The solution of Bloch equations for flowing spins during a selective pulse using a finite difference method

The movement of spins during periods of selective pulses result in a modulation of the signal intensity and phase of the received magnetic resonance imaging (MRI) signal, and is a major cause of signal loss from vessels imaged with slice-selective pulses. Methods are well developed for compensation of phase perturbations for spins flowing at constant velocity during the time of applied gradients. However, for spins flowing during selective pulses, the magnitude of the amplitude and phase perturbations has not been understood nor to this time has any method of flow compensation been proposed. This is due in part to the difficulty in using the Bloch equations to quantify the amplitude and phase modulation during radiofrequency (rf) excitation since solutions cannot be obtained analytically. In this paper a finite difference method is used to solve Bloch equations for flowing spins during a 90 degrees selective pulse. Compared with stationary spins, the magnetization distribution for flowing spins exhibits a shift of the slice profile in the direction of the flow, an expansion of the profile, phase shifts, and changes in profile shape. The profiles show residual phase errors which become more severe with higher flow velocities, with flow compensation schemes which apply in the case of spins flowing during applied gradients, and in the absence of an rf pulse. The measurement and understanding of the magnetization distribution is important to designing pulse sequences that compensate for flow. Flow compensated pulse sequences are necessary to reduce image flow artifacts and to increase signal of vessels in MR angiographic images.