07-03 MR Imaging and k-Space
What we have said about optical lenses holds, in a similar way, for k-space in MR imaging (Figure 07-05). As the lens, k-space collects image raw data for Fourier transform. One of the main differences is the shape. Lenses are round, k-space is rectangular.
Figure 07-05: |
In k-space, the iris of the camera is replaced by gradient strength, in one direction for frequency-encoding, in the other direction for phase-encoding (Figure 07-06).
The coordinates of k-space are called ‘spatial frequencies’ (measured in cycles per millimeter). They are filled depending on gradient strength of the frequency-encoding gradient (readout gradient: red arrow; x-direction) and phase-encoding gradient (preparation gradient: blue arrow; y-direction), moving from low gradient strength (-1) to zero gradient strength in the center (0) and high gradient strength (+1).
Figure 07-06: |
In MR imaging, k is divided into three dimensions (kx, ky, and kz) which define a domain or a space. Only two of them are commonly included, kx and ky. The third, kz, is the slice-selecting gradient which is mostly disregarded in k-space.
The points at the center of this raw data matrix represent small gradients; increasing the offset from the center corresponds to increasing gradient strength [⇒ Ljunggren; ⇒ Twieg].
Again, in an MR image the low spatial frequencies determine the gross signal levels (and hence contrast), while the higher spatial frequencies principally determine the edge definition (sharpness), as shown in Figure 07-07.
Figure 07-07: |
The definition of small objects is an integral part of the contrast and requires high spatial frequencies; thus, in this situation the high spatial frequencies also contribute to contrast. The maximum signal intensity is recorded close to the center of k-space since the net read and phase gradients applied for these points are relatively small, resulting in less dephasing.