Uniqueness and reconstruction in magnetic resonance-electrical impedance tomography (MR-EIT)

Date
2003
Authors
İder, Y. Z.
Onart, S.
Lionheart, W. R. B.
Advisor
Instructor
Source Title
Physiological Measurement
Print ISSN
0967-3334
Electronic ISSN
Publisher
Institute of Physics Publishing
Volume
24
Issue
2
Pages
591 - 604
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

Magnetic resonance-electrical impedance tomography (MR-EIT) was first proposed in 1992. Since then various reconstruction algorithms have been suggested and applied. These algorithms use peripheral voltage measurements and internal current density measurements in different combinations. In this study the problem of MR-EIT is treated as a hyperbolic system of first-order partial differential equations, and three numerical methods are proposed for its solution. This approach is not utilized in any of the algorithms proposed earlier. The numerical solution methods are integration along equipotential surfaces (method of characteristics), integration on a Cartesian grid, and inversion of a system matrix derived by a finite difference formulation. It is shown that if some uniqueness conditions are satisfied, then using at least two injected current patterns, resistivity can be reconstructed apart from a multiplicative constant. This constant can then be identified using a single voltage measurement. The methods proposed are direct, non-iterative, and valid and feasible for 3D reconstructions. They can also be used to easily obtain slice and field-of-view images from a 3D object. 2D simulations are made to illustrate the performance of the algorithms.

Course
Other identifiers
Book Title
Keywords
EIT, Electrical impedance tomography, Hyperbolic system of partial differential equations, Image reconstruction, Magnetic resonance-electrical impedance tomography, Medical imaging, Method of characteristics, MR-EIT, Algorithm, Computer assisted impedance tomography, Density, Electric current, Electric potential, Image reconstruction, Imaging, Mathematical analysis, Measurement, Nuclear magnetic resonance imaging, Simulation, Algorithms, Computer Simulation, Electric Impedance, Magnetic resonance spectroscopy, Models, theoretical
Citation
Published Version (Please cite this version)