07-04 Filling k-Space with Data and Image Reconstruction
In most MR imaging sequences applied in clinical routine today, raw data are placed in a rectangular k-space grid [⇒ Edelstein].
In a standard spin-echo sequence, each 90° pulse creates a new line (Figure 07-08). The length of the line is determined by the strength of the frequency-encoding gradient and the sampling time, its position by the strength of the phase-encoding gradient.
The position of the line is determined as follows. After the initial 90° excitation pulse, the spins evolve in the direction given by the phase-encoding gradient Gy and the frequency-encoding gradient Gx (yellow arrow in Figure 07-09a).
They are then turned around by the 180° pulse (red/magenta arrow). Then the frequency encoding gradient is switched on again and sampling starts. This is repeated for different amplitudes of the phase-encoding gradient until k-space is filled (Figure 07-09b).
The time needed for such an imaging experiment is the number of phase-encoding steps (NGy) multiplied by the repetition time (TR) and the number of excitations (NEX):
NGy × TR × NEX
Now we have filled the data matrix with each row containing information from one echo. Each data point is then Fourier-transformed in the x-direction, which leads to a new data matrix where every point in each column contains information stemming from a certain frequency; the phase information differs point-by-point per row. The second Fourier transform is performed in the y-direction to extract phase information. This again leads to a new data matrix containing combined phase and frequency information. The output is a matrix showing a modulus or magnitude image which corresponds to the bulk of MR signals from each point. Phase correction might be necessary to correct for phase jumps between 0° and 360°.
Among the main parameters influenced by k-space are the speed of acquisition, spatial resolution, field-of-view, contrast, and artifacts. Details can be found in some dedicated papers [Review articles:⇒ Hennig; ⇒ Mezrich; ⇒ Pelc; ⇒ Peters].