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

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.

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.

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.

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.