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

Ziyalder, Y. and Onart, Serkan and Lionheart, W. R. B. (2003) Uniqueness and reconstruction in magnetic resonance - electrical impedance tomography (MR - EIT). Physiological Measurement, 24 (2). pp. 591-604. ISSN 0967-3334

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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.

Item Type:	Article
Uncontrolled Keywords:	Electrical impedance tomography, EIT, magnetic resonance-electrical impedance tomography, MR–EIT, medical imaging, image reconstruction, method of characteristics, hyperbolic system of partial differential equations
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
Depositing User:	Ms Lucy van Russelt
Date Deposited:	07 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/446

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