A simple geometrical description of the TrueFISP ideal transient and steady-state signal

An intuitive approach is presented for assessment of the TrueFISP signal behavior in the transient phase and the steady state, based on geometrical considerations in combination with the Bloch equations. Short formulations are derived for the zenith and phase angle determining the direction of the magnetization vector for which a smooth monoexponential decay is obtained even at considerable off-resonance frequencies, thus compactly defining the target of various preparation schemes proposed in literature. A pictorial explanation is provided to illustrate how the interplay between RF excitation and relaxation governs the TrueFISP transient phase and steady state. Closed form expressions are developed that describe the signal evolution, accounting for the influence of T-1, T-2, flip angle, and resonance frequency offset in agreement with recently published studies. These results are obtained directly from basic assumptions, without the need for abstract mathematical treatment or further approximations. The validity of the conceptual framework and the analytical description is verified by simulations based on the Bloch equations as well as with MR phantom experiments. The theory may be used for contrast calculations and has the potential to facilitate improved parameter quantification with magnetization prepared TrueFISP experiments accounting for off-resonance effects.