Basic principles

1
Basic principles




After reading this chapter, you will be able to:



  • Describe the structure of the atom.
  • Explain the mechanisms of alignment and precession.
  • Understand the concept of resonance and signal generation.

INTRODUCTION


The basic principles of magnetic resonance imaging (MRI) form the foundation for further understanding of this complex subject. It is important to grasp these ideas before moving on to more complicated topics in this book.


There are essentially two ways of explaining the fundamentals of MRI: classically and via quantum mechanics. Classical theory (accredited to Sir Isaac Newton and often called Newtonian theory) provides a mechanical view of how the universe (and therefore how MRI) works. Using classical theory, MRI is explained using the concepts of mass, spin, and angular momentum on a large or bulk scale. Quantum theory (accredited to several individuals including Max Planck, Albert Einstein, and Paul Dirac) operates at a much smaller, subatomic scale and refers to the energy levels of protons, neutrons, and electrons. Although classical theory is often used to describe physical principles on a large scale and quantum theory on a subatomic level, there is evidence that all physical principles are explained using quantum concepts [1]. However, for our purposes, this chapter mainly relies on classical perspectives because they are generally easier to understand. Quantum theory is only used to provide more detail when required.


In this chapter, we explore the properties of atoms and their interactions with magnetic fields as well as the mechanisms of excitation and relaxation.


ATOMIC STRUCTURE


All things are made of atoms. Atoms are organized into molecules, which are two or more atoms arranged together. The most abundant atom in the human body is hydrogen, but there are other elements such as oxygen, carbon, and nitrogen. Hydrogen is most commonly found in molecules of water (where two hydrogen atoms are arranged with one oxygen atom; H2O) and fat (where hydrogen atoms are arranged with carbon and oxygen atoms; the number of each depends on the type of fat).


The atom consists of a central nucleus and orbiting electrons (Figure 1.1). The nucleus is very small, one millionth of a billionth of the total volume of an atom, but it contains all the atom’s mass. This mass comes mainly from particles called nucleons, which are subdivided into protons and neutrons. Atoms are characterized in two ways.

Diagram shows atom with markings for neutron (no charge), proton (positive), and electron (negative).

Figure 1.1 The atom.



  • The atomic number is the sum of the protons in the nucleus. This number gives an atom its chemical identity.
  • The mass number or atomic weight is the sum of the protons and neutrons in the nucleus.

The number of neutrons and protons in a nucleus is usually balanced so that the mass number is an even number. In some atoms, however, there are slightly more or fewer neutrons than protons. Atoms of elements with the same number of protons but a different number of neutrons are called isotopes.


Electrons are particles that spin around the nucleus. Traditionally, this is thought of as analogous to planets orbiting around the sun with electrons moving in distinct shells. However, according to quantum theory, the position of an electron is not predictable as it depends on the energy of an individual electron at any moment in time (this is called Heisenberg’s Uncertainty Principle).


Some of the particles in the atom possess an electrical charge. Protons have a positive electrical charge, neutrons have no net charge, and electrons are negatively charged. Atoms are electrically stable if the number of negatively charged electrons equals the number of positively charged protons. This balance is sometimes altered by applying energy to knock out electrons from the atom. This produces a deficit in the number of electrons compared with protons and causes electrical instability. Atoms in which this occurs are called ions and the process of knocking out electrons is called ionization.


MOTION IN THE ATOM


Three types of motion are present within the atom (Figure 1.1):



  • Electrons spinning on their own axis
  • Electrons orbiting the nucleus
  • The nucleus itself spinning about its own axis.

The principles of MRI rely on the spinning motion of specific nuclei present in biological tissues. There are a limited number of spin values depending on the atomic and mass numbers. A nucleus has no spin if it has an even atomic and mass number, e.g. six protons and six neutrons, mass number 12. In nuclei that have an even mass number caused by an even number of protons and neutrons, half of the nucleons spin in one direction and half in the other. The forces of rotation cancel out, and the nucleus itself has no net spin.


However, in nuclei with an odd number of protons, an odd number of neutrons, or an odd number of both protons and neutrons, the spin directions are not equal and opposite, so the nucleus itself has a net spin or angular momentum. Typically, these are nuclei that have an odd number of protons (or odd atomic number) and therefore an odd mass number. This means that their spin has a half-integral value, e.g. inline. However, this phenomenon also occurs in nuclei with an odd number of both protons and neutrons resulting in an even mass number. This means that it has a whole integral spin value, e.g. 1, 2, 3. Examples are 6lithium (which is made up of three protons and three neutrons) and 14nitrogen (seven protons and seven neutrons). However, these elements are largely unobservable in MRI so, in general, only nuclei with an odd mass number or atomic weight are used. These are known as MR-active nuclei.


MR-ACTIVE NUCLEI


MR-active nuclei are characterized by their tendency to align their axis of rotation to an applied magnetic field. This occurs because they have angular momentum or spin and, as they contain positively charged protons, they possess an electrical charge. The law of electromagnetic induction (determined by Michael Faraday in 1833) refers to the connection between electric and magnetic fields and motion (explained later in this chapter). Faraday’s law determines that a moving electric field produces a magnetic field and vice versa.


MR-active nuclei have a net electrical charge (electric field) and are spinning (motion), and, therefore, automatically acquire a magnetic field. In classical theory, this magnetic field is denoted by a magnetic moment. The magnetic moment of each nucleus has vector properties, i.e. it has size (or magnitude) and direction. The total magnetic moment of the nucleus is the vector sum of all the magnetic moments of protons in the nucleus.


