Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 32

k y

III

First line

II

k x

Last line

FIGURE 1.16 k-space path for 2-D Fourier transform.

1.10.1 K-S PACE T RAJECTORIES

By applying Equation 1.42 to a field gradient sequence, a path in k -space can be

traced out. Consider again the sequence diagram of Figure 1.14 ; let us trace the

paths in the k -space generated by the three time intervals as shown in Figure 1.14.
Figure 1.16 shows the path(s) in k-space corresponding to intervals II and III.
Each different phase encode takes us to a new starting point on the left during
interval II; during interval III, only the readout gradient is applied, ensuring that k
travels horizontally from left to right at constant speed. Such trajectory is due to
the x-gradient (readout gradient), shape, which has a negative compensation lobe
before the sampling period that allows the k-space to be sampled symmetrically
with the readout gradient; i.e., during the readout period, k goes from

k max to k max .
The important parts of the paths are where the MR signal is being sampled
for processing into an image. In a straightforward FT imaging procedure, the whole
track in k-space should be a rectilinear scan, preferably with a square aspect ratio,
because this implies equal spatial resolution along both axes.

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1.11 IMAGING METHODS

There are numerous variations on the basic MRI sequences described earlier. Other
than the RF pulse shapes and repetitions (gradient echo, spin echo, inversion recovery,
etc.), there are many aspects that distinguish them from one another; for example, data
acquisition and image reconstruction velocity. There exist a number of rapid imaging
techniques that could be grouped under echo-planar imaging (EPI), spiral imaging,
and, more recently, parallel imaging. Another important aspect that characterizes