Interaction of the Nuclear Spin with Magnetic Fields

MRI requires that the signal-generating protons be placed in a strong static magnetic field. It is conventional to denote the applied magnetic field by a vector quantity, B0. The typical magnetic field strength used in brain imaging is 1.5 T (approximately 30,000 times stronger than the earth's magnetic field). The spatial

Proton Parallel Antiparallel
Figure 1 Key concepts related to MRI signal creation.

homogeneity of the magnetic field also plays an important role in defining feasibility of imaging. Typically, the magnetic field must vary less than 100 parts per million (ppm) over the entire brain volume and less than about 1 ppm over any particular imaging voxel. An important attribute of MRI is that the magnetic field readily penetrates bony structures, permitting MRI to "see" the brain through the bony cranium.

C. The Larmor Relationship

Figure 1 illustrates how the proton nuclear spins (equivalent to spinning bar magnets) behave in an imposed magnetic field. They tend to align parallel to (with) or antiparallel to (against) the magnetic field. Such behavior is readily appreciated when two magnets are manipulated in the macroscopic world. When a smaller magnet is placed inside a larger one, the smaller magnet's north pole tends to point toward the north pole of the larger magnet. ''North to south'' orientation has some stability, but a perpendicular orientation of the two magnets is highly unstable. In the quantum world, magnetic alignments are expressed in terms of their probabilities. Alignment in the parallel configuration is only slightly more probable compared to that of the antiparallel configuration. Furthermore, in the quantum world, the alignment is not perfect. The spin causes the nuclear magnet to ''precess'' about the applied magnetic field at a constant angle in each of the two allowed configurations. The precession frequency, n, (the number of precession cycles per second), is a linear function of the applied magnetic field n = gBo

Precession characteristics such as these are found in everyday mechanical systems (e.g., gyroscopes). The relationship between the precession frequency and the applied magnetic field on the orbital motion of an electron was described in 1897 by Sir Joseph Larmor. Accordingly, even in the context of MRI, the expression that relates precessional frequency to magnetic field strength is known as the Larmor relationship. The Larmor relationship indicates that the precession frequency is directly proportional to the magnetic field strength, with g (the gyromagnetic ratio) being a constant of proportionality that is a unique property of the type of nucleus. For the proton, g is approximately 42 million cycles per second per Tesla. Therefore, the characteristic frequency at which the nuclear spins precess about the commonly used applied magnetic field strength (1.5 T) is 63.8 MHz.

D. Behavior of Large Ensembles of Nuclear Spins

A single nuclear spin would produce a signal that is far too weak to detect. Therefore, it is necessary to consider how large numbers of nuclear spins behave in a collective sense to understand how a measurable MRI signal is produced. It is the 1020 protons in the typical MRI voxel that produce the signal used for image formation. Some of the spins are oriented antiparallel to the applied field, whereas others are oriented parallel to the applied field (Fig. 2). Nature tends to favor the parallel configuration because this represents an energetically more stable (lower energy) state. However, the two possible configurations do not differ to a great extent in their energy stability, and there are almost equal numbers of spins in the two configurations. The magnetic field from each of the spins in the antiparallel configuration is canceled by a spin in the parallel configuration, but there are spins in the parallel configuration that not canceled by antiparallel spins. These ''uncanceled'' parallel spins act cohesively as an ensemble. They collectively behave as a bar magnet oriented perfectly parallel with B0. It is common practice to refer to the magnetic properties of the ensemble as the ''bulk nuclear spin magnetization'' or ''magnetization.'' The angle between the magnetization and B0 is lost because each nuclear spin precesses about the applied field independently of the others. Nature imposes no constraints on where along

Figure 2 Ensembles of nuclear spins create a magnetization parallel to the applied magnetic field.

each precession circle each spin happens to be, and the transverse component nuclear spin magnetization perpendicular to B0 is zero. It is important to also emphasize that the bulk magnetization produced by an ensemble of many nuclear spins behaves differently than does the spin magnetization from a single spin. The bulk magnetization from an ensemble of nuclear spins can attain any arbitrary orientation relative to B0. Its behavior is not "quantized" as is the case for a single spin's magnetization.

