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

Fast and silent MRI using nonlinear gradient fields at the ultrasonic gradient switching frequency of 20 kHz with a Point Spread Function framework reconstruction

PURPOSE

To demonstrate the feasibility of using a nonlinear gradient field for spatial encoding at the ultrasonic switching frequency of 20 kHz and present a framework to reconstruct data acquired in this way.

METHODS

Nonlinear encoding at 20 kHz was realized by using a single-axis silent gradient insert for imaging in the periphery, that, is the nonlinear region, of the gradient field. The gradient insert induces a rapidly oscillating gradient field in the phase-encode direction, which enables nonlinear encoding when combined with a Cartesian readout from the linear whole-body gradients. Data from a 2D gradient echo sequence were reconstructed using a point spread function (PSF) framework. Accelerated scans were also simulated via retrospective undersampling (R = 1 to R = 8) to determine the effectiveness of the PSF-framework for accelerated imaging.

RESULTS

Using a nonlinear gradient field switched at 20 kHz and the PSF-framework resulted in images of comparable quality to images from conventional Cartesian linear encoding. At increased acceleration factors (R ≤ 8), the PSF-framework outperformed linear SENSE reconstructions by improved controlling of aliasing artifacts.

CONCLUSION

Using the PSF-framework, images of comparable quality to conventional SENSE reconstructions are possible via combining traditional linear and ultrasonic oscillating nonlinear encoding fields. Using nonlinear gradient fields relaxes the demand for strictly linear gradient fields, enabling much higher slew rates with a reduced risk of peripheral nerve stimulation or cardiac stimulation, which could aid in extension to ultrasonic whole-body MRI. The lack of aliasing artifacts also highlights the potential of accelerated imaging using the PSF-framework.

Use of nonlinear pulsed magnetic fields for spatial encoding in magnetic resonance imaging

This study examines the use of nonlinear magnetic field coils for spatial encoding in magnetic resonance imaging. Existing theories on imaging with such coils share a complex reconstruction process that originates from a suboptimal signal interpretation in the spatial-frequency domain (k-space). In this study, a new solution to this problem is proposed, namely a two-step reconstruction process, in which in the first step, the image signal is converted into a frequency spectrum, and in the second step, the spectrum, which represents the distorted image, is geometrically and intensity corrected to obtain an undistorted image. This theory has been verified by numerical simulations and experimentally using a straight wire as a coil model for an extremely nonlinear magnetic field. The results of this study facilitate the use of simple encoding coil designs that can feature low inductance, allowing for much faster switching times and higher magnetic field gradients.

Accelerated 2D Cartesian MRI with an 8-channel local B0 coil array combined with parallel imaging

PURPOSE

In MRI, the magnetization of nuclear spins is spatially encoded with linear gradients and radiofrequency receivers sensitivity profiles to produce images, which inherently leads to a long scan time. Cartesian MRI, as widely adopted for clinical scans, can be accelerated with parallel imaging and rapid magnetic field modulation during signal readout. Here, by using an 8-channel localB 0 $$ {\mathrm{B}}_0 $$ coil array, the modulation scheme optimized for sampling efficiency is investigated to speed up 2D Cartesian scans.

THEORY AND METHODS

An 8-channel localB 0 $$ {\mathrm{B}}_0 $$ coil array is made to carry sinusoidal currents during signal readout to accelerate 2D Cartesian scans. An MRI sampling theory based on reproducing kernel Hilbert space is exploited to visualize the efficiency of nonlinear encoding in arbitrary sampling duration. A field calibration method using current monitors for localB 0 $$ {\mathrm{B}}_0 $$ coils and the ESPIRiT algorithm is proposed to facilitate image reconstruction. Image acceleration with various modulation field shapes, aliasing control, and distinct modulation frequencies are scrutinized to find an optimized modulation scheme. A safety evaluation is conducted. In vivo 2D Cartesian scans are accelerated by the localB 0 $$ {\mathrm{B}}_0 $$ coils.

RESULTS

For 2D Cartesian MRI, the optimal modulation field by this localB 0 $$ {\mathrm{B}}_0 $$ array converges to a nearly linear gradient field. With the field calibration technique, it accelerates the in vivo scans (i.e., proved safe) by threefold and eightfold free of visible artifacts, without and with SENSE, respectively.

CONCLUSION

The nonlinear encoding analysis tool, the field calibration method, the safety evaluation procedures, and the in vivo reconstructed scans make significant steps to push MRI speed further with the localB 0 $$ {\mathrm{B}}_0 $$ coil array.

A Siamese-Transport Domain Adaptation Framework for 3D MRI Classification of Gliomas and Alzheimer's Diseases

Accurate and fully automated brain structure examination and prediction from 3D volumetric magnetic resonance imaging (MRI) is a necessary step in medical imaging analysis, which can assist greatly in clinical diagnosis. Traditional deep learning models suffer from severe performance degradation when applied to clinically acquired unlabeled data. The performance degradation is mainly caused by domain discrepancy such as different device types and parameter settings for data acquisition. However, existing approaches focus on the reduction of domain discrepancies but ignore the entanglement of semantic features and domain information. In this article, we explore the feature invariance of categories and domains in different projection spaces and propose a Siamese-Transport Domain Adaptation (STDA) method using a joint optimal transport theory and contrastive learning for automatic 3D MRI classification and glioma multi-grade prediction. Specifically, the learning framework updates the distribution of features across domains and categories by Siamese transport network training with an Optimal Cost Transfer Strategy (OCTS) and a Mutual Invariant Constraint (MIC) in two projective spaces to find multiple invariants in potential heterogeneity. We design three sets of transfer task scenarios with different source and target domains, and demonstrate that STDA yields substantially higher generalization performance than other state-of-the-art unsupervised domain adaptation (UDA) methods. The method is applicable on 3D MRI data from glioma to Alzheimer's disease and has promising applications in the future clinical diagnosis and treatment of brain diseases.

