting reconstructed apparent conductivity images of the phantom as ion mobility images, we discuss the meaning of the apparent conductivity seen by a certain probing method. In designing MREIT imaging experiments, the ion mobility imaging method using the proposed stable conductivity phantom will enable us to estimate a distinguishable conductivity contrast for a given set of imaging parameters.

Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions.

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.

Regional absolute conductivity reconstruction using projected current density in MREIT

Magnetic resonance electrical impedance tomography (MREIT) is a non-invasive technique for imaging the internal conductivity distribution in tissue within an MRI scanner, utilizing the magnetic flux density, which is introduced when a current is injected into the tissue from external electrodes. This magnetic flux alters the MRI signal, so that appropriate reconstruction can provide a map of the additional z-component of the magnetic field (B(z)) as well as the internal current density distribution that created it. To extract the internal electrical properties of the subject, including the conductivity and/or the current density distribution, MREIT techniques use the relationship between the external injection current and the z-component of the magnetic flux density B = (B(x), B(y), B(z)). The tissue studied typically contains defective regions, regions with a low MRI signal and/or low MRI signal-to-noise-ratio, due to the low density of nuclear magnetic resonance spins, short T(2) or T*(2) relaxation times, as well as regions with very low electrical conductivity, through which very little current traverses. These defective regions provide noisy B(z) data, which can severely degrade the overall reconstructed conductivity distribution. Injecting two independent currents through surface electrodes, this paper proposes a new direct method to reconstruct a regional absolute isotropic conductivity distribution in a region of interest (ROI) while avoiding the defective regions. First, the proposed method reconstructs the contrast of conductivity using the transversal J-substitution algorithm, which blocks the propagation of severe accumulated noise from the defective region to the ROI. Second, the proposed method reconstructs the regional projected current density using the relationships between the internal current density, which stems from a current injection on the surface, and the measured B(z) data. Combining the contrast conductivity distribution in the entire imaging slice and the reconstructed regional projected current density, we propose a direct non-iterative algorithm to reconstruct the absolute conductivity in the ROI. The numerical simulations in the presence of various degrees of noise, as well as a phantom MRI imaging experiment showed that the proposed method reconstructs the regional absolute conductivity in a ROI within a subject including the defective regions. In the simulation experiment, the relative L₂-mode errors of the reconstructed regional and global conductivities were 0.79 and 0.43, respectively, using a noise level of 50 db in the defective region.