MAGNETIC RESONANCE ELECTRICAL IMPEDANCE TOMOGRAPHY (MREIT) : SIMULATION STUDY OF J-SUBSTITUTION ALGORITHM

OHIN KWON, JIN KEUN SEO, EUNG JE WOO, AND JEONG-ROCK YOON

In Electrical Impedance Tomography (EIT), we try to reconstruct a cross-sectional resistivity (or conductivity) image of a subject using boundary voltage and current measurements. Since 1980s, several static EIT image reconstruction algorithms have been published [1], [2]. Static imaging in EIT is a kind of inverse problem showing inherently severe ill-posed characteristics [2], [3]. There are two major problems in EIT static imaging. One is the modeling error in capturing the boundary shape of the subject for the construction of computer model. The other is the inherent low sensitivity of boundary measurements to any changes of internal tissue resistivity values. For these reasons, static EIT imaging is still far from clinical applications.

Lately, a new MRI technique has been developed for the measurements of the internal current density distribution [4]–[8]. While we inject current through electrodes attached on the boundary of a subject, MR images are obtained using a spin-echo sequence synchronized with current pulses. Since the injected current generates small magnetic field, these MR images include the effects of injection current as perturbation in the phase of images. Given MR images with phase perturbation, we can compute the magnitude of current density at each pixel of the MR image. Gamba and Delpy successfully measured the current density distribution in an intact piglet head using this technique [4]. Even though currently this requires rotating the subject within the main magnet, we believe that more practical and accurate method will be available soon.

We propose utilizing internal current density data from MRI system to reconstruct static crosssectional resistivity images. We call this new imaging method MREIT (Magnetic Resonance Electrical Impedance Tomography). Since MR images of a subject are available, we can minimize the modeling error in boundary shape of the subject. Furthermore, the internal current density data eliminate the severe sensitivity problem in conventional EIT image reconstruction. The major disadvantage of MREIT is the requirement of the expensive MRI system. However, since MRI is becoming more common in modern clinical situation, the advantage of getting accurate high-resolution resistivity images will overcome the cost problem. Furthermore, MREIT will be a new enhancement in conventional MRI system providing both MR images and static resistivity images.

In 1994, a new EIT image reconstruction algorithm was proposed using internal current density distribution measured by MRI technique [9]. By adjusting resistivity distribution of a computer model of a subject, they tried to minimize the error between the measured current density from the subject and the computed current density of the model using the finite element method. However, the algorithm did not utilize the internal current density data effectively resulting in a poor spatial resolution and convergence characteristics. In this paper, we assume that internal current density distribution is available from an MRI system including added current injection capability. We propose a new static resistivity image reconstruction algorithm called J-substitution algorithm.

Several results from computer simulations will show that accurate high-resolution static resistivity imaging with improved convergence characteristics is possible.

References

[1] J. G. Webster, ed., Electrical Impedance Tomography, Bristol, UK, Adam Hilger, 1990.

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[4] H. R. Gamba and D. T. Delpy, “Measurement of electrical current density distribution within the tissues of the head by magnetic resonance imaging,” Med. Biol. Eng. Comp., vol. 36, pp. 165-170, 1998.

[5] G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Measurement of nonuniform current density by magnetic resonance,” IEEE Trans. Med. Imag., vol. 10, no. 3, pp. 362-374, 1991.

[6] G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Sensitivity of magnetic-resonance current density imaging,” J. Mag. Res., vol. 97, pp. 235-254, 1992.

[7] G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Electromagnetic considerations for RF current density imaging,” IEEE Trans. Med. Imag., vol. 14, pp. 515-524, 1995.

[8] Y. Z. Ider and L. T. Muftuler, “Measurement of ac magnetic field distribution using magnetic resonance imaging,” IEEE Trans. Med. Imag., vol. 16, no. 5, pp. 617-622, 1997.

[9] E. J. Woo, S. Y. Lee, and C. W. Mun, “Impedance tomography using internal current density distribution measured by nuclear magnetic resonance,” SPIE, vol. 2299, pp. 377-385, 1994.

   E-mail address: oikwon@math.snu.ac.kr
   E-mail address: seoj@bubble.yonsei.ac.kr
   E-mail address: ejwoo@khu.ac.kr
   E-mail address: jryoon@numer.kaist.ac.kr