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;

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.

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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].




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