Designing optimal universal pulses using second-order, large-scale, non-linear optimization

作者：Anand Christopher Kumar; Bain Alex D^*; Curtis Andrew Thomas; Nie Zhenghua

来源：Journal of Magnetic Resonance, 2012, 219: 61-74.

DOI：10.1016/j.jmr.2012.04.004

• CPMG experiments
• Nonlinear second-order optimization
• Optimal broadband universal rotation pulses
• RF inhomogeneity
• R-2 estimation

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. %26lt;br%26gt;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 +/-gamma B-1. Finally, we compare our optimal refocusing pulse with other published refocusing pulses by doing CPMG experiments.

• 出版日期2012-6