0
Research Papers

New Formulation of Magnetization Equation for Flowing Nuclear Spin Under Nuclear Magnetic Resonance/Magnetic Resonance Imaging Excitation

[+] Author and Article Information
Dilip K. De

Department of Physics,
Covenant University,
Cannan Land,
Ota 112233, Ogun State, Nigeria
e-mails: dlpd770@gmail.com;
dipak61@yahoo.com

Manuscript received September 2, 2017; final manuscript received January 19, 2018; published online February 21, 2018. Assoc. Editor: Shijia Zhao.

ASME J of Medical Diagnostics 1(2), 021003 (Feb 21, 2018) (7 pages) Paper No: JESMDT-17-2031; doi: 10.1115/1.4039100 History: Received September 02, 2017; Revised January 19, 2018

We have obtained from the Bloch nuclear magnetic resonance (NMR) equations the correct dependence of the single component My and Mz at resonance (NMR/magnetic resonance imaging (MRI)) on relaxation times, rf B1 field (pulsed or continuous), blood(nuclear spin) flow velocity, etc., in the rotating frame of reference. We find that the new formulation for the first time uniquely describes the true relationship between individual single component My or Mz of magnetization of flowing nuclear spin with the above quantities (excluding diffusion and gradient fields) during NMR/MRI excitation. The equations are applicable for both continuous wave (CW) and pulsed NMR experiments with or without flow of spins. Our approaches can be extended easily to include gradient fields and diffusion of spins, if needed in NMR/MRI experiments. We also discuss the application of our equations to a specific case of magnetic resonance (MR) excitation scheme: Free induction decay. The new equations and further equations that can be derived with the methodologies used here can advance the techniques of noninvasive blood flow estimation by MR and also accurate extraction of parameters of clinical importance by enabling accurate simulation of the MR images (of blood flow and tissue) and comparison with experimental MR images. The detailed simulations from the equations will be published in the next paper.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Singer, J. R. , Carr, H. Y. , Millman, S. , and Wehrli, F. W. , 1993, Physics Today, 46(1), p. 15.
Hollingworth, W. , Todd, C. J. , Bell, M. I. , Arafat, Q. , Girling, S. , Karia, K. R. , and Dixon, A. K. , 2000, “ The Diagnostic and Therapeutic Impact of MRI: An Observational Multi-Centre Study,” Clin. Radiol., 55(11), pp. 825–831. [CrossRef] [PubMed]
The Royal College of Radiologists, 2017, “ Magnetic Resonance Imaging (MRI) Equipment, Operations and Planning in the NHS—Report From the Clinical Imaging Board,” The Royal College of Radiologists, London, accessed Feb. 6, 2018, https://www.rcr.ac.uk/sites/default/files/cib_mri_equipment_report.pdf
McRobbie, D. W. , Moore, E. A. , Graves, M. J. , and Prince, M. R. , 2007, MRI From Picture to Proton, Cambridge University Press, Cambridge, UK.
Lauterbur, P. C. , 1973, “ Image Formation by Induced Local Interactions: Examples of Employing Nuclear Magnetic Resonance,” Nature, 242(5394), pp. 190–191. [CrossRef]
Filler, A. , 2009, “ Magnetic Resonance Neography and Diffusion Tensor Imaging: Origins, History, and Clinical Impact of the First 50,000 Cases With an Assessment of Efficacy and Utility in a Prospective 5000-Patient Group,” Neurosurgery, 65(Suppl. 4), pp. A29–A43. [CrossRef] [PubMed]
Lauterbur, P. C. , 1974, “ Magnetic Resonance Zeugmatography,” Pure Appl. Chem., 40(1–2), pp. 149–157.
Benjamin, B. S. , 2016, “ First MRI and Ultrasound Scanning,” Pennsylvania State University, University Park, PA, accessed Feb. 6, 2018, http://benbeck.co.uk/firsts/1_Technology/scanningt.htm
Wakefield, J., 2000, “ The Indomitable MRI,” Smithsonian Magazine, Washington, DC, accessed Feb. 6, 2018, https://www.smithsonianmag.com/science-nature/the-indomitable-mri-29126670/
Damadian, R. , Goldsmith, M. , and Minkoff, L. , 1977, “ NMR in Cancer: XVI. FONAR Image of the Live Human Body,” Physiol. Chem. Phys., 9(1), pp. 97–100. [PubMed]
Hinshaw, W. S. , Bottomley, P. A. , and Holland, G. N. , 1977, “ Radiographic Thin-Section Image of the Human Wrist by Nuclear Magnetic Resonance,” Nature, 270(5639), pp. 722–723. [CrossRef] [PubMed]
De, D. K. , 2013, “ NMR/MRI Blood Flow Magnetization Equation in the Rotating Frame—Part I,” Adv. Sci. Eng. Med., 5(11), pp. 1216–1224.
Scheidegger, M. B. , Maier, S. E. , and Boesiger, P. , 1991, “ FID-Acquired Echoes (FAcE), A Short Echo Time Imaging Method for Flow Artifact Suppression,” Magn. Reson. Imaging, 9(4), pp. 517–534. [CrossRef] [PubMed]
