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

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• 作者：Christopher Kumar Anand^a ; Alex D. Bain^b ; ^{bain@mcmaster.ca} ; Andrew Thomas Curtis^c ; Zhenghua Nie^a
• 关键词：CPMG experiments ; Nonlinear second-order optimization ; Optimal broadband universal rotation pulses ; RF inhomogeneity ; R2 estimation
• 刊名：Journal of Magnetic Resonance
• 出版年：2012
• 期刊代码：126_10907807
• 类别：ch
• 出版时间：June, 2012
• 卷：219
• 期：Complete
• 页码：61-74
• 文件大小：967 K

摘要

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 B₀ and B₁. 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 R₂ measurements for offsets within 卤纬B₁. Finally, we compare our optimal refocusing pulse with other published refocusing pulses by doing CPMG experiments.