title: Radiofrequency pulse design using nonlinear gradient magnetic fields.
abstract: OBJECTIVE
  An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields.
  
  
  METHODS
  The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments.
  
  
  RESULTS
  The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity.
  
  
  CONCLUSIONS
  An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest.
authors.affiliation: Department of Diagnostic Radiology, Yale University, New Haven, Connecticut, USA.
authors.forename: Emre
authors.initials: E
authors.lastname: Kopanoglu
authors.affiliation: Department of Diagnostic Radiology, Yale University, New Haven, Connecticut, USA.|Department of Neurosurgery, Yale University, New Haven, Connecticut, USA.|Department of Biomedical Engineering, Yale University, New Haven, Connecticut, USA.
authors.forename: R Todd
authors.initials: RT
authors.lastname: Constable
mesh_terms: D000465:Algorithms; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D019047:Phantoms, Imaging; D011846:Radio Waves
keywords: RF pulse design; high order gradient fields; k-space trajectory design; multidimensional excitation; nonlinear gradient fields