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The design of excitation pulses for spin systems using optimal control theory: With application to NMR spectroscopy
Author(s) -
Gershenzon Naum I.,
Miller David F.,
Skinner Thomas E.
Publication year - 2008
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.867
Subject(s) - excitation , bloch equations , optimal control , magnetization , physics , computational physics , pulse (music) , spectroscopy , amplitude , magnetization transfer , spin (aerodynamics) , field (mathematics) , nuclear magnetic resonance , computer science , magnetic field , optics , mathematics , quantum mechanics , mathematical optimization , magnetic resonance imaging , medicine , detector , pure mathematics , radiology , thermodynamics
Abstract This paper considers the use of optimal control theory in designing radio frequency excitation pulses for magnetic spin systems satisfying Bloch dynamics. Such pulses are required in applications of nuclear magnetic resonance to initially transfer sample magnetization vectors to the transverse plane. Once transferred, signals released by nuclei as they respond to a static magnetic field normal to the transverse plane are then analyzed and interpreted. Continuous time deterministic optimal control theory is employed to determine time‐dependent pulse amplitudes and frequencies that minimize the distance between final magnetization vectors and a chosen target vector. Pulses are designed to excite a range of resonant frequencies and to tolerate miscalibration errors in applied fields. The model presented permits a unified treatment of the control problem as considered by a variety of authors, and a thorough mathematical analysis of the existence, and characteristics of, optimal excitation pulses. Practical numerical algorithms for designing optimal pulses are given, and the effectiveness of the algorithms is illustrated by comparing the pulses that they generate with those commonly used in high‐resolution spectroscopy. Copyright © 2008 John Wiley & Sons, Ltd.