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

Stochastic-offset-enhanced restricted slice excitation and 180° refocusing designs with spatially non-linear ΔB0 shim array fields

PURPOSE

Developing a general framework with a novel stochastic offset strategy for the design of optimized RF pulses and time-varying spatially non-linear ΔB0 shim array fields for restricted slice excitation and refocusing with refined magnetization profiles within the intervals of the fixed voxels.

METHODS

Our framework uses the decomposition property of the Bloch equations to enable joint design of RF-pulses and shim array fields for restricted slice excitation and refocusing with auto-differentiation optimization. Bloch simulations are performed independently on orthogonal basis vectors, Mx, My, and Mz, which enables designs for arbitrary initial magnetizations. Requirements for refocusing pulse designs are derived from the extended phase graph formalism obviating time-consuming sub-voxel isochromatic simulations to model the effects of crusher gradients. To refine resultant slice-profiles because of voxelwise optimization functions, we propose an algorithm that stochastically offsets spatial points at which loss is computed during optimization.

RESULTS

We first applied our proposed design framework to standard slice-selective excitation and refocusing pulses in the absence of non-linear ΔB0 shim array fields and compared them against pulses designed with Shinnar-Le Roux algorithm. Next, we demonstrated our technique in a simulated setup of fetal brain imaging in pregnancy for restricted-slice excitation and refocusing of the fetal brain.

CONCLUSIONS

Our proposed framework for optimizing RF pulse and time-varying spatially non-linear ΔB0 shim array fields achieve high fidelity restricted-slice excitation and refocusing for fetal MRI, which could enable zoomed fast-spin-echo-MRI and other applications.

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.

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.

Mitigation of B1+ inhomogeneity using spatially selective excitation with jointly designed quadratic spatial encoding magnetic fields and RF shimming

PURPOSE

The inhomogeneity of flip angle distribution is a major challenge impeding the application of high-field MRI. We report a method combining spatially selective excitation using generalized spatial encoding magnetic fields (SAGS) with radiofrequency (RF) shimming to achieve homogeneous excitation. This method can be an alternative approach to address the challenge of B1+ inhomogeneity using nonlinear gradients.

METHODS

We proposed a two-step algorithm that jointly optimizes the combination of nonlinear spatial encoding magnetic fields and the combination of multiple RF transmitter coils and then optimizes the locations, RF amplitudes, and phases of the spokes.

RESULTS

Our results show that jointly designed SAGS and RF shimming can provide a more homogeneous flip angle distribution than using SAGS or RF shimming alone. Compared with RF shimming alone, our approach can reduce the relative standard deviation of flip angle by 56% and 52% using phantom and human head data, respectively.

CONCLUSION

The jointly designed SAGS and RF shimming method can be used to achieve homogeneous flip angle distributions when fully parallel RF transmission is not available. Magn Reson Med 78:577-587, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Parallel transmission for ultrahigh-field imaging

The development of MRI systems operating at or above 7 T has provided researchers with a new window into the human body, yielding improved imaging speed, resolution and signal-to-noise ratio. In order to fully realise the potential of ultrahigh-field MRI, a range of technical hurdles must be overcome. The non-uniformity of the transmit field is one of such issues, as it leads to non-uniform images with spatially varying contrast. Parallel transmission (i.e. the use of multiple independent transmission channels) provides previously unavailable degrees of freedom that allow full spatial and temporal control of the radiofrequency (RF) fields. This review discusses the many ways in which these degrees of freedom can be used, ranging from making more uniform transmit fields to the design of subject-tailored RF pulses for both uniform excitation and spatial selection, and also the control of the specific absorption rate. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

Reduced field of view imaging using a static second-order gradient for functional MRI applications

PURPOSE

Imaging using reduced FOV excitation allows higher resolution or signal-to-noise ratio (SNR) per scan time but often requires long radiofrequency pulses. The goal of this study was to improve a recent reduced field of view (FOV) method that uses a second-order shim gradient to decrease pulse length and evaluate its use in functional MRI (fMRI) applications.

THEORY AND METHODS

The method, which was initially limited to excite thin disc-shaped regions at the isocenter, was extended to excite thicker regions off the isocenter and produced accurate excitation profiles on a grid phantom. Visual stimulation fMRI scans were performed with full and reduced FOV. The resolution of the time series images and functional activation maps were assessed using the full-width half-maxima of the autocorrelation functions (FACFs) of the noise images and the activation map values, respectively.

RESULTS

The resolution was higher in the reduced FOV time series images (4.1% ± 3.7% FACF reduction, P < 0.02) and functional activation maps (3.1% ± 3.4% FACF reduction, P < 0.01), but the SNR was lower (by 26.5% ± 16.9%). However, for a few subjects, the targeted region could not be localized to the reduced FOV due to the low Z2 gradient strength.

CONCLUSION

The results of this study suggest that the proposed method is feasible, though it would benefit from a stronger gradient coil.

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.