The Principles of Magnetic Resonance, and Associated Hardware

ANDREW WEBB

C.J. Gorter Center for High Field MRI, Department of Radiology, Leiden University Medical Center, Leiden, The Netherlands

1.1 Introduction

The diversity of magnetic resonance (MR) experiments is enormous, ranging from simple one-dimensional proton nuclear magnetic resonance (NMR) spectroscopy through multi-dimensional multi-nuclear spectra to full three-dimensional magnetic resonance imaging (MRI) of morphology and function in animals and humans. Some examples of the types of data produced from different MR experiments are shown in Figure 1.1.

Despite the widely different information content of these data, the fundamental hardware systems for NMR spectroscopy (in both the liquid and solid states) and MRI (human and animal) are very similar. The basic components include the following:

(i) The magnet, which polarizes the nuclei and produces a net magnetization within the sample.

(ii) The radiofrequency coil(s), which transmit pulses of electromagnetic (EM) energy into the sample and detect the precessing magnetization, which constitutes the MR signal.

(iii) Magnetic field gradient coils, which induce a spatial dependence of the nuclear precession frequency and can be used for coherence order selection, measurements of diffusion, and MRI.

(iv) Shim coils, which are used to produce as homogeneous a magnetic field as possible throughout the sample, (v) The receiver electronics and circuitry, which amplify, filter and digitize the MR signal for data storage and post-processing.

The physical arrangement of components (i) to (iv) is shown in Figure 1.2 for a vertical bore magnet.

In addition, there are a series of electronic components used to switch the gradients on and off, to produce high power RF pulses, and to amplify and digitize the signal. A simplified block diagram of a generalized MR system is shown in Figure 1.3.

Table 1.1 gives an idea of the characteristics and performance of components in typical commercial NMR and MRI systems. The system performances of each of the components in the table are explained in greater detail in the relevant sections throughout the book.

In the following sections in this chapter the basic phenomena involved in magnetic resonance are explained briefly, with links to the relevant system hardware. There are a large number of MR books dealing with the basic theory of high-resolution liquid-state NMR, solid-state NMR and MRI, and readers are advised to consult these tomes for much more in-depth analyses of different aspects of basic MR theory.

1.2 The Superconducting Magnet and Nuclear Polarization

The role of the magnet is to polarize the nuclei to produce a net magnetization within the sample. For NMR spectroscopy and MRI, almost all magnets are superconducting. The magnetic field should be temporally stable and homogeneous to within parts-per-billion (ppb) throughout the sample. Most magnets are actively shielded, i.e. the fringe field does not extend significantly outside the physical dimensions of the magnet itself. Magnet design is considered in detail in Chapter 2 of this book, as well as Appendix 1A at the end of this chapter.

All nuclei with an odd atomic weight and/or an odd atomic number possess a fundamental quantum mechanical property termed "spin" and are termed "spin-active" or "NMR-active". The most important spin-active nuclei include 1H, 13C, 15N, 23Na, 17O, 31P and 2H. Notably spin-inactive are nuclei such as 16O and 12C. Considering the proton as the simplest example, the property of spin can be viewed as the proton spinning around an internal axis of rotation giving it a certain value of angular momentum (P). Since the proton is a charged particle, this rotation results in a magnetic moment (µ). This magnetic moment produces an associated magnetic field, which has a configuration similar to that of a bar magnet. The magnitude of P is quantized in terms of the nuclear spin quantum number (7):

[MATHEMATICAL EXPRESSION OMITTED] (1.1)

where h is Planck's constant (6.63 x 10-34 Js). In the following analysis a spin 1/2 nucleus (I = 1/2) is considered, corresponding to 1H, 13C, 15N, and 31P in the previous list. In this case:

[MATHEMATICAL EXPRESSION OMITTED] (1.2)

The magnitudes of the magnetic moment and the angular momentum of the proton are related by:

[MATHEMATICAL EXPRESSION OMITTED] (1.3)

where ? is the nuclear gyromagnetic ratio, and has a specific value for different nuclei, with protons having the highest ? (with the exception of tritium). For protons therefore:

[MATHEMATICAL EXPRESSION OMITTED] (1.4)

µ contains three components (µx, µy and µz), each of which can have any value within the conditions governed by eqn (1.4): this situation is shown in Figure 1.4(a). However, in the presence of a strong magnetic field, B0, µz is quantized with values given by:

µz = ?h/2p mI (1.5)

where mI is the nuclear magnetic quantum number, and can take values I, I – 1 ... –I. In the case of a proton, m1 = [+ or -]1/2 and so:

µz = [+ or -]?h/4p (1.6)

The orientation of µ with respect to B0 is shown in Figure 1.4(b). The interaction of the static magnetic (B0) field with µz results in Zeeman splitting, producing two energy levels: one in which µz aligns parallel to B0 (the lower energy state) and the other anti-parallel (the higher energy state).

The net magnetization, M0, of a sample containing Ns protons is proportional to the difference in populations between the two energy levels, which is dictated by Boltzmann's equation:

[MATHEMATICAL EXPRESSION OMITTED] (1.7)

Eqn (1.7) shows that the net polarization of a sample is proportional to the strength of the main magnetic field. However, since the energy difference between the two levels is very small, so is the population difference. For example, at an operating magnetic field of 11.7 tesla for every one million protons, there is a population difference of only ~40 protons between the parallel and anti-parallel orientations.

1.3 The Transmitter Coil to Generate Radiofrequency Pulses

In order to detect an MR signal, energy must be applied to the nuclear spin system to stimulate transitions between the two energy levels. A pulse of EM energy is applied at the specific resonance frequency (f0), which corresponds to the energy difference between the two levels...