The k-Space Raster

Although the schematic of Fig. 3 allows us to appreciate the concept of obtaining spatial resolution in the measurement, it is almost impossible to understand and 

Rewriting Eq. (2) for the general case of the variation of resonance frequency with spatial position r we find  

A transformation into the rotating frame of reference and integrating over the sample volume allows us to rewrite Eq. (7) as 

Mansfield and Grannell (76) simplified the interpretation of Eq. (8) and the development of imaging pulse sequences by introducing the concept of k-space, where the k-space vector is defined as k — (yGr/Zm). It follows that Eq. (8) can now 

Thus the imaging experiment is seen as acquisition of data in the time domain, sampling the k-space raster, followed by Fourier transformation to the frequency domain, which in turn is directly related to real space. 

While the simple schematic of Fig. 4 allows us to appreciate the concept of obtaining spatial resolution in the measurement, it is almost impossible to understand and design MRI pulse sequences using this approach. Instead, the approach used is that of the so-called k-space raster, introduced by Mansfield (1977). 

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This section introduces the reader to the basic principles of MRI and the concept of the k-space raster. The basic MRI pulse sequence, the spin-echo imaging sequence, is described at this point. For more detailed discussion of the background theory of MRI the interested reader should refer to texts by Callaghan5 and Kimmich.6... 

Fig. 6. (a) Schematic representation of a simple slice-selective 2-D spin-echo pulse sequence. In this pulse sequence the magnetic field gradient (G, ) is varied for successive acquisitions of different rows of the k-space raster, (b) The corresponding k-space raster used to show how we interpret the pulse sequence. Following a sufficient Ti-relaxation period, the sequence is repeated to acquire a second row of the k-space raster. Acquisition of each row of k-space requires a separate r.f. excitation and application of a G,-gradient of different magnitude. 

In this example, the gradient applied in the y-direction is referred to as the phase encoding gradient. Phase encoding refers to the action of an applied gradient that is responsible for moving the acquisition through the k-space raster. In this case, the... 

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