Excitation and geometrically matched local encoding of curved slices

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.

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.

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.

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.

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.

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.

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.

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.

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.

Simultaneous functional MRI acquisition of distributed brain regions with high temporal resolution using a 2D-selective radiofrequency excitation

PURPOSE

To perform simultaneous functional MRI of multiple, distributed brain regions at high temporal resolution using a 2D-selective radiofrequency (2DRF) excitation.

METHODS

A tailored 2DRF excitation is used to excite several, small regions-of-interest distributed in the brain. They are acquired in a single projection image with an appropriately chosen orientation such that the different regions-of-interest can be discriminated by their position in the projection plane. Thus, they are excited and acquired simultaneously with a temporal resolution comparable to that of a single-slice measurement. The feasibility of this approach for functional neuroimaging (in-plane resolution 2 × 2 mm(2) ) at high temporal resolution (80 ms) is demonstrated in healthy volunteers for regions-of-interest in the visual and motor system using checkerboard and finger tapping block-design paradigms.

RESULTS

Task-related brain activation could be observed in both the visual and the motor system simultaneously with a high temporal resolution. For an onset shift of 240 ms for half of the checkerboard, a delay of the hemodynamic response in the corresponding hemisphere of the visual cortex could be detected.

CONCLUSION

Limiting the excited magnetization to the desired target regions with a 2DRF excitation reduces the imaging sampling requirements which can improve the temporal resolution significantly.

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.