Multidimensionally encoded magnetic resonance imaging

Practical utilization of nonlinear spatial encoding: Fast field mapping and FRONSAC-wave

PURPOSE

To study the additional value of FRONSAC encoding in 2D and 3D wave sequences, implementing a simple strategy to trajectory mapping for FRONSAC encoding gradients.

THEORY AND METHODS

The nonlinear gradient trajectory for each voxel was estimated by exploiting the sparsity of the point spread function in the frequency domain. Simulations and in-vivo experiments were used to analyze the performance of combinations of wave and FRONSAC encoding.

RESULTS

Field mapping using the simplified approach produced similar image quality with much shorter calibration time than the comprehensive mapping schemes utilized in previous work. In-vivo human brain images showed that the addition of FRONSAC encoding could improve wave image quality, particularly at very high undersampling factors and in the context of limited wave amplitudes. These results were further supported by g-factor maps.

CONCLUSION

Results show that FRONSAC can be used to improve image quality of wave at very high undersampling rates or in slew-limited acquisitions. Our study illustrates the potential of the proposed fast field mapping approach.

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.

Clinical Potential of a New Approach to MRI Acceleration

Fast ROtary Nonlinear Spatial ACquisition (FRONSAC) was recently introduced as a new strategy that applies nonlinear gradients as a small perturbation to improve image quality in highly undersampled MRI. In addition to experimentally showing the previously simulated improvement to image quality, this work introduces the insight that Cartesian-FRONSAC retains many desirable features of Cartesian imaging. Cartesian-FRONSAC preserves the existing linear gradient waveforms of the Cartesian sequence while adding oscillating nonlinear gradient waveforms. Experiments show that performance is essentially identical to Cartesian imaging in terms of (1) resilience to experimental imperfections, like timing errors or off-resonance spins, (2) accommodating scan geometry changes without the need for recalibration or additional field mapping, (3) contrast generation, as in turbo spin echo. Despite these similarities to Cartesian imaging, which provides poor parallel imaging performance, Cartesian-FRONSAC consistently shows reduced undersampling artifacts and better response to advanced reconstruction techniques. A final experiment shows that hardware requirements are also flexible. Cartesian-FRONSAC improves accelerated imaging while retaining the robustness and flexibility critical to real clinical use.

Magnetic Resonance Imaging technology-bridging the gap between noninvasive human imaging and optical microscopy

Technological advances in Magnetic Resonance Imaging (MRI) have provided substantial gains in the sensitivity and specificity of functional neuroimaging. Mounting evidence demonstrates that the hemodynamic changes utilized in functional MRI can be far more spatially and thus neuronally specific than previously believed. This has motivated a push toward novel, high-resolution MR imaging strategies that can match this biological resolution limit while recording from the entire human brain. Although sensitivity increases are a necessary component, new MR encoding technologies are required to convert improved sensitivity into higher resolution. These new sampling strategies improve image acquisition efficiency and enable increased image encoding in the time-frame needed to follow hemodynamic changes associated with brain activation.

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.

O-space with high resolution readouts outperforms radial imaging

PURPOSE

While O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts.

THEORY AND METHODS

A sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging.

RESULTS

Experimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image.

CONCLUSIONS

High resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.

Fast rotary nonlinear spatial acquisition (FRONSAC) imaging

PURPOSE

Nonlinear spatial encoding magnetic fields (SEMs) have been studied to reconstruct images from a minimum number of echoes. Previous work has also explored single shot trajectories in nonlinear SEMs. However, the search continues for optimal schemes that apply nonlinear SEMs to improve spatial encoding efficiency and image quality.

THEORY AND METHODS

We enhance the encoding efficiency of standard linear gradient trajectories by adding a rapidly rotating nonlinear SEM of moderate amplitude, the so called FRONSAC (Fast ROtary Nonlinear Spatial ACquisition) imaging. This additional gradient greatly improves the image quality of highly undersampled single-shot trajectories, including EPI, Spiral, and Rosette trajectories.

