Nuclear magnetic resonance: The contrast imaging problem

2011 ◽  
Author(s):  
Bernard Bonnard ◽  
Monique Chyba ◽  
Steffen J. Glaser ◽  
John Marriott ◽  
Dominique Sugny
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Contrast Imaging ◽  
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

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.

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.

scholarly journals Geometric and Numerical Methods in the Contrast Imaging Problem in Nuclear Magnetic Resonance

2014 ◽  
Vol 135 (1) ◽  
pp. 5-45 ◽  
Author(s):  
Bernard Bonnard ◽  
Mathieu Claeys ◽  
Olivier Cots ◽  
Pierre Martinon
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Numerical Methods ◽  
Contrast Imaging ◽  
Nuclear Magnetic

An emerging technology: Nuclear magnetic resonance microscopy

1988 ◽  
Vol 46 ◽  
pp. 1000-1001
Author(s):  
M.J. Hennessy ◽  
E. Kwok
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Relaxation Times ◽  
Basic Research ◽  
Local Environment ◽  
Magnetic Resonance Images ◽  
Nmr Microscopy ◽  
Mri Scans ◽  
Temperature Relaxation ◽  
Nuclear Magnetic

Much progress in nuclear magnetic resonance microscope has been made in the last few years as a result of improved instrumentation and techniques being made available through basic research in magnetic resonance imaging (MRI) technologies for medicine. Nuclear magnetic resonance (NMR) was first observed in the hydrogen nucleus in water by Bloch, Purcell and Pound over 40 years ago. Today, in medicine, virtually all commercial MRI scans are made of water bound in tissue. This is also true for NMR microscopy, which has focussed mainly on biological applications. The reason water is the favored molecule for NMR is because water is,the most abundant molecule in biology. It is also the most NMR sensitive having the largest nuclear magnetic moment and having reasonable room temperature relaxation times (from 10 ms to 3 sec). The contrast seen in magnetic resonance images is due mostly to distribution of water relaxation times in sample which are extremely sensitive to the local environment.

Nuclear magnetic resonance microscopy

1989 ◽  
Vol 47 ◽  
pp. 828-829
Author(s):  
Paul C. Lauterbur
Keyword(s):  
Magnetic Field ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Magnetic Fields ◽  
Signal To Noise ◽  
Field Gradients ◽  
Useful Signal ◽  
Magnetic Field Gradients ◽  
Observation Times ◽  
Nuclear Magnetic

Nuclear magnetic resonance imaging can reach microscopic resolution, as was noted many years ago, but the first serious attempt to explore the limits of the possibilities was made by Hedges. Resolution is ultimately limited under most circumstances by the signal-to-noise ratio, which is greater for small radio receiver coils, high magnetic fields and long observation times. The strongest signals in biological applications are obtained from water protons; for the usual magnetic fields used in NMR experiments (2-14 tesla), receiver coils of one to several millimeters in diameter, and observation times of a number of minutes, the volume resolution will be limited to a few hundred or thousand cubic micrometers. The proportions of voxels may be freely chosen within wide limits by varying the details of the imaging procedure. For isotropic resolution, therefore, objects of the order of (10μm) may be distinguished.Because the spatial coordinates are encoded by magnetic field gradients, the NMR resonance frequency differences, which determine the potential spatial resolution, may be made very large. As noted above, however, the corresponding volumes may become too small to give useful signal-to-noise ratios. In the presence of magnetic field gradients there will also be a loss of signal strength and resolution because molecular diffusion causes the coherence of the NMR signal to decay more rapidly than it otherwise would. This phenomenon is especially important in microscopic imaging.

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