Time optimal control-based RF pulse design under gradient imperfections

Christoph S. Aigner*, Armin Rund, Samy Abo Seada, Anthony N. Price, Joseph V. Hajnal, Shaihan J. Malik, Karl Kunisch, Rudolf Stollberger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)561-574
Number of pages14
JournalMagnetic Resonance in Medicine
Issue number2
Early online date23 Aug 2019
Publication statusE-pub ahead of print - 23 Aug 2019


  • gradient imperfections
  • gradient impulse response function
  • pulse design
  • simultaneous multi-slice excitation
  • time optimal control


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