Correcting image distortions from a nonlinear B 1 + $$ {\boldsymbol{B}}_{\mathbf{1}}^{+} $$ -gradient field in frequency-modulated Rabi-encoded echoes

PURPOSE

To correct image distortions that result from nonlinear spatial variation in the transmit RF field amplitude (B 1 + $$ {B}_1^{+} $$ ) when performing spatial encoding with the method called frequency-modulated Rabi encoded echoes (FREE).

THEORY AND METHODS

An algorithm developed to correct image distortion resulting from the use of nonlinear static field (B0 ) gradients in standard MRI is adapted herein to correct image distortion arising from a nonlinearB 1 + $$ {B}_1^{+} $$ -gradient field in FREE. From aB 1 + $$ {B}_1^{+} $$ -map, the algorithm performs linear interpolation and intensity scaling to correct the image. The quality of the distortion correction is evaluated in 1.5T images of a grid phantom and human occipital lobe.

RESULTS

An expanded theoretical description of FREE revealed the symmetry between thisB 1 + $$ {B}_1^{+} $$ -gradient field spatial-encoding and standard B0 -gradient field spatial-encoding. The adapted distortion-correction algorithm substantially reduced image distortions arising in the spatial dimension that was encoded by the nonlinearB 1 + $$ {B}_1^{+} $$ gradient of a circular surface coil.

CONCLUSION

Image processing based on straightforward linear interpolation and intensity scaling, as previously applied in conventional MRI, can effectively reduce distortions in FREE images acquired with nonlinearB 1 + $$ {B}_1^{+} $$ -gradient fields.

Germany's journey toward 14 Tesla human magnetic resonance

Multiple sites within Germany operate human MRI systems with magnetic fields either at 7 Tesla or 9.4 Tesla. In 2013, these sites formed a network to facilitate and harmonize the research being conducted at the different sites and make this technology available to a larger community of researchers and clinicians not only within Germany, but also worldwide. The German Ultrahigh Field Imaging (GUFI) network has defined a strategic goal to establish a 14 Tesla whole-body human MRI system as a national research resource in Germany as the next progression in magnetic field strength. This paper summarizes the history of this initiative, the current status, the motivation for pursuing MR imaging and spectroscopy at such a high magnetic field strength, and the technical and funding challenges involved. It focuses on the scientific and science policy process from the perspective in Germany, and is not intended to be a comprehensive systematic review of the benefits and technical challenges of higher field strengths.

Advancements in Gradient System Performance for Clinical and Research MRI

In magnetic resonance imaging (MRI), spatial field gradients are applied along each axis to encode the location of the nuclear spin in the frequency domain. During recent years, the development of new gradient technologies has been focused on the generation of stronger and faster gradient fields for imaging with higher spatial and temporal resolution. This benefits imaging methods, such as brain diffusion and functional MRI, and enables human imaging at ultra-high field MRI. In addition to improving gradient performance, new technologies have been presented to minimize peripheral nerve stimulation and gradient-related acoustic noise, both generated by the rapid switching of strong gradient fields. This review will provide a general background on the gradient system and update on the state-of-the-art gradient technology. EVIDENCE LEVEL: 5 TECHNICAL EFFICACY: Stage 1.

MaxGIRF: Image reconstruction incorporating concomitant field and gradient impulse response function effects

Purpose

To develop and evaluate an improved strategy for compensating concomitant field effects in non‐Cartesian MRI at the time of image reconstruction.

Theory

We present a higher‐order reconstruction method, denoted as MaxGIRF, for non‐Cartesian imaging that simultaneously corrects off‐resonance, concomitant fields, and trajectory errors without requiring specialized hardware. Gradient impulse response functions are used to predict actual gradient waveforms, which are in turn used to estimate the spatiotemporally varying concomitant fields based on analytic expressions. The result, in combination with a reference field map, is an encoding matrix that incorporates a correction for all three effects.

Methods

The MaxGIRF reconstruction is applied to noiseless phantom simulations, spiral gradient‐echo imaging of an International Society for Magnetic Resonance in Medicine/National Institute of Standards and Technology phantom, and axial and sagittal multislice spiral spin‐echo imaging of a healthy volunteer at 0.55 T. The MaxGIRF reconstruction was compared against previously established concomitant field‐compensation and image‐correction methods. Reconstructed images are evaluated qualitatively and quantitatively using normalized RMS error. Finally, a low‐rank approximation of MaxGIRF is used to reduce computational burden. The accuracy of the low‐rank approximation is studied as a function of minimum rank.

Results

The MaxGIRF reconstruction successfully mitigated blurring artifacts both in phantoms and in vivo and was effective in regions where concomitant fields counteract static off‐resonance, superior to the comparator method. A minimum rank of 8 and 30 for axial and sagittal scans, respectively, gave less than 2% error compared with the full‐rank reconstruction.

Conclusions

The MaxGIRF reconstruction simultaneously corrects off‐resonance, trajectory errors, and concomitant field effects. The impact of this method is greatest when imaging with longer readouts and/or at lower field strength.

