scholarly journals Geometric Optimal Control of the Contrast Imaging Problem in Nuclear Magnetic Resonance

2012 ◽  
Vol 57 (8) ◽  
pp. 1957-1969 ◽  
Author(s):  
B. Bonnard ◽  
O. Cots ◽  
S. J. Glaser ◽  
M. Lapert ◽  
D. Sugny ◽  
...  
Keyword(s):  
Optimal Control ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Contrast Imaging ◽  
Geometric Optimal Control ◽  
Nuclear Magnetic

scholarly journals A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Bernard Bonnard ◽  
Steffen J. Glaser ◽  
Dominique Sugny
Keyword(s):  
Optimal Control ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Magnetization Vector ◽  
Conjugate Points ◽  
Sufficient Optimality Conditions ◽  
Contrast Imaging ◽  
Geometric Framework ◽  
Geometric Optimal Control ◽  
Nuclear Magnetic

We present a geometric framework to analyze optimal control problems of uncoupled spin 1/2 particles occurring in nuclear magnetic resonance. According to the Pontryagin's maximum principle, the optimal trajectories are solutions of a pseudo-Hamiltonian system. This computation is completed by sufficient optimality conditions based on the concept of conjugate points related to Lagrangian singularities. This approach is applied to analyze two relevant optimal control issues in NMR: the saturation control problem, that is, the problem of steering in minimum time a single spin 1/2 particle from the equilibrium point to the zero magnetization vector, and the contrast imaging problem. The analysis is completed by numerical computations and experimental results.

On the application of geometric optimal control theory to Nuclear Magnetic Resonance

2013 ◽  
Vol 3 (4) ◽  
pp. 375-396 ◽  
Author(s):  
Elie Assémat ◽  
◽  
Marc Lapert ◽  
Dominique Sugny ◽  
Steffen J. Glaser ◽  
...  
Keyword(s):  
Optimal Control ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Geometric Optimal Control ◽  
Nuclear Magnetic

scholarly journals Algebraic geometric classification of the singular flow in the contrast imaging problem in nuclear magnetic resonance

2013 ◽  
Vol 3 (4) ◽  
pp. 397-432 ◽  
Author(s):  
Bernard Bonnard ◽  
◽  
Monique Chyba ◽  
Alain Jacquemard ◽  
John Marriott ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Contrast Imaging ◽  
Singular Flow ◽  
Nuclear Magnetic

Optimal control of the inversion of two spins in Nuclear Magnetic Resonance

2012 ◽  
Vol 405 ◽  
pp. 71-75 ◽  
Author(s):  
E. Assémat ◽  
L. Attar ◽  
M.-J. Penouilh ◽  
M. Picquet ◽  
A. Tabard ◽  
...  
Keyword(s):  
Optimal Control ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Nuclear Magnetic

scholarly journals GEOMETRIC NUMERICAL METHODS AND RESULTS IN THE CONTRAST IMAGING PROBLEM IN NUCLEAR MAGNETIC RESONANCE

2013 ◽  
Vol 24 (01) ◽  
pp. 187-212 ◽  
Author(s):  
B. BONNARD ◽  
O. COTS
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Numerical Methods ◽  
Order Conditions ◽  
Continuation Methods ◽  
Contrast Imaging ◽  
Blood Samples ◽  
Mayer Problem ◽  
The Pontryagin Maximum Principle ◽  
Nuclear Magnetic

The purpose of this paper is to present numerical methods and results about the contrast imaging problem in nuclear magnetic resonance which corresponds to a Mayer problem in optimal control. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system given by the Pontryagin Maximum Principle and sufficient second order conditions are described. They form the geometric foundations of the HAMPATH code which combines shooting and continuation methods, see Ref. 9. The main contribution of this paper is to present a numerical analysis of the contrast imaging problem in NMR in the case of deoxygenated/oxygenated blood samples as an application of the aforementioned techniques.

Optimal Broadband Pulse Design with Limited RF Amplitude in Nuclear Magnetic Resonance

2014 ◽  
Vol 543-547 ◽  
pp. 2288-2291
Author(s):  
Shu Lin Zhang ◽  
Yan Chang ◽  
Xiao Dong Yang
Keyword(s):  
Optimal Control ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Optimal Control Theory ◽  
Excitation Pulse ◽  
Design Criteria ◽  
State Transfer ◽  
Shaped Pulse ◽  
Broadband Pulse ◽  
Nuclear Magnetic

In this paper, we introduce an optimal control theory (OCT) based method for design of broadband excitation pulse with limited radio frequency (RF) amplitude in nuclear magnetic resonance (NMR). The capability of the optimized pulse was verified by the following design criteria: the state transfer of 1H fromtoover resonance offsets of, the pulse duration is 1ms with maximum RF amplitude of 10 kHz. The simulation result demonstrates that the optimal control-based shaped pulse is much more adaptable to broadband excitation, providing a better performance than traditional hard pulse.

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