# Spatial encoding

5
Spatial encoding

After reading this chapter, you will be able to:

• Describe gradients and how they work.
• Explain slice-selection.
• Understand how gradients spatially locate signal in a slice.
• Apply what you have learned to explore how gradients are used in common pulse sequences.

## INTRODUCTION

In Chapter 1, we learned that a radio frequency (RF) excitation pulse is applied at 90° to B0 at the precessional frequency of the magnetic moments of hydrogen nuclei to cause them to resonate. The RF excitation pulse gives energy to the hydrogen nuclei. This creates magnetization in the transverse plane and puts individual magnetic moments of hydrogen nuclei into phase. The resultant coherent transverse magnetization precesses at the Larmor frequency of hydrogen in the transverse plane.

A voltage or signal is therefore induced in the receiver coil positioned in the transverse plane. It is caused by oscillation of coherent transverse magnetization relative to the receiver coil. This signal is an alternating voltage that has a frequency equal to the Larmor frequency regardless of the origin of signal. As all magnetic moments precess at the same frequency, all signals oscillate at the same frequency so the system cannot spatially locate it. In other words, the MRI system has no idea where individual signals are coming from because they all have the same frequency.

To produce an image, the MRI system must calculate how much signal is coming from each three-dimensional location in the patient. This location is called a voxel. The simplest way to do this is to first locate a slice and then locate signal at each two-dimensional location within it. This location is called a pixel. The process is called spatial encoding, and it is performed by gradients. In this chapter, the mechanisms of gradients are discussed in relation to spatial encoding. Scan tips are also used to link the theory of spatial encoding to practice.

## MECHANISM OF GRADIENTS

The concept of gradients was first introduced in Chapter 4 and is further discussed in Chapter 9. When no gradient is applied, all magnetic moments of the hydrogen nuclei precess at the same frequency as they experience the same field strength (in fact inhomogeneities in the field cause magnetic moments to precess at slightly different frequencies, but these changes are relatively small compared with those imposed by a gradient). To locate individual signals, the main magnetic field is altered so that it slopes in a linear and, therefore, predictable way. Graded or sloped magnetic fields are generated by cylindrical electromagnets situated in the warm bore of the cryostat. These coils are called gradient coils, and, at certain time points within a pulse sequence, current is passed through each of these coils. According to Faraday’s law of electromagnetic induction, when current is passed through a gradient coil, a magnetic field is induced around it (see Chapter 1). This magnetic field is superimposed onto the main magnetic field (B0) in such a way that the magnetic field strength along the axis of the gradient coil is sloped.

Look at Figures 5.1 and 5.2. In Figure 5.1, a gradient is applied that increases the magnetic field strength toward the right-hand side of the magnet (shown in red) and decreases it toward the left-hand side (blue). Figure 5.2 shows that the gradient coil has three terminals, one at each end of the coil and one in the middle. Current is passed through these terminals into the gradient coil. These terminals enable control of the direction of the current flowing through the gradient coil. This, in turn, determines gradient polarity. The polarity of a gradient depends on which end of the gradient magnetic field is higher than B0 and which is lower. If current flows clockwise through the coil, then the magnetic field induced around the coil adds to B0. This increases the magnetic field strength relative to B0. If the current flows anticlockwise through the coil, then the magnetic field induced around the coil subtracts from B0 and decreases the magnetic field strength relative to B0. The middle of the axis of the gradient remains at the field strength of the main magnetic field even when the gradient is switched on. This is called the magnetic isocenter.

Therefore, to achieve the gradient polarity shown in Figure 5.1, current is applied clockwise through the gradient coil on the right-hand side of Figure 5.2 from the center to the right-hand terminal. The current is also applied anticlockwise through the gradient coil on the left-hand side of Figure 5.2 from the center to the left-hand terminal. The combination of these two currents produces a linear alteration in (or sloped) magnetic field strength from a low magnetic field on the left that gradually increases to the right. In all gradient diagrams in this book, gradient fields higher than the magnetic isocenter are shown in red and those lower in blue.

The Larmor equation states that the precessional frequency of magnetic moments of hydrogen nuclei increases or decreases depending on the magnetic field strength they experience at different points along the gradient (see Figure 5.1). The precessional frequency increases when the magnetic field increases, and decreases when the magnetic field decreases. Magnetic moments of hydrogen nuclei experiencing an increased field strength due to the gradient speed up, i.e. their precessional frequency increases. Magnetic moments of hydrogen nuclei experiencing a decreased magnetic field strength slow down, i.e. their precessional frequency decreases. Therefore, the position of a spin located along a gradient is identified according to the precessional frequency of its magnetic moment (Table 5.1) (Equation (5.1)). The changes in field strength and therefore frequency imposed by gradients are quite small. They usually vary the magnetic field and therefore the frequency of magnetic moments of spins located along them by less than 1% .

