Iterative fitting approach to CR-MREPT
Electrical properties (conductivity, and permittivity, ) imaging, reveals information about the contrast between tissues. Magnetic Resonance Electrical Properties Tomography (MREPT) is one of the electrical properties imaging techniques, which provides conductivity and permittivity images at Larmor frequency using the perturbations in the transmit magnetic eld, B+ 1 . Standard-MREPT (std-MREPT) method is the simplest method for obtaining electrical properties from the B+ 1 eld distribution, however it su ers from the boundary artifacts between tissue transitions. In order to eliminate this artifact, many methods are proposed. One such method is the Convection Reaction equation based MREPT (cr-MREPT). cr-MREPT method solves the boundary artifact problem, however Low Convective Field (LCF) artifact occurs in the resulting electrical property images. In this thesis, Iterative Fitting Approach to cr-MREPT is developed for investigating the possibility of elimination of LCF artifact. In this method, forward problem of obtaining magnetic eld with the given electrical properties inside the region of interest is solved iteratively and electrical properties are updated at each iteration until the di erence between the solution of the forward problem and the measured magnetic eld is small. Forward problem is a di usion convection reaction partial di erential equation and the solution for the magnetic eld is obtained by the Finite Di erence Method. By using the norm of the difference between the solution of the forward problem and the measured magnetic eld, electrical properties are obtained via Gauss-Newton method. Obtaining electrical property updates at each iteration, is not a well conditioned problem therefore Tikhonov and Total Variation regularizations are implemented to solve this problem. For the realization of the Total Variation regularization, Primal Dual Interior Point Method (PDIPM) is used. Using the COMSOL Multiphysics, simulation phantoms are modeled and B+ 1 data for each phantom is generated for electrical property reconstructions. 2D simulation phantom, modeled as an in- nitely long cylindrical object, is assumed to be under the e ect of the clockwise rotating radio-frequency (RF) eld. Second phantom modeled, is a cylindrical object with nite length and z- independent electrical properties, that is placed in a Quadrature Birdcage Coil (QBC). Third phantom modeled is a cylindrical object placed in a QBC, with z- dependent electrical properties. In addition to the simulation phantoms, z- independent experimental phantoms are also created for MRI experiments. Conductivity reconstructions of 2D simulation phantom, do not su er from LCF artifact and have accurate conductivity values for both Tikhonov and Total Variation regularizations. While, 2D center slice reconstructions of the zindependent simulation and experimental phantoms do not have LCF artifact, resulting conductivity values are lower than the expected conductivity values. These low conductivity values are obtained because of the inaccurate solution of the forward problem in 2D for 3D phantoms. When Iterative Fitting Approach is extended to 3D, such that solution of the forward problem is also obtained in 3D, resulting electrical property reconstruction does not have LCF artifact and obtained conductivity values are as expected for both z- independent simulation and experimental phantom. Reconstructions obtained for the z- dependent simulation phantom shows that electrical properties varying all 3 directions can be accurately reconstructed using Iterative Fitting Approach. For Iterative Fitting Approach reconstructions, voxel size of 2 mm is used for the 3D experimental phantom and voxel size of 1.5 mm is used for all simulation phantoms and 2D experimental phantom. Reconstructions obtained for all phantom with Iterative Fitting Approach are LCF artifact free. Conductivity reconstructions obtained using Tikhonov and Total Variation regularizations have similar resolutions (1-2 pixels) but Total Variation regularization results in smoother conductivity values inside the tissues compared to the Tikhonov regularization.