Équations de Bloch

En physique et chimie, dans la résonance magnétique nucléaire (RMN), l' et la résonance paramagnétique électronique (RPE), les équations de Bloch sont un ensemble d’équations macroscopiques de calcul de l'aimantation nucléaire M = (Mx, My, Mz) en fonction du temps lorsque les temps de relaxation T1 et T2 sont présents. Les équations de Bloch sont parfois appelées équations du mouvement de l'aimantation nucléaire. Ces équations ont été introduites par Félix Bloch en 1946 et sont analogues aux équations de Maxwell-Bloch qui décrivent l'effet d'un champ électromagnétique sur un système à deux niveaux et les relaxations qu'on y peut observer. Ces équations ne sont pas microscopiques : elles ne décrivent pas l'équation de mouvement de moments magnétiques individuels. Ceux-ci sont gouvernés et décrits par les lois de mécanique quantique. Les équations de Bloch sont macroscopiques : elles décrivent les équations de mouvement de l'aimantation nucléaire macroscopique qui peut être obtenue en a

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Compressed Quantitative MRI: Bloch Response Recovery through iterated projection

Gilles Puy, Pierre Vandergheynst, Yves Wiaux

Inspired by the recently proposed Magnetic Resonance Fin- gerprinting technique, we develop a principled compressed sensing framework for quantitative MRI. The three key com- ponents are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the Bloch equations. We show that, as long as the ex- citation sequence possesses an appropriate form of persistent excitation, we are able to achieve accurate recovery of the proton density, T1, T2 and off-resonance maps simultane- ously from a limited number of samples.

2014

Chargement

A Compressed Sensing Framework for Magnetic Resonance Fingerprinting

Gilles Puy, Pierre Vandergheynst, Yves Wiaux

Inspired by the recently proposed Magnetic Resonance Fingerprinting (MRF) technique we develop a principled compressed sensing framework for quantitative MRI. The three key components are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the Bloch equations. We show that, as long as the excitation sequence possesses an appropriate form of persistent excitation, we are able to achieve accurate recovery the proton density, T1, T2 and off-resonance maps simultaneously from a limited number of samples.

Siam Publications2014

Chargement

Long-lived states to sustain hyperpolarized magnetization

Puneet Ahuja, Jean-Philippe Ansermet, Geoffrey Bodenhausen, Arnaud Comment, Sami Jannin, Riddhiman Sarkar, Paul Romeo Vasos

Major breakthroughs have recently been reported that can help overcome two inherent drawbacks of NMR: the lack of sensitivity and the limited memory of longitudinal magnetization. Dynamic nuclear polarization (DNP) couples nuclear spins to the large reservoir of electrons, thus making it possible to detect dilute endogenous substances in magnetic resonance spectroscopy (MRS) and magnetic resonance imaging (MRI). We have designed a method to preserve enhanced ("hyperpolarized") magnetization by conversion into long-lived states (LLS). It is shown that these enhanced long-lived states can be generated for proton spins, which afford sensitive detection. Even in complex molecules such as peptides, long-lived proton states can be sustained effectively over time intervals on the order of tens of seconds, thus allowing hyperpolarized substrates to reach target areas and affording access to slow metabolic pathways. The natural abundance carbon-13 polarization has been enhanced ex situ by almost four orders of magnitude in the dipeptide Ala-Gly. The sample was transferred by the dissolution process to a high-resolution magnet where the carbon-13 polarization was converted into a long-lived state associated with a pair of protons. In Ala-Gly, the lifetime TLLS associated with the two nonequivalent H glycine protons, sustained by suitable radio-frequency irradiation, was found to be seven times longer than their spin-lattice relaxation time constant (TLLS/T1 = 7). At desired intervals, small fractions of the populations of long-lived states were converted into observable magnetization. This opens the way to observing slow chemical reactions and slow transport phenomena such as diffusion by enhanced magnetic resonance.

2009

Chargement

CH-314: Structural analysis

The aim of this course is to treat three of the major techniques for structural characterization of molecules: mass spectrometry, NMR, and X-ray techniques.

CH-401: Advanced nuclear magnetic resonance

Principles of Magnetic Resonance Imaging (MRI) and applications to medical imaging. Principles of modern multi-dimensional NMR in liquids and solids. Structure determination of proteins & materials. Measurement of molecular dynamics. Principles of Hyperpolarization.

PHYS-438: Fundamentals of biomedical imaging

The goal of this course is to illustrate how modern principles of basic science approaches are integrated into the major biomedical imaging modalities of importance to biology and medicine, with an emphasis on those of interest to in vivo.