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 T₂ 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. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.