Performance evaluation of matrix gradient coils.

OBJECTIVE: In 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 METHODS: An 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. RESULTS: A 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. CONCLUSIONS: The 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.

Single-shot imaging with higher-dimensional encoding using magnetic field monitoring and concomitant field correction.

PURPOSE: PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field-of-view. Higher-dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher-dimensional single-shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived. METHODS: A dynamic field camera was built for encoding field calibration. Concomitant fields of linear and nonlinear spatial encoding magnetic fields were analyzed. A combined basis consisting of spherical harmonics and concomitant terms was proposed and used for encoding field calibration and image reconstruction. RESULTS: A good agreement between the analytical solution for the concomitant fields and the magnetic field simulations of the custom-built PatLoc SEM coil was observed. Substantial image quality improvements were obtained using a dynamic field camera for encoding field calibration combined with the proposed combined basis. CONCLUSION: The importance of trajectory calibration for single-shot higher-dimensional encoding is demonstrated using the combined basis including spherical harmonics and concomitant terms, which treats the concomitant fields as an integral part of the encoding.

Monoplanar gradient system for imaging with nonlinear gradients.

OBJECT: In this paper we present a monoplanar gradient system capable of imaging a volume comparable with that covered by linear gradient systems. Such a system has been designed and implemented. MATERIALS AND METHODS: Building such a system was made possible by relaxing the constraint of global linearity and replacing it with a requirement for local orthogonality. A framework was derived for optimization of local orthogonality within the physical boundaries and geometric constraints. Spatial encoding of magnetic fields was optimized for their local orthogonality over a large field of view. RESULTS: A coil design consisting of straight wire segments was optimized, implemented, and integrated into a 3T human scanner to show the feasibility of this approach. Initial MR images are shown and further applications of the derived optimization method and the nonlinear planar gradient system are discussed. CONCLUSION: Encoding fields generated by the prototype encoding system were shown to be locally orthogonal and able to encode a cylindrical volume sufficient for some abdomen imaging applications for humans.

Stages: sub-Fourier dynamic shim updating using nonlinear magnetic field phase preparation.

Heterogeneity of the static magnetic field in magnetic resonance imaging may cause image artifacts and degradation in image quality. The field heterogeneity can be reduced by dynamically adjusting shim fields or dynamic shim updating, in which magnetic field homogeneity is optimized for each tomographic slice to improve image quality. A limitation of this approach is that a new magnetic field can be applied only once for each slice, otherwise image quality would improve somewhere to its detriment elsewhere in the slice. The motivation of this work is to overcome this limitation and develop a technique using nonlinear magnetic fields to dynamically shim the static magnetic field within a single Fourier-encoded volume or slice, called sub-Fourier dynamic shim updating. However, the nonlinear magnetic fields are not used as shim fields; instead, they impart a strong spatial dependence to the acquired MR signal by nonlinear phase preparation, which may be exploited to locally improve magnetic field homogeneity during acquisition. A theoretical description of the method is detailed, simulations and a proof-of-principle experiment are performed using a magnet coil with a known field geometry. The method is shown to remove artifacts associated with magnetic field homogeneity in balanced steady-state free-precession pulse sequences. We anticipate that this method will be useful to improve the quality of magnetic resonance images by removing deleterious artifacts associated with a heterogeneous static magnetic field.

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.

Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields.

It has recently been demonstrated that nonlinear encoding fields result in a spatially varying resolution. This work develops an automated procedure to design single-shot trajectories that create a local resolution improvement in a region of interest. The technique is based on the design of optimized local k-space trajectories and can be applied to arbitrary hardware configurations that employ any number of linear and nonlinear encoding fields. The trajectories designed in this work are tested with the currently available hardware setup consisting of three standard linear gradients and two quadrupolar encoding fields generated from a custom-built gradient insert. A field camera is used to measure the actual encoding trajectories up to third-order terms, enabling accurate reconstructions of these demanding single-shot trajectories, although the eddy current and concomitant field terms of the gradient insert have not been completely characterized. The local resolution improvement is demonstrated in phantom and in vivo experiments.

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.

Practical considerations for in vivo MRI with higher dimensional spatial encoding.

