Taşınım denkleminin çözümüne dayalı manyetik rezonans elektriksel empedans tomografi ve 3B Fourier dönüşümü-manyetik rezonans akım yoğunluğu görüntüleme

In Magnetic Resonance Electrical Impedance Tomography (MREIT) and Magnetic Resonance Current Density Imaging (MRCDI), current is injected into a conductive object such as the human-body via surface electrodes. The resulting internal current generates a magnetic flux density distribution which is measured using a Magnetic Resonance Imaging (MRI) system. Utilizing this measured data, MREIT is the inverse problem of reconstructing the internal electrical conductivity distribution and MRCDI is the inverse problem of reconstructing a current density distribution. There are hardware and reconstruction algorithm development aspects of MREIT and MRCDI. On the hardware side, an MRI compatible constant current source is designed and manufactured. On the other side, two reconstruction algorithms are developed one for MREIT and one for MRCDI. Most algorithms for MREIT concentrate on utilizing the Laplacian of only one component of the magnetic flux density (del2Bz). In this thesis, a new algorithm is proposed to solve this del2Bz-based MREIT problem which is mathematically formulated as a steady state scalar pure convection equation. Numerical methods developed for the solution of the more general convection-diffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in the proposed algorithm the streamline upwind Petrov Galerkin (SUPG) stabilization method is incorporated into Galerkin weighted residual Finite Element Method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. It is found that for the case of two orthogonal current injections the SUPG method is beneficial when there is noise in the magnetic flux density data or when there are sharp variations in conductivity. It is also found that the algorithm can be used to reconstruct conductivity using data from only one current injection if SUPG is used. For MRCDI, a novel iterative Fourier transform based MRCDI algorithm, which utilizes one component of magnetic flux density, is developed for 3D problems. The projected current is reconstructed on any slice using del2Bz data for that slice only. The algorithm is applied to simulated as well as actual data from phantoms. Effect of noise in measurement data on the performance of the algorithm is also investigated.