The TrueFISP sequence (1) (also referred to as balanced or fully refocused SSFP, balanced FFE, or FIESTA) is best known for its high SNR efficiency in the steady state, particularly for compartments with a high T 2 /T 1 ratio. Useful information may also be provided by signal acquisition during the transient phase before the steady state is reached. This first became feasible with introduction of the ␣/2 RF preparation pulse, preceding the acquisition module at a time TR/2 (2). In this context, an inversion-prepared TrueFISP sequence was presented for T 1 -weighted imaging, a principle that was proposed later for T 1 quantification (3). However, it was thereupon demonstrated that the temporal evolution of the transient signal actually depends on both longitudinal and transverse relaxation and that this property can be exploited for simultaneous quantification of T 1 and T 2 (4). For magnetization at resonance frequency and for TR Ͻ Ͻ T 1,2 , the transient signal behavior can be described with a simple closed formula (5). Recently, analytic expressions were presented for the calculation of T 1 , T 2 , and spin density from the fit parameters that are obtained by fitting an IR TrueFISP signal time course to a three-parameter monoexponential function (6). The technique works well on the human brain, but the presence of off-resonances poses problems in that it yields modified relaxation parameters and the ␣/2 preparation scheme is suboptimal so that signal fluctuations may impair the early echoes.Various preparation schemes have been proposed for avoiding these initial signal oscillations even for off-resonant magnetization, such as the use of a series RF pulses with linearly increasing flip angles (7,8). An elaborate procedure was also presented for the development of tailored preparation schemes, employing the ShinnarLeRoux (SLR) algorithm for selective RF pulse design and combined with preceding magnitude calibration (9). It is based on eigenvector calculations, using a matrix formalism that was introduced as an early tool for the assessment of signal behavior in periodic pulse sequences (10). The approach is particularly useful for analysis of the True-FISP sequence, since here the net integrals of all gradients within a TR cycle are zero. Hence, ideally no positiondependent dephasing takes place so that it is appropriate to describe the magnetization at a certain frequency by a single vector. With use of matrix notation, an analytic expression can be derived for the steady-state signal of TrueFISP sequences, which is a rather complex function of the parameters involved (T 1 , T 2 , M 0 , TR, flip angle, and frequency offset) (11)(12)(13)(14)(15)(16)(17)(18)(19). Recently, matrix-based mathematics were successfully used to assess the TrueFISP signal decay in the transient phase at off-resonance frequencies, applied in combination with suitable approximations and rather abstract mathematical procedures based on spinor formalism and perturbation theory (20,21).In this paper, the behavior of the magnetization vecto...