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Boundary Value-Free Magnetic Resonance Electrical Properties Tomography Based on the Generalized Cauchy Formula with the Complex-Derivative Boundary Condition

By Motofumi Fushimi and Takaaki Nara
Progress In Electromagnetics Research M, Vol. 96, 1-8, 2020


Recently, magnetic-resonance-based electrical properties tomography, by which the electrical properties (EPs), namely conductivity and permittivity, of biological tissues are reconstructed, has been an active area of study. We previously proposed an explicit reconstruction method based on the Dbar equation and its explicit solution given by the generalized Cauchy formula. In this method, as in some other conventional methods, the values of EPs on the boundary of the region of interest must be specified by the Dirichlet boundary condition of the partial differential equation. However, it is difficult to know the precise values in practical situations. In this paper, we propose a novel method that reconstructs EPs without the prior information of boundary EP values by deriving a new representation formula of the solution of the Dbar equation with the complex-derivative boundary condition. Numerical simulations and phantom experiments show that the proposed method can reconstruct EPs without knowledge of the boundary EP values. Therefore, the proposed method greatly enhances the applicability of the current EPT methods to practical situations.


Motofumi Fushimi and Takaaki Nara, "Boundary Value-Free Magnetic Resonance Electrical Properties Tomography Based on the Generalized Cauchy Formula with the Complex-Derivative Boundary Condition," Progress In Electromagnetics Research M, Vol. 96, 1-8, 2020.


    1. Joines, W. T., Y. Zhang, C. Li, and R. L. Jirtle, "The measured electrical properties of normal and malignant human tissues from 50 to 900 MHz," Med. Phys., Vol. 21, No. 4, 547-550, 1994.

    2. Lazebnik, M., D. Popovic, L. McCartney, C. B. Watkins, M. J. Lindstrom, J. Harter, S. Sewall, T. Ogilvie, A. Magliocco, T. M. Breslin, W. Temple, D. Mew, J. H. Booske, M. Okoniewski, and S. C. Hagness, "A large-scale study of the ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries," Phys. Med. Biol., Vol. 52, No. 20, 6093-6115, 2007.

    3. Li, Z., W. Wang, Z. Cai, S. Han, S. Lin, L. He, M. Chen, D. Pan, G. Deng, S. Duan, and S. X. Xin, "Variation in the dielectric properties of freshly excised colorectal cancerous tissues at different tumor stages," Bioelectromagnetics, Vol. 38, No. 7, 522-532, 2017.

    4. Zhang, X., J. Liu, and B. He, "Magnetic-resonance-based electrical properties tomography: A review," IEEE Rev. Biomed. Eng., Vol. 7, 87-96, 2014.

    5. Katscher, U. and C. A. T. van den Berg, "Electric properties tomography: Biochemical, physical and technical background, evaluation and clinical applications," NMR Biomed., Vol. 30, No. 8, 1-15, 2017.

    6. Liu, J., Y. Wang, U. Katscher, and B. He, "Electrical properties tomography based on B1 maps in MRI: Principles, applications, and challenges," IEEE Trans. Biomed. Eng., Vol. 64, No. 11, 2515-2530, 2017.

    7. Schenck, J. F., "The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds," Med. Phys., Vol. 23, No. 6, 815-850, 1996.

    8. Haacke, E. M., L. S. Petropoulos, E. W. Nilges, and D. H. Wu, "Extraction of conductivity and permittivity using magnetic resonance imaging," Phys. Med. Biol., Vol. 36, No. 6, 723-734, 1991.

    9. Wen, H., "Noninvasive quantitative mapping of conductivity and dielectric distributions using RF wave propagation effects in high-field MRI," Proc. SPIE Med. Imag., Vol. 5030, 471-477, San Diego, CA, USA, 2003.

    10. Seo, J. K., M.-O. Kim, J. Lee, N. Choi, E. J. Woo, H. J. Kim, O. I. Kwon, and D.-H. Kim, "Error analysis of nonconstant admittivity for MR-based electric property imaging," IEEE Trans. Med. Imag., Vol. 31, No. 2, 430-437, 2012.

    11. Hafalir, F. S., O. F. Oran, N. Gurler, and Y. Z. Ider, "Convection-reaction equation based magnetic resonance electrical properties tomography (cr-MREPT)," IEEE Trans. Med. Imag., Vol. 33, No. 3, 777-793, 2014.

    12. Balidemaj, E., C. A. van den Berg, J. Trinks, A. L. van Lier, A. J. Nederveen, L. J. A. Stalpers, H. Crezee, and R. F. Remis, "CSI-EPT: A contrast source inversion approach for improved MRI-based electric properties tomography," IEEE Trans. Med. Imag., Vol. 34, No. 9, 1788-1796, 2015.

    13. Arduino, A., L. Zilberti, M. Chiampi, and O. Bottauscio, "CSI-EPT in presence of RF-shield for MR-coils," IEEE Trans. Med. Imag., Vol. 36, No. 7, 1396-1404, 2017.

    14. Hampe, N., M. Herrmann, T. Amthor, C. Findeklee, M. Doneva, and U. Katscher, "Dictionarybased electric properties tomography," Magn. Reson. Med., Vol. 81, No. 1, 342-349, 2018.

    15. Nara, T., T. Furuichi, and M. Fushimi, "An explicit reconstruction method for magnetic resonance electrical property tomography base on the generalized Cauchy formula," Inverse Problems, Vol. 33, No. 10, 105005, 2017.

    16. Fushimi, M. and T. Nara, "A boundary-value-free reconstruction method for magnetic resonance electrical properties tomography based on the Neumann-type integral formula over a circular region," SICE JCMSI, Vol. 10, No. 6, 571-578, 2017.

    17. Vekua, I., Generalized Analytic Functions, Pergamon Press, 1962.

    18. Katscher, U., T. Voigt, C. Findeklee, P. Vernickel, K. Nehrke, and O. Dossel, "Determination of electric conductivity and local SAR via B1 mapping," IEEE Trans. Med. Imag., Vol. 28, No. 9, 1365-1374, 2009.

    19. Gurler, N. and Y. Z. Ider, "Numerical methods and software tools for simulation, design, and resonant mode analysis of radio frequency birdcage coils used in MRI," Concepts Magn. Reson. Part B, Vol. 45B, No. 1, 13-22, 2015.

    20. Shepp, L. A. and B. F. Logan, "The Fourier reconstruction of a head selection," IEEE Trans. Nucl. Sci., Vol. 21, No. 3, 21-43, 1974.

    21. Insko, E. K. and L. Bolinger, "Mapping of the radiofrequency field," J. Magn. Reson., Vol. 103, No. 1, 82-85, 1993.