Kiwan Jeon

MREIT conductivity imaging of the postmortem canine abdomen using CoReHA.

Magnetic resonance electrical impedance tomography (MREIT) is a new bio-imaging modality providing cross-sectional conductivity images from measurements of internal magnetic flux densities produced by externally injected currents. Recent experimental results of postmortem and in vivo imaging of the canine brain demonstrated its feasibility by showing conductivity images with meaningful contrast among different brain tissues. MREIT image reconstructions involve a series of data processing steps such as k-space data handling, phase unwrapping, image segmentation, meshing, modelling, finite element computation, denoising and so on. To facilitate experimental studies, we need a software tool that automates these data processing steps. In this paper, we summarize such an MREIT software package called CoReHA (conductivity reconstructor using harmonic algorithms). Performing imaging experiments of the postmortem canine abdomen, we demonstrate how CoReHA can be utilized in MREIT. The abdomen with a relatively large field of view and various organs imposes new technical challenges when it is chosen as an imaging domain. Summarizing a few improvements in the experimental MREIT technique, we report our first conductivity images of the postmortem canine abdomen. Illustrating reconstructed conductivity images, we discuss how they discern different organs including the kidney, spleen, stomach and small intestine. We elaborate, as an example, that conductivity images of the kidney show clear contrast among cortex, internal medulla, renal pelvis and urethra. We end this paper with a brief discussion on future work using different animal models.

Local Harmonic

Magnetic resonance electrical impedance tomography (MREIT) attempts to provide conductivity images of an electrically conducting object with a high spatial resolution. When we inject current into the object, it produces internal distributions of current density J and magnetic flux density B=(Bx,By,Bz). By using a magnetic resonance imaging (MRI) scanner, we can measure Bz data where z is the direction of the main magnetic field of the scanner. Conductivity images are reconstructed based on the relation between the injection current and Bz data. The harmonic Bz algorithm was the first constructive MREIT imaging method and it has been quite successful in previous numerical and experimental studies. Its performance is, however, degraded when the imaging object contains low-conductivity regions such as bones and lungs. To overcome this difficulty, we carefully analyzed the structure of a current density distribution near such problematic regions and proposed a new technique, called the local harmonic Bz algorithm. We first reconstruct conductivity values in local regions with a low conductivity contrast, separated from those problematic regions. Then, the method of characteristics is employed to find conductivity values in the problematic regions. One of the most interesting observations of the new algorithm is that it can provide a scaled conductivity image in a local region without knowing conductivity values outside the region. We present the performance of the new algorithm by using computer simulation methods.

B_z

In magnetic resonance electrical impedance tomography, among several conductivity image reconstruction algorithms, the harmonic Bz algorithm has been successfully applied to Bz data from phantoms and animals. The algorithm is, however, sensitive to measurement noise in Bz data. Especially, in in vivo animal and human experiments where injection current amplitudes are limited within a few milliampere at most, measured Bz data tend to have a low SNR. In addition, magnetic resonance (MR) signal void in outer layers of bones and gas-filled organs, for example, produces salt-pepper noise in the MR phase and, consequently, Bz images. The Bz images typically present areas of sloped transitions, which can be assimilated to ramps. Conductivity contrasts change ramp slopes in Bz images and it is critical to preserve positions of those ramps to correctly recover edges in conductivity images. In this paper, we propose a ramp-preserving denoising method utilizing a structure tensor. Using an eigenvalue analysis, we identified local regions of salt-pepper noise. Outside the identified local regions, we applied an anisotropic smoothing to reduce noise while preserving their ramp structures. Inside the local regions of salt-pepper noise, we used an isotropic smoothing. After validating the proposed denoising method through numerical simulations, we applied it to in vivo animal imaging experiments. Both numerical simulation and experimental results show significant improvements in the quality of reconstructed conductivity images.

