Application of the limited-memory quasi-Newton algorithm for multi-dimensional, large flip-angle RF pulses at 7T

  • Mads S. VindingEmail author
  • Daniel Brenner
  • Desmond H. Y. Tse
  • Sebastian Vellmer
  • Thomas Vosegaard
  • Dieter Suter
  • Tony Stöcker
  • Ivan I. MaximovEmail author
Research Article



Ultrahigh field MRI provides great opportunities for medical diagnostics and research. However, ultrahigh field MRI also brings challenges, such as larger magnetic susceptibility induced field changes. Parallel-transmit radio-frequency pulses can ameliorate these complications while performing advanced tasks in routine applications. To address one class of such pulses, we propose an optimal-control algorithm as a tool for designing advanced multi-dimensional, large flip-angle, radio-frequency pulses. We contrast initial conditions, constraints, and field correction abilities against increasing pulse trajectory acceleration factors.

Materials and methods

On an 8-channel 7T system, we demonstrate the quasi-Newton algorithm with pulse designs for reduced field-of-view imaging with an oil phantom and in vivo with scans of the human brain stem. We used echo-planar imaging with 2D spatial-selective pulses. Pulses are computed sufficiently rapid for routine applications.


Our dataset was quantitatively analyzed with the conventional mean-square-error metric and the structural-similarity index from image processing. Analysis of both full and reduced field-of-view scans benefit from utilizing both complementary measures.


We obtained excellent outer-volume suppression with our proposed method, thus enabling reduced field-of-view imaging using pulse trajectory acceleration factors up to 4.


MRI RF pulse design Parallel transmit Ultrahigh field MRI 



MSV and TV acknowledge support from the Danish Council for Strategic Research, the Danish National Research Foundation (DNRF59), the Ministry of Higher Education and Science (AU-2010-612-181), the Lundbeck Foundation, Aarhus University Research Foundation, and the Programme Commission on Strategic Growth Technologies, Innovation Fund Denmark (0603-00439B). IIM, SV, and DS thank Deutsche Forschungsgemeinschaft grant (SU 192/32-1) for support of this work, and Dr. Daniel Edelhoff and Mr. Raphael Mocek for assistance in the experiments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Supplementary material

10334_2016_580_MOESM1_ESM.docx (78 kb)
Supplementary material 1 (DOCX 78 kb)


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Copyright information

© ESMRMB 2016

Authors and Affiliations

  1. 1.Department of Chemistry, Center for Ultrahigh-Field NMR Spectroscopy, Interdisciplinary Nanoscience Center (iNANO)Aarhus UniversityAarhusDenmark
  2. 2.German Center for Neurodegenerative Diseases DZNEBonnGermany
  3. 3.Department of Neuropsychology and Psychopharmacology, Faculty of Psychology and NeuroscienceMaastricht UniversityMaastrichtThe Netherlands
  4. 4.Experimental Physics IIITU Dortmund UniversityDortmundGermany
  5. 5.Department of Physics and AstronomyUniversity of BonnBonnGermany

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