This work analyses relaxation in balanced non-steady-state free precession sequences. Transforming the Bloch equation to polar coordinates gives insights in the spin dynamics and provides the basis for robust numerical optimization of the excitation pattern. The employed optimal control algorithm results in spin trajectories that allow for parameter mapping with considerably reduced noise, as shown in in vivo MR-fingerprinting experiments. The simple shapes of the optimized spin trajectories provide a basis for further analysis of the encoding process of relaxation times for parameter mapping.
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