Robust dual-angle T 1 measurement in magnetization transfer spectroscopy by time-optimal control

Magnetization transfer spectroscopy relies heavily on the robust determination of $T_1$ relaxation times of nuclei participating in metabolic exchange. Challenges arise due to the use of surface RF coils for transmission (high $B_1^{+}$ variation) and the broad resonance band of most X nuclei. These challenges are particularly pronounced when fast $T_1$ mapping methods, such as the dual-angle method, are employed. Consequently, in this work, we develop resonance offset and $B_1^{+}$ robust excitation RF pulses for ³¹P magnetization transfer spectroscopy at 7T through ensemble-based time-optimal control. In our approach, we introduce a cost functional for designing robust pulses, incorporating the full Bloch equations as constraints, which are solved using symmetric operator splitting techniques. The optimal control design of the RF pulses developed demonstrates improved accuracy, desired phase properties, and reduced RF power when applied to dual-angle $T_1$ mapping, thereby improving the precision of exchange-rate measurements, as demonstrated in a preclinical in vivo study quantifying brain creatine kinase activity.