title: Designing optimal universal pulses using second-order, large-scale, non-linear optimization.
abstract: Recently, RF pulse design using first-order and quasi-second-order pulses has been actively investigated. We present a full second-order design method capable of incorporating relaxation, inhomogeneity in B(0) and B(1). Our model is formulated as a generic optimization problem making it easy to incorporate diverse pulse sequence features. To tame the computational cost, we present a method of calculating second derivatives in at most a constant multiple of the first derivative calculation time, this is further accelerated by using symbolic solutions of the Bloch equations. We illustrate the relative merits and performance of quasi-Newton and full second-order optimization with a series of examples, showing that even a pulse already optimized using other methods can be visibly improved. To be useful in CPMG experiments, a universal refocusing pulse should be independent of the delay time and insensitive of the relaxation time and RF inhomogeneity. We design such a pulse and show that, using it, we can obtain reliable R(2) measurements for offsets within ±γB(1). Finally, we compare our optimal refocusing pulse with other published refocusing pulses by doing CPMG experiments.
authors.affiliation: Department of Computing and Software, McMaster University, Hamilton, ON, Canada L8S 4K1.
authors.forename: Christopher Kumar
authors.initials: CK
authors.lastname: Anand
authors.forename: Alex D
authors.initials: AD
authors.lastname: Bain
authors.forename: Andrew Thomas
authors.initials: AT
authors.lastname: Curtis
authors.forename: Zhenghua
authors.initials: Z
authors.lastname: Nie
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D009682:Magnetic Resonance Spectroscopy / Q000379:methods*; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted