Magnetic Resonance Imaging

Huimin Wu, PhD

LEARNING OBJECTIVES

1. Name the three main types of coils used in a magnetic resonance (MR) scanner.
2. Define the Larmor frequency and its relationship with the static magnetic field.
3. Describe the basic principles of the three main types of MR pulse sequences: spin echo (SE), gradient echo (GE), and inversion recovery (IR).
4. Explain the rationale of parameter selection for an SE pulse sequence to produce T1-, T2-, or proton-weighted images.
5. Identify different types of artifacts on MR images and explain their possible causes.
6. Define specific absorption rate (SAR).
7. Describe the four different MR safety zones.
8. Magnetic resonance imaging (MRI) is a commonly used and highly valued clinical imaging modality, primarily attributed to its offered exquisite soft-tissue contrast through a multitude of mechanisms and its use of nonionizing radiation. The phenomenon of MR is the underlying mechanism of MRI.

BASIC CONCEPTS

Magnetism

Magnetism results from the organized motion of electric charge. Magnetic fields exist as dipoles and are commonly depicted by lines that originate from the North Pole and return to the South Pole with the density of these lines, that is, the number of lines per unit area, proportional to the local field strength (Figure 6.1). Magnetic field strength produced by a dipole, B, decreases approximately as the inverse square of the distance from the dipole. Two commonly used units for B are Tesla (T) and Gauss (G), and 1 T = 10 000 G. The earth’s magnetic field strength is about 0.5 G, whereas that of today’s clinical MR scanners is typically on the order of a few Teslas.

Magnets

All MRI scanners need a main magnet that produces a strong, stable, and homogeneous magnetic field. MRI magnets can be classified into three types by the way the field is generated:

Permanent magnets—They are made of materials magnetized to keep the magnetic field permanently. Permanent magnets use permanently magnetized iron (or other alloys). They require no power consumption, need no cooling, and are of low cost.

Resistive electromagnets—They produce a magnetic field by running electric currents through wirings that are typically iron cored or air cored. These magnets require a large constant flow of current and significant cooling during operation due to electrical resistance of the magnet coils.

FIG. 6.1 • A small magnetic dipole resulting from the spinning of a hydrogen nucleus (proton). It behaves like a bar magnet and can be depicted by field lines going from the north pole to the south pole. Reprinted with permission from Atlas SW. Magnetic Resonance Imaging of the Brain and Spine. 5th ed. Philadelphia, PA: Wolters Kluwer; 2017.

Superconducting electromagnets—Superconductivity is a unique characteristic exhibited by certain types of metals with zero resistance to electric currents when their temperature drops below a critical point close to the absolute zero. A superconducting magnet is built by immersing metal wires made by special alloys like niobium-titanium in liquid helium whose temperature is below 4 K; in this way, electric currents large enough to produce a clinically desired field strength (≥1 T) may run through the wires without overheating issues. Care should be taken to ensure the proper state and temperature of liquid helium because, once its temperature rises above the critical point, resistance heating from the electric current running through the wires will boil the helium and eventually lead to a quench of the system.

Superconducting magnets are predominantly used in diagnostic MR scanners, typically requiring a high field strength (>0.5 T) for sufficient signal-to-noise ratio (SNR). On the other hand, both permanent magnets and resistive electromagnets are mostly seen in low-field systems. Permanent magnets are limited by their bulk and weight, and resistive electromagnets by the maximum currents allowed without generating excessive heat by resistance.

Coils

An MR scanner consists of multiple coils of wire stacked or nested, each serving a different purpose (Figure 6.2).

Main coils

As previously mentioned, the main coils establish the main magnetic field to induce nonzero bulk magnetization as a foundation for signal production. Large currents run through the static coils to produce the desired field strength, typically at 1.5 or 3 T. The static coils are immersed in cryogen, whose temperature is near the absolute zero degree (Figure 6.3).

Shim coils

Shim coils are used to introduce small adjustments to the main magnetic field to increase its homogeneity within the imaging field of view (FOV).

Radiofrequency coils

RF coils transmit and receive signals. The RF transmit coil produces a rotating magnetic field to flip the magnetization. The RF receive coil detects the induced electric current of precessing magnetization via electromagnetic induction. There are volume coils (eg, body coil in Figure 6.2), array coils, and surface coils.

FIG. 6.2 • A simplified illustration of the relative positions of the coils on a cylindrical magnetic resonance scanner, including the main coils (aka the magnet), the shim coils, the gradient coils, and the radiofrequency (RF) coils (denoted as body coil as that is often the built-in RF coil of a system). Reprinted with permission from Garcia MJ. Noninvasive Cardiovascular Imaging: A Multimodality Approach. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2010.

FIG. 6.3 • A cross-sectional view of the surroundings of the main coils on a scanner. Reprinted with permission from Andolina VF, Lillé SL. Mammographic Imaging. 3rd ed. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2011.

Gradient coils

The gradient coils generate linearly varying magnetic fields in multiple dimensions; these gradient fields encode spatial information into the detected signal so that images can be correctly reconstructed. Three sets of gradient coils are typically mounted on an MR scanner, responsible for the gradient fields in the x-, y-, and z-directions separately (Figure 6.4).

Nuclei capable of MR signal production

Atomic and subatomic particles possess a property called spin angular momentum (also known as spin). Nuclear spin is traditionally denoted by the letter I. Protons, neutrons, and electrons all have spin = ½. Nuclei containing even numbers of both protons and neutrons have I = 0. Nuclei with odd numbers of both protons and neutrons have spin quantum numbers that are positive integers. The remaining nuclei (odd/even and even/odd) all have spins that are half integers. Only nuclei with nonzero spins (I ≠ 0) can absorb and emit electromagnetic radiation and undergo “resonance” when placed in a magnetic field. Only a small number of nuclei have the potential for MR signal production, and their values in clinical use are dependent on the strength of the nuclear magnetic moment, the physiologic concentration, and the isotopic abundance.

The nucleus of hydrogen (¹H), or the proton equivalently, becomes the major focus for MR signal production, because of its strong nuclear magnetic moment, its great abundance, and its wide availability in water (˜70% of body weight in an adult) and fat molecules.

Some other nuclei, like ²³Na and ³¹P, have also been used in clinical applications, but their use has been limited primarily due to their low abundance in human body.

While the notion of spin is fundamentally a quantum mechanical concept, one can use classical physics to understand most of the principles of MRI. Consider Figure 6.1, the spin of proton can be seen as a rotation of the nucleus about some axis, giving the proton a magnetic dipole moment (u) similar to a small bar magnet.

FIG. 6.4 • The three sets of gradient coils on a magnetic resonance system, including the z-axis gradient coil (A), the x-axis gradient coil (B), and the y-axis gradient coil (C). The conical arrows indicate the flow of the current in the coils. Note that the x– and y-axis coils are equivalent but rotated by 90°. Reprinted with permission from Bammer R. MR and CT Perfusion and Pharmacokinetic Imaging: Clinical Applications and Theoretical Principles. Philadelphia, PA: Wolters Kluwer; 2016.

Behaviors of spins inside a static magnetic field

Precession

A spin placed inside a static magnetic field,

, experience a torque that is perpendicular to both the magnetic field and angular momentum (Figure 6.5). The torque causes the spin to precess around the direction of the magnetic field similarly as a spinning top precesses around a gravitational field (Figure 6.6). The precessing frequency of the proton, proportional to the applied magnetic field strength, can be characterized by the Larmor equation:

where f is the precession frequency, B₀ is the magnitude of the static magnetic field, and

is a constant called the gyromagnetic ratio that depends on the type of the nucleus. The gyromagnetic ratio for the hydrogen nucleus, or the proton, is 42.58 MHz/T, so the Larmor frequency of the proton on 1.5 and 3 T systems are 42.58 × 1.5 = 63.87 MHz and 42.58 × 3 = 127.68 MHz, respectively.

FIG. 6.5 • Paramagnetic and diamagnetic materials in magnetic fields. Paramagnetic materials increase the local magnetic field, whereas diamagnetic ones decrease the local field. They introduce inhomogeneity into the main magnetic field. Reprinted with permission from Bushberg JT, Seibert JA, Leidholdt EM, Boone JM. Essential Physics of Medical Imaging. 3rd ed. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2012.

The precessing directions of the spins, defined using the right-hand rule, are not the same for all spins. Some spins precess in the direction parallel to that of B₀, whereas others do so in the direction antiparallel. The two different directions, parallel and antiparallel, also correspond to two discrete different energy levels, with the former being the ground state and the latter at a higher level. The energy difference between the two states is proportional to B₀; the higher the field strength, the more energy separation between parallel and antiparallel spins.

FIG. 6.6 • The precession of an individual proton in the presence of an external magnetic field (in analogy to a spin top in the presence of a gravitational field). Reprinted with permission from Berquist TH. MRI of the Musculoskeletal System. 6th ed. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2013; Adapted from Fullerton GD. Basic concepts for nuclear magnetic resonance imaging. Magn Reson Imaging. 1982;1:39-55. Copyright © 1982 Elsevier. With permission.

FIG. 6.7 • The formation of net magnetization. Each proton spin has its magnetic moment (left) inherent to the spin. When there is no external magnetic field, each individual moment has its random orientation, and, as a group together, they show zero net magnetization (middle). When there is an external magnetic field, proton spins align themselves with the field into two groups, one parallel to the external field, and the other antiparallel. There is always, however, a slightly larger number of parallel spins than antiparallel spins at equilibrium (because the parallel spins are at a more stable, lower energy state) and that results in a nonzero net magnetic moment, or magnetization vector, in the direction parallel to the applied external field (right).

FIG. 6.8 • The laboratory versus the rotating frames of reference in the depiction of proton spin’s behaviors. A, The laboratory frame of reference is simply the stationary 3D Cartesian coordinate system, in which the precessing motion of proton spins in a magnetic field are observed. B, The rotating frame of reference is a 3D Cartesian coordinate system that is spinning at the Larmor frequency about the z-axis; the proton spins look stationary to the observer in this frame of reference. The rotating frame of reference is convenient in the understanding of proton spin’s behaviors when the precessing motion is “removed.” Reprinted with permission from Bushberg JT, Seibert JA, Leidholdt EM, Boone JM. Essential Physics of Medical Imaging. 3rd ed. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2012.

Net magnetization

At equilibrium, a slight majority exists in the parallel direction with lower energy. Owing to the excess of protons that precess in the parallel direction, a nonzero net magnetization vector forms as a combination of all individual spins, in the direction parallel to that of the static magnetic field (Figure 6.7). The net magnetization vector is referred to as

, and varies linearly with

. It serves as the source of the MR signal to be detected for imaging purposes.

Frame of reference

Two frames of reference have been used in understanding the behavior of the spins under the influence of static and RF magnetic fields. They are described as follows (Figure 6.8):

The laboratory frame is a stationary reference frame from the observer’s point of view. The sample magnetic moment vector precesses about the z-axis in a circular geometry.
The rotating frame is a spinning axis system, whereby the x′ to y′ axes rotate at an angular frequency equal to the Larmor frequency. In this frame, the sample magnetic moment vector appears to be stationary when precessing at the resonance frequency.

The RF excitation of the magnetization can be more clearly described using the rotating frame of reference, whereas the observed returning signal and its frequency content are explained using the laboratory (stationary) frame of reference.

As a convention, the direction of the applied magnetic field is considered the longitudinal direction, or the z-direction; in cylindrical scanners, this direction aligns with cranial-caudal axis, and is also referred to as the longitudinal axis. The plane perpendicular to the z-direction is the transverse plane in which the x-direction is typically aligned with the left-right direction of human body and the y-direction the anterior-posterior direction.

IMAGE FORMATION

Once nonzero net magnetic vectors are is in place within tissues, the process of image formation ensues by manipulation of these vectors. This process is divided into the following steps: signal production, signal detection, and signal localization.

Signal production

Excitation

Protons precess inside a static magnetic field at a frequency proportional to its strength, B₀; when an additional time-varying magnetic field, often denoted as

, is applied whose oscillation frequency is equal to the precessional frequency of protons, MR occurs involving energy absorption and motion synchronization. The process of the resonance leads to changes in both the z– and the transverse (x–y) components of the net magnetization vector (Figure 6.9), described as follows:

As is applied, , the z-component of the net magnetization vector, initially equal to , first decreases until zero and then increases in the opposite direction until it reaches −. It can be explained as follows. The applied RF magnetic field, , can be considered as a train of energy packets; when the frequency of matches that of the proton precession, the energy of each packet is equal to the difference between the energy levels of parallel and antiparallel spins, and as a result, the low-energy parallel spins will absorb the RF energy and become high-energy antiparallel spins. becomes zero when the parallel and antiparallel spins are equal in number.
In the meantime, , the transverse component of the magnetization vector, increases from zero until it reaches the maximum at . This is due to the synchronization effect has on the precessional phases of individual proton spins. Before is applied, all proton spins are at random phases, and their transverse components cancel out one another. After is applied, its synchronization effect results in coherence in the precessional motion of the spins and a nonzero transverse component.

