Introduction 1 Atomic structure 1 Motion in the atom 2 MR active nuclei 2 The hydrogen nucleus 4 Alignment 4 Precession 8 The Larmor equation 9 Resonance 11 The MR signal 15 The free induction decay signal (FID) 16 Relaxation 16 T1 recovery 16 T2 decay 16 Pulse timing parameters 19
Introduction
The basic principles of magnetic resonance imaging (MRI) form the foundation for further understanding of this complex subject. It is important that these ideas are fully grasped before moving on to areas that are more complicated. There are essentially two ways of explaining the fundamentals of MRI: classically and via quantum physics. Any discussion requires both, so we have attempted to integrate the two versions. Within this chapter, the properties of atoms and their interactions with magnetic fields, excitation and relaxation are discussed.
Atomic structure
All things are made of atoms, including the human body. Atoms are very small. Half a million lined up together are narrower than a human hair. Atoms are organized in molecules, which are two or more atoms arranged together. The most abundant atom in the body is hydrogen. This 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. The atomic number is the sum of the protons in the nucleus. This number gives an atom its chemical identity. The mass number is the sum of the protons and neutrons in the nucleus. The number of neutrons and protons in a nucleus are 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. Nuclei with an odd mass number (a different number of protons to neutrons) are important in MRI (see later).
Electrons are particles that spin around the nucleus. Traditionally this is thought of as being analogous to planets orbiting around the sun. In reality, electrons exist around the nucleus in a cloud; the outermost dimension of the cloud is the edge of the atom. The position of an electron in the cloud is not predictable as it depends on the energy of an individual electron at any moment in time (physicists call this Heisenberg's Uncertainty Principle). The number of electrons, however, is usually the same as the number of protons in the nucleus.
Protons have a positive electrical charge, neutrons have no net charge and electrons are negatively charged. So 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 external energy to knock out electrons from the atom. This causes a deficit in the number of electrons compared with protons and causes electrical instability. Atoms in which this has occurred are called ions.
Motion in the atom
Three types of motion are present within the atom (Figure 1.1). These are:
• 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. This spin derives from the individual spins of protons and neutrons within the nucleus. Pairs of subatomic particles automatically spin in opposite directions but at the same rate as their partners. In nuclei that have an even mass number, i.e. the number of protons equals the number of neutrons, half spin in one direction and half in the other. The nucleus itself has no net spin. However, in nuclei with odd mass numbers, i.e. where the number of neutrons is slightly more or less than the number of protons, spin directions are not equal and opposite, so the nucleus itself has a net spin or angular momentum. 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 electrical charge. The law of electromagnetic induction (set out by Michael Faraday in 1833) refers to three individual forces – motion, magnetism and charge – and states that if two of these are present, then the third is automatically induced. MR active nuclei that have a net charge and are spinning (motion), automatically acquire a magnetic moment and can align with an external magnetic field.
Important examples of MR active nuclei, together with their mass numbers are listed below:
hydrogen 1 carbon 13 nitrogen 15 oxygen 17 fluorine 19 sodium 23 phosphorus 31
Although neutrons have no net charge, their subatomic particles are not evenly arranged over the surface of the neutron and this imbalance enables the nucleus in which the neutron is situated to be MR active as long as the mass number is odd. Alignment is measured as the total sum of the nuclear magnetic moments and is expressed as a vector quantity. The strength of the total magnetic moment is specific to every nucleus and determines the sensitivity to magnetic resonance.
The hydrogen nucleus
The isotope of the hydrogen nucleus called protium is the MR active nucleus used in clinical MRI. This contains a single proton (atomic and mass number 1). It is used because hydrogen is very abundant in the human body, and because its solitary proton gives it a relatively large magnetic moment. Both of these characteristics enable utilization of the maximum amount of available magnetization in the body. From now on in this book when the terms spin, nucleus or hydrogen nucleus are used we are referring to this particular isotope of hydrogen.
