Magnetic resonance imaging (MRI) is an imaging modality that noninvasively measures magnetic fields by selectively exciting the magnetization of protons inside the body. When combined with an understanding of electromagnetic theory, MRI can be used in a novel way to provide a powerful tool for measuring the electromagnetic fields and electrical properties of biological tissues. This thesis presents the analytical, numerical, processing and experimental components of a successful implementation of Low-Frequency Current Density Impedance Imaging (LF-CDII), an impedance imaging method based on MRI measurements. The accuracy, stability and noise tolerance of this technique are examined. The first in-vivo LF-CDII experiment was conducted with a clinical MRI scanner, and the conductivity distribution of the heart of a live piglet was obtained. Both the simulation and experimental results show that LF-CDII can be used as a reliable tool for accurate noninvasive, quantitative imaging of tissue conductivities. This thesis also presents new data processing algorithms, imaging procedures and hardware development for the measurement of electromagnetic fields at radio frequencies, based on Polar Decomposition Radio Frequency Current Density Imaging (PD-RFCDI). The method was tested on both numerical models and experiments on phantoms. The results show that the techniques presented here are able to successfully image current density fields without the strict restrictions on the direction and magnitude of the currents required in previous versions of RFCDI.

Biological tissues are generally conductive and knowing the current distribution in these tissues is of great importance in many biomedical applications. Radio frequency current density imaging (RF-CDI) is a technology that measures current density distributions at the Larmor frequency utilizing magnetic resonance imaging (MRI). RF-CDI computes the applied current density, J, from the non-invasively measured magnetic field, H, produced by J. The previously implemented RF-CDI techniques could only image a single slice at a time. The previous method for RF current density reconstruction only computed one component of J. Moreover, this reconstruction required an assumption about H, which may be easily violated. These technical constraints have limited the potential biomedical applications of RF-CDI. In this thesis, we address the limitations of RF-CDI mentioned above. First, we implement a multi-slice RF-CDI sequence with a clinical MRI system and characterize its sensitivity to MRI random noise. Second, we present a novel method to fully reconstruct all three components of J without relying on any assumption of H. The central idea of our approach is to rotate the sample by 180 degrees in the horizontal plane to collect adequate MR data from two opposite sample orientations to compute one component of J. Furthermore, this approach can be extended to reconstruct the other two components of J by adding one additional sample orientation in the horizontal plane. This method has been verified by simulations and electrolytic phantom experiments. We have therefore demonstrated for the first time the feasibility of imaging the magnitude and phase of all components of the RF current density vector. The work presented in this thesis is expected to significantly enhance RF-CDI to image biological subjects. The current density vector J or any component of J can be measured over multiple slices without the compromise of motions of organs and tissues caused by gravitational force, thanks to the method of horizontal rotations. In addition, the reconstruction of the complex conductivity of biological tissues becomes possible due to the current advance in RF-CDI presented here.

Magnetic resonance imaging (MRI) is an imaging modality that noninvasively measures magnetic fields by selectively exciting the magnetization of protons inside the body. When combined with an understanding of electromagnetic theory, MRI can be used in a novel way to provide a powerful tool for measuring the electromagnetic fields and electrical properties of biological tissues. This thesis presents the analytical, numerical, processing and experimental components of a successful implementation of Low-Frequency Current Density Impedance Imaging (LF-CDII), an impedance imaging method based on MRI measurements. The accuracy, stability and noise tolerance of this technique are examined. The first in-vivo LF-CDII experiment was conducted with a clinical MRI scanner, and the conductivity distribution of the heart of a live piglet was obtained. Both the simulation and experimental results show that LF-CDII can be used as a reliable tool for accurate noninvasive, quantitative imaging of tissue conductivities. This thesis also presents new data processing algorithms, imaging procedures and hardware development for the measurement of electromagnetic fields at radio frequencies, based on Polar Decomposition Radio Frequency Current Density Imaging (PD-RFCDI). The method was tested on both numerical models and experiments on phantoms. The results show that the techniques presented here are able to successfully image current density fields without the strict restrictions on the direction and magnitude of the currents required in previous versions of RFCDI.

Biological tissues are generally conductive and knowing the current distribution in these tissues is of great importance in many biomedical applications. Radio frequency current density imaging (RF-CDI) is a technology that measures current density distributions at the Larmor frequency utilizing magnetic resonance imaging (MRI). RF-CDI computes the applied current density, J, from the non-invasively measured magnetic field, H, produced by J. The previously implemented RF-CDI techniques could only image a single slice at a time. The previous method for RF current density reconstruction only computed one component of J. Moreover, this reconstruction required an assumption about H, which may be easily violated. These technical constraints have limited the potential biomedical applications of RF-CDI. In this thesis, we address the limitations of RF-CDI mentioned above. First, we implement a multi-slice RF-CDI sequence with a clinical MRI system and characterize its sensitivity to MRI random noise. Second, we present a novel method to fully reconstruct all three components of J without relying on any assumption of H. The central idea of our approach is to rotate the sample by 180 degrees in the horizontal plane to collect adequate MR data from two opposite sample orientations to compute one component of J. Furthermore, this approach can be extended to reconstruct the other two components of J by adding one additional sample orientation in the horizontal plane. This method has been verified by simulations and electrolytic phantom experiments. We have therefore demonstrated for the first time the feasibility of imaging the magnitude and phase of all components of the RF current density vector. The work presented in this thesis is expected to significantly enhance RF-CDI to image biological subjects. The current density vector J or any component of J can be measured over multiple slices without the compromise of motions of organs and tissues caused by gravitational force, thanks to the method of horizontal rotations. In addition, the reconstruction of the complex conductivity of biological tissues becomes possible due to the current advance in RF-CDI presented here.