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Design of an insertable cone-shaped gradient coil matrix for head imaging with a volumetric finite-difference method

Matrix gradient coils have received increasing interest in generating arbitrary-shaped magnetic fields for various magnetic resonance imaging applications. In this paper, a novel cone-shaped matrix gradient coil is proposed to design a multifunctional insertable system for head imaging. Using a volumetric finite-difference-based method, the matrix coil is designed to have comprised several coil elements that can implement localized imaging and control eddy current, dissipated power, and minimum wire gap. With the lowest total dissipated power, various current configurations are selected to generate multiple gradient fields within a large, spheroidal region of interest (ROI) and two small spherical sub-ROIs. The numerical computation results show that the designed matrix coil offers high flexibility in generating a local gradient field capable of improving the local resolution. In addition, with enhanced coil performance, the cone-shaped structure provides a patient-friendly solution for head imaging.

A portable scanner for magnetic resonance imaging of the brain

Access to scanners for magnetic resonance imaging (MRI) is typically limited by cost and by infrastructure requirements. Here, we report the design and testing of a portable prototype scanner for brain MRI that uses a compact and lightweight permanent rare-earth magnet with a built-in readout field gradient. The 122-kg low-field (80 mT) magnet has a Halbach cylinder design that results in a minimal stray field and requires neither cryogenics nor external power. The built-in magnetic field gradient reduces the reliance on high-power gradient drivers, lowering the overall requirements for power and cooling, and reducing acoustic noise. Imperfections in the encoding fields are mitigated with a generalized iterative image reconstruction technique that leverages previous characterization of the field patterns. In healthy adult volunteers, the scanner can generate T1-weighted, T2-weighted and proton density-weighted brain images with a spatial resolution of 2.2 × 1.3 × 6.8 mm³. Future versions of the scanner could improve the accessibility of brain MRI at the point of care, particularly for critically ill patients.

A numerical study of pre-polarisation switching in ultra-low field magnetic resonance imaging using dynamic permanent magnet arrays

Dynamically adjustable permanent magnet arrays have been proposed to generate switchable magnetic fields for pre-polarisation in Ultra-Low Field magnetic resonance imaging. However, the optimal switching dynamics of the pre-polarisation magnetic field as well as the energy requirements, mechanical forces and stresses during switching of the pre-polarisation field have not been evaluated. We analysed these requirements numerically and estimated the magnetic resonance signal strength and image quality for two practical switching modes in an instrument suitable for scanning the human head. Von Mises stress analysis showed that although magnetic forces were significantly higher for two specific rungs, the structural integrity of magnet rungs would not be compromised. Our simulations suggest that a significantly higher signal yield is obtained by switching off the pre-polarisation field with the angular velocity in each rung dependent on its location.

Development and validation of 3D MP-SSFP to enable MRI in inhomogeneous magnetic fields

PURPOSE

We demonstrate the feasibility of MRI with missing-pulse steady-state free precession (MP-SSFP) in a 4T magnet with artificially degraded homogeneity.

METHODS

T₁ , T₂ , and diffusion contrast of MP-SSFP was simulated with constant and alternate radiofrequency (RF) phase using an extended phase graph. To validate MP-SSFP performance in human brain imaging, MP-SSFP was tested with two types of artificially introduced inhomogeneous magnetic fields: (1) a pure linear gradient field, and (2) a pseudo-linear gradient field introduced by mounting a head-gradient set at 36 cm from the magnet isocenter. Image distortion induced by the nonlinear inhomogeneous field was corrected using B₀ mapping measured with MP-SSFP.

RESULTS

The maximum flip angle in MP-SSFP was limited to ≤10° because of the large range of resonance frequencies in the inhomogeneous magnetic fields tested in this study. Under this flip-angle limitation, MP-SSFP with constant RF phase provided advantages of higher signal-to-noise ratio and insensitivity to B₁ ⁺ field inhomogeneity as compared with an alternate RF phase. In diffusion simulation, the steady-state magnetization in constant RF phase MP-SSFP increased with an increase of static field gradient up to 8 to 21 mT/m depending on simulation parameters. Experimental results at 4T validated these findings. In human brain imaging, MP-SSFP preserved sufficient signal intensities, but images showed severe image distortion from the pseudo-linear inhomogeneous field. However, following distortion correction, good-quality brain images were achieved.

CONCLUSION

MP-SSFP appears to be a feasible MRI technique for brain imaging in an inhomogeneous magnetic field.

Switching Circuit Optimization for Matrix Gradient Coils

Matrix gradient coils with up to 84 coil elements were recently introduced for magnetic resonance imaging. Ideally, each element is driven by a dedicated amplifier, which may be technically and financially infeasible. Instead, several elements can be connected in series (called a “cluster”) and driven by a single amplifier. In previous works, a set of clusters, called a “configuration,” was sought to approximate a target field shape. Because a magnetic resonance pulse sequence requires several distinct field shapes, a mechanism to switch between configurations is needed. This can be achieved by a hypothetical switching circuit connecting all terminals of all elements with each other and with the amplifiers. For a predefined set of configurations, a switching circuit can be designed to require only a limited amount of switches. Here we introduce an algorithm to minimize the number of switches without affecting the ability of the configurations to accurately create the desired fields. The problem is modeled using graph theory and split into 2 sequential combinatorial optimization problems that are solved using simulated annealing. For the investigated cases, the results show that compared to unoptimized switching circuits, the reduction of switches in optimized circuits ranges from 8% to up to 44% (average of 31%). This substantial reduction is achieved without impeding circuit functionality. This study shows how technical effort associated with implementation and operation of a matrix gradient coil is related to different hardware setups and how to reduce this effort.