The hydrogen nucleus as a magnet
The laws of electromagnetism state that a magnetic field is created when a charged particle moves. The hydrogen nucleus contains one positively charged proton that spins, i.e. it moves. Therefore the hydrogen 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 the classical theory of the principles of MRI. The magnetic moment of each nucleus has vector properties, i.e. it has size and direction and is denoted by an arrow. The direction of the vector designates the direction of the magnetic moment, and the length of the vector designates the size of the magnetic moment as in Figure 1.2.
Alignment
In the absence of an applied magnetic field, the magnetic moments of the hydrogen nuclei are randomly orientated. 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 the hydrogen nuclei align with this magnetic field. Some of the hydrogen nuclei align parallel with the magnetic field (in the same direction), while a smaller number of the nuclei align anti-parallel to the magnetic field (in the opposite direction) as in Figure 1.3.
Quantum theory (first discovered by Max Planck in 1900) describes the properties of electromagnetic radiation in terms of discrete quantities of energy called quanta. Applying quantum theory to MRI, hydrogen nuclei possess energy in two discrete quantities or populations termed low and high (Figure 1.4). Low-energy nuclei align their magnetic moments parallel to the external field (shown as a white arrow on Figure 1.4) and are termed spin-up nuclei (shown in blue in Figure 1.4). High-energy nuclei align their magnetic moments in the anti-parallel direction and are termed spin-down nuclei (shown in red in Figure 1.4).
The factors affecting which hydrogen nuclei align parallel and which align anti-parallel are determined by the strength of the external magnetic field and the thermal energy level of the nuclei. Low thermal energy nuclei do not possess enough energy to oppose the magnetic field in the anti-parallel direction. High thermal energy nuclei, however, do possess enough energy to oppose this field, and as the strength of the magnetic field increases, fewer nuclei have enough energy to do so. The thermal energy of a nucleus is mainly determined by the temperature of the patient. In clinical applications this cannot be significantly altered and is not important. This is called thermal equilibrium. Under these circumstances it is the strength of the external field that determines the relative quantities of spin-up to spin-down nuclei.
In thermal equilibrium there are always fewer high-energy nuclei than low-energy nuclei, therefore the magnetic moments of the nuclei aligned parallel to the magnetic field cancel out the smaller number of magnetic moments aligned anti-parallel. As there is a larger number aligned parallel, there is always a small excess in this direction that produces a net magnetic moment (Figure 1.5). Other MR active nuclei also align with the magnetic field and produce their own small net magnetic moments.
These magnetic moments are not used in clinical MRI because they do not exist in enough abundance in the body to be imaged adequately, as their net magnetic moments are very small. The net magnetic moment of hydrogen, however, produces a significant magnetic vector that is used in clinical MRI. This is called the net magnetization vector (NMV) and reflects the relative balance between spin-up and spin-down nuclei.
Precession
Each hydrogen nucleus is spinning on its axis as in Figure 1.6. The influence of B0 produces an additional spin or wobble of the magnetic moments of hydrogen around B0. This secondary spin is called precession and causes the magnetic moments to follow a circular path around B0. This path is called the precessional path and the speed at which they wobble around B0 is called the precessional frequency. The unit of precessional frequency is megahertz (MHz) where 1Hz is one cycle or rotation per second and 1MHz is one million cycles or rotations per second.
Combining Figure 1.6 with what we now know about quantum physics, it is possible to appreciate that there are two populations of hydrogen nuclei: some high-energy, spin-down nuclei and a greater number of low-energy, spin-up hydrogen nuclei. The magnetic moments of all these nuclei precess around B0 on a circular precessional path (Figure 1.7).
The Larmor equation
The value of the precessional frequency is governed by the Larmor equation. The Larmor equation states that:
ω0 = B0 x λ
where:
ω0 is the precessional frequency
B0 is the magnetic field strength of the magnet
λ is the gyromagnetic ratio.
The gyromagnetic ratio expresses the relationship between the angular momentum and the magnetic moment of each MR active nucleus. It is constant and is expressed as the precessional frequency of a specific MR active nucleus at 1T. The unit of the gyromagnetic ratio is therefore MHz/T.