Gradients also cause magnetic moments of the hydrogen nuclei to change phase. This is because as the frequency of magnetic moments increases they, gain phase relative to the magnetic moments of other hydrogen nuclei. Likewise, as the frequency of magnetic moments decreases, they lose phase relative to the magnetic moments of other hydrogen nuclei. The watch analogy discussed in Chapter 1 comes in handy when learning about gradients and understanding why they alter frequency and phase. Imagine that the magnetic moments of hydrogen nuclei sitting along a gradient are watches. When no gradient is switched on, the precessional frequency of the hands of these watches is the same because they all experience the same field strength (B0).

Imagine that the gradient illustrated in Figure 5.1 is switched on. At the magnetic isocenter, the hands of the watch at this location continue to precess at the same frequency as they were precessing when there was no gradient. This is because there is no change in field strength at the isocenter even when gradients are applied. However, the watches situated to the right-hand side of the magnetic isocenter experience a progressively increased magnetic field strength. As precessional frequency is proportional to the magnetic field strength, the hands of these watches precess increasingly faster and therefore tell a time ahead of the watch located at the magnetic isocenter. This means that they gain phase relative to the watch at the magnetic isocenter.

Similarly, the watches situated to the left-hand side of the magnetic isocenter experience a progressively decreased magnetic field strength. As precessional frequency is proportional to the magnetic field strength, the hands of these watches precess increasingly slower, and therefore they tell a time behind that of the watch located at the magnetic isocenter. This means that they lose phase relative to the watch at the magnetic isocenter. The farther away from the magnetic isocenter a watch is located, the greater the difference in time (either ahead or behind) between them and the watch at the magnetic isocenter. The degree of difference depends on the amplitude or steepness of the gradient.

Gradient amplitude determines the rate of change of the magnetic field strength along the gradient axis. Steep gradient slopes alter the magnetic field strength between two points more than shallow gradient slopes. Steep gradient slopes therefore alter the precessional frequency of magnetic moments of hydrogen nuclei between two points more than shallow gradient slopes (Figure 5.3). Another way of saying this is that steep gradient slopes cause a large difference in precessional frequency and therefore phase between the magnetic moments of hydrogen nuclei situated along the gradient. Shallow gradient slopes cause a small difference in precessional frequency and therefore phase between the same two points.

There are three gradient coils situated within the bore of the magnet, and these are named according to the axis along which they act when they are switched on. Figure 5.4 shows these directions in a typical superconducting magnet. However, some manufacturers may use a different system, so it is important to check the convention on your scanner.

• The z gradient alters the magnetic field strength along the z-(long) axis of the magnet (from head to foot of the patient).
• The y gradient alters the magnetic field strength along the y-(vertical) axis of the magnet (from the back to the front of the patient).
• The x gradient alters the magnetic field strength along the x-(horizontal) axis of the magnet (from right to left of the patient) (Table 5.3).

The magnetic isocenter is the center point of the axis of all three gradients and the bore of the magnet. The magnetic field strength and therefore the precessional frequency and phase remain unaltered here even when the gradients are applied. Permanent magnets (see Chapter 9) have different axes. The z-axis is vertical, not horizontal, as shown in Figure 5.4.

Gradients perform many important tasks during a pulse sequence as described in Chapters 3 and 4. Can you remember what these are? Gradients are used to either dephase or rephase the magnetic moments of nuclei. However, gradients also perform the following three main tasks. Their purpose is to spatially locate or encode signal depending on where it is located along these three gradients.

• Slice-selection. Locating a slice within the selected scan plane.
• Spatially locating (encoding) signal along the long axis of the slice – this is called frequency encoding.
• Spatially locating (encoding) signal along the short axis of the slice – this is called phase encoding.

Now let’s explore each of these processes in turn.

## SLICE-SELECTION

### How does it work?

When a gradient coil is switched on, the magnetic field strength and therefore the precessional frequency of magnetic moments of hydrogen nuclei located along its axis are altered in a linear and predictable way. Therefore, magnetic moments of hydrogen nuclei located at any point along the axis of the gradient have a specific precessional frequency, and this is dependent on the amplitude of the gradient and the position of the nucleus along the gradient (Equation (5.1)).

A slice is selectively excited by transmitting an RF excitation pulse that is oscillating at the same or similar frequency to the precessional frequency of the magnetic moments of hydrogen nuclei in the slice. Consequently, resonance occurs in these nuclei. Nuclei situated in other slices along the gradient do not resonate because their precessional frequencies are different due to the presence of the gradient.

The selected scan plane determines which of the three gradients performs slice-selection during the RF excitation pulse (Figure 5.6). Typically, they are as follows (although some manufacturers may vary, so please check the convention on your scanner).

• The z gradient alters the field strength and precessional frequency along the z-axis of the magnet and therefore selects axial slices (head to foot of the patient).
• The x gradient alters the field strength and the precessional frequency along the x-axis of the magnet and therefore selects sagittal slices (left to right of the patient).
• The y gradient alters the field strength and the precessional frequency along the y-axis of the magnet and therefore selects coronal slices (back to front of the patient).
• Oblique slices are selected using two or three gradients in combination.