Biomedical Engineering Letters

, Volume 8, Issue 3, pp 273–282 | Cite as

Electrodeless conductivity tensor imaging (CTI) using MRI: basic theory and animal experiments

  • Saurav Z. K. Sajib
  • Oh In Kwon
  • Hyung Joong Kim
  • Eung Je WooEmail author
Original Article


The electrical conductivity is a passive material property primarily determined by concentrations of charge carriers and their mobility. The macroscopic conductivity of a biological tissue at low frequency may exhibit anisotropy related with its structural directionality. When expressed as a tensor and properly quantified, the conductivity tensor can provide diagnostic information of numerous diseases. Imaging conductivity distributions inside the human body requires probing it by externally injecting conduction currents or inducing eddy currents. At low frequency, the Faraday induction is negligible and it has been necessary in most practical cases to inject currents through surface electrodes. Here we report a novel method to reconstruct conductivity tensor images using an MRI scanner without current injection. This electrodeless method of conductivity tensor imaging (CTI) utilizes B1 mapping to recover a high-frequency isotropic conductivity image which is influenced by contents in both extracellular and intracellular spaces. Multi-b diffusion weighted imaging is then utilized to extract the effects of the extracellular space and incorporate its directional structural property. Implementing the novel CTI method in a clinical MRI scanner, we reconstructed in vivo conductivity tensor images of canine brains. Depending on the details of the implementation, it may produce conductivity contrast images for conductivity weighted imaging (CWI). Clinical applications of CTI and CWI may include imaging of tumor, ischemia, inflammation, cirrhosis, and other diseases. CTI can provide patient-specific models for source imaging, transcranial dc stimulation, deep brain stimulation, and electroporation.


Conductivity tensor imaging (CTI) Diffusion weighted imaging Magnetic resonance electrical properties tomography Anisotropy 



This work was supported by the National Research Foundation of Korea (NRF) and Korea Institute of Radiological and Medical Sciences (KIRAMS) Grants funded by the Korea government (Nos. 2015R1D1A1A09058104, 2016R1A2B4014534, 2017R1A2A1A05001330, and 50461-2018). The authors thank Dr. W. C. Jeong for his helps in animal experiments.

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest to declare.

Ethical approval

All animal procedures were approved by the institutional animal care and use committee of Kyung Hee University (KHUASP-14-25). All methods were carried out in accordance with the relevant guidelines and regulations.