RESULTS

Our simulations, including noise and dephasing effects, test the effect of adding FRONSAC gradients, demonstrating the applicability of this approach. Performance is explained by demonstrating the additional k-space sampling the nonlinear gradient provides. Studies of the optimal amplitude and frequency of the additional FRONSAC field are presented, and the role of enhanced sampling during the readout demonstrated. Dynamic field mapping in a second-order gradient system shows the proposed gradient waveforms are feasible.

CONCLUSION

Images resulting from highly undersampled existing k-space trajectories, such as EPI, Spiral, and Rosette, are greatly enhanced simply by adding a rotating nonlinear SEM field.

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.

Combining parallel detection of proton echo planar spectroscopic imaging (PEPSI) measurements with a data-consistency constraint improves SNR

One major challenge of MRSI is the poor signal-to-noise ratio (SNR), which can be improved by using a surface coil array. Here we propose to exploit the spatial sensitivity of different channels of a coil array to enforce the k-space data consistency (DC) in order to suppress noise and consequently to improve MRSI SNR. MRSI data were collected using a proton echo planar spectroscopic imaging (PEPSI) sequence at 3 T using a 32-channel coil array and were averaged with one, two and eight measurements (avg-1, avg-2 and avg-8). The DC constraint was applied using a regularization parameter λ of 1, 2, 3, 5 or 10. Metabolite concentrations were quantified using LCModel. Our results show that the suppression of noise by applying the DC constraint to PEPSI reconstruction yields up to 32% and 27% SNR gain for avg-1 and avg-2 data with λ = 5, respectively. According to the reported Cramer-Rao lower bounds, the improvement in metabolic fitting was significant (p < 0.01) when the DC constraint was applied with λ ≥ 2. Using the DC constraint with λ = 3 or 5 can minimize both root-mean-square errors and spatial variation for all subjects using the avg-8 data set as reference values. Our results suggest that MRSI reconstructed with a DC constraint can save around 70% of scanning time to obtain images and spectra with similar SNRs using λ = 5.

Multi-slice MRI with the dynamic multi-coil technique

To date, spatial encoding for MRI is based on linear X, Y and Z field gradients generated by dedicated X, Y and Z wire patterns. We recently introduced the dynamic multi-coil technique (DYNAMITE) for the generation of magnetic field shapes for biomedical MR applications from a set of individually driven localized coils. The benefits for B0 magnetic field homogenization have been shown, as well as proof of principle of radial and algebraic MRI. In this study the potential of DYNAMITE MRI is explored further and the first multi-slice MRI implementation in which all gradient fields are purely DYNAMITE based is presented. The obtained image fidelity is shown to be virtually identical to that of a conventional MRI system with dedicated X, Y and Z gradient coils. Comparable image quality is a milestone towards the establishment of fully functional DYNAMITE MRI (and shim) systems.

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.

A 32-channel combined RF and B0 shim array for 3T brain imaging

PURPOSE

We add user-controllable direct currents (DC) to the individual elements of a 32-channel radio-frequency (RF) receive array to provide B0 shimming ability while preserving the array's reception sensitivity and parallel imaging performance.

METHODS

Shim performance using constrained DC current (± 2.5A) is simulated for brain arrays ranging from 8 to 128 elements. A 32-channel 3-tesla brain array is realized using inductive chokes to bridge the tuning capacitors on each RF loop. The RF and B0 shimming performance is assessed in bench and imaging measurements.

RESULTS

The addition of DC currents to the 32-channel RF array is achieved with minimal disruption of the RF performance and/or negative side effects such as conductor heating or mechanical torques. The shimming results agree well with simulations and show performance superior to third-order spherical harmonic (SH) shimming. Imaging tests show the ability to reduce the standard frontal lobe susceptibility-induced fields and improve echo planar imaging geometric distortion. The simulation of 64- and 128-channel brain arrays suggest that even further shimming improvement is possible (equivalent to up to 6th-order SH shim coils).

CONCLUSION

Including user-controlled shim currents on the loops of a conventional highly parallel brain array coil is feasible with modest current levels and produces improved B0 shimming performance over standard second-order SH shimming.

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.

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.