Time optimal control-based RF pulse design under gradient imperfections

Abstract

Purpose: This study incorporates a gradient system imperfection model into an optimal control framework for radio frequency (RF) pulse design.

Theory and methods: The joint design of minimum-time RF and slice selective gradient shapes is posed as an optimal control problem. Hardware limitations such as maximal amplitudes for RF and slice selective gradient or its slew rate are included as hard constraints to assure practical applicability of the optimized waveforms. In order to guarantee the performance of the optimized waveform with possible gradient system disturbances such as limited system bandwidth and eddy currents, a measured gradient impulse response function (GIRF) for a specific system is integrated into the optimization.

Results: The method generates optimized RF and pre-distorted slice selective gradient shapes for refocusing that are able to fully compensate the modeled imperfections of the gradient system under investigation. The results nearly regenerate the optimal results of an idealized gradient system. The numerical Bloch simulations are validated by phantom and in-vivo experiments on 2 3T scanners.

Conclusions: The presented design approach demonstrates the successful correction of gradient system imperfections within an optimal control framework for RF pulse design.

Keywords: gradient imperfections; gradient impulse response function; pulse design; simultaneous multi-slice excitation; time optimal control.