Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Evaluation of the Magnetized Magnitudes of the Flowing Nuclear Spins Using Solving Bloch Equations by Finite Difference Method in MRI

Document Type : Research Paper

Authors

S Bahrami 1
M Boroshaki 1
M Ashoor 2

1 Department of Energy Engineering, Sharif University

2 Radiation Application Research School, Nuclear Science and Technology Research Institute, AEOI

https://doi.org/10.24200/nst.2018.187
Abstract
The distribution of the magnetized magnitudes of the flowing nuclear spins has a key role to evaluate the radiofrequency pulses used in the magnetic resonance angiography (MRA). In this study, a finite difference method is used to solve Bloch equations for the flowing nuclear spins during and after a 90° rectangular selective pulse which is important for optimization of the pulse sequence. The results of the simulation indicate that the magnitudes are deformed due to the flowing nuclear spins, while their velocity is increased. The maximum variations are created on the transverse magnitudes namely, Mx and My. The symmetry on these profiles disappear by increasing the velocity. In contrast, no variation on the longitudinal magnitude namely Mz is observed, except a shift on the velocity direction. The sensitivity of these profiles at low velocities for the rectangular selective pulse is more than that of the sinc type, which probably it may be used for characterizing the capillary space. In general, one may obtain the distribution of magnitudes for pulses with various flip angles, as well as, the combination of different pulses. The results may be employed to improve mapping indices in the MRA as well as assessment pulse sequences on the flowing nuclear spins.

Highlights

[1] J.A. Roberts, S-E. Kim, H-C. Yoon, J.S. McNally, J.R. Hadley, L.K. Findeiss, G.S. Treiman, D.L. Parker, Reproducibility of Lumen and vessel wall measurements in Carotid magnetic resonance imaging, The Open Cardiovascular and Thoracic Surgery Journal, 5 (2012) 1-7.

 [2] R. Tyen, D. Saloner, L-D. Jou, S. Berger, MR Imaging of flow through tortuous vessels: A numerical simulation, Magnetic Resonance in Medicine, 31 (1994) 184-195.

 [3] J.T. Ngo, P.G. Morris, General solution to the NMR excitation problem for noninteracting spins, Magnetic Resonance in Medicine, (2005) DOI: 10.1002/mrm.1910050303.

 [4] P. Mansfield, A.A. Maudsley, P.G. Morris, I.L. Pykett, Selective pulses in NMR imaging: A reply to criticism, J. Magn. Reson., 33 (1979) 261–274.

 [5] J.E. Tanner, E.O. Stejskal, Restricted self-diffusion of protons in colloidal systems by the pulsed-gradient, spin-echo method, J. Chem. Phys., 49 (1968) 1768.

 [6] C. Yuan, G.T. Gullberg, D.L. Parker, The solution of Bloch equations for flowing spins during a selective pulse using a finite difference method, Medical Physics, 14 (1987) 914.

 [7] E.O. Stejskal, Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow, Phys., 43 (1965) 3597.

 [8] L. Lapidus, G.F. Pinder, Numerical solution of partial differential equations in science and engineering, Wiley, (1982) Chapter 6.

 [9] C. Yuan, G.T. Gullberg, D.L. Parker, Flow-induced phase effects and compensation technique for slice-selective pulses, Magnetic Resonance in Medicine, 9 (1989)161-176.

Keywords

Magnetization
Bloch equations
Flowing nuclear spins
Finite element method
Magnetic resonance imaging angiography
[1] J.A. Roberts, S-E. Kim, H-C. Yoon, J.S. McNally, J.R. Hadley, L.K. Findeiss, G.S. Treiman, D.L. Parker, Reproducibility of Lumen and vessel wall measurements in Carotid magnetic resonance imaging, The Open Cardiovascular and Thoracic Surgery Journal, 5 (2012) 1-7.
 [2] R. Tyen, D. Saloner, L-D. Jou, S. Berger, MR Imaging of flow through tortuous vessels: A numerical simulation, Magnetic Resonance in Medicine, 31 (1994) 184-195.
 [3] J.T. Ngo, P.G. Morris, General solution to the NMR excitation problem for noninteracting spins, Magnetic Resonance in Medicine, (2005) DOI: 10.1002/mrm.1910050303.
 [4] P. Mansfield, A.A. Maudsley, P.G. Morris, I.L. Pykett, Selective pulses in NMR imaging: A reply to criticism, J. Magn. Reson., 33 (1979) 261–274.
 [5] J.E. Tanner, E.O. Stejskal, Restricted self-diffusion of protons in colloidal systems by the pulsed-gradient, spin-echo method, J. Chem. Phys., 49 (1968) 1768.
 [6] C. Yuan, G.T. Gullberg, D.L. Parker, The solution of Bloch equations for flowing spins during a selective pulse using a finite difference method, Medical Physics, 14 (1987) 914.
 [7] E.O. Stejskal, Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow, Phys., 43 (1965) 3597.
 [8] L. Lapidus, G.F. Pinder, Numerical solution of partial differential equations in science and engineering, Wiley, (1982) Chapter 6.
 [9] C. Yuan, G.T. Gullberg, D.L. Parker, Flow-induced phase effects and compensation technique for slice-selective pulses, Magnetic Resonance in Medicine, 9 (1989)161-176.

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