The Analysis of nonanalytical flow phenomena in magnetic resonance imaging using a finite difference method

In magnetic resonance (MR) imaging, moving spins have a significant effect on the received signal, which is seen, depending upon the pulse sequence utilized, as a modulation in signal intensity and/or phase relative to that of stationary spins. This can be used as an advantage to image vessels by using pulse sequences with timing parameters for radiofrequency (RF) and magnetic gradient wave forms that enhance the signal from flowing spins. However, clinical MR images show this seemingly significant advantage is a disadvantage in the presence of pulsatile flow which causes variations in signal strengths and phases that result in image artifacts. The artifacts vary with flow pattern, flow velocity, pulse flip angle, and imaging pulse sequence. An in-depth study into quantifying the effect of flowing spins on image quality has not been done due in part to the difficulty to quantify the amplitude and phase modulation during RF excitation since solutions to the Bloch equations cannot be obtained analytically. This dissertation studies flow problems in MR imaging that cannot be analyzed by analytically solving Bloch equations but require obtaining solutions through numerical methods. In particular, the study focuses on non-analytical flow phenomena experienced by spins flowing during time varying RF pulses. A finite difference method was derived for solving the Bloch equations and a computer simulation program was developed to simulate two-dimensional Fourier transform MR imaging. The combination of the finite difference method and the computer simulation program was used to analyze the degree to which variations in flow induced phase shifts and time-of-flight signal amplitude cause flow artifacts in MR imaging. One-dimensional and two-dimensional flow was studied for slice-selective 90°, 90°-180° hyperbolic scent RF pulse and was shown to be a nonlinear function of spin velocity and flip angle. Flow artifacts were simulated for one-dimensional pulsatile flow and an effective compensation scheme was developed to correct for flow induced phase shifts. Also, a theoretical model was developed to predict time-of flight signal amplitude variations and a technique was developed to correct the image artifacts that results from these variations. The study of one-dimensional flow was extended to a study to two-dimensional flow around a stenotic lesion. The magnetic resonance signal amplitude and phase was spatially mapped across the two-dimensional flow vector field through vertical flow regions and differences in signal amplitude and phase between one- and two-dimensional flows were observed. Based upon this work significant progress has been made in quantifying and simulating MR imaging of flow in the cardiovascular systems.