Conjugate gradient variants for $${\ell}_{p}$$-regularized image reconstruction in low-field MRI

We consider the MRI physics in a low-field MRI scanner, in which permanent magnets are used to generate a magnetic field in the millitesla range. A model describing the relationship between measured signal and image is derived, resulting in an ill-posed inverse problem. In order to solve it, a regularization penalty is added to the least-squares minimization problem. We generalize the conjugate gradient minimal error (CGME) algorithm to the weighted and regularized least-squares problem. Analysis of the convergence of generalized CGME (GCGME) and the classical generalized conjugate gradient least squares (GCGLS) shows that GCGME can be expected to converge faster for ill-conditioned regularization matrices. The $${\ell}_{p}$$ℓp-regularized problem is solved using iterative reweighted least squares for $$p=1$$p=1 and $$p=\frac{1}{2}$$p=12, with both cases leading to an increasingly ill-conditioned regularization matrix. Numerical results show that GCGME needs a significantly lower number of iterations to converge than GCGLS.

Design of sparse Halbach magnet arrays for portable MRI using a genetic algorithm

Permanent magnet arrays offer several attributes attractive for the development of a low-cost portable MRI scanner for brain imaging. They offer the potential for a relatively lightweight, low to mid-field system with no cryogenics, a small fringe field, and no electrical power requirements or heat dissipation needs. The cylindrical Halbach array, however, requires external shimming or mechanical adjustments to produce B0 fields with standard MRI homogeneity levels (e.g., 0.1 ppm over FOV), particularly when constrained or truncated geometries are needed, such as a head-only magnet where the magnet length is constrained by the shoulders. For portable scanners using rotation of the magnet for spatial encoding with generalized projections, the spatial pattern of the field is important since it acts as the encoding field. In either a static or rotating magnet, it will be important to be able to optimize the field pattern of cylindrical Halbach arrays in a way that retains construction simplicity. To achieve this, we present a method for designing an optimized cylindrical Halbach magnet using the genetic algorithm to achieve either homogeneity (for standard MRI applications) or a favorable spatial encoding field pattern (for rotational spatial encoding applications). We compare the chosen designs against a standard, fully populated sparse Halbach design, and evaluate optimized spatial encoding fields using point-spread-function and image simulations. We validate the calculations by comparing to the measured field of a constructed magnet. The experimentally implemented design produced fields in good agreement with the predicted fields, and the genetic algorithm was successful in improving the chosen metrics. For the uniform target field, an order of magnitude homogeneity improvement was achieved compared to the un-optimized, fully populated design. For the rotational encoding design the resolution uniformity is improved by 95% compared to a uniformly populated design.

Optimization of Coil Element Configurations for a Matrix Gradient Coil

Recently, matrix gradient coils (also termed multi-coils or multi-coil arrays) were introduced for imaging and B₀ shimming with 24, 48, and even 84 coil elements. However, in imaging applications, providing one amplifier per coil element is not always feasible due to high cost and technical complexity. In this simulation study, we show that an 84-channel matrix gradient coil (head insert for brain imaging) is able to create a wide variety of field shapes even if the number of amplifiers is reduced. An optimization algorithm was implemented that obtains groups of coil elements, such that a desired target field can be created by driving each group with an amplifier. This limits the number of amplifiers to the number of coil element groups. Simulated annealing is used due to the NP-hard combinatorial nature of the given problem. A spherical harmonic basis set up to the full third order within a sphere of 20-cm diameter in the center of the coil was investigated as target fields. We show that the median normalized least squares error for all target fields is below approximately 5% for 12 or more amplifiers. At the same time, the dissipated power stays within reasonable limits. With a relatively small set of amplifiers, switches can be used to sequentially generate spherical harmonics up to third order. The costs associated with a matrix gradient coil can be lowered, which increases the practical utility of matrix gradient coils.

A z-gradient array for simultaneous multi-slice excitation with a single-band RF pulse

PURPOSE

Multi-slice radiofrequency (RF) pulses have higher specific absorption rates, more peak RF power, and longer pulse durations than single-slice RF pulses. Gradient field design techniques using a z-gradient array are investigated for exciting multiple slices with a single-band RF pulse.

THEORY AND METHODS

Two different field design methods are formulated to solve for the required current values of the gradient array elements for the given slice locations. The method requirements are specified, optimization problems are formulated for the minimum current norm and an analytical solution is provided. A 9-channel z-gradient coil array driven by independent, custom-designed gradient amplifiers is used to validate the theory.

RESULTS

Performance measures such as normalized slice thickness error, gradient strength per unit norm current, power dissipation, and maximum amplitude of the magnetic field are provided for various slice locations and numbers of slices. Two and 3 slices are excited by a single-band RF pulse in simulations and phantom experiments.

CONCLUSION

The possibility of multi-slice excitation with a single-band RF pulse using a z-gradient array is validated in simulations and phantom experiments. Magn Reson Med 80:400-412, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Simultaneous use of linear and nonlinear gradients for B1+ inhomogeneity correction

The simultaneous use of linear spatial encoding magnetic fields (L-SEMs) and nonlinear spatial encoding magnetic fields (N-SEMs) in B₁⁺ inhomogeneity problems is formulated and demonstrated with both simulations and experiments. Independent excitation k-space variables for N-SEMs are formulated for the simultaneous use of L-SEMs and N-SEMs by assuming a small tip angle. The formulation shows that, when N-SEMs are considered as an independent excitation k-space variable, numerous different k-space trajectories and frequency weightings differing in dimension, length, and energy can be designed for a given target transverse magnetization distribution. The advantage of simultaneous use of L-SEMs and N-SEMs is demonstrated by B₁⁺ inhomogeneity correction with spoke excitation. To fully utilize the independent k-space formulations, global optimizations are performed for 1D, 2D RF power limited, and 2D RF power unlimited simulations and experiments. Three different cases are compared: L-SEMs alone, N-SEMs alone, and both used simultaneously. In all cases, the simultaneous use of L-SEMs and N-SEMs leads to a decreased standard deviation in the ROI compared with using only L-SEMs or N-SEMs. The simultaneous use of L-SEMs and N-SEMs results in better B₁⁺ inhomogeneity correction than using only L-SEMs or N-SEMs due to the increased number of degrees of freedom.

