Analytical solution and verification of diffusion effect in SSFP

Assuming that the SSFP magnetization response maintains a steady state which is periodic in the presence of diffusion, we can solve for the diffusion effect in such sequences. Formulating a Fourier series decomposition solution to the Bloch-Torrey equation and imposing the steady-state condition, analytical expressions describing the signal decay due to diffusion are developed. Magnetization responses for any system and sequence parameters can then be obtained. Also, sensitivity to b factor changes is quite different than standard diffusion measurement techniques. Assumptions made in the solution are verified via finite difference solutions and simulations of the Bloch-Torrey equation.