OBJECT: This work seeks to examine practical aspects of in vivo imaging when spatial encoding is performed with three or more encoding channels for a 2D image. MATERIALS AND METHODS: The recently developed 4-Dimensional Radial In/Out (4D-RIO) trajectory is compared in simulations to an alternative higher-order encoding scheme referred to as O-space imaging. Direct comparison of local k-space representations leads to the proposal of a modification to the O-space imaging trajectory based on a scheme of prephasing to improve the reconstructed image quality. Data were collected using a 4D-RIO acquisition in vivo in the human brain and several image reconstructions were compared, exploiting the property that the dense encoding matrix, after a 1D or 2D Fourier transform, can be approximated by a sparse matrix by discarding entries below a chosen magnitude. RESULTS: The proposed prephasing scheme for the O-space trajectory shows a marked improvement in quality in the simulated image reconstruction. In experiments, 4D-RIO data acquired in vivo in the human brain can be reconstructed to a reasonable quality using only 5 % of the encoding matrix--massively reducing computer memory requirements for a practical reconstruction. CONCLUSION: Trajectory design and reconstruction techniques such as these may prove especially useful when extending generalized higher-order encoding methods to 3D images.

Comparison of LC-MS and LC-DAD Methods of Detecting Abused Piperazine Designer Drugs.

Recreational use of piperazine designer drugs is a serious threat to human health. These compounds act on the body in a similar fashion to illegal drugs. They induce psychostimulatory effects as well as visual and auditory hallucinations to varying degrees. In many cases of poisoning and deaths, the presence of two or even several psychoactive substances have been demonstrated. Piperazine derivatives are often found in such mixtures and pose a great analytical problem during their identification. Additionally, some piperazine derivatives can be detected in biological material as a result of metabolic changes to related drugs. Therefore, it is necessary to correctly identify these compounds and ensure repeatability of determinations. This article presents a comparison of the methods used to detect abused piperazine designer drugs using liquid chromatography in combination with a diode-array detector (LC-DAD) or mass spectrometer (LC-MS). Each of methods can be used independently for determinations, obtaining reliable results in a short time of analysis. These methods can also complement each other, providing qualitative and quantitative confirmation of results. The proposed methods provide analytical confirmation of poisoning and may be helpful in toxicological diagnostics.

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.

Rapid Targeted Method of Detecting Abused Piperazine Designer Drugs.

Piperazine derivatives belong to the popular psychostimulating compounds from the group of designer drugs. They are an alternative to illegal drugs such as ecstasy and amphetamines. They are being searched by consumers for recreational use due to their stimulating and hallucinogenic effects. Many NPS-related poisonings and deaths have been reported where piperazines have been found. However, a major problem is the potential lack of laboratory confirmation of the involvement of piperazine derivatives in the occurrence of poisoning. Although many methods have been published, piperazine derivatives are not always included in a routine analytical approach or targeted toxicological analysis. There is an increasing need to provide qualitative evidence for the presence of piperazine derivatives and to ensure reproducible quantification. This article describes a new rapid method of detecting piperazine derivatives in biological material, using LC-MS. All target analytes were separated in a 15 min run time and identified based on the precursor ion, at least two product ions, and the retention time. Stable isotopically labeled (SIL) internal standards: BZP-D7, mCPP-D8 and TFMPP-D4 were used for analysis, obtaining the highest level of confidence in the results. The proposed detection method provides the analytical confirmation of poisoning with piperazine designer drugs.

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.

Piperazine derivatives as dangerous abused compounds.

Piperazine derivatives are a group of compounds with a psychostimulant effect. They are an alternative to illegal drugs. They are being searched for recreational use due to their psychoactive and hallucinogenic effects. The high popularity of these compounds can be noticed all over the world due to easy purchase, lack of legal regulations and incorrect assessment of the safety of use. The recreational use of piperazine derivatives can often result in chronic and acute health problems and additionally with unpredictable remote effects. It is also common to take mixtures of psychoactive compounds. This hinders the correct diagnosis and treatment of patients with poisoning. The presented work is an illustration of the wide problem of piperazine derivatives abuse. The health effects and the possibility of identifying these compounds in preparations and biological material are described.

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.

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

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 x 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.