Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2017, Article ID 3035479, 9 pages
https://doi.org/10.1155/2017/3035479
Research Article

The Magnetic Field Produced by the Heart and Its Influence on MRI

Department of Physics, Oakland University, Rochester, MI, USA

Correspondence should be addressed to Bradley J. Roth; ude.dnalkao@htor

Received 5 February 2017; Accepted 20 April 2017; Published 10 May 2017

Academic Editor: Seungik Baek

Copyright © 2017 Dan Xu and Bradley J. Roth. 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.

Linked References

  1. H. Kamei, K. Iramina, K. Yoshifcawa, and S. Ueno, “Neuronal current distribution imaging using magnetic resonance,” IEEE Transactions on Magnetics, vol. 35, no. 5, pp. 4109–4111, 1999. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Bodurka and P. A. Bandettini, “Toward direct mapping of neuronal activity: MRI detection of ultraweak, transient magnetic field changes,” Magnetic Resonance in Medicine, vol. 47, no. 6, pp. 1052–1058, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. P. A. Bandettini, N. Petridou, and J. Bodurka, “Direct detection of neuronal activity with MRI: Fantasy, possibility, or reality?” Applied Magnetic Resonance, vol. 29, no. 1, pp. 65–88, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. A. M. Cassarà, G. E. Hagberg, M. Bianciardi, M. Migliore, and B. Maraviglia, “Realistic simulations of neuronal activity: a contribution to the debate on direct detection of neuronal currents by MRI,” NeuroImage, vol. 39, no. 1, pp. 87–106, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. P. Sundaram, A. Nummenmaa, W. Wells et al., “Direct neural current imaging in an intact cerebellum with magnetic resonance imaging,” NeuroImage, vol. 132, pp. 477–490, 2016. View at Publisher · View at Google Scholar · View at Scopus
  6. W. I. Jay, R. S. Wijesinghe, B. D. Dolasinski, and B. J. Roth, “Is it possible to detect dendrite currents using presently available magnetic resonance imaging techniques?” Medical and Biological Engineering and Computing, vol. 50, no. 7, pp. 651–657, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Huang, “Detecting neuronal currents with MRI: a human study,” Magnetic Resonance in Medicine, vol. 71, no. 2, pp. 756–762, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. G. E. Hagberg, M. Bianciardi, and B. Maraviglia, “Challenges for detection of neuronal currents by MRI,” Magnetic Resonance Imaging, vol. 24, no. 4, pp. 483–493, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Xu and B. J. Roth, “The magnetic field produced by the heart and its influence on MRI,” in Proceedings of SIAM Conference, Great Lakes Section, Dearborn, Mich, USA, April, 2010.
  10. N. A. Trayanova, B. J. Roth, and L. J. Maiden, “The Response of a spherical heart to a uniform electric field: a bidomain analysis of cardiac stimulation,” IEEE Transactions on Biomedical Engineering, vol. 40, no. 9, pp. 899–908, 1993. View at Publisher · View at Google Scholar · View at Scopus
  11. R. A. Murdick and B. J. Roth, “A comparative model of two mechanisms from which a magnetic field arises in the heart,” Journal of Applied Physics, vol. 95, no. 9, pp. 5116–5122, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. C. S. Henriquez, “Simulating the electrical behavior of cardiac tissue using the bidomain model,” Critical Reviews in Biomedical Engineering, vol. 21, pp. 1–77, 1993. View at Google Scholar
  13. J. C. Neu and W. Krassowska, “Homogenization of syncytial tissues,” Critical Reviews in Biomedical Engineering, vol. 21, pp. 137–199, 1993. View at Google Scholar
  14. B. J. Roth and J. P. Wikswo, “A bidomain model for the extracellular potential and magnetic field of cardiac tissue,” IEEE Transactions on Biomedical Engineering, vol. 33, no. 4, pp. 467–469, 1986. View at Publisher · View at Google Scholar · View at Scopus
  15. B. J. Roth, “A comparison of two boundary conditions used with the bidomain model of cardiac tissue,” Annals of Biomedical Engineering, vol. 19, no. 6, pp. 669–678, 1991. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Krassowska and J. C. Neu, “Effective boundary conditions for syncytial tissues,” IEEE Transactions on Biomedical Engineering, vol. 41, no. 2, pp. 143–150, 1994. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs and Mathematical Tables, Dover Publications, New York, NY, USA, 1965.
  18. B. J. Roth, “Electrical conductivity values used with the bidomain model of cardiac tissue,” IEEE Transactions on Biomedical Engineering, vol. 44, no. 4, pp. 326–328, 1997. View at Publisher · View at Google Scholar · View at Scopus
