Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 421619, 12 pages
Research Article

Noninvasive Measurement of Conductivity Anisotropy at Larmor Frequency Using MRI

1Department of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749, Republic of Korea
2Department of Computational Science & Engineering, Yonsei University, Seoul 120-749, Republic of Korea

Received 15 October 2012; Revised 2 January 2013; Accepted 18 January 2013

Academic Editor: Ulrich Katscher

Copyright © 2013 Joonsung Lee et al. 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.


Anisotropic electrical properties can be found in biological tissues such as muscles and nerves. Conductivity tensor is a simplified model to express the effective electrical anisotropic information and depends on the imaging resolution. The determination of the conductivity tensor should be based on Ohm's law. In other words, the measurement of partial information of current density and the electric fields should be made. Since the direct measurements of the electric field and the current density are difficult, we use MRI to measure their partial information such as B1 map; it measures circulating current density and circulating electric field. In this work, the ratio of the two circulating fields, termed circulating admittivity, is proposed as measures of the conductivity anisotropy at Larmor frequency. Given eigenvectors of the conductivity tensor, quantitative measurement of the eigenvalues can be achieved from circulating admittivity for special tissue models. Without eigenvectors, qualitative information of anisotropy still can be acquired from circulating admittivity. The limitation of the circulating admittivity is that at least two components of the magnetic fields should be measured to capture anisotropic information.