Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)
Author(s)
Advisor
İder, Y. ZiyaDate
2013Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Tomographic imaging of electrical conductivity and permittivity of tissues may
be used for diagnostic purposes as well as for estimating local specific absorption
rate (SAR) distributions. Magnetic Resonance Electrical Properties Tomography
(MREPT) aims at noninvasively obtaining conductivity and permittivity images
at RF frequencies of MRI systems. MREPT algorithms are based on measuring
the B1 field which is perturbed by the electrical properties of the imaged object.
In this study, the relation between the electrical properties and the measured
B
+
1 field is formulated, for the first time as, the well-known convection-reaction
equation. The suggested novel algorithm, called “cr-MREPT”, is based on the
solution of this equation, and in contrast to previously proposed algorithms, it is
applicable in practice not only for regions where electrical properties are relatively
constant but also for regions where they vary. The convection-reaction equation
is solved using a triangular mesh based finite difference method and also finite
element method (FEM).
The convective field of the convection-reaction equation depends on the spatial
derivatives of the B
+
1 field. In the regions where the magnitude of convective
field is low, a spot-like artifact is observed in the reconstructed conductivity
and dielectric permittivity images. For eliminating this artifact, two different
methods are developed, namely “constrained cr-MREPT” and “double-excitation
cr-MREPT”. In the constrained cr-MREPT method, in the region where the
magnitude of convective field is low, the electrical properties are reconstructed
by neglecting the convective term in the equation. The obtained solution is
used as a constraint for solving electrical properties in the whole domain. In
the double-excitation cr-MREPT method, two B1 excitations, which create two
convective field distributions having low magnitude of convective field in different locations, are applied separately. The electrical properties are then reconstructed
simultaneously using data from these two applied B
+
1 field.
These methods are tested with both simulation and experimental data from
phantoms. As seen from results, successful electrical property reconstructions
are obtained in all regions including electrical property transition region. The
performance of cr-MREPT method against noise is also investigated.
Keywords
B1 mappingconductivity imaging
convection-reaction equation
Magnetic Resonance Electrical Properties Tomography
MREPT
MREIT
permittivity imaging
quantitative MRI
triangular mesh
FEM