In Vivo NMR Spectroscopy

Principles and Techniques

Robin A. de Graaf

• Publisher: Wiley-Interscience
• Year: 2013
• ISBN:
  9781118681305
• Edition: 2
• Topic: Sciences physiques
• Subtopic: Spectroscopie et analyse du spectre

This is the second edition of a unique book in the field of in vivo NMR covering in detail the technical and biophysical aspects of the technique.

The contents of the book are appropriate to both beginners and experienced users of in vivo NMR spectroscopy. The new edition is focussed on bringing the reader practical insights and advice, but is also geared towards use as a study aid and in NMR courses. Recent advances in NMR spectroscopy, like high field NMR, hyperpolarized NMR and new localization and editing techniques have been included. An extensive and updated treatment of radiofrequency pulses is given, together with several tables and recipes for their generation.

Solutions to the exercises within this text can be found here

1

Basic Principles

1.1 Introduction

The field of spectroscopy is in general concerned with the interaction between matter and electromagnetic radiation. Atoms and molecules have a range of discrete energy levels corresponding to different electronic, vibrational or rotational states. The interaction between atoms and electromagnetic radiation is characterized by the absorption and emission of photons, such that the energy of the photons exactly matches an energy level difference in the atom. Since the energy of a photon is proportional to the frequency, the different forms of spectroscopy are often distinguished on the basis of the frequencies involved. For instance, absorption and emission between electronic states of the outer electrons typically require frequencies in the ultraviolet (UV) range, hence giving rise to UV spectroscopy. Molecular vibrational modes are characterized by frequencies just below visible red light and are thus studied with infrared (IR) spectroscopy. Nuclear magnetic resonance (NMR) spectroscopy uses radiofrequencies, which are typically in the range of 10–800 MHz.

NMR is the study of the magnetic properties (and energies) of nuclei. The absorption and emission of electromagnetic radiation can be observed when the nuclei are placed in a (strong) external magnetic field. Purcell, Torrey and Pound [1] at MIT, Cambridge and Bloch, Hansen and Packard [2] at Stanford simultaneously, but independently discovered NMR in 1946. In 1952 Bloch and Purcell shared the Nobel Prize for physics in recognition of their pioneering achievements [1–4]. At this stage, NMR was purely an experiment for physicists to determine the nuclear magnetic moments of nuclei. NMR could only develop into one of the most versatile forms of spectroscopy after the discovery that nuclei within the same molecule absorb energy at different resonance frequencies. These so-called chemical shift effects, which are directly related to the chemical environment of the nuclei, were first observed in 1950 by Proctor and Yu [5], and independently by Dickinson [6].

In the first two decades, NMR spectra were recorded in a continuous wave mode in which the magnetic field strength or the radiofrequency (RF) was swept through the spectral area of interest, whilst keeping the other fixed. In 1966, NMR was revolutionized by Ernst and Anderson [7] who introduced pulsed NMR in combination with Fourier transformation. Pulsed or Fourier transform NMR is at the heart of all modern NMR experiments.

The induced energy level difference of nuclei in an external magnetic field is very small when compared with the thermal energy, making it that the energy levels are almost equally populated. As a result the absorption of photons is very low, making NMR a very insensitive technique when compared with the other forms of spectroscopy. However, the low energy absorption makes NMR also a noninvasive and nondestructive technique, ideally suited for in vivo measurements. It is believed that, by observing the water signal from his own finger, Bloch was the first to use NMR on a living system. Soon after the discovery of NMR, others showed the utility of using NMR to study living objects. In 1950, Shaw and Elsken [8] used proton NMR to investigate the water content of vegetable material. Odebald and Lindstrom [9] obtained proton NMR signals from a number of mammalian preparations in 1955. Continued interest in defining and explaining the properties of water in biological tissues led to the promising report of Damadian in 1971 [10] that NMR properties (relaxation times) of malignant tumorous tissue significantly differs from normal tissue, suggesting that (proton) NMR may have diagnostic value. In the early 1970s, the first experiments of NMR spectroscopy on intact living tissues were reported. Moon and Richards [11] used ³¹P NMR on intact red blood cells and showed how the intracellular pH can be determined from chemical shift differences. In 1974, Hoult et al. [12] reported the first study of ³¹P NMR to study intact, excised rat hind leg.

Around the same time reports on in vivo NMR spectroscopy appeared, Lauterbur [13] and Mansfield and Grannell [14] described the first reports of a major application of modern NMR, namely in vivo NMR imaging or magnetic resonance imaging (MRI). By applying position dependent magnetic fields in addition to the static magnetic field, they were able to reconstruct the spatial distribution of the spins in the form of an image. Lauterbur and Mansfield shared the 2003 Nobel Prize in medicine. In vivo NMR spectroscopy or magnetic resonance spectroscopy (MRS) and MRI have evolved from relatively simple one or two RF pulse sequences to complex techniques involving spatial localization, water and lipid suppression and spectral editing for MRS and time-varying magnetic field gradients, ultra fast and multiparametric acquisition schemes for MRI.

In this chapter the basic phenomenon of NMR is considered. After establishing the Larmor resonance condition with a combination of classical and quantum mechanical arguments, the NMR phenomenon is approached from a more practical point of view with the aid of the macroscopic Bloch equations. The phenomena of chemical shift, scalar coupling and spin echoes will be described, as well as some elementary processing of the NMR signal.

1.2 Classical Description

NMR is based on the concept of nuclear spin. Before discussing the properties of nuclear spins, some relations from classical physics will be introduced which will simplify further discussions. Although classical physics is incapable of describing the quantum mechanical spin, it can be used to create a familiar frame of reference in which the existence of a spin angular momentum can be visualized.

Motion (linear or rotational) always has a corresponding momentum (linear or angular). For an object of mass m and velocity v, the linear momentum p is given by:

(1.1)

Conceptually, momentum can be thought of as the tendency for an object to continue its motion. The momentum only changes when an external force F is applied, in accordance with Newton’s second law:

(1.2)

where a is the acceleration. In the absence of external forces, the object does not accelerate (or decelerate) and the linear momentum and hence the speed is constant.

Now consider an object rotating with constant velocity about a fixed point at a distance r. This motion is described with an angular momentum vector L, defined as:

(1.3)

Therefore, the magnitude of L is mvr and its direction is perpendicular to the plane of motion. Angular momentum can only be changed when an ...