Gerrit Schultz

Parallel imaging in non-bijective, curvilinear magnetic field gradients: a concept study.

ObjectivesThe 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 methodsAs 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.

Simultaneously driven linear and nonlinear spatial encoding fields in MRI

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.

Reconstruction of MRI data encoded with arbitrarily shaped, curvilinear, nonbijective magnetic fields

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. Magn Reson Med, 2010.

Localization by nonlinear phase preparation and k‐space trajectory design

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 three‐dimensional 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, 2012.

Reconstruction of MRI data encoded by multiple nonbijective curvilinear magnetic fields.

Parallel imaging technique using localized gradients (PatLoc) uses the combination of surface gradient coils generating nonbijective curvilinear magnetic fields for spatial encoding. PatLoc imaging using one pair of multipolar spatial encoding magnetic fields (SEMs) has two major caveats: (1) The direct inversion of the encoding matrix requires exact determination of multiple locations which are ambiguously encoded by the SEMs. (2) Reconstructed images have a prominent loss of spatial resolution at the center of field‐of‐view using a symmetric coil array for signal detection. This study shows that a PatLoc system actually has a higher degree of freedom in spatial encoding to mitigate the two challenges mentioned above. Specifically, a PatLoc system can generate not only multipolar but also linear SEMs, which can be used to reduce the loss of spatial resolution at the field‐of‐view center. Here, we present an efficient and generalized image reconstruction method for PatLoc imaging using multiple SEMs without explicitly identifying the locations where SEM encoding is not unique. Reconstructions using simulations and empirical experimental data are compared with those using conventional linear gradients to demonstrate that the general combination of SEMs can improve image reconstructions. Magn Reson Med, 2012.

Reconstruction of undersampled radial PatLoc imaging using total generalized variation.

In the case of radial imaging with nonlinear spatial encoding fields, a prominent star‐shaped artifact has been observed if a spin distribution is encoded with an undersampled trajectory. This work presents a new iterative reconstruction method based on the total generalized variation, which reduces this artifact. For this approach, a sampling operator (as well as its adjoint) is needed that maps data from PatLoc k‐space to the final image space. It is shown that this can be realized as a type‐3 nonuniform fast Fourier transform, which is implemented by a combination of a type‐1 and type‐2 nonuniform fast Fourier transform. Using this operator, it is also possible to implement an iterative conjugate gradient SENSE based method for PatLoc reconstruction, which leads to a significant reduction of computation time in comparison to conventional PatLoc image reconstruction methods. Results from numerical simulations and in vivo PatLoc measurements with as few as 16 radial projections are presented, which demonstrate significant improvements in image quality with the total generalized variation‐based approach. Magn Reson Med, 2013.

Excitation and geometrically matched local encoding of curved slices

In this work, the concept of excitation and geometrically matched local in‐plane encoding of curved slices (ExLoc) is introduced. ExLoc is based on a set of locally near‐orthogonal spatial encoding magnetic fields, thus maintaining a local rectangular shape of the individual voxels and avoiding potential problems arising due to highly irregular voxel shapes. Unlike existing methods for exciting curved slices based on multidimensional radiofrequency‐pulses, excitation and geometrically matched local encoding of curved slices does not require long duration or computationally expensive radiofrequency‐pulses. As each encoding field consists of a superposition of potentially arbitrary (spatially linear or nonlinear) magnetic field components, the resulting field shape can be adapted with high flexibility to the specific region of interest. For extended nonplanar structures, this results in improved relevant volume coverage for fewer excited slices and thus increased efficiency. In addition to the mathematical description for the generation of dedicated encoding fields and data reconstruction, a verification of the ExLoc concept in phantom experiments and examples for in vivo curved single and multislice imaging are presented. Magn Reson Med, 2013.

Radial Imaging With Multipolar Magnetic Encoding Fields

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.

MR image reconstruction from generalized projections.

Currently, the time required for image reconstruction is prohibitively long if data are acquired using multidimensional imaging trajectories that make use of multichannel systems equipped with nonlinear gradients. Methods are presented that reduce the computational complexity of the iterative time‐domain reconstruction algorithm down from O(N4) to O(N3).

Performance evaluation of matrix gradient coils.

ObjectiveIn this paper, we present a new performance measure of a matrix coil (also known as multi-coil) from the perspective of efficient, local, non-linear encoding without explicitly considering target encoding fields.Materials and methodsAn optimization problem based on a joint optimization for the non-linear encoding fields is formulated. Based on the derived objective function, a figure of merit of a matrix coil is defined, which is a generalization of a previously known resistive figure of merit for traditional gradient coils.ResultsA cylindrical matrix coil design with a high number of elements is used to illustrate the proposed performance measure. The results are analyzed to reveal novel features of matrix coil designs, which allowed us to optimize coil parameters, such as number of coil elements. A comparison to a scaled, existing multi-coil is also provided to demonstrate the use of the proposed performance parameter.ConclusionsThe assessment of a matrix gradient coil profits from using a single performance parameter that takes the local encoding performance of the coil into account in relation to the dissipated power.