Important examples of MR-active nuclei, together with their mass numbers are listed below:



  • 1H (hydrogen)
  • 13C (carbon)
  • 15N (nitrogen)
  • 17O (oxygen)
  • 19F (fluorine)
  • 23Na (sodium).

Table 1.1 Characteristics of common elements in the human body.


































Element Protons Neutrons Nuclear spin % Natural abundance
1H (protium) 1 0 1/2 99.985
13C (carbon) 6 7 1/2 1.10
15 N (nitrogen) 7 8 1/2 0.366
17O (oxygen) 8 9 5/2 0.038

THE HYDROGEN NUCLEUS


The isotope of hydrogen called protium is the most commonly used MR-active nucleus in MRI. It has a mass and atomic number of 1, so the nucleus consists of a single proton and has no neutrons. It is used because hydrogen is very abundant in the human body and because the solitary proton gives it a relatively large magnetic moment. These characteristics mean that the maximum amount of available magnetization in the body is utilized.


Faraday’s law of electromagnetic induction states that a magnetic field is created by a charged moving particle (that creates an electric field). The protium nucleus contains one positively charged proton that spins, i.e. it moves. Therefore, the nucleus has a magnetic field induced around it and acts as a small magnet. The magnet of each hydrogen nucleus has a north and a south pole of equal strength. The north/south axis of each nucleus is represented by a magnetic moment and is used in classical theory.


In diagrams in this book, the magnetic moment is shown by an arrow. The length of the arrow represents the magnitude of the magnetic moment or the strength of the magnetic field that surrounds the nucleus. The direction of the arrow denotes the direction of alignment of the magnetic moment as in Figure 1.2.

Diagram shows nuclear magnetic moment on left, bar magnet in middle, and magnetic vector on right.

Figure 1.2 The magnetic moment of the hydrogen nucleus.


Table 1.2 Things to remember – basics of the atom.











Hydrogen is the most abundant element in the human body
Nuclei that are available for MRI are those that exhibit a net spin
As all nuclei contain at least one positively charged proton, those that also spin have a magnetic field induced around them
An arrow called a magnetic moment denotes the magnetic field of a nucleus in classical theory

ALIGNMENT


In the absence of an applied magnetic field, the magnetic moments of hydrogen nuclei are randomly orientated and produce no overall magnetic effect. However, when placed in a strong static external magnetic field (shown as a white arrow on Figure 1.3 and termed B0), the magnetic moments of hydrogen nuclei orientate with this magnetic field. This is called alignment. Alignment is best described using classical and quantum theories as follows.

Image described by caption and surrounding text.

Figure 1.3 Alignment – classical theory.


Classical theory uses the direction of the magnetic moments of spins (hydrogen nuclei) to illustrate alignment.



  • Parallel alignment: Alignment of magnetic moments in the same direction as the main B0 field (also referred to as spin-up).
  • Antiparallel alignment: Alignment of magnetic moments in the opposite direction to the main B0 field (also referred to as spin-down) (Figure 1.3).

After alignment, there are always more spins with their magnetic moments aligned parallel than antiparallel. The net magnetism of the patient (termed the net magnetic vector, NMV) is therefore aligned parallel to the main B0 field in the longitudinal plane or z-axis.


Quantum theory uses the energy level of the spins (or hydrogen nuclei) to illustrate alignment. Protons of hydrogen nuclei couple with the external magnetic field B0 (termed Zeeman interaction) and cause a discrete number of energy states. For hydrogen nuclei, there are only two possible energy states (Figure 1.4):



  • Low-energy nuclei do not have enough energy to oppose the main B0 field (shown as a white arrow on Figure 1.4). These are nuclei that align their magnetic moments parallel or spin-up to the main B0 field in the classical description (shown in blue in Figure 1.4).
  • High-energy nuclei do have enough energy to oppose the main B0 field. These are nuclei that align their magnetic moments antiparallel or spin-down to the main B0 field in the classical description (shown in red in Figure 1.4).
Image described by caption and surrounding text.

Figure 1.4 Alignment – quantum theory.


Quantum theory explains why hydrogen nuclei only possess two energy states – high or low (Equation (1.1)). This means that the magnetic moments of hydrogen spins only align in the parallel or antiparallel directions. They cannot orientate themselves in any other direction. The number of spins in each energy level is predicted by the Boltzmann equation (Equation (1.2)). The difference in energy between these two states is proportional to the strength of the external magnetic field (B0) (ΔE in the Boltzmann equation). As B0 increases, the difference in energy between the two energy states increases, and nuclei therefore require more energy to align their magnetic moments in opposition to the main field. Boltzmann’s equation also shows that the patient’s temperature is an important factor that determines whether a spin is in the high- or low-energy population. In clinical imaging, however, thermal effects are largely discounted, as the patient’s temperature is usually similar inside and outside the magnetic field. This is called thermal equilibrium.










Equation 1.1
Number of energy states = 2S + 1 S is the spin quantum number. The value of S for hydrogen is ½ This equation explains why hydrogen can only possess two energy states. If S = ½, then the number of energy states is 2 × ½ + 1 = 2

Mar 9, 2019 | Posted by in MAGNETIC RESONANCE IMAGING | Comments Off on Basic principles
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