Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR.
Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.
Skinner
Thomas E
TE
Physics Department, Wright State University, Dayton, OH 45435, USA. thomas.skinner@wright.edu
Reiss
Timo O
TO
Luy
Burkhard
B
Khaneja
Navin
N
Glaser
Steffen J
SJ
D000465:Algorithms; D003198:Computer Simulation; D017076:Computer-Aided Design; D017666:Deuterium Oxide / Q000737:chemistry; D008239:Lysine / Q000737:chemistry; D015233:Models, Statistical; D019906:Nuclear Magnetic Resonance, Biomolecular / Q000379:methods*; D011786:Quality Control; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013269:Stochastic Processes; D013598:Systems Theory
D017666:Deuterium Oxide; D008239:Lysine