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Mathematical Problems in Engineering
Volume 2013, Article ID 635713, 6 pages
Research Article

Mathematical Modeling, Computation, and Experimental Imaging of Thin-Layer Objects by Magnetic Resonance Imaging

Institute of Measurement Science, Slovak Academy of Sciences, 84104 Bratislava, Slovakia

Received 14 May 2013; Revised 25 September 2013; Accepted 11 November 2013

Academic Editor: Eihab M. Abdel-Rahman

Copyright © 2013 Ivan Frollo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Imaging of thin layers using magnetic resonance imaging (MRI) methods belongs to the special procedures that serve for imaging of weak magnetic materials (weak ferromagnetic, diamagnetic, or paramagnetic). The objective of the paper is to present mathematical models appropriate for magnetic field calculations in the vicinity of thin organic or inorganic materials with defined magnetic susceptibility. Computation is similar to the double layer theory. Thin plane layers in their vicinity create a deformation of the neighboring magnetic field. Calculations with results in the form of analytic functions were derived for rectangular, circular, and general shaped samples. For experimental verification, an MRI 0.2 Tesla esaote Opera imager was used. For experiments, a homogeneous parallelepiped block (reference medium)—a container filled with doped water—was used. The resultant images correspond to the magnetic field variations in the vicinity of the samples. For data detection, classical gradient-echo (GRE) imaging methods, susceptible to magnetic field inhomogeneities, were used. Experiments proved that the proposed method was effective for thin organic and soft magnetic materials testing using magnetic resonance imaging methods.