Analytical solution to the transient phase of steady‐state free precession sequences

The transient phase of short-TR steady-state free precession (SSFP) sequences exhibits an often striking complexity and is not only important for nonequilibrium applications (e.g., rapid T(1)-measurements), but can also cause severe artifacts in conventional imaging. In both cases, balanced SSFP sequences are practically (with regard to preparation efficiency) and conceptually (concerning the theoretical understanding of the decay) easier to handle their unbalanced counterparts, for which currently no theory is available. Based on a decomposition of coherence pathways into irreducible subpaths, an exact mathematical solution to the transient phase of unbalanced SSFP sequences is presented in this article, which also includes the known results for balanced SSFP and the steady state of arbitrary SSFP sequences as special cases. As an application, it is shown that the familiar Look-Locker expression for the accelerated magnetization recovery in RF-spoiled sequences is only valid for T(2)-->0. In addition to oscillatory perturbations, systematic deviations from the monoexponential decay are observed for T(2) > 0 as a consequence of memory effects.