Boesiger, P. , Scheidegger, M. B. , Maier, S. E. , Liu, K. , and Maier, D. , 1992, “ Visualization and Quantification of the Human Blood Flow by Magnetic Resonance Imaging,” J. Biomed. Eng., 25(1), pp. 55–67.
Liu, K. , 1992, “ Magnetic Resonance Imaging for Imaging for the Acquisition of Vectorial Flow Velocity Pattern and Accurate Vessel Geometry,” Ph.D. thesis, University and ETH Zurich, Switzerland.
Ståhlberg, F. , Søndergaard, L. , Thomsen, C. , and Henriksen, O. , 1992, “ Quantification of Complex Flow Using MR Phase Imaging—A Study of Parameters Influencing the Phase/Velocity Relation,” Magn. Reson. Imaging, 10(1), pp. 13–23. [CrossRef] [PubMed]
Srivastava, V. P. , 2007, “ A Theoretical Model for Blood Flow in Small Vessels,” Appl. Appl. Math., 2, pp. 51–65.
Schmalbrock, P. , Yuan, C. , Chakers, D. W. , Koli, J. , and Pelc, N. J. , 1990, “ Volume MR Angiography: Methods to Achieve Very Short Echo Times,” Radiology, 175(3), pp. 861–865. [CrossRef] [PubMed]
De, D. K. , 1990, “ Theoretical Investigation of Estimation of Steady and Pulsatile Blood Flow Rates and Vessel Cross Sections by CW NMR Excitation,” Phys. Med. Biol., 35(2), pp. 197–211. [CrossRef] [PubMed]
Odoh, E. O. , and De, D. K. , 2009, “ Theoretical Investigation and Computation of Time Dependent CW NMR Blood-Flow Signal for the Estimation of Blood Flow Parameters,” Afr. Phys. Rev., 3(0012), pp. 65–75.
Maleki, N. , Dai, W. , and Alsop, D. C. , 2011, “ Blood Flow Quantification of the Human Retina With MRI: NMR,” Biomedicine, 24(1), pp. 104–111.
Varela, M. , Groves, A. M. , Arichi, T. , and Hajnal, J. V. , 2012, “ Mean Cerebral Blood Flow Measurements Using Phase Contrast MRI in the First Year of Life,” NMR Biomed., 25(9), pp. 1063–1072.
Awojoyogbe, O. B. , 2002, “ A Mathematical Model of Bloch NMR Equations for Quantitative Analysis of Blood Flow in Blood Vessels With Changing Cross-Section I,” Phys. A, 303(1–2), pp. 163–175. [CrossRef]
Onwu, O. S. , Dada, O. M. , and Awojoyogbe, O. B. , 2014, “ Physics and Mathematics of Magnetic Resonance Imaging for Nanomedicine: An Overview,” World J. Transl. Med., 3(1), pp. 17–30. [CrossRef]
Jain, V. , Langham, M. C. , and Wehrli, F. W. , 2010, “ MRI Estimation of Global Brain Oxygen Consumption Rate,” J. Cereb. Blood Flow Metab., 30(9), pp. 1598–1607.
Odoh, E. O. , and De, D. K. , 2009, “ Analytical Solutions of NMR Bloch Equations for Human Blood Flow by Laplace Transform,” J. Inst. Math. Comput. Sci. (India)., 22(2), pp. 77–85.
Bonekamp, D. , Degaonkar, M. , and Barker, P. B. , 2011, “ Quantitative Cerebral Blood Flow in Dynamic Susceptibility Contrast MRI Using Total Cerebral Flow From Phase Contrast Magnetic Resonance Angiography,” Magn. Reson. Med., 66(1), pp. 57–66. [CrossRef] [PubMed]
Ebrahimi, B. , 2008, “ Mathematical Regularization and Phantom Evaluation,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
Reddy, R., 2018, “ Bloch Equations,” Center for Magnetic Resonance & Optical Imaging, Philadelphia, PA, accessed Feb. 6, 2018, http://www.mmrrcc.upenn.edu/mediawiki/images/4/4d/Bloch_equations_Feb_2010_ol.pdf
Wang, S. , 1966, Solid State Electronics (International Series in Pure and Applied Physics), 1st ed., McGraw-Hill Book Company, New York, p. 507.
Farrar, T. C. , An Introduction to Pulse NMR Spectroscopy, Farragut Press, Chicago, IL.
Farrar, T. C. , and Becker, E. D. , 1971, Pulse and Fourier Transform NMR, Academic Press, New York.

Figures

Grahic Jump Location
Fig. 1

Rotational frame of axes (xyz) in relation to the fixed Laboratory frame of axes (X0Y0Z0). X-axis of the rotational frame makes an angle ω0t with the X0-axis of the laboratory frame at time t. ω0 = γBo = 2πfo. fo is the NMR resonance frequency. The oscillating rf B1 field is applied along the X0-axis along which the blood flow is considered to take place. Along the x-axis of the rotating frame, the rf B10 field is independent of time. The magnetization component My, which is function of B10, T1, T2, flow velocity, etc., produces the signal in the detector coil placed in quadrature mode to the exciter coil (see Fig. 2).

Grahic Jump Location
Fig. 2

The relative disposition of the exciter coil (AB) and the detector coil (CD) in quadrature mode to be employed in the blood flow estimation by NMR

Grahic Jump Location
Fig. 3

The 90 deg FID sequence. Pulse repetition not shown [32].

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In