Signal Modelling
The steady-state longitudinal magnetization of an ideal variable flip angle experiment can be analytically solved from the Bloch equations for the spoiled gradient echo pulse sequence {θn–TR}:

where Mz is the longitudinal magnetization, M0 is the magnetization at thermal equilibrium, TR is the pulse sequence repetition time (Figure 1), and θn is the excitation flip angle. The Mz curves of different T1 values for a range of θn and TR values are shown in Figure 2.
Figure 2. Variable flip angle technique signal curves (Eq. 1) for three different T1 values, approximating the main types of tissue in the brain at 3T.
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