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

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.

Keywords

• magnetization
• bloch equations
• flowing nuclear spins
• finite element method
• magnetic resonance imaging angiography