## InPlane Imaging Frequency Encoding and Phase Encoding

Once the nuclear spins from a particular slice are excited, it is necessary to have methods of measuring how the MRI signal varies within the imaging plane. For two-dimensional imaging, two orthogonal coordinate directions are interrogated by application of magnetic field gradients that vary along these coordinate directions. Typically, frequency encoding and phase encoding gradients are used. To avoid confusing locations along the two orthogonal axes, the frequency encoding and phase encoding gradients are applied at different times during the pulse sequence. Figure 9 illustrates the general concepts. A magnetic field gradient is imposed such that the signal frequency is higher on the left compared to the right. (Note that it is customary in MRI to display the subject's left on the viewer's right.) This causes the signal frequency to depend on position along the left-right axis. A plot of signal amplitude versus frequency in the presence of this left-right frequency encoding gradient would give a one-dimensional image in which signal amplitude is projected down the columns along the anterior-posterior axis onto the left-right axis. The signal amplitude along this one-dimensional image defines the total amount of MRI signal generated by anterior-posterior columns. To obtain a two-dimensional image, a phase encoding gradient must also be used. In Fig. 9, the phase encoding gradient is applied along the anterior-posterior direction, causing the signal phase to depend on the position along the anterior-posterior direction. Phase encoding must be used because the signal frequency is already used for left-right encoding. Phase encoding is more complicated compared to frequency encoding. It is necessary to perform a number of phase-encoded signal measurements using different levels of the phase encoding to fully unravel the relationship between the position and phase. Typically, if it is desired to obtain a resolution of 256 image lines in the phase encode direction, then it is necessary to make on the order of 256 independent phase-encoded measurements.

The previous paragraph described the most commonly employed procedure for in-plane imaging. Several additional variant techniques have been

Figure 9 Frequency and phase encoding using applied magnetic field gradients with frequency measurement for in-plane imaging.

designed for specific purposes. The 3D acquisition techniques described previously use phase encoding in two dimensions and frequency encoding in one dimension without slice selection. This permits the slices to be made thinner than is typically possible when using conventional slice selection techniques. Another variant is known as echo planar imaging (EPI). In EPI, the frequency encoding and phase encoding are combined in a manner that speeds the imaging process considerably compared to conventional MRI. However, efficiency of EPI is partially offset by an increased susceptibility to artifacts arising from B0 imperfections.

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