E. The Magnetic Resonance Signal

In MRI, images are formed from the electrical "signals" generated by each of the volume elements in the tissue. The bulk magnetization resultant from the ensemble of spins in each of the volume elements generates the MRI signals. In order to detect the MRI signal, it is necessary to first disturb the bulk magnetization away from the equilibrium configuration shown in Figure 2. This is done using a radiofrequency (RF) transmitter pulse (Fig. 3). The working part of the RF pulse is a second magnetic field, which is usually referred to as Bx. The magnetic field differs from B0 in that it oscillates. In order to be effective, must oscillate at a frequency that is very near to the

Larmor frequency (e.g., 63.8 MHz for 1.5 T). When this is the case, there is a coupling between B1 and the nuclear spin precessions that causes the bulk magnetization to be rotated away from its equilibrium position toward the transverse plane perpendicular to B0. Energy from the B1 field is used to excite the magnetization to a nonequilibrium configuration. Figure 3 shows the result of a 90° pulse in which the magnetization is twisted through an angle of 90° into the transverse plane. Coupling between the bulk magnetization and a B1 field having the appropriate oscillatory frequency is an example of the phenomenon known in physics as resonance. The oscillatory B1 field is created by the flow of alternating electric current through a coil of wire (i.e., the RF coil) that is placed near the tissue being imaged. The alternating electric current frequency must be very near the Larmor frequency (typically 63.8 MHz) to create the appropriate oscillation frequency for B1. Use of RF is a central part of radio and television broadcasting; therefore, one often hears that MRI results from an interaction between "radio waves'' and nuclear spins. However, as has already been stated, only oscillating magnetic fields are used in MRI, and it is not correct to state that radio waves are used in MRI.

Once the magnetization has been disturbed as shown in Fig. 3, it precesses about the transverse plane

Figure 3 Perturbation of the magnetization with a radiofrequency pulse and the resultant free induction decay signal.

at the Larmor frequency. This precessional motion can be detected with a coil of wire (i.e., the RF coil) that is placed near the tissue of interest. The motion of the magnetization generates a voltage oscillating at the Larmor frequency in the coil. Therefore, one can describe the phenomenon by saying that the nuclear spins transmit a radio frequency signal on a characteristic radio "channel" that is detected by the MRI scanner. Note, however, that radio waves per se are not involved in this signal-generation process. The signal subsequently decays as illustrated in the graph shown in Fig. 3. The maximal signal amplitude (voltage) is proportional to the magnetization, which in turn is principally dependent on the number of nuclear spins in the ensemble, although other factors (described later) also play a role. The MRI signal that results immediately from a 90° pulse is known as a free induction decay (FID). It is often advantageous to cause the signal to appear sometime after the transmitter RF pulse is finished. One way of doing this is to form a spin echo. Spin echo MRI signals oscillate at the Larmor frequency just as FID signals do. However, they build up and then disappear at some defined period of time after the transmitter pulse is completed (Fig. 4). The time that elapses between the initial transmitter pulse and the formation of the echo is known as the time-to-echo (TE). The amplitude of the spin echo signal decays as the TE is progressively lengthened, as illustrated in the graph shown in Fig. 4. This will be discussed in more detail later.

Formation of a spin echo requires the use of two RF pulses given in a carefully prescribed manner. A series of pulses is referred to as a pulse sequence. In a broader sense, pulse sequences, which can be quite complicated, are frequently used in MRI to manipulate the magnetization in a defined manner so as to accentuate certain aspects of the MRI signal or for developing contrast. The spin echo pulse sequence is one of the simplest of a large and growing body of MRI pulse sequences.

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