Iterative Fitting Approach to CR-MREPT
Electrical properties (conductivity, σ, and permittivity, ϵ) 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 field, B+. Standard-MREPT (std-MREPT) method is the simplest method for obtaining electrical properties from the B+ field distribution, however it suffers 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 inves- tigating the possibility of elimination of LCF artifact. In this method, forward problem of obtaining magnetic field with the given electrical properties inside the region of interest is solved iteratively and electrical properties are updated at each iteration until the difference between the solution of the forward problem and the measured magnetic field is small. Forward problem is a diffusion con- vection reaction partial differential equation and the solution for the magnetic field is obtained by Finite Difference Method. By using the norm of the differ- ence between the solution of the forward problem and the measured magnetic field, 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 H+ data for each phantom is generated for electrical property reconstructions. 2D simulation phantom is modeled as an infinitely long cylindrical object is assumed to be under the effect of the clockwise rotating radio-frequency (RF) field. Second phantom modeled, is a cylindrical object with finite 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 simulation phantoms are also created for MRI experiments.
For the 2D Iterative Fitting Approach reconstructions, pixel size of 1.5 mm is used. Conductivity reconstructions of 2D simulation phantom , do not suffer from LCF artifact and have accurate conductivity values for both Tikhonov and Total Variation regularizations. While, 2D center slice reconstructions of the z- independent 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 ob- tained conductivity values are as expected for both z- independent simulation and experimental phantom. For the 3D Iterative Fitting Approach reconstructions, voxel size of 2 mm is used for the experimental phantom. Reconstructions ob- tained for the z- dependent simulation phantom shows that electrical properties varying all 3 directions can be accurately reconstructed using Iterative Fitting Approach.
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.