When a person is placed into the bore of the magnet, his or her protons will align in the direction of the main magnetic field. Magnetic moments are not stationary; they precess about the z axis. But because the protons lack phase coherence, the transverse component of their magnetic moments are completely random and sum to zero. Therefore, the net magnetization is completely longitudinal. Longitudinal magnetization is static, and therefore no signal is measurable.

The orientation of any magnet can be influenced simply by exposure to a magnetic field oriented in a different direction (Figure I2-1). Radiofrequency (RF) excitation operates on this principle. An RF pulse is a relatively weak magnetic field oriented in the xy plane that pulls the magnetic moments away from the longitudinal direction toward the transverse plane. Distinct from B₀, the magnetic field of the RF pulse is referred to as B₁ (“B one”).

In addition to tipping the magnetization into the transverse plane, the RF pulse also achieves phase coherence. This means that with RF excitation, all the magnetic moments of the protons precess together around the z axis at 64 MHz (Figure I1-11). Because of the properties of electromagnetic induction, a coherent M_xy can induce an oscillating current in a nearby receiver coil. Hence, an RF pulse creates MR signal by converting static longitudinal magnetization into coherently precessing transverse magnetization.

There is one additional condition necessary for RF excitation. In the superconducting magnet, even though the net magnetization, M, is a stationary vector aligned with the z axis, the individual magnetic moments (μ) precess around the z axis at the Larmor frequency, or about 64 MHz at 1.5 T. For the RF pulse to have any effect on these protons, B₁ must also spin around the z axis at the same 64 MHz frequency. In other words, B₁ must resonate with the protons, as in “Magnetic Resonance Imaging.” As long as the B₁ magnetic field rotates around the xy plane at the same frequency as the protons are precessing, it will be able to engage and pull the magnetization vector down toward the xy plane (Figure I2-2).

When B₁ resonates with the precessing protons, it causes M to be tipped away from the z axis and into the xy plane. Protons that are not precessing at the same frequency as B₁ will not be affected. This observation has important implications. To excite all the protons in the field of view with an RF pulse at 64 MHz, all the protons must precess at 64 MHz. For this to occur, the magnetic field must be exactly 1.5 T throughout the field of view. Magnetic field inhomogeneity, either intentional (created by the use of gradient coils) or unintentional (created by metal in the subject’s body, for example), will cause protons to deviate from the expected Larmor frequency. Then, only the subset of the protons that still precess at 64 MHz will be excited. Consequently, B₀ inhomogeneity can be a substantial source of image artifacts (Figure I2-3). However, under
certain circumstances, the necessity for resonance can also be used to advantage, for example, in the selective excitation of single slices of tissue (Chapter I-5).

The flip angle, α (alpha), is defined as the angle the magnetization vector is tipped away from the z axis by the RF pulse (Figure I2-4). For example, if the the flip angle is 10 or 15°, the magnetization vector is tipped only slightly away from the z axis. A flip angle of 90° tips the vector completely into the xy plane. Once tipped, the magnetization vector precesses around the z axis at the Larmor frequency (Figure I2-4).

The amount of measurable signal resulting from an RF excitation pulse is equal to the transverse component of M, M_xy. The longitudinal component, M_z, reflects the signal that is available for measurement following the next RF pulse. From Chapter I-1, Figure I1-5,

M_xy = M sin α

M_z = M cos α

The magnetization vector can also be tipped beyond the xy plane to angles greater than 90°. For example, if tipped 180°, M is longitudinal but points in the opposite direction along the z axis (Figure I2-4). How a rotating magnetic field in the xy plane can cause protons to flip 180° will be explained in the next section.

It is also worth noting that repeatedly tipping the magnetization with several RF pulses in rapid succession causes a cumulative increase in the flip angle that is the sum of each individual RF pulse’s effect. For example, if three identical 15° RF pulses are applied back-to-back, then the net effect would be a 45° flip angle. Similarly, if the vector is tipped 180° and then tipped another 180°, for a total of 360°, the magnetization vector will again be at 0° or back where it started.

Sometimes it is useful to consider the flip angle in terms of its fraction of a full 360° cycle. For example, a 90° flip angle represents one-quarter of a cycle, while 45° is one-eighth of a cycle.

To understand how to achieve a desired flip angle, a more thorough explanation of the RF pulse is needed.

RF excitation can be thought of as a magnetic field, B₁, rotating in the xy plane at the Larmor frequency. To simplify
matters, it can be helpful to ignore the rotational behavior of B₁ and simply consider it to be a stationary magnetic field, say along the x axis (Figure I2-5). (This is sometimes referred to as a “rotating frame of reference.”) As soon as B₁ is turned on, the net magnetization will be inclined to align in the same direction as B₁. The main magnetic field, B₀, is still on, of course, and so the protons remain primarily aligned in the z-axis direction. Nevertheless, B₁ will have a real, albeit small, effect on magnetization.

How can magnetic moments precess around the axis of B₁

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