FIG. 6.9 • A net magnetization vector in a static magnetic field flips away from its initial vertical direction after a second radiofrequency pulse at the Larmor frequency is applied. The trajectory followed by the vector differs because it is observed in the laboratory frame of reference (left) versus the rotating frame of reference (right). The rotating frame of reference is preferred due to the simplified view of the vector’s behaviors. Reprinted with permission from Garcia MJ. Noninvasive Cardiovascular Imaging: A Multimodality Approach. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2010.

In rotating frame, the net magnetization M can be viewed as being progressively tipped away by continuous application of B₁. The flip angle is a quantity that describes the angle between

and the net magnetization vector at the end of the application of

. The flip angle, depending on the needs of different pulse sequences, varies from 0° to 180°. A desired flip angle of

is achieved by varying the strength or the duration of

(Figure 6.10). Following Faraday’s Law of Induction, wherein a changing magnetic field induces a voltage in a nearby conductor, the precessing magnetization induces an electrical current in the receive coil that’s oriented perpendicular to the direction of the main magnetic field. This signal is then amplified, digitized, filtered, and stored as MR signal that will later be used for image reconstruction.

Once the RF field is turned off, the net magnetization vector will return to its equilibrium through a relaxation process. This relaxation process includes two separate subprocesses for

and

, in the longitudinal and transverse dimensions, respectively (Figure 6.11).

Longitudinal relaxation

For

, once the RF field becomes zero, it will recover toward the net magnetization vector at equilibrium,

. The underlying process is the turnover of individual proton spins, from higher energy antiparallel to lower energy parallel by releasing energy into the surrounding environment (often called the lattice). This recovery process, aka the spin-lattice relaxation, involves energy exchange between protons and the surrounding environment following an exponential behavior. The time constant of the relaxation process, defined as the time it takes for

to change from 0% to 63% of

, is T1.

Energy emission from spins to the surrounding environment must be stimulated through encounter of the nucleus with another magnetic field fluctuating near the Larmor frequency. The trend of variation can be explained as follows (Figure 6.12 and Table 6.1):

For tissues of solid type, all the molecules are tightly bound to each other; they form a lattice that vibrates at a narrow range of low frequencies, usually distinctly different from the Larmor frequency, and absorbs only a small fraction of the energy released during the longitudinal relaxation. As a result, such tissues have long T1.

FIG. 6.10 • The flip angle of the net magnetization vector. The flip angle is the angular displacement of the net magnetization vector from its initial or equilibrium position, viewed in the rotating frame. It is determined by both the amplitude and the duration of the applied B₁ field (at the Larmor frequency). The illustrations here include small (A; <45°), large (B; 75°-90°), and common (C; 90° and 180°) angles. Reprinted with permission from Bushberg JT, Seibert JA, Leidholdt EM, Boone JM. Essential Physics of Medical Imaging. 3rd ed. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2012.

For tissues of liquid type, like cerebral spinal fluid, or water itself, all the molecules are nearly free and form a highly loose lattice. Such a lattice allows a wide range of frequencies in their molecular vibration; only a small fraction of these frequencies may be close enough to the Larmor frequency to allow absorption of energy released during the longitudinal relaxation. These tissues too have long T1.
For tissues that exhibit both solid and liquid behaviors, their molecular vibrations have a range of frequencies that are near the Larmor frequency, which leads to the absorption of a substantial amount of energy released during the longitudinal relaxation and therefore a shorter relaxation process back to the equilibrium. These tissues have a short T1 as a result.

FIG. 6.11 • T1 and T2 relaxations as observed in a rotating frame of reference. (A) shows changes in spin magnetization in the rotating frame, and (B) relaxation and decay curves. Reprinted with permission from Bammer R. MR and CT Perfusion and Pharmacokinetic Imaging: Clinical Applications and Theoretical Principles. Philadelphia, PA: Wolters Kluwer; 2016.

T1 is not a constant for the same tissue; it varies by the strength of the static magnetic field, B₀. In general, T1 becomes longer as B₀ increases; longer T1 is expected for the same tissue at 3 T than at 1.5 T.

