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: From lens to MR imaging. If you compare this figure with Figure 06-20, you would position k-space before the second Fourier transform.

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: The k-space raw data matrix consists of an area to be filled with the information nee­ded to form an MR image.

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: k-Space with spatial frequency filtering. Figures a1 and a2: Regular k-space with image reconstruction. Figures b1 and b2: Same k-space as in (a) with filtering of the high frequencies; the reconstructed image has lost sharpness, it looks blurred; however, image contrast has hardly been affected. Figures c1 and c2: Spatial frequency fil­te­ring of the low frequencies; the re­con­struc­ted image has lost image contrast, but image details have hardly been affected. Figures d1 and d2: Low pass filtering in the readout direction, ... Figures e1 and e2: ... high pass filtering in the preparation direction. The signal amplitude (or mag­ni­tu­de) cor­res­ponds with the absolute brightness on the image because k-space is the re­pre­sen­ta­tion of the amplitudes of the sampled echoes. Therefore, the highest intensity is in the center. Simulation software: MR Image Expert®

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.