k-space

Abstract: The application of a new Fourier transform technique to magnetic resonance spectroscopy is explored. The method consists of applying a sequence of short rf pulses to the sample to be investigated and Fourier‐transforming the response of the system. The main advantages of this technique compared with the usual spectral sweep method are the much shorter time required to record a spectrum and the higher inherent sensitivity. It is shown theoretically and experimentally that it is possible to enhance the sensitivity of high resolution proton magnetic resonance spectroscopy in a restricted time up to a factor of ten or more. The time necessary to achieve the same sensitivity is a factor of 100 shorter than with conventional methods. The enhancement of the sensitivity is essentially given by the square root of the ratio of line width to total width of the spectrum. The method is of particular advantage for complicated high resolution spectra with much fine structure.

Abstract: New, efficient reconstruction procedures are proposed for sensitivity encoding (SENSE) with arbitrary k-space trajectories. The presented methods combine gridding principles with so-called conjugate-gradient iteration. In this fashion, the bulk of the work of reconstruction can be performed by fast Fourier transform (FFT), reducing the complexity of data processing to the same order of magnitude as in conventional gridding reconstruction. Using the proposed method, SENSE becomes practical with nonstandard k-space trajectories, enabling considerable scan time reduction with respect to mere gradient encoding. This is illustrated by imaging simulations with spiral, radial, and random k-space patterns. Simulations were also used for investigating the convergence behavior of the proposed algorithm and its dependence on the factor by which gradient encoding is reduced. The in vivo feasibility of non-Cartesian SENSE imaging with iterative reconstruction is demonstrated by examples of brain and cardiac imaging using spiral trajectories. In brain imaging with six receiver coils, the number of spiral interleaves was reduced by factors ranging from 2 to 6. In cardiac real-time imaging with four coils, spiral SENSE permitted reducing the scan time per image from 112 ms to 56 ms, thus doubling the frame-rate. Magn Reson Med 46:638–651, 2001. © 2001 Wiley-Liss, Inc.

Abstract: A method for obtaining the three-dimensional distribution of chemical shifts in a spatially inhomogeneous sample using Fourier transform NMR is presented. The method uses a sequence of pulsed field gradients to measure the Fourier transform of the desired distribution on a rectangular grid in (k,t) space. Simple Fourier inversion then recovers the original distribution. An estimated signal/noise ratio of 20 in 10 min is obtained for an "image" of the distribution of a 10 mM phosphorylated metabolite in the human head at a field of 20 kG with 2-cm resolution.