Algorithm With Domain Decomposition in MREIT: Computer Simulation Study

The topological derivative-based non-iterative imaging algorithm has demonstrated its applicability in limited-aperture inverse scattering problems. However, this has been confirmed through many experimental simulation results, and the reason behind this applicability has not been satisfactorily explained. In this paper, we identify the mathematical structure and certain properties of topological derivatives for the imaging of two-dimensional crack-like thin penetrable electromagnetic inhomogeneities that are completely embedded in a homogeneous material. To this end, we establish a relationship with an infinite series of Bessel functions of integer order of the first kind. Based on the derived structure, we discover a necessary condition for applying topological derivatives in limited-aperture inverse scattering problems, and thus confirm why topological derivatives can be applied. Furthermore, we analyze the structure of multi-frequency topological derivative, and identify why this improves the single-frequency topological derivative in limited-aperture inverse scattering problems. Various numerical simulations are conducted with noisy data, and the results support the derived structure and exhibit certain properties of single- and multi-frequency topological derivatives.

Ramp-Preserving Denoising for Conductivity Image Reconstruction in Magnetic Resonance Electrical Impedance Tomography

This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.

A study on the topological derivative-based imaging of thin electromagnetic inhomogeneities in limited-aperture problems

The goal of magnetic resonance electrical impedance tomography (MREIT) is to produce a tomographic image of a conductivity distribution inside an electrically conducting object. Injecting current into the object, we measure a z-component Bz of an induced magnetic flux density using an MRI scanner. Based on the relation between the conductivity and measured Bz data, we may reconstruct cross-sectional images of the conductivity distribution. In a two-dimensional imaging slice, we can see that conductivity changes along equipotential lines are determined by the measured Bz data. Since the equipotential lines themselves depend nonlinearly on the unknown conductivity distribution, it is not possible to recover the conductivity distribution directly from measured Bz data. Conductivity image reconstruction algorithms such as the harmonic Bz algorithm utilize an iterative procedure to update conductivity values and in each iteration we need to solve an elliptic boundary value problem with a presumed conductivity distribution. This iteration is often troublesome in practice due to excessive amounts of noise in some local regions where weak MR signals are produced. This motivated us to develop a non-iterative reconstruction algorithm which does not depend on a global structure of the conductivity distribution. In this paper, we propose a new MREIT conductivity image reconstruction algorithm, called the non-iterative harmonic Bz algorithm, which provides a conductivity image directly from measured Bz data. From numerical simulations, we found that the new method produces absolute images of a conductivity distribution with a high accuracy by maximizing the use of reliable Bz data. It effectively reduces adverse effects of excessive noise in some local regions of weak MR signals by restricting the influences within them.

Analysis of MUSIC-type imaging functional for single, thin electromagnetic inhomogeneity in limited-view inverse scattering problem

Conductivity imaging based on the current-injection MRI technique has been developed in magnetic resonance electrical impedance tomography. Current injected through a pair of surface electrodes induces a magnetic flux density distribution inside an imaging object, which results in additional magnetic field inhomogeneity. We can extract phase changes related to the current injection and obtain an image of the induced magnetic flux density. Without rotating the object inside the bore, we can measure only one component B(z) of the magnetic flux density B = (B(x), B(y), B(z)). Based on a relation between the internal conductivity distribution and B(z) data subject to multiple current injections, one may reconstruct cross-sectional conductivity images. As the image reconstruction algorithm, we have been using the harmonic B(z) algorithm in numerous experimental studies. Performing conductivity imaging of intact animal and human subjects, we found technical difficulties that originated from the MR signal void phenomena in the local regions of bones, lungs and gas-filled tubular organs. Measured B(z) data inside such a problematic region contain an excessive amount of noise that deteriorates the conductivity image quality. In order to alleviate this technical problem, we applied hybrid methods incorporating ramp-preserving denoising, harmonic inpainting with isotropic diffusion and ROI imaging using the local harmonic B(z) algorithm. These methods allow us to produce conductivity images of intact animals with best achievable quality. We suggest guidelines to choose a hybrid method depending on the overall noise level and existence of distinct problematic regions of MR signal void.

Non-iterative harmonic Bz algorithm in MREIT

Magnetic resonance electrical impedance tomography (MREIT) aims to visualize a conductivity distribution inside the human body. In MREIT, we inject current to produce a current density

Integration of the denoising, inpainting and local harmonic Bz algorithm for MREIT imaging of intact animals

\mathbf{J}

Analysis and Blocking of Error Propagation by Region-Dependent Noisy Data in MREIT

and magnetic flux density