Reconstruction of MRI data encoded by multiple nonbijective curvilinear magnetic fields

SiMultaneous Acquisition of Spatial Harmonics (SMASH) is a new fast-imaging technique that increases MR image acquisition speed by an integer factor over existing fast-imaging methods, without significant sacrifices in spatial resolution or signal-to-noise ratio. Image acquisition time is reduced by exploiting spatial information inherent in the geometry of a surface coil array to substitute for some of the phase encoding usually produced by magnetic field gradients. This allows for partially parallel image acquisitions using many of the existing fast-imaging sequences. Unlike the data combination algorithms of prior proposals for parallel imaging, SMASH reconstruction involves a small set of MR signal combinations prior to Fourier transformation, which can be advantageous for artifact handling and practical implementation. A twofold savings in image acquisition time is demonstrated here using commercial phased array coils on two different MR-imaging systems. Larger time savings factors can be expected for appropriate coil designs.

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. Copyright 2001 Wiley-Liss, Inc.

Objectives The paper presents a novel and more generalized concept for spatial encoding by non-unidirectional, non- bijective spatial encoding magnetic fields (SEMs). In combination with parallel local receiver coils these fields allow one to overcome the current limitations of neuronal nerve stimulation. Additionally the geometry of such fields can be adapted to anatomy. Materials and methods As an example of such a parallel imaging technique using localized gradients (PatLoc)- system, we present a polar gradient system consisting of 2 × 8 rectangular current loops in octagonal arrangement, which generates a radial magnetic field gradient. By inverting the direction of current in alternating loops, a near sinusoidal field variation in the circumferential direction is produced. Ambiguities in spatial assignment are resolved by use of multiple receiver coils and parallel reconstruction. Simulations demonstrate the potential advantages and limitations of this approach. Results and conclusions The exact behaviour of PatLoc fields with respect to peripheral nerve stimulation needs to be tested in practice. Based on geometrical considerations SEMs of radial geometry allow for about three times faster gradient switching compared to conventional head gradient inserts and even more compared to whole body gradients. The strong nonlinear geometry of the fields needs to be considered for practical applications.