  1. 1.
    Grimnes S, Martinsen OG. Bioimpedance and bioelectricity basics. Waltham: Academic Press; 2015.Google Scholar
  2. 2.
    Seo JK, Kim DH, Lee J, Kwon OI, Sajib SZK, Woo EJ. Electrical tissue property imaging using MRI at dc and Larmor frequency. Inverse Probl. 2012;28:8.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Metherall P, Barber DC, Smallwood RH, Brown BH. Three-dimensional electrical impedance tomography. Nature. 1996;380:509–12.CrossRefGoogle Scholar
  4. 4.
    Holder D. Electrical impedance tomography: methods, History and Applications. Bristol: IOP Publishing; 2005.Google Scholar
  5. 5.
    Frerichs I, Amato MBP, van Kaam AH, Tingay DG, Zhao Z, Grychtol B, Bodenstein M, Gagnon H, Bohm SH, Teschner E, Stenqvist O, Mauri T, Torsani V, Camporota L, Schibler A, Wolf GK, Gommers D, Leonhardt S, Adler A, TREND study group. Chest electrical impedance tomography examination, data analysis, terminology, clinical use and recommendations: consensus statement of the TRanslational EIT development study group. Thorax. 2017;72:83–93.CrossRefGoogle Scholar
  6. 6.
    Seo JK, Woo EJ. Magnetic resonance electrical impedance tomography (MREIT). SIAM Rev. 2011;53:40–68.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Seo JK, Woo EJ. Electrical tissue property imaging at low frequency using MREIT. IEEE Trans Biomed Eng. 2014;61:1390–9.CrossRefGoogle Scholar
  8. 8.
    Sajib SZK, Katoch N, Kim HJ, Kwon OI, Woo EJ. Software toolbox for low-frequency conductivity and ciurrent density imaging using MRI. IEEE Trans Biomed Eng. 2017;64:2505–14.CrossRefGoogle Scholar
  9. 9.
    Ammari H, Qiu L, Santosa F, Zhang W. Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction. Inverse Probl. 2017;33:125006.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ammari H, Garnier J, Giovangigli L, Jing W, Seo JK. Spectroscopic imaging of a dilute cell suspension. J Math Pures Appl. 2016;105:603–61.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Tuch DS, Wedeen VJ, Dale AM, George JS, Belliveau JW. Conductivity tensor mapping of the human brain using diffusion tensor MRI. Proc Nat Acad Sci. 2001;98:11697–701.CrossRefGoogle Scholar
  12. 12.
    Jeong WC, Sajib SZK, Katoch N, Kim HJ, Kwon OI, Woo EJ. Anisotropic conductivity tensor imaging of in vivo canine brain using DT-MREIT. IEEE Trans Med Imaging. 2017;36:124–31.CrossRefGoogle Scholar
  13. 13.
    Katscher U, Voigt T, Findeklee C, Vernickel P, Nehrke K, Dossel O. Determination of electrical conductivity and local SAR via B1 mapping. IEEE Trans Med Imaging. 2009;28:1365–74.CrossRefGoogle Scholar
  14. 14.
    Voigt T, Katscher U, Doessel O. Quantitative conductivity and permittivity imaging of the human brain using electric properties tomography. Magn Reson Med. 2011;66:456–66.CrossRefGoogle Scholar
  15. 15.
    Lee J, Shin J, Kim DH. MR-based conductivity imaging using multiple receiver coils. Magn Res Med. 2016;76:530–9.CrossRefGoogle Scholar
  16. 16.
    Stanisz GJ, Wright GA, Henkelman RM, Szafer A. An analytical model of restricted diffusion in bovine optic nerve. Magn Res Med. 1997;37:103–11.CrossRefGoogle Scholar
  17. 17.
    Le Bihan D. Looking into the functional architecture of the brain with diffusion MRI. Nature Rev Neurosci. 2003;4:469–80.CrossRefGoogle Scholar
  18. 18.
    Mattiello J, Basser PJ, Le Bihan D. Analytical expression for the b matrix in NMR diffusion imaging and spectroscopy. J Magn Reson Ser A. 1994;108:131–41.CrossRefGoogle Scholar
  19. 19.
    Madelin G, Kline R, Walvivk R, Regatte RR. A method for estimating intracellular sodium concentration and extracellular volume fraction in brain in vivo using sodium magnetic resonance imaging. Sci Rep. 2014;4:47–63.Google Scholar
  20. 20.
    Wojcieszyn JW, Schlegel RA, Wu ES, Jacobson KA. Diffusion of injected macromolecules within the cytoplasm of living cells. Proc Natl Acad Sci. 1981;78:4407–10.CrossRefGoogle Scholar
  21. 21.
    Kao HP, Abney JR, Verkman AS. Determinants of the translational mobility of a small solute in cell cytoplasm. J Cell Biol. 1993;120:175–84.CrossRefGoogle Scholar
  22. 22.
    Zhang H, Schneider T, Wheeler-Kingshott CA, Alexander DC. NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. NeuroImage. 2012;61:1000–116.CrossRefGoogle Scholar
  23. 23.
    Hoy AR, Koay CG, Kecskemeti SR, Alexander AL. Optimization of a free water elimination two-compartment model for diffusion tensor imaging. NeuroImage. 2014;103:323–33.CrossRefGoogle Scholar
  24. 24.
    Clark CA, Hedehus M, Moseley ME. In vivo mapping of the fast and slow diffusion tensors in human brain. Magn Reson Med. 2002;47:623–8.CrossRefGoogle Scholar
  25. 25.
    Maier SE, Vajapeyam S, Mamata H, Westin CF, Jolesz FA, Mulkern RV. Biexponential diffusion tensor analysis of human brain diffusion data. Magn Reson Med. 2004;51:321–30.CrossRefGoogle Scholar
  26. 26.
    Basser PJ, Le Bihan D, Mattiello J. Estimation of the effective self diffusion tensor from the NMR spin echo. J Magn Reson Ser B. 1994;103:399–412.CrossRefGoogle Scholar
  27. 27.
