Imaging Methods with Advanced $\vec k$-Space Trajectories

Abstract

In the previous chapter we have shown that for MR imaging the transverse magnetization of Spin-Echo sequences is sampled on linear sets of the Carte-sian points in the $\vec k$ plane (see Fig. 2.6; for 2D methods we speak of the $\vec k$ plane, for 3D methods we use $\vec k$ space). An image is generated by “reconstruction”, which is done by applying a fast Fourier transform to these sampled data (“raw data”). The temporal evolution of the k value after excitation, called the trajectory through the $\vec k$ plane, determines the time on which a certain cartesian point is reached. This trajectory is specified by the time integral of the gradient (see (2.26)). Other and/or faster trajectories through the $\vec k$ plane than those of conventional sequences are also possible. The choice of such trajectories determines the time at which the transverse magnetization is sampled and opens the possibility of finding faster imaging methods and/or shorter echo times. In this chapter we shall give a global survey of such imaging methods by looking at their trajectory through the $\vec k$ plane. This appears to be a clarifying way to introduce new sequences in those cases, in which all magnetization arises from one single previous excitation. When there is still magnetization present from earlier excitations (when TR < T ₂), the $\vec k$ plane description of this chapter is not adequate and must be complemented with a more complete description of the “steady state”. This will be the subject of Chap. 4. The search for faster imaging methods is powered by the desired increase in the system throughput, by the possibility to “freeze” motion and thus avoiding motion artifacts, and by dynamic imaging, aimed at studying time-dependent processes (for example, the distribution of contrast agents through tissue as a function of time).