Steady-state free precession experiments and exact treatment of diffusion in a uniform gradient

We derive an analytic solution for the magnetization of spins diffusing in a constant gradient field while applying a long stream of rf pulses, which is known as the steady-state free precession (SSFP) sequence. We calculate the diffusion-dependent amplitude of the free induction decay (FID) and higher order echoes for pulses with arbitrary flip angle alpha and pulse spacing T-R. Stopped-SSFP experiments were performed in a permanent gradient field and the amplitudes of the first three higher order echoes were measured for a range of values of alpha and T-R. Theoretical results are in excellent agreement with experimental results, using no adjustable parameters. We identify various diffusion regimes in a rather large parameter space of pulsing and relaxation times, diffusion coefficient, and flip angle and discuss the interplay of the relevant time scales present in the problem. This phase diagram provides a road map for designing experiments which enhance or suppress the sensitivity to diffusion. We delineate the limits of validity of the widely used ansatz put forth by Kaiser, Bartholdi, and Ernst in their seminal paper. (C) 2001 American Institute of Physics.