Magnetic Resonance Electrical Impedance Tomography (MREIT) reconstructs conductivity distribution with internal current density (MRCDI) and boundary voltage measurements. There are many algorithms proposed for the solution of MREIT inverse problem which can be divided into two groups: Current density (J) and magnetic flux density (B) based reconstruction algorithms. In this thesis, J-based MREIT reconstruction algorithms are implemented and optimized with modifications. These algorithms are simulated with five conductivity models which have different geometries and conductivity values. Results of simulation are discussed and reconstruction algorithms are compared according to their performances. Equipotential-Projection algorithm has lower error percentages than other algorithms for noise-free case whereas Hybrid algorithm has the best performance for noisy cases. Although J-substitution and Hybrid algorithms have relatively long reconstruction times, they produced the best images perceptually. v Integration along Cartesian Grid Lines and Integration along Equipotential Lines algorithms diverge as noise level increases. Equipotential-Projection algorithm has erroneous lines starting from corners of FOV especially for noisy cases whereas Solution as a Linear Equation System has a typical grid artifact. When performance with data of experiment 1 is considered, only Solution as a Linear Equation System algorithm partially reconstructed all elements which show that it is robust to noise. Equipotential-Projection algorithm reconstructed resistive element partially and other algorithms failed in reconstruction of conductivity distribution. Experimental results obtained with a higher conductivity contrast show that Solution as a Linear Equation System, J-Substitution and Hybrid algorithms reconstructed both phantom elements and Hybrid algorithm is superior to other algorithms in percentage error comparison.

Data acquisition and image reconstruction tasks of METU Magnetic Resonance Imaging (MRI) System are used to be performed by a 15 year-old technology. This system is incapable of transmitting control signals simultaneously and has memory limitations. Control software is written mostly in assembly language, which is hard to modify, with very limited user interface functionality, and time consuming. In order to improve the system, a LabVIEW based data acquisition system consisting of a NI-6713 D/A card (to generate RF envelope, gradients, etc.) and a NI-6110E A/D card (to digitize echo signals) from National Instruments is programmed and integrated to the system, and a pulse sequence design, data acquisition and image reconstruction front-end is designed and implemented. Apart from that, a new method that can be used in Magnetic Resonance Current Density Imaging (MRCDI) experiments is proposed. In this method the readily built gradient coil of the MRI scanner is utilized to induce current in the imaging volume. Magnetic fields created by induced currents are measured for various amplitude levels, and it is proved that inducing current with this method is possible.

In magnetic resonance electrical impedance tomography (MR-EIT), crosssectional images of a conductivity distribution are reconstructed. When current is injected to a conductor, it generates a magnetic field, which can be measured by a magnetic resonance imaging (MRI) scanner. MR-EIT reconstruction algorithms can be grouped into two: current density based reconstruction algorithms (Type-I) and magnetic flux density based reconstruction algorithms (Type-II). The aim of this study is to implement a series of reconstruction algorithms for MR-EIT, proposed by several research groups, and compare their performance under the same circumstances. Five direct and one iterative Type-I algorithms, and an iterative Type-II algorithm are investigated. Reconstruction errors and spatial resolution are quantified and compared. Noise levels corresponding to system SNR 60, 30 and 20 are considered. Iterative algorithms provide the lowest errors for the noise- free case. For the noisy cases, the iterative Type-I algorithm yields a lower error than the Type-II, although it can diverge for SNR lower than 20. Both of them suffer significant blurring effects, especially at SNR 20. Another two algorithms make use of integration in the reconstruction, producing intermediate errors, but with high blurring effects. Equipotential lines are calculated for two reconstruction algorithms. These lines may not be found accurately when SNR is lower than 20. Another disadvantage is that some pixels may not be covered and, therefore, cannot be reconstructed. Finally, the algorithm involving the solution of a linear system provides the less blurred images with intermediate error values. It is also very robust against noise.

Magnetic Resonance Electrical Impedance Tomography (MREIT) algorithms using current density distribution have been proposed in the literature. The current density distribution can be determined by using Magnetic Resonance Current Density Imaging (MRCDI) technique. In MRCDI technique, all three components of magnetic flux density should be measured. Hence, object should be rotated inside the magnet which is not trivial even for small size objects and remains as a strong limitation to clinical applicability of the technique. In this thesis, 2D MRCDI problem is investigated in detail and an analytical relation is found between Bz, Jx and Jy. This study makes it easy to understand the behavior of Bz due to changes in Jx and Jy. Furthermore, a novel 2D MRCDI reconstruction algorithm using one component of B is proposed. Iterative FT-MRCDI algorithm is also implemented. The algorithms are tested with simulation and experimental models. In simulations, error in the reconstructed current density changes between 0.27% - 23.00% using the proposed algorithm and 7.41% - 37.45% using the iterative FT-MRCDI algorithm for various SNR levels. The proposed algorithm is superior to the iterative FT-MRCDI algorithm in reconstruction time comparison. In experimental models, the classical MRCDI algorithm has the best reconstruction performance when the algorithms are compared by evaluating the reconstructed current density images perceptually. However, the J-substitution algorithm reconstructs the best conductivity image by using J obtained from the proposed algorithm. Finally, the iterative FT-MRCDI algorithm shows the best performance when the reconstructed current density images are verified by using divergence theorem.