Advanced Methods for Radial Data Sampling in Magnetic Resonance Imaging

In magnetic resonance imaging (MRI), the received signal corresponds to the Fourier transform of the object's spin density, which can be sampled selectively by switching time varying gradient fields. Most conventional MRI techniques perform a line-by-line sampling of the Fourier transform, although in general arbitrary sampling schemes can be employed. In this thesis, the use of radial trajectories is discussed, which sample the Fourier transform along coinciding spokes. The imaging properties of this alternative acquisition technique are investigated in detail: while it offers several promising advantages over the conventional Cartesian approach, these salient properties are accompanied by a number of serious complications that so far hamper a more frequent use of radial techniques in routine applications.One of the major problems consists in the higher complexity of the image reconstruction. In particular, existing approaches require 57% more Fourier lines relative to the Cartesian technique in order to sufficiently sample the data space. To overcome this limitation and the corresponding prolongation of the measurement time, this work describes the development of a novel method that allows for reasonable image reconstructions from a clearly reduced number of acquisitions. The reconstruction approach is based on the formulation as an inverse problem, which is solved with an iterative non-linear optimization technique. To compensate for the omitted acquisition steps, prior knowledge is incorporated using a set of penalty functions that prevent the selection of implausible solutions. The total variation of the estimate is employed as the main penalty term, which effectively suppresses radial undersampling artifacts for objects that are piecewise-constant. In addition, the approach exploits localized sensitivities of multi-coil arrays in a parallel imaging manner and copes with experimental phase variations to ensure the applicability in real MRI scenarios. The coil sensitivities are estimated from the same data in a preceding step, which avoids the recording of additional reference information. Global smoothness of the coil profiles is assumed and incorporated using a quadratic penalization of the pixel differences.The effectiveness of the reconstruction method is demonstrated in studies of water phantoms and the human brain in vivo. The results reveal that the technique yields reasonable images from only a few k-space lines, which is not possible with current Cartesian techniques. As a first real-world application, the performance of the new method is evaluated for the case of a single-shot MRI sequence based on stimulated echoes, which was adapted to the radial acquisition scheme. Because in single-shot MRI the number of obtainable k-space lines is limited, the combination with the proposed image reconstruction method results in a much higher spatial resolution than for the corresponding Cartesian case. Experimentally, a resolution enhancement up to a factor of four could be demonstrated for studies of the human brain. In a further step, the reconstruction method is extended to handle complex acquisition scenarios where data inconsistencies arise from spin relaxation or saturation effects. By employing a non-linear model of the received MRI signal, the extended approach is capable of merging such data in a reasonable way and enables exploiting respective acquisition techniques to reduce the overall measurement time. In the specific case of a radial fast spin-echo acquisition, the extended approach directly yields quantitative proton-density and relaxivity information, which offers motion-robust T2 mapping from only a single radial data set.Finally, it is shown that a minimization of the total variation can be exploited not only to fill k-space gaps in-between the measured lines but also to extrapolate the data beyond the measured part of k-space. As demonstrated for Cartesian sampling, this idea leads to a suppression of Gibbs ringing artifacts without noticeable loss of resolution. These results confirm that constraining the total variation is an effective concept to compensate for incomplete MRI acquisitions.