Objectives The paper presents a novel and more generalized concept for spatial encoding by non-unidirectional, nonbijective 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 conclusionsThe 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.

A basic framework for image reconstruction from spatial encoding by curvilinear, nonbijective magnetic encoding fields in combination with multiple receivers is presented. The theory was developed in the context of the recently introduced parallel imaging technique using localized gradients (PatLoc) approach. In this new imaging modality, the linear gradient fields are generalized to arbitrarily shaped, nonbijective spatial encoding magnetic fields, which lead to ambiguous encoding. Ambiguities are resolved by adaptation of concepts developed for parallel imaging. Based on theoretical considerations, a practical algorithm for Cartesian trajectories is derived in the case that the conventional gradient coils are replaced by coils for PatLoc. The reconstruction method extends Cartesian sensitivity encoding (SENSE) reconstruction with an additional voxelwise intensity-correction step. Spatially varying resolution, signal-to-noise ratio, and truncation artifacts are described and analyzed. Theoretical considerations are validated by two-dimensional simulations based on multipolar encoding fields and they are confirmed by applying the reconstruction algorithm to initial experimental data.

Spatial encoding in MRI is conventionally achieved by the application of switchable linear encoding fields. The general concept of the recently introduced PatLoc (Parallel Imaging Technique using Localized Gradients) encoding is to use nonlinear fields to achieve spatial encoding. Relaxing the requirement that the encoding fields must be linear may lead to improved gradient performance or reduced peripheral nerve stimulation. In this work, a custom‐built insert coil capable of generating two independent quadratic encoding fields was driven with high‐performance amplifiers within a clinical MR system. In combination with the three linear encoding fields, the combined hardware is capable of independently manipulating five spatial encoding fields. With the linear z‐gradient used for slice‐selection, there remain four separate channels to encode a 2D‐image. To compare trajectories of such multidimensional encoding, the concept of a local k‐space is developed. Through simulations, reconstructions using six gradient‐encoding strategies were compared, including Cartesian encoding separately or simultaneously on both PatLoc and linear gradients as well as two versions of a radial‐based in/out trajectory. Corresponding experiments confirmed that such multidimensional encoding is practically achievable and demonstrated that the new radial‐based trajectory offers the PatLoc property of variable spatial resolution while maintaining finite resolution across the entire field‐of‐view. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.

We present reconstruction methods for radial magnetic resonance imaging (MRI) data which were spatially encoded using a pair of orthogonal multipolar magnetic fields for in-plane encoding and parallel imaging. It is shown that a direct method exists in addition to iterative reconstruction. Standard direct projection reconstruction algorithms can be combined with a previously developed direct reconstruction for multipolar encoding fields acquired with Cartesian trajectories. The algorithm is simplified by recasting the reconstruction problem into polar coordinates. In this formulation distortion and aliasing become separate effects. Distortion occurs only along the radial direction and aliasing along the azimuthal direction. Moreover, aliased points are equidistantly distributed in this representation, and, consequently, Cartesian SENSE is directly applicable with highly effective unfolding properties for radio-frequency coils arranged with a radial symmetry. The direct and iterative methods are applied to simulated data to analyze basic properties of the algorithms and for the first time also measured in vivo data are presented. The results are compared to linear spatial encoding using a radial trajectory and quadrupolar encoding using a Cartesian trajectory. The direct reconstruction gives good results for fully sampled datasets. Undersampled datasets, however, show star-shaped artifacts, which are significantly reduced with the iterative reconstruction.

A technique is described to localize MR signals from a target volume using nonlinear pulsed magnetic fields and spatial encoding trajectories designed using local k-space theory. The concept of local k-space is outlined theoretically, and this principle is applied to simulated phantom and cardiac MRI data in the presence of surface and quadrupolar gradient coil phase modulation. Phantom and in vivo human brain images are obtained using a custom, high-performance quadrupolar gradient coil integrated with a whole-body 3-T MRI system to demonstrate target localization using three-dimensional T 2 *-weighted spoiled gradient echo, two-dimensional segmented, multiple gradient encoded spin echo, and threedimensional balanced steady-state free precession acquisitions. This method may provide a practical alternative to selective radiofrequency excitation at ultra-high-field, particularly for steady-state applications where repetition time (TR) must be minimized and when the amount of energy deposited in human tissues is prohibitive. There are several limitations to the approach including the spatial variation in resolution, high frequency aliasing artifacts, and spatial variation in echo times and contrast. Magn Reson Med 67:1620-1632,