Iterative fitting approach to CR-MREPT
Author(s)
Advisor
İder, Yusuf ZiyaDate
2019-06Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
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.
Keywords
Magnetic Resonance Imaging (MRI)Inverse problem
Magnetic Resonance Electrical Properties Tomography (MREPT)
Convection-Reaction Equation Based MREPT (cr-MREPT)
Conductivity
Tikhonov regularization
Total variation regularization