The gyromagnetic ratio of hydrogen is 42.57MHz/T. Other MR active nuclei have different gyromagnetic ratios, so have different precessional frequencies at the same field strength. In addition, hydrogen has a different precessional frequency at different field strengths. For example:
• at 1.5T the precessional frequency of hydrogen is 63.86MHz (42.57MHz x 1.5T)
• at 1.0T the precessional frequency of hydrogen is 42.57MHz (42.57MHz x 1.0T)
• at 0.5T the precessional frequency of hydrogen is 21.28MHz (42.57MHz x 0.5T).
The precessional frequency is often called the Larmor frequency, because it is determined by the Larmor equation.
Resonance
Resonance is a phenomenon that occurs when an object is exposed to an oscillating perturbation that has a frequency close to its own natural frequency of oscillation. When a nucleus is exposed to an external perturbation that has an oscillation similar to its own natural frequency, the nucleus gains energy from the external force. The nucleus gains energy and resonates if the energy is delivered at exactly the same precessional frequency. If energy is delivered at a different frequency to that of the Larmor frequency of the nucleus, resonance does not occur.
Energy at the precessional frequency of hydrogen at all field strengths in clinical MRI corresponds to the radio frequency (RF) band of the electromagnetic spectrum (Figure 1.8). For resonance of hydrogen to occur, an RF pulse of energy at exactly the Larmor frequency of hydrogen must be applied. Other MR active nuclei that have aligned with B0 do not resonate, because their precessional frequencies are different to that of hydrogen. This is because their gyromagnetic ratios are different to that of hydrogen.
The application of an RF pulse that causes resonance to occur is termed excitation. This absorption of energy causes an increase in the number of spin-down hydrogen nuclei populations as some of the spin-up (shown in blue in Figure 1.9) nuclei gain energy via resonance and become high-energy nuclei (shown in red in Figure 1.9). The energy difference between the two populations corresponds to the energy required to produce resonance via excitation. As the field strength increases, the energy difference between the two populations also increases so that more energy (higher frequencies) are required to produce resonance.
The results of resonance
One of the results of resonance is that the NMV moves out of alignment away from B0. This occurs because some of the low-energy nuclei are given enough energy via resonance to join the high-energy population. As the NMV reflects the balance between the low and high-energy populations, resonance causes the NMV to no longer lie parallel to B0 but at an angle to it. The angle to which the NMV moves out of alignment is called the flip angle (Figure 1.10). The magnitude of the flip angle depends on the amplitude and duration of the RF pulse. Usually the flip angle is 90°, i.e. the NMV is given enough energy by the RF pulse to move through 90° relative to B0. However, as the NMV is a vector, even if flip angles other than 90° are used, there is always a component of magnetization in a plane perpendicular to B0.
• B0 is now termed the longitudinal plane.
• The plane at 90° to B0 is termed the transverse plane.
With a flip angle of 90 the nuclei are given sufficient energy so that the longitudinal NMV is completely transferred into a transverse NMV. This transverse NMV rotates in the transverse plane at the Larmor frequency. When flip angles less than 90° are used, only a portion of the NMV is transferred to the transverse plane. This represents a smaller number of low-energy spins becoming high-energy spins as a result of excitation. If flip angles greater than 90 are used, this represents a larger number of high-energy spins to low-energy spins. The NMV merely reflects the balance between the spin-up to spin-down populations.
The other result of resonance is that the magnetic moments of hydrogen nuclei move into phase with each other. Phase is the position of each magnetic moment on the precessional path around B0. Magnetic moments that are in phase (or coherent) are in the same place on the precessional path around B0 at any given time. Magnetic moments that are out of phase (or incoherent) are not in the same place on the precessional path. When resonance occurs, all the magnetic moments move to the same position on the precessional path and are then in phase (Figure 1.11).
(Continues...)
Excerpted from MRI in Practice by Catherine Westbrook Carolyn Kaut Roth John Talbot Copyright © 2011 by Blackwell Publishing Ltd.. Excerpted by permission of John Wiley & Sons. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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