An analytical description of balanced steady-state free precession with finite radio-frequency excitation

Conceptually, the only flaw in the standard steady-state free precession theory is the assumption of quasi-instantaneous radio-frequency pulses, and 10-20% signal deviations from theory are observed for common balanced steady-state free precession protocols. This discrepancy in the steady-state signal can be resolved by a simple T(2) substitution taking into account reduced transverse relaxation effects during finite radio-frequency excitation. However, finite radio-frequency effects may also affect the transient phase of balanced steady-state free precession, its contrast or its spin-echo nature and thereby have an adverse effect on common steady-state free precession magnetization preparation methods. As a result, an in-depth understanding of finite radio-frequency effects is not only of fundamental theoretical interest but also has direct practical implications. In this article, an analytical solution for balanced steady-state free precession with finite radio-frequency pulses is derived for the transient phase (under ideal conditions) and in the steady state demonstrating that balanced steady-state free precession key features are preserved but revealing an unexpected dependency of finite radio-frequency effects on relaxation times for the transient decay. Finally, the mathematical framework reveals that finite radio-frequency theory can be understood as a generalization of alternating repetition time and fluctuating equilibrium steady-state free precession sequence schemes.