Development and implementation of an 84-channel matrix gradient coil

PURPOSE

Design, implement, integrate, and characterize a customized coil system that allows for generating spatial encoding magnetic fields (SEMs) in a highly-flexible fashion.

METHODS

A gradient coil with a high number of individual elements was designed. Dimensions of the coil were chosen to mimic a whole-body gradient system, scaled down to a head insert. Mechanical shape and wire layout of each element were optimized to increase the local gradient strength while minimizing eddy current effects and simultaneously considering manufacturing constraints.

RESULTS

Resulting wire layout and mechanical design is presented. A prototype matrix gradient coil with 12 × 7 = 84 elements consisting of two element types was realized and characterized. Measured eddy currents are <1% of the original field. The coil is shown to be capable of creating nonlinear, and linear SEMs. In a DSV of 0.22 m gradient strengths between 24 mT∕m and 78 mT∕m could be realized locally with maximum currents of 150 A. Initial proof-of-concept imaging experiments using linear and nonlinear encoding fields are demonstrated.

CONCLUSION

A shielded matrix gradient coil setup capable of generating encoding fields in a highly-flexible manner was designed and implemented. The presented setup is expected to serve as a basis for validating novel imaging techniques that rely on nonlinear spatial encoding fields. Magn Reson Med 79:1181-1191, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Experimental O-space turbo spin echo imaging

PURPOSE

Turbo spin echo (TSE) imaging reduces imaging time by acquiring multiple echoes per repetition (TR), requiring fewer TRs. O-space can also require fewer TRs by using a combination of nonlinear magnetic gradient fields and surface coil arrays. Although to date, O-space has only been demonstrated for gradient echo imaging, it is valuable to combine these two techniques. However, collecting multiple O-space echoes per TR is difficult because of the different local k-space trajectories and variable T2-weighting.

THEORY AND METHODS

A practical scheme is demonstrated to combine the benefits of TSE and O-space for highly accelerated T2-weighted images. The scheme uses a modified acquisition order and filtered projection reconstruction to reduce artifacts caused by T2 decay, while retaining T2 contrast that corresponds to a specific echo time.

RESULTS

The experiments revealed that the proposed method can produce highly accelerated T2-weighted images. Moreover, the method can generate multiple images with different T2 contrasts from a single dataset.

CONCLUSIONS

The proposed O-space TSE imaging method requires fewer echoes than conventional TSE and fewer repetitions than conventional O-space imaging. It retains resilience to undersampling, clearly outperforming Cartesian SENSE at high levels of undersampling, and can generate undistorted images with a range of T2 contrast from a single acquired dataset.

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.

Local field of view imaging for alias-free undersampling with nonlinear spatial encoding magnetic fields

PURPOSE

Nonlinear spatial encoding magnetic fields result in an inhomogeneous image resolution. Within this study, this characteristic property of nonlinear encoding is investigated with regard to its potential to accelerate MRI acquisitions.

THEORY

A dependency between k-space coverage and local resolvability of the image causes k-space samples to have a spatially localized contribution to the reconstruction of the spin density. On the basis of this observation, a concept for alias-free data undersampling is developed, which is referred to as the local field of view concept.

METHODS

On the basis of this concept, a fast sampling trajectory is developed. It is evaluated with simulations and experiments (both using a phantom and in vivo) for MRI with, as an example, pure quadrupolar encoding fields. To demonstrate that the concept is only applicable to (spatially) nonlinear encoding, a comparison with linear encoding is provided.

RESULTS

Application of the local field of view concept results in a localized adaptation of the image resolution by undersampling higher frequency k-space samples without introducing aliasing.

CONCLUSIONS

A new effect of nonlinear spatial encoding magnetic fields was found, which allows more efficient data sampling and at the same time counterbalancing the natural variation in image resolution.

Radiofrequency pulse design using nonlinear gradient magnetic fields

PURPOSE

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields.

THEORY AND METHODS

The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments.

RESULTS

The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity.

CONCLUSION

An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest.

Trajectory optimization based on the signal-to-noise ratio for spatial encoding with nonlinear encoding fields

PURPOSE

Multiple nonlinear gradient fields offer many potential benefits for spatial encoding including reduced acquisition time, fewer artefacts and region-specific imaging, although designing a suitable trajectory for such a setup is difficult. This work aims to optimize encoding trajectories for multiple nonlinear gradient fields based on the image signal-to-noise ratio.

THEORY AND METHODS

Image signal-to-noise ratio is directly linked to the covariance of the reconstructed pixels, which can be calculated recursively for each projection of the trajectory under a Bayesian formulation. An evolutionary algorithm is used to find the higher-dimensional projections that minimize the pixel covariance, incorporating receive coil profiles, intravoxel dephasing, and reconstruction regularization. The resulting trajectories are tested through simulations and experiments.

RESULTS

The optimized trajectories produce images with higher resolution and fewer artefacts compared with traditional approaches, particularly for high undersampling. However, higher-dimensional projection experiments strongly depend on accurate hardware and calibration.

