title: Design of multidimensional Shinnar-Le Roux radiofrequency pulses.
abstract: OBJECTIVE
  To generalize the conventional Shinnar-Le Roux method for the design of multidimensional radiofrequency pulses.
  
  
  METHODS
  Using echo-planar gradients, the multidimensional radiofrequency pulse design problem was converted into a series of one-dimensional polynomial design problems. Each of the one-dimensional polynomial design problems was solved efficiently. B0 inhomogeneity compensation and design of spatial-spectral pulses were also considered.
  
  
  RESULTS
  The proposed method was used to design two-dimensional excitation and refocusing pulses. The results were validated through Bloch equation simulation and experiments on a 3.0 T scanner. Large-tip-angle, equiripple-error, multidimensional excitation was achieved with ripple levels closely matching the design specifications.
  
  
  CONCLUSIONS
  The conventional Shinnar-Le Roux method can be extended to design multidimensional radiofrequency pulses. The proposed method achieves almost equiripple excitation errors, allows easy control of the tradeoff among design parameters, and is computationally efficient.
authors.affiliation: Department of Electrical and Computer Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
authors.forename: Chao
authors.initials: C
authors.lastname: Ma
authors.forename: Zhi-Pei
authors.initials: ZP
authors.lastname: Liang
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D009682:Magnetic Resonance Spectroscopy / Q000295:instrumentation / Q000379:methods*; D019047:Phantoms, Imaging; D011846:Radio Waves; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: Shinnar-Le Roux; multidimensional radiofrequency pulse; radiofrequency pulse design