  19. B. J. Roth, Longitudinal Resistance in Strands of Cardiac Muscle [Ph.D. thesis], Vanderbilt University, Nashville, Tenn, USA, 1987.
  20. B. J. Roth, W.-Q. Guo, and J. Wikswo, “The effects of spiral anisotropy on the electric potential and the magnetic field at the apex of the heart,” Mathematical Biosciences, vol. 88, no. 2, pp. 191–221, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. K. K. McBride, B. J. Roth, V. Y. Sidorov, J. P. Wikswo, and F. J. Baudenbacher, “Measurements of transmembrane potential and magnetic field at the apex of the heart,” Biophysical Journal, vol. 99, no. 10, pp. 3113–3118, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. J. R. Holzer, L. E. Fong, V. Y. Sidorov, J. P. Wikswo Jr., and F. Baudenbacher, “High resolution magnetic images of planar wave fronts reveal bidomain properties of cardiac tissue,” Biophysical Journal, vol. 87, no. 6, pp. 4326–4332, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Koch, “Recent advances in magnetocardiography,” Journal of Electrocardiology, vol. 37, pp. 117–122, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. B. J. Roth, “How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle,” Journal of Mathematical Biology, vol. 30, no. 6, pp. 633–646, 1992. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Joy, G. Scott, and M. Henkelman, “In vivo detection of applied electric currents by magnetic resonance imaging,” Magnetic Resonance Imaging, vol. 7, no. 1, pp. 89–94, 1989. View at Publisher · View at Google Scholar · View at Scopus
  26. G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Sensitivity of magnetic-resonance current-density imaging,” Journal of Magnetic Resonance, vol. 97, no. 2, pp. 235–254, 1992. View at Publisher · View at Google Scholar · View at Scopus
  27. G. C. Scott, M. L. G. Joy, R. L. Armstrong, and R. M. Henkelman, “Measurement of nonuniform current density by magnetic resonance,” IEEE Transactions on Medical Imaging, vol. 10, no. 3, pp. 362–374, 1991. View at Publisher · View at Google Scholar · View at Scopus
  28. R. S. Yoon, T. P. DeMonte, K. F. Hasanov, D. B. Jorgenson, and M. L. G. Joy, “Measurement of thoracic current flow in pigs for the study of defibrillation and cardioversion,” IEEE Transactions on Biomedical Engineering, vol. 50, no. 10, pp. 1167–1173, 2003. View at Publisher · View at Google Scholar · View at Scopus
  29. R. K. Hobbie and B. J. Roth, Intermediate Physics for Medicine and Biology, Springer, New York, NY, USA, 5 edition, 2015. View at MathSciNet
  30. S. Ogawa, T. Lee, A. S. Nayak, and P. Glynn, “Oxygenation‐sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields,” Magnetic Resonance in Medicine, vol. 14, no. 1, pp. 68–78, 1990. View at Publisher · View at Google Scholar · View at Scopus
  31. R. H. Kraus Jr., P. Volegov, A. Matlachov, and M. Espy, “Toward direct neural current imaging by resonant mechanisms at ultra-low field,” NeuroImage, vol. 39, no. 1, pp. 310–317, 2008. View at Publisher · View at Google Scholar · View at Scopus
  32. A. M. Cassarà and B. Maraviglia, “Microscopic investigation of the resonant mechanism for the implementation of nc-MRI at ultra-low field MRI,” NeuroImage, vol. 41, no. 4, pp. 1228–1241, 2008. View at Publisher · View at Google Scholar · View at Scopus
  33. M. N. J. Paley, L. S. Chow, E. H. Whitby, and G. G. Cook, “Modelling of axonal fields in the optic nerve for direct MR detection studies,” Image and Vision Computing, vol. 27, no. 4, pp. 331–341, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. R. S. Wijesinghe and B. J. Roth, “Detection of peripheral nerve and skeletal muscle action currents using magnetic resonance imaging,” Annals of Biomedical Engineering, vol. 37, no. 11, pp. 2402–2406, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. E. A. Lima, A. Irimia, and J. P. Wikswo, “The magnetic inverse problem,” in The SQUID Handbook, J. Clarke and A. I. Braginski, Eds., vol. 2, Applications, pp. 139–267, Wiley-VCH, Weinheim, Germany, 2006. View at Google Scholar
  36. J. P. Wikswo, “Noninvasive magnetic detection of cardiac mechanical activity: Theory,” Medical Physics, vol. 7, no. 4, pp. 297–306, 1980. View at Publisher · View at Google Scholar · View at Scopus
  37. J. P. Wikswo, J. E. Opfer, and W. M. Fairbank, “Noninvasive magnetic detection of cardiac mechanical activity: experiments,” Medical Physics, vol. 7, no. 4, pp. 307–314, 1980. View at Publisher · View at Google Scholar · View at Scopus