CONCLUSION

Computer-based optimization provides an efficient means to explore the large trajectory space created by the use of multiple nonlinear encoding fields. The optimization framework, as presented here, is necessary to fully exploit the advantages of nonlinear fields. Magn Reson Med 76:104-117, 2016. © 2015 Wiley Periodicals, Inc.

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.

Image reconstruction in k-space from MR data encoded with ambiguous gradient fields

PURPOSE

In this work, the limits of image reconstruction in k-space are explored when non-bijective gradient fields are used for spatial encoding.

THEORY

The image space analogy between parallel imaging and imaging with non-bijective encoding fields is partially broken in k-space. As a consequence, it is hypothesized and proven that ambiguities can only be resolved partially in k-space, and not completely as is the case in image space.

METHODS

Image-space and k-space based reconstruction algorithms for multi-channel radiofrequency data acquisitions are programmed and tested using numerical simulations as well as in vivo measurement data.

RESULTS

The hypothesis is verified based on an analysis of reconstructed images. It is found that non-bijective gradient fields have the effect that densely sampled autocalibration data, used for k-space reconstruction, provide less information than a separate scan of the receiver coil sensitivity maps, used for image space reconstruction. Consequently, in k-space only the undersampling artifact can be unfolded, whereas in image space, it is also possible to resolve aliasing that is caused by the non-bijectivity of the gradient fields.

CONCLUSION

For standard imaging, reconstruction in image space and in k-space is nearly equivalent, whereas there is a fundamental difference with practical consequences for the selection of image reconstruction algorithms when non-bijective encoding fields are involved.

Pseudo-random center placement O-space imaging for improved incoherence compressed sensing parallel MRI

PURPOSE

Nonlinear spatial encoding magnetic (SEM) field strategies such as O-space imaging have previously reported dispersed artifacts during accelerated scans. Compressed sensing (CS) has shown a sparsity-promoting convex program allows image reconstruction from a reduced data set when using the appropriate sampling. The development of a pseudo-random center placement (CP) O-space CS approach optimizes incoherence through SEM field modulation to reconstruct an image with reduced error.

THEORY AND METHODS

The incoherence parameter determines the sparsity levels for which CS is valid and the related transform point spread function measures the maximum interference for a single point. The O-space acquisition is optimized for CS by perturbing the Z(2) strength within 30% of the nominal value and demonstrated on a human 3T scanner.

RESULTS

Pseudo-random CP O-space imaging is shown to improve incoherence between the sensing and sparse domains. Images indicate pseudo-random CP O-space has reduced mean squared error compared with a typical linear SEM field acquisition method.

CONCLUSION

Pseudo-random CP O-space imaging, with a nonlinear SEM field designed for CS, is shown to reduce mean squared error of images at high acceleration over linear encoding methods for a 2D slice when using an eight channel circumferential receiver array for parallel imaging.

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.

Two-dimensional imaging in a lightweight portable MRI scanner without gradient coils

PURPOSE

As the premiere modality for brain imaging, MRI could find wider applicability if lightweight, portable systems were available for siting in unconventional locations such as intensive care units, physician offices, surgical suites, ambulances, emergency rooms, sports facilities, or rural healthcare sites.

METHODS

We construct and validate a truly portable (<100 kg) and silent proof-of-concept MRI scanner which replaces conventional gradient encoding with a rotating lightweight cryogen-free, low-field magnet. When rotated about the object, the inhomogeneous field pattern is used as a rotating spatial encoding magnetic field (rSEM) to create generalized projections which encode the iteratively reconstructed two-dimensional (2D) image. Multiple receive channels are used to disambiguate the nonbijective encoding field.

RESULTS

The system is validated with experimental images of 2D test phantoms. Similar to other nonlinear field encoding schemes, the spatial resolution is position dependent with blurring in the center, but is shown to be likely sufficient for many medical applications.

CONCLUSION

The presented MRI scanner demonstrates the potential for portability by simultaneously relaxing the magnet homogeneity criteria and eliminating the gradient coil. This new architecture and encoding scheme shows convincing proof of concept images that are expected to be further improved with refinement of the calibration and methodology.

Single echo MRI

Purpose

Previous nonlinear gradient research has focused on trajectories that reconstruct images with a minimum number of echoes. Here we describe sequences where the nonlinear gradients vary in time to acquire the image in a single readout. The readout is designed to be very smooth so that it can be compressed to minimal time without violating peripheral nerve stimulation limits, yielding an image from a single 4 ms echo.

Theory and Methods

This sequence was inspired by considering the code of each voxel, i.e. the phase accumulation that a voxel follows through the readout, an approach connected to traditional encoding theory. We present simulations for the initial sequence, a low slew rate analog, and higher resolution reconstructions.

Results

Extremely fast acquisitions are achievable, though as one would expect, SNR is reduced relative to the slower Cartesian sampling schemes because of the high gradient strengths.

Conclusions

The prospect that nonlinear gradients can acquire images in a single <10 ms echo makes this a novel and interesting approach to image encoding.

Accelerating sequences in the presence of metal by exploiting the spatial distribution of off-resonance

PURPOSE

To demonstrate feasibility of exploiting the spatial distribution of off-resonance surrounding metallic implants for accelerating multispectral imaging techniques.

THEORY AND METHODS

Multispectral imaging (MSI) techniques perform time-consuming independent three-dimensional acquisitions with varying radio frequency offsets to address the extreme off-resonance from metallic implants. Each off-resonance bin provides a unique spatial sensitivity that is analogous to the sensitivity of a receiver coil and, therefore, provides a unique opportunity for acceleration. Fully sampled MSI was performed to demonstrate retrospective acceleration. A uniform sampling pattern across off-resonance bins was compared with several adaptive sampling strategies using a total hip replacement phantom. Monte Carlo simulations were performed to compare noise propagation of two of these strategies. With a total knee replacement phantom, positive and negative off-resonance bins were strategically sampled with respect to the B0 field to minimize aliasing. Reconstructions were performed with a parallel imaging framework to demonstrate retrospective acceleration.