    Sekino M, Yamaguchi K. Conductivity tensor imaging of the brain using diffusion-weighted magnetic resonance imaging. J Appl Phys. 2003;93:6730–2.CrossRefGoogle Scholar
  28. 28.
    Hansen AJ. Effect of anoxia on ion distribution in the brain. Physiol Rev. 1985;65:101–48.CrossRefGoogle Scholar
  29. 29.
    Volkov AG, Paula S, Deamer DW. Two mechanisms of permeation of small neutral molecules and hydrated ions across phospholipid bilayers. Bioelectrochem Bioenerg. 1997;93:153–60.CrossRefGoogle Scholar
  30. 30.
    Haacke EM, Petropoulos LS, Nilges EW, Wu DH. Extraction of conductivity and permittivity using magnetic resonance imaging. Phys Med Biol. 1991;36:723–34.CrossRefGoogle Scholar
  31. 31.
    Hoult DI. The principle of reciprocity in signal strength calculations: mathematical guide. Concepts Magn Reson. 2000;12:173–87.CrossRefGoogle Scholar
  32. 32.
    Stollberger R, Wach P. Imaging of the active B1 field in vivo. Mag Res Med. 1996;36:246–51.CrossRefGoogle Scholar
  33. 33.
    Kwon OI, Jeong WC, Sajib SZK, Kim HJ, Woo EJ, Oh TI. Reconstruction of dual-frequency conductivity by optimization of phase map in MREIT and MREPT. BioMed Eng OnLine. 2014;13:1–15.CrossRefGoogle Scholar
  34. 34.
    Wen H. Non-invasive quantitative mapping of conductivity and dielectric distributions using the RF wave propagation effects in high field MRI. Concepts Magn Reson. 2003;12:173–87.Google Scholar
  35. 35.
    van Lier ALHMW, Brunner DO, Pruessmann KP, Klomp DW, Luijten PR, Lagendijk JJ, van den Berg CAT. B1(+) phase mapping at 7 T and its application for in vivo electrical conductivity mapping. Magn Reson Med. 2012;67:552–61.CrossRefGoogle Scholar
  36. 36.
    Katscher U, Djamshidi K, Voigt T, Ivancevic M, Abe H, Newstead G, Keupp J. Estimation of breast tumor conductivity using parabolic phase fitting. Proc Intl Soc Mag Reson Med. 2012;20:3482.Google Scholar
  37. 37.
    Seo JK, Ghim M, Lee J, Choi N, Woo EJ, Kim HJ, Kwon OI, Kim DH. Error analysis for electrical property imaging using MREPT. IEEE Trans Med Imaging. 2012;31:430–7.CrossRefGoogle Scholar
  38. 38.
    Gurler N, Ider YZ. Gradient-based electrical conductivity imaging using MR phase. Magn Reson Med. 2016;77:137–50.CrossRefGoogle Scholar
  39. 39.
    Mansfield P. Multi-planar image formation using NMR spin-echo. J Phys C Solid State Phys. 1977;10:L55–8.CrossRefGoogle Scholar
  40. 40.
    Kwon OI, Woo EJ, Du YP, Hwang D. A tissue-relaxation-dependent neighbouring method for robust mapping of the myelin water fraction. Neuro Image. 2013;74:12–21.Google Scholar
  41. 41.
    Gabriel C, Gabriel S, Corthout E. The dielectric properties of biological tissues: I. Literature survey. Phys Med Biol. 1996;41:2231–49.CrossRefGoogle Scholar
  42. 42.
    Katscher U, Kim DH, Seo JK. Recent progress and future challenges in MR electric properties tomography. Comput Math Meth Med. 2013;2013:546–62.MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Liu J, Zhang X, Schmitter S, Van de Moortele PF, He B. Gradient-based electrical properties tomography (gEPT): a robust method for mapping electrical properties of biological tissues in vivo using magnetic resonance imaging. Magn Reson Med. 2015;74:634–46.CrossRefGoogle Scholar
  44. 44.
    Turner R, Le Bihan D, Maier J, Vavrek R, Hedges LK, Pekar J. Echo-planar imaging of intravoxel incoherent motion. Radiology. 1990;177:407–14.CrossRefGoogle Scholar
  45. 45.
    Basser PJ, Jones DK. Diffusion-tensor MRI: theory, experiment design and data analysis—a technical review NMR. Biomedicine. 2002;15:456–67.Google Scholar
  46. 46.
    Leemans A, Jeurissen B, Sijbers J, Jones DK. ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data. Proc Intl Soc Mag Reson Med. 2009;17:35–7.Google Scholar
  47. 47.
    Muftuler LT, Hamamura MJ, Birgul O, Nalcioglu O. In vivo MRI electrical impedance tomography (MREIT) of tumors. Technol Cancer Res Treat. 2006;5:381–7.Google Scholar
  48. 48.
    Gao G, Zhu SA, He B. Estimation of electrical conductivity distribution within the human head from magnetic flux density measurement. Phys Med Biol. 2005;50:2675–87.CrossRefGoogle Scholar
  49. 49.
    Kwon OI, Sajib SZK, Sersa I, Oh TI, Jeong WC, Kim HJ, Woo EJ. Current density imaging during transcranial direct current stimulation using DT-MRI and MREIT: algorithm development and numerical simulations. IEEE Trans Biomed Eng. 2016;63:168–75.CrossRefGoogle Scholar
  50. 50.
    Kranjc M, Bajd F, Sersa I, Woo EJ, Miklavcic D. Ex vivo and in silico feasibility study of monitoring electric field distribution in tissue during electroporation based treatments. PLoS ONE. 2012;7:e45737.CrossRefGoogle Scholar

Copyright information

© Korean Society of Medical and Biological Engineering and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Saurav Z. K. Sajib
    • 1
  • Oh In Kwon
    • 2
  • Hyung Joong Kim
    • 1
  • Eung Je Woo
    • 1
    Email author
  1. 1.Department of Biomedical EngineeringKyung Hee UniversitySeoulKorea
  2. 2.Department of MathematicsKonkuk UniversitySeoulKorea

Personalised recommendations