It is known that steady-state ring-locked trajectories are formed on an elliptical manifold under a constant amplitude and constant frequency excitation envelope. Here we demonstrate that the excitation envelope can be expressed in terms of the spin-system parameters and a target steady-state trajectory, providing control of the magnetisation on the steady-state ellipsoid when spin-system parameters, such as the relaxation constants, are known. Conversely, we exploit this relationship between excitation parameters and unknown relaxation constants to develop a volume relaxometry technique, which can potentially be extended to relaxation mapping due to the elliptical nature of balanced SSFP.
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