### Learning objectives

After reading this chapter, you should be able:

• To explain the effect of bipolar gradients on the magnetic field, precession frequency and spin phase
• List the stages of spatial encoding in 2D and 3D imaging
• Describe the principle of a selective RF pulse
• Explain the relationship between amplitude, gradient application time and dephasing
• Present the similarities and differences between frequency spatial encoding and phase encoding
• Look at the relationship between spatial encoding and the notion of spatial frequency

### Key points

• Selecting the slice plane and spatial encoding of each voxel involves the use of magnetic field gradients. The intensity of the magnetic field varies regularly along the gradient application axis. These magnetic field gradients are characterized by amplitude(greater or lesser field variation for the same unit of distance), direction, duration and moment of application.
• The slice selection gradient modifies the precession frequency of the protons such that an RF wave of the same frequency will cause them to shift (resonance). The selective pulse bandwith and gradient amplitude will determine the slice thickness.
• The slice selection gradient is simultaneously applied to all the RF pulses.
• The phase encoding gradient (GPE) differentiates the « rows ». GPE is regularly incremented, as many times as there are rows to receive, leading to different phase shifts for each voxe line. The frequency encoding gradient (GFE) differentiates the « columns ». Its application gives distinct frequencies to each voxel column.
• In 3D imaging, more phase encoding steps, applied in the third spatial direction, are added to each of these phase encoding steps, thus lengthening acquisition time. 3D imaging improves spatial resolution and the signal to noise ratio.
• Phase and frequency encoding can be compared to a sieve that is sensitive to spatial distribution, in the horizontal and vertical directions, and whose fineness varies according to gradient value.
• The entire set of data is combined in the RF signal simultaneously received on applying the GFE (still called the readout gradient). All the signals of the same slice are recorded in a matrix then processed to form an image of the slice plane.

### References

1. Elster. Questions and answers in magnetic resonance imaging. 1994:ix, 278 p.
2. McRobbie. MRI from picture to proton. 2003:xi, 359 p.
3. NessAiver. All you really need to know about MRI physics. 1997
4. Kastler. Comprendre l'IRM. 2006
5. Gibby. Basic principles of magnetic resonance imaging. Neurosurgery clinics of North America. 2005 Jan;16(1):1-64.
6. Hennig. K-space sampling strategies. European radiology. 1999;9(6):1020-31.
7. Cox. k-Space partition diagrams: a graphical tool for analysis of MRI pulse sequences. Magn Reson Med. 2000 Jan;43(1):160-2.
8. Paschal and Morris. K-space in the clinic. J Magn Reson Imaging. 2004 Feb;19(2):145-59.