Chapter 1
Production of net magnetization

Magnetic resonance (MR) is a measurement technique used to examine atoms and molecules. It is based upon the interaction between an applied magnetic field and a particle that possesses spin and charge. While electrons and other subatomic particles possess spin (or more precisely, spin angular momentum) and can be examined using MR techniques, this book focuses on nuclei and the use of MR techniques for their study, formally known as Nuclear Magnetic Resonance, or NMR. Nuclear spin, or more precisely nuclear spin angular momentum, is one of several intrinsic properties of an atom and its value depends on the precise atomic composition. Every element in the Periodic Table except argon and cerium has at least one naturally occurring isotope that possesses nuclear spin. Thus, in principle, nearly every element can be examined using MR, and the basic ideas of resonance absorption and relaxation are common for all of these elements. The precise details will vary from nucleus to nucleus and from system to system.

1.1 Magnetic fields

Magnetic fields are produced by and surround electric currents, whether these currents are macroscopic currents such as those running through wires or microscopic currents such as those around an atom of iron. The magnetic field can be represented as a vector, meaning that it has both a magnitude and a direction, and is usually denoted by the variable B.1 For example, the B field at the center of a circular loop of current-carrying wire points in the direction of the axis of the loop (perpendicular to the plane of the loop and therefore perpendicular to the current flow) and it has a magnitude that is proportional to the current in the loop. The magnitude of the field is related to the strength of the magnetic force on wires or magnetic materials, and the direction of the field is perpendicular to the direction of the force.

Magnetic fields often vary over time and/or space, and will be coupled to the electric field, producing electromagnetic waves. Magnetic fields, particularly those in electromagnetic waves, are characterized by their frequency (the time between two consecutive "peaks" in the field). In MR, there are magnetic fields, which are constant in time, which vary at acoustic frequencies (a few kilohertz), and which vary at radio frequencies (RF) (several megahertz).

1.2 Nuclear spin

The structure of an atom is an essential component of the MR experiment. Atoms consist of three fundamental particles: protons, which possess a positive charge; neutrons, which have no charge; and electrons, which have a negative charge. The protons and neutrons are located in the nucleus or core of an atom; thus all nuclei are positively charged. The electrons are located in shells or orbitals surrounding the nucleus. The characteristic chemical reactions of elements depend upon the particular number of each of these particles. The properties most commonly used to categorize elements are the atomic number and the atomic weight. The atomic number is the number of protons in the nucleus and is the primary index used to differentiate atoms. All atoms of an element have the same atomic number and undergo the same chemical reactions. The atomic weight is the sum of the number of protons and the number of neutrons. Atoms with the same atomic number but different atomic weights are called isotopes. Isotopes of an element will undergo the same chemical reactions, but at different reaction rates.

A third property of the nucleus is spin or intrinsic spin angular momentum. Classically, nuclei with spin can be considered to be always rotating about an axis at a constant rate. This self-rotation axis is perpendicular to the direction of rotation (Figure 1.1). A limited number of values for the spin are found in nature; that is, the spin, I, is quantized to certain discrete values. These values depend on the atomic number and atomic weight of the particular nucleus. There are three groups of values for I: zero, integral, and half-integral values. A nucleus has no spin (I = 0) if it has an even atomic weight and an even atomic number; for example, 12C (6 protons and 6 neutrons) or 16O (8 protons and 8 neutrons). Such a nucleus does not interact with an external magnetic field and cannot be studied using MR. A nucleus has an integral value for I (e.g., 1, 2, 3) if it has an even atomic weight and an odd atomic number; for example, 2H (1 proton and 1 neutron) or 6Li (3 protons and 3 neutrons). A nucleus has a half-integral value for I (e.g., 1/2, 3/2, 5/2) if it has an odd atomic weight. Table 1.1 lists the spin and isotopic composition for several elements commonly found in biological systems. The 1H nucleus, consisting of a single proton, is a natural choice for probing the body using MR techniques for several reasons. It has a spin of 1/2 and is the most abundant isotope for hydrogen. Its response to an applied magnetic field is one of the largest found in nature. Since the body is composed of tissues that contain primarily water and fat, both of which contain hydrogen, a significant MR signal can be produced naturally by normal tissues.

Figure 1.1 A rotating nucleus (spin) with a positive charge produces a magnetic field known as the magnetic moment oriented parallel to the axis of rotation (a). This arrangement is analogous to a bar magnet in which the magnetic field is considered to be oriented from the south to the north pole (b).

Table 1.1 Constants for Selected Nuclei of Biological Interest

Source: Adapted from Ian Mills (ed.), Quantities, Units, and Symbols in Physical Chemistry, IUPAC, Physical Chemistry Division, Blackwell, Oxford, UK, 1989.

While a rigorous mathematical description of a nucleus with spin and its interactions requires the use of quantum mechanical principles, most of MR can be described using the concepts of classical mechanics, particularly in describing the actions of a nucleus with spin. The subsequent discussions of MR phenomena in this book use a classical approach. In addition, while the concepts of resonance absorption and relaxation apply to all nuclei with spin, the descriptions in this book focus on 1H (commonly referred to as a proton) since most imaging experiments visualize the 1H nucleus.

1.3 Nuclear magnetic moments

Recall that the nucleus is the location of the positively charged protons. When this charge rotates due to the nuclear spin, a local magnetic field or magnetic moment is induced about the nucleus. This magnetic moment will be oriented parallel to the axis of rotation. Since the nuclear spin is constant in magnitude, its associated magnetic moment will also be constant in magnitude. This magnetic moment is fundamental to MR. A bar magnet provides a useful analogy. A bar magnet has a north and a south pole, or, more precisely, a magnitude and orientation to the magnetic field can be defined. The axis of rotation for a nucleus with spin can similarly be viewed as a vector with a definite orientation and magnitude (Figure 1.1). This orientation of the nuclear spin and the changes induced in it due to the experimental manipulations that the nucleus undergoes provide the basis for the MR signal.

In general, MR measurements are made on collections of spins rather than on an individual spin....