FIG. 6.12 • Relaxation times (T1 and T2) exhibit trends with tissue types. They are fundamentally affected by tissue characteristics like molecular motion, molecular size, and interactions among molecules. Typically, solid tissues, fluid tissues, and tissues of certain viscosity fall on the left side, the right side, and the middle of the graph, respectively. Reprinted with permission from Bushberg JT, Seibert JA, Leidholdt EM, Boone JM. Essential Physics of Medical Imaging. 3rd ed. Philadelphia, PA: Wolters Kluwer Health/Lippincott Williams & Wilkins; 2012.

Table 6.1 T1 AND T2 VALUES FOR COMMON TYPES OF TISSUES

Tissue	T1 at 0.5 T (ms)	T1 at 1.5 T (ms)	T2 (ms)
Fat	210	260	80
Liver	350	500	40
Muscle	550	870	45
White matter	500	780	90
Gray matter	650	920	100
Cerebrospinal fluid	1800	2400	160

FIG. 6.13 • The comparison of T2 versus T2^* decay. Reprinted with permission from Huda W. Review of Radiologic Physics. 4th ed. Philadelphia, PA: Wolters Kluwer; 2016.

Transverse relaxation

For

, once the RF field is turned off, it will decrease toward zero because of the loss of phase coherence among proton spins. The relaxation process is often called spin-spin relaxation, because it is fundamentally caused by interactions among proton spins. The mechanism of this process is explained as follows:

Recall that spins precess at Larmor frequency, which is determined by the magnetic field they experience. In tissue, the magnetic field that each nucleus experiences is not exactly equal to the externally applied magnetic field B0. This microscopic neighborhood around a spin can cause the spin to experience a field slightly larger or smaller than B0. In addition, the spins in tissue are constantly in random thermal motion, so the microscopic neighborhoods of spins are continuously changing. The net result is that spins being tipped into the transverse plane progressively accumulate different amount of phase due to spatially variant and temporally changing precession frequencies. When the spins get out of synchronization with one another (losing coherence), the net transverse magnetization decays exponentially over time. The time it takes for the transverse magnetization to decrease to 37% of the initial magnetization is referred to as the T2 relaxation time (Figure 6.12).

Like T1, T2 also varies with the tissue type. However, its trend of variation differs from that of T1, which is described as follows (Figure 6.12 and Table 6.1):

For tissues of solid type, there are a large number of interactions among adjacent proton spins at every moment, simply because all the molecules are tightly bound to each other. The proton spins therefore get out of sync in their precession very rapidly, resulting in short T2.

FIG. 6.14 • Spin magnetization and signal reception. Radiofrequency excitation tips a fraction of the equilibrium magnetization into the transverse (x–y) plane. The resulting transverse magnetization

rotates around the main magnetic field

at the Larmor frequency. This rotation and thus temporal change in magnetization direction induce a detectable magnetic resonance (MR) signal in a receive coil surrounding the object or patient. Relaxation effects and inhomogeneity within the imaged sample result in a signal reduction over time, leading to a characteristic MR signal, also referred to as the free induction decay. Reprinted with permission from Bammer R. MR and CT Perfusion and Pharmacokinetic Imaging: Clinical Applications and Theoretical Principles. Philadelphia, PA: Wolters Kluwer; 2016.

For tissues of liquid type, there are few interactions among proton spins at any moment, because the molecules are distant from each other. It therefore takes a long time for the proton spins to lose their coherence, resulting in a long T2.
For tissues that exhibit both solid and liquid behaviors, intermediate T2 constants are expected.

T2, in theory, varies by B₀, but the variation is much smaller than that of T1. T2 is practically considered as constant with respect to B₀. In free induction decay (FID; Figure 6.13), the transverse magnetization diminishes much faster than would be predicted by natural atomic and molecular mechanisms (measured by T2). The factors that exacerbate the decay include B₀ inhomogeneity, susceptibility-induced field distortions produced by the tissue, velocity distribution, etc. The decay due to these macroscopic field disruption factors may be recovered with special designed pulse sequence. The time constant that characterizes the decay from all factors is T2^* (T2^* < T2).

Signal detection

The precessing transverse component of the magnetization (M_xy) can be detected using a receive coil oriented perpendicular to the direction of the main magnetic field (Figure 6.14). They can be the same coil used for producing

, or a dedicated receiving coil. According to Faraday’s Law of Induction, when
a changing magnetic field induces a voltage in a nearby conductor, the precessing magnetization induces an electrical current in the receive coil. This signal is then amplified, digitized, filtered, and stored as MR signal that will later be used for image reconstruction. The produced signal at any time point is a function of both the magnitude and the phase (or the direction) of

at the time point.