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Department of CSE

Yonsei University

262 Seongsanno, Seodaemun-gu

Seoul 120-749, Korea

Tel: 82-2-2123-6122

E-mail: seoj@yonsei.ac.kr

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Mathematics and Biomedical Imaging Lab

**1. ****MREIT (Magnetic Resonance Electrical Impedance Tomography)**

Numerous experiences have shown that practically measurable data sets in EIT system are insufficient for a robust reconstruction of a high-resolution static conductivity image due to its ill-posed nature and formidable influences of errors in forward modeling. To overcome the inherent ill-posed characteristics in EIT, MREIT system has been proposed in the early 1990s to use the internal data of magnetic flux density B=(B_x,B_y,B_z) which is induced by an externally injected current.

MREIT uses an MRI scanner as a tool to measure the z-component B_z of the magnetic flux density where z is the axial magnetization direction of the MRI scanner. In 2001, Seo-Woo-Kwon-Yoon developed the first constructive B_z-based MREIT algorithm called the harmonic B_z algorithm and its numerical simulations showed that high-resolution conductivity image reconstructions are possible. This novel algorithm is based on the key observation that the Laplacian of B_z probes changes in log of the conductivity distribution along any equipotential curve having its tangent to the transversal projection of the induced current vector field (J_x,J_y,J_z). Since then, imaging techniques in MREIT have been advanced rapidly and now reached the stage of in vivo animal and human experiments.

**2. Frequency-derivative electrical impedance tomography (fdEIT) **

Seo-EJ Woo proposed fdEIT to deal with technical difficulties of a conventional static EIT imaging method caused by unknown boundary geometry, uncertainty in electrode positions and other systematic measurement artifacts. In fdEIT, we try to produce images showing changes of a complex conductivity distribution with respect to frequency. Simultaneously injecting currents with at least two frequencies, we find differences of measured boundary voltages between those frequencies. In most previous studies, real parts of frequency-difference voltage data were used to reconstruct conductivity changes and imaginary parts to reconstruct permittivity changes.

This conventional approach is neglecting the interplay of conductivity and permittivity upon measured boundary voltage data. Our group proposed an improved fdEIT image reconstruction algorithm that properly handles the interaction. It uses weighted frequency differences of complex voltage data and a complex sensitivity matrix to reconstruct frequency-difference images of conductivity and permittivity. We found that there were two major sources of image contrast in fdEIT. The first is a contrast in conductivity and permittivity values between an anomaly and background. The second is a frequency-dependency of conductivity and permittivity distributions to be imaged. We note that even for the case where conductivity and permittivity do not change with frequency, the fdEIT algorithm may show a contrast in frequency-difference images of conductivity and permittivity distributions. On the other hand, even if conductivity and permittivity values significantly change with frequency, there is an example where we cannot find any contrast. ** **__Multi-frequency trans-admittance scanner____ __