ON THE APPLICATION OF GEOMETRIC OPTIMAL CONTROL THEORY TO NUCLEAR MAGNETIC RESONANCE

被引：7

作者：

Assemat, Elie ^{[1
]}

Lapert, Marc ^{[1
]}

Sugny, Dominique ^{[1
]}

Glaser, Steffen J. ^{[2
]}

机构：

[1] Univ Bourgogne, CNRS, UMR 5209, Lab Interdisciplinaire Carnot Bourgogne ICB, F-21078 Dijon, France

[2] Tech Univ Munich, Dept Chem, D-85747 Garching, Germany

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2013年 / 3卷 / 04期

关键词：

Geometrical optimal control; Nuclear Magnetic Resonance; Pontryagin Maximum Principle; contrast problem; BROAD-BAND EXCITATION; IMAGING PROBLEM; SPIN DYNAMICS; PULSES; INVERSION; DESIGN; SPECTROSCOPY; TRAJECTORIES; SYSTEMS; LIMITS;

D O I：

10.3934/mcrf.2013.3.375

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present some applications of geometric optimal control theory to control problems in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). Using the Pontryagin Maximum Principle (PMP), the optimal trajectories are found as solutions of a pseudo-Hamiltonian system. This computation can be completed by second-order optimality conditions based on the concept of conjugate points. After a brief physical introduction to NMR, this approach is applied to analyze two relevant optimal control issues in NMR and MRI: the control of a spin 1/2 particle in presence of radiation damping effect and the maximization of the contrast in MRI. The theoretical analysis is completed by numerical computations. This work has been made possible by the central and essential role of B. Bonnard, who has been at the heart of this project since 2009.

引用

页码：375 / 396

页数：22

共 50 条

[41] Miniature nuclear magnetic resonance spectrometer using a partially enclosed permanent magnet [J].

Lu, Rongsheng ;

Zhou, Xinlong ;

Yin, Qifeng ;

Hu, Jianxiong ;

Ni, Zhonghua .

INSTRUMENTATION SCIENCE & TECHNOLOGY, 2017, 45 (03) :324-337

[42] Control flow strategy in a receiver coil for nuclear magnetic resonance for imaging [J].

Barbaraci, Gabriele .

JOURNAL OF VIBRATION AND CONTROL, 2021, 27 (23-24) :2711-2723

[43] Universal quantum control in zero-field nuclear magnetic resonance [J].

Bian, Ji ;

Jiang, Min ;

Cui, Jiangyu ;

Liu, Xiaomei ;

Chen, Botao ;

Ji, Yunlan ;

Zhang, Bo ;

Blanchard, John ;

Peng, Xinhua ;

Du, Jiangfeng .

PHYSICAL REVIEW A, 2017, 95 (05)

[44] Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. II. Singlet spin locking [J].

Pileio, Giuseppe ;

Levitt, Malcolm H. .

JOURNAL OF CHEMICAL PHYSICS, 2009, 130 (21)

[45] Numerical optimal control of spin systems at zero magnetic field [J].

Jiang, Min ;

Bian, Ji ;

Liu, Xiaomei ;

Wang, Hengyan ;

Ji, Yunlan ;

Zhang, Bo ;

Peng, Xinhua ;

Du, Jiangfeng .

PHYSICAL REVIEW A, 2018, 97 (06)

[46] Combining Mercury Intrusion and Nuclear Magnetic Resonance Measurements Using Percolation Theory [J].

Daigle, Hugh ;

Johnson, Andrew .

TRANSPORT IN POROUS MEDIA, 2016, 111 (03) :669-679

[47] Combining Mercury Intrusion and Nuclear Magnetic Resonance Measurements Using Percolation Theory [J].

Hugh Daigle ;

Andrew Johnson .

Transport in Porous Media, 2016, 111 :669-679

[48] Development of a miniature permanent magnetic circuit for nuclear magnetic resonance chip [J].

Lu Rongsheng ;

Yi Hong ;

Wu Weiping ;

Ni Zhonghua .

CHINESE JOURNAL OF MECHANICAL ENGINEERING, 2013, 26 (04) :689-694

[49] Exact two-component relativistic theory for nuclear magnetic resonance parameters [J].

Sun, Qiming ;

Liu, Wenjian ;

Xiao, Yunlong ;

Cheng, Lan .

JOURNAL OF CHEMICAL PHYSICS, 2009, 131 (08)

[50] Nuclear magnetic resonance in manganites [J].

K. N. Mikhalev ;

Z. N. Volkova ;

A. P. Gerashchenko .

The Physics of Metals and Metallography, 2014, 115 :1139-1159

← 1 2 3 4 5 →