Optimal control design of turbo spin-echo sequences with applications to parallel-transmit systems

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Purpose: The design of turbo spin-echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient-specific sequences online. Theory and Methods: The extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations. Results: Standard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two-dimensional and three-dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields. Conclusion: The optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient-specific fashion. Magn Reson Med 77:361–373, 2017.

Original languageEnglish
Pages (from-to)361-373
Number of pages13
JournalMagnetic Resonance in Medicine
Issue number1
Publication statusPublished - Jan 2017


  • direct signal control
  • extended phase graph
  • fast spin-echo
  • optimal control
  • parallel transmit radiofrequency
  • turbo spin-echo

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