Magnetic Resonance RF Pulse Design by Optimal Control With Physical Constraints

Optimal control approaches have proved useful in designing RF pulses for large tip-angle applications. A typical challenge for optimal control design is the inclusion of constraints resulting from physiological or technical limitations that assure the realizability of the optimized pulses. In this paper, we show how to treat such inequality constraints, in particular, amplitude constraints on the B1 field, the slice-selective gradient, and its slew rate, as well as constraints on the slice profile accuracy. For the latter, a pointwise profile error and additional phase constraints are prescribed. Here, a penalization method is introduced that corresponds to a higher order tracking instead of the common quadratic tracking. The order is driven to infinity in the course of the optimization. We jointly optimize for the RF and slice-selective gradient waveform. The amplitude constraints on these control variables are treated efficiently by semismooth Newton or quasi-Newton methods. The method is flexible, adapting to many optimization goals. As an application, we reduce the power of refocusing pulses, which is important for spin echo-based applications with a short echo spacing. Here, the optimization method is tested in numerical experiments for reducing the pulse power of simultaneous multislice refocusing pulses. The results are validated by phantom and in-vivo experiments.