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 hig her order echoes for pulses with arbitrary flip angle alpha and pulse spaci ng T-R. Stopped-SSFP experiments were performed in a permanent gradient fie ld 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 excellen t agreement with experimental results, using no adjustable parameters. We i dentify various diffusion regimes in a rather large parameter space of puls ing and relaxation times, diffusion coefficient, and flip angle and discuss the interplay of the relevant time scales present in the problem. This "ph ase 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 the ir seminal paper. (C) 2001 American Institute of Physics.