RESULTS

An adaptive sampling scheme dramatically improved reconstruction quality, which was supported by the noise propagation analysis. Independent acceleration of negative and positive off-resonance bins demonstrated reduced overlapping of aliased signal to improve the reconstruction.

CONCLUSION

This work presents the feasibility of acceleration in the presence of metal by exploiting the spatial sensitivities of off-resonance bins.

MR image reconstruction from generalized projections

PURPOSE

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(N(4)) to O(N(3)).

THEORY

For generalized projections, a large class of multidimensional imaging trajectories, the encoding matrix can be focused to sparse bands by introducing an appropriate filter function along the frequency-encoding direction. The reconstruction can be speeded up by ignoring values below a predefined threshold level.

METHODS

Two methods are presented that differ in how the filter is incorporated into the reconstruction algorithm. The first method represents, without implementation of a threshold, a weighted version of the time-domain method, while the second method is equivalent to it.

RESULTS

Simulation and measurement results show that image reconstruction from high-resolution imaging data can be speeded up by up to two orders of magnitude. While the weighted reconstruction requires more iterations to reach an optimum than the second method, it is less sensitive to thresholding.

CONCLUSION

For complex spatial encoding strategies that involve nonlinear gradient fields, fast and accurate image reconstruction methods are provided that are particularly efficient for high-resolution anatomical imaging.

Spatial encoding using the nonlinear field perturbations from magnetic materials

PURPOSE

A proof-of-concept study was performed to assess the technical feasibility of using magnetic materials to generate spatial encoding fields.

THEORY AND METHODS

Spatially varying magnetic fields were generated by the placement of markers with different volume susceptibilities within the imaging volume. No linear gradients were used for spatial encoding during the signal acquisition. A signal-encoding model is described for reconstructing the images encoded with these field perturbations. Simulation and proof-of-concept experimental results are presented. Experiments were performed using field perturbations from a cylindrical marker as an example of the new encoding fields. Based on this experimental setup, annular rings were reconstructed from signals encoded with the new fields.

RESULTS

Simulation results were presented for different acquisition parameters. Proof-of-concept was supported by the correspondence of regions in an image reconstructed from experimental data compared to those in a conventional gradient-echo image. Experimental results showed that inclusions of dimensions 1.5 mm in size could be resolved with the experimental setup.

CONCLUSION

This study shows the technical feasibility of using magnetic markers to produce encoding fields. Magnetic materials will allow generating spatial encoding fields, which can be tailored to an imaging application with less complexity and at lower cost compared to the use of gradient inserts.

Pushing the limits of in vivo diffusion MRI for the Human Connectome Project

Perhaps more than any other "-omics" endeavor, the accuracy and level of detail obtained from mapping the major connection pathways in the living human brain with diffusion MRI depend on the capabilities of the imaging technology used. The current tools are remarkable; allowing the formation of an "image" of the water diffusion probability distribution in regions of complex crossing fibers at each of half a million voxels in the brain. Nonetheless our ability to map the connection pathways is limited by the image sensitivity and resolution, and also the contrast and resolution in encoding of the diffusion probability distribution. The goal of our Human Connectome Project (HCP) is to address these limiting factors by re-engineering the scanner from the ground up to optimize the high b-value, high angular resolution diffusion imaging needed for sensitive and accurate mapping of the brain's structural connections. Our efforts were directed based on the relative contributions of each scanner component. The gradient subsection was a major focus since gradient amplitude is central to determining the diffusion contrast, the amount of T2 signal loss, and the blurring of the water PDF over the course of the diffusion time. By implementing a novel 4-port drive geometry and optimizing size and linearity for the brain, we demonstrate a whole-body sized scanner with G(max) = 300 mT/m on each axis capable of the sustained duty cycle needed for diffusion imaging. The system is capable of slewing the gradient at a rate of 200 T/m/s as needed for the EPI image encoding. In order to enhance the efficiency of the diffusion sequence we implemented a FOV shifting approach to Simultaneous MultiSlice (SMS) EPI capable of unaliasing 3 slices excited simultaneously with a modest g-factor penalty allowing us to diffusion encode whole brain volumes with low TR and TE. Finally we combine the multi-slice approach with a compressive sampling reconstruction to sufficiently undersample q-space to achieve a DSI scan in less than 5 min. To augment this accelerated imaging approach we developed a 64-channel, tight-fitting brain array coil and show its performance benefit compared to a commercial 32-channel coil at all locations in the brain for these accelerated acquisitions. The technical challenges of developing the over-all system are discussed as well as results from SNR comparisons, ODF metrics and fiber tracking comparisons. The ultra-high gradients yielded substantial and immediate gains in the sensitivity through reduction of TE and improved signal detection and increased efficiency of the DSI or HARDI acquisition, accuracy and resolution of diffusion tractography, as defined by identification of known structure and fiber crossing.

Efficient concomitant and remanence field artifact reduction in ultra-low-field MRI using a frequency-space formulation

PURPOSE

For ultra-low-field MRI, the spatial-encoding magnetic fields generated by gradient coils can have strong concomitant fields leading to prominent image distortion. Additionally, using superconducting magnet to pre-polarize magnetization can improve the signal-to-noise ratio of ultra-low-field MRI. Yet the spatially inhomogeneous remanence field due to the permanently trapped flux inside a superconducting pre-polarizing coil modulates magnetization and causes further image distortion.

METHOD

We propose a two-stage frequency-space (f-x) formulation to accurately describe the dynamics of spatially-encoded magnetization under the influence of concomitant and remanence fields, which allows for correcting image distortion due to concomitant and remanence fields.

RESULTS

Our method is computationally efficient as it uses a combination of the fast Fourier transform algorithm and a linear equation solver. With sufficiently dense discretization in solving the linear equation, the performance of this f-x method was found to be stable among different choices of the regularization parameter and the regularization matrix.

CONCLUSION

We present this method together with numerical simulations and experimental data to demonstrate how concomitant and remanence field artifacts in ultra-low-field MRI can be corrected efficiently.

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.

In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration

Recently, spatial encoding with nonlinear magnetic fields has drawn attention for its potential to achieve faster gradient switching within safety limits, tailored resolution in regions of interest, and improved parallel imaging using encoding fields that complement the sensitivity profiles of radio frequency receive arrays. Proposed methods can broadly be divided into those that use phase encoding (Cartesian-trajectory PatLoc and COGNAC) and those that acquire nonlinear projections (O-Space, Null space imaging, radial PatLoc, and 4D-RIO). Nonlinear projection data are most often reconstructed with iterative algorithms that backproject data using the full encoding matrix. Just like conventional radial sequences that use linear spatial encoding magnetic fields, nonlinear projection methods are more sensitive than phase encoding methods to imperfect calibration of the encoding fields. In this work, voxel-wise phase evolution is mapped at each acquired point in an O-Space trajectory using a variant of chemical shift imaging, capturing all spin dynamics caused by encoding fields, eddy currents, and pulse timing. Phase map calibration is then applied to data acquired from a high-power, 12 cm, Z2 insert coil with an eight-channel radio frequency transmit-receive array on a 3T human scanner. We show the first experimental proof-of-concept O-Space images on in vivo and phantom samples, paving the way for more in-depth exploration of O-Space and similar imaging methods.

PexLoc-Parallel excitation using local encoding magnetic fields with nonlinear and nonbijective spatial profiles

With the recent proposal of using magnetic fields that are nonlinear by design for spatial encoding, new flexibility has been introduced to MR imaging. The new degrees of freedom in shaping the spatially encoding magnetic fields (SEMs) can be used to locally adapt the imaging resolution to features of the imaged object, e.g., anatomical structures, to reduce peripheral nerve stimulation during in vivo experiments or to increase the gradient switching speed by reducing the inductance of the coils producing the SEMs and thus accelerate the imaging process. In this work, the potential of nonlinear and nonbijective SEMs for spatial encoding during transmission in multidimensional spatially selective excitation is explored. Methods for multidimensional spatially selective excitation radiofrequency pulse design based on nonlinear encoding fields are introduced, and it is shown how encoding ambiguities can be resolved using parallel transmission. In simulations and phantom experiments, the feasibility of selective excitation using nonlinear, nonbijective SEMs is demonstrated, and it is shown that the spatial resolution with which the target distribution of the transverse magnetization can be realized varies locally. Thus, the resolution of the target pattern can be increased in some regions compared with conventional linear encoding. Furthermore, experimental proof of principle of accelerated two-dimensional spatially selective excitation using nonlinear SEMs is provided in this study.

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.

Null space imaging: nonlinear magnetic encoding fields designed complementary to receiver coil sensitivities for improved acceleration in parallel imaging

To increase image acquisition efficiency, we develop alternative gradient encoding strategies designed to provide spatial encoding complementary to the spatial encoding provided by the multiple receiver coil elements in parallel image acquisitions. Intuitively, complementary encoding is achieved when the magnetic field encoding gradients are designed to encode spatial information where receiver spatial encoding is ambiguous, for example, along sensitivity isocontours. Specifically, the method generates a basis set for the null space of the coil sensitivities with the singular value decomposition and calculates encoding fields from the null space vectors. A set of nonlinear gradients is used as projection imaging readout magnetic fields, replacing the conventional linear readout field and phase encoding. Multiple encoding fields are used as projections to capture the null space information, hence the term null space imaging. The method is compared to conventional Cartesian SENSitivity Encoding as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The null space imaging approach yields a parallel imaging method that provides high acceleration factors with a limited number of receiver coil array elements through increased time efficiency in spatial encoding.

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.

The Role of Nonlinear Gradients in Parallel Imaging: A k-Space Based Analysis

Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.

Multidimensionally encoded magnetic resonance imaging

Magnetic resonance imaging (MRI) typically achieves spatial encoding by measuring the projection of a q-dimensional object over q-dimensional spatial bases created by linear spatial encoding magnetic fields (SEMs). Recently, imaging strategies using nonlinear SEMs have demonstrated potential advantages for reconstructing images with higher spatiotemporal resolution and reducing peripheral nerve stimulation. In practice, nonlinear SEMs and linear SEMs can be used jointly to further improve the image reconstruction performance. Here, we propose the multidimensionally encoded (MDE) MRI to map a q-dimensional object onto a p-dimensional encoding space where p > q. MDE MRI is a theoretical framework linking imaging strategies using linear and nonlinear SEMs. Using a system of eight surface SEM coils with an eight-channel radiofrequency coil array, we demonstrate the five-dimensional MDE MRI for a two-dimensional object as a further generalization of PatLoc imaging and O-space imaging. We also present a method of optimizing spatial bases in MDE MRI. Results show that MDE MRI with a higher dimensional encoding space can reconstruct images more efficiently and with a smaller reconstruction error when the k-space sampling distribution and the number of samples are controlled.

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.

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.