Shinnar-Le Roux Algorithm Research Articles

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

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. 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. 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. 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.

SLfRank: Shinnar-Le-Roux Pulse Design With Reduced Energy and Accurate Phase Profiles Using Rank Factorization.

The Shinnar-Le-Roux (SLR) algorithm is widely used to design frequency selective pulses with large flip angles. We improve its design process to generate pulses with lower energy (by as much as 26%) and more accurate phase profiles. Concretely, the SLR algorithm consists of two steps: (1) an invertible transform between frequency selective pulses and polynomial pairs that represent Cayley-Klein (CK) parameters and (2) the design of the CK polynomial pair to match the desired magnetization profiles. Because the CK polynomial pair is bi-linearly coupled, the original algorithm sequentially solves for each polynomial instead of jointly. This results in sub-optimal pulses. Instead, we leverage a convex relaxation technique, commonly used for low rank matrix recovery, to address the bi-linearity. Our numerical experiments show that the resulting pulses are almost always globally optimal in practice. For slice excitation, the proposed algorithm results in more accurate linear phase profiles. And in general the improved pulses have lower energy than the original SLR pulses.

Selective excitation localized by the Bloch-Siegert shift and a gradient.

To perform -selective excitation using the Bloch-Siegert shift for spatial localization. A -selective excitation is produced by an radiofrequency (RF) pulse consisting of two summed component pulses: an off-resonant pulse that induces a -dependent Bloch-Siegert frequency shift and a frequency-selective excitation pulse. The passband of the pulse can be tailored by adjusting the frequency content of the frequency-selective pulse, as in conventional gradient-localized excitation. Fine magnetization profile control is achieved by using the Shinnar-Le Roux algorithm to design the frequency-selective excitation pulse. Simulations analyzed the pulses' robustness to off-resonance, their suitability for multi-echo spin echo pulse sequences, and how their performance compares to that of rotating-frame selective excitation pulses. The pulses were evaluated experimentally on a 47.5 mT MRI scanner using an RF gradient transmit coil. Multiphoton resonances produced by the pulses were characterized and their distribution across predicted. With correction for varying across the desired profile, the proposed pulses produced selective excitation with the specified profile characteristics. The pulses were robust against off-resonance and RF amplifier distortion, and suitable for multi-echo pulse sequences. Experimental profiles closely matched simulated patterns. The Bloch-Siegert shift can be used to perform -gradient-free selective excitation, enabling the excitation of slices or slabs in RF gradient-encoded MRI.

Semi-adiabatic Shinnar–Le Roux pulses and their application to diffusion tensor imaging of humans at 7T

The adiabatic Shinnar–Le Roux (SLR) algorithm for radiofrequency (RF) pulse design enables systematic control of pulse parameters such as bandwidth, RF energy distribution and duration. Some applications, such as diffusion-weighted imaging (DWI) at high magnetic fields, would benefit from RF pulses that can provide greater B1 insensitivity while adhering to echo time and specific absorption rate (SAR) limits. In this study, the adiabatic SLR algorithm was employed to generate 6-ms and 4-ms 180° semi-adiabatic RF pulses which were used to replace the refocusing pulses in a twice-refocused spin echo (TRSE) diffusion-weighted echo planar imaging (DW-EPI) sequence to create two versions of a twice-refocused adiabatic spin echo (TRASE) sequence. The two versions were designed for different trade-offs between adiabaticity and echo time. Since a pair of identical refocusing pulses is applied, the quadratic phase imposed by the first is unwound by the second, preserving the linear phase created by the excitation pulse. In vivo images of the human brain obtained at 7Testa (7T) demonstrate that both versions of the TRASE sequence developed in this study achieve more homogeneous signal in the diffusion-weighted images than the conventional TRSE sequence. Semi-adiabatic SLR pulses offer a more B1-insensitive solution for diffusion preparation at 7T, while operating within SAR constraints. This method may be coupled with any EPI readout trajectory and parallel imaging scheme to provide more uniform coverage for diffusion tensor imaging at 7T and 3T.

Hadamard slice encoding for reduced‐FOV diffusion‐weighted imaging

To improve the clinical utility of diffusion-weighted imaging (DWI) by extending the slice coverage of a high-resolution reduced field-of-view technique. Challenges in achieving high spatial resolution restrict the use of DWI in assessment of small structures such as the spinal cord. A reduced field-of-view method with 2D echo-planar radiofrequency (RF) excitation was recently proposed for high-resolution DWI. Here, a Hadamard slice-encoding scheme is proposed to double the slice coverage by exploiting the periodicity of the 2D echo-planar RF excitation profile. A 2D echo-planar RF pulse and matching multiband refocusing RF pulses were designed using the Shinnar-Le Roux algorithm to reduce band interference, and variable-rate selective excitation to shorten the pulse durations. Hadamard-encoded images were resolved through a phase-preserving image reconstruction. The performance of the method was evaluated via simulations, phantom experiments, and in vivo high-resolution axial DWI of spinal cord. The proposed scheme successfully extends the slice coverage, while preserving the sharp excitation profile and the reliable fat suppression of the original method. For in vivo axial DWI of the spinal cord, an in-plane resolution of 0.7 × 0.7 mm(2) was achieved with 16 slices. The proposed Hadamard slice-encoding scheme doubles the slice coverage of the 2D echo-planar RF reduced field-of-view method without any scan-time penalty.

Near-contiguous spin echo imaging using matched-phase RF and its application in velocity-selective arterial spin labeling.

The minimum slice spacing in multislice imaging is limited by inter-slice crosstalk due to an imperfect slice profile. This study sought to minimize the slice spacing using matched-phase RF pulses and demonstrate its application in cerebral blood flow imaging using velocity-selective arterial spin labeling. A spin-echo matched-phase 90°-180° RF pair was designed using Shinnar-Le Roux algorithm in order to improve the slice profile of longitudinal magnetization, which plays a more critical role in creating interslice crosstalk than transverse magnetization. Both transverse and longitudinal slice profiles were compared between matched-phase RF and sinc-based RF pulses in simulations and measurements. Velocity-selective arterial spin labeling was performed in normal volunteers using both RF pulses and standard deviation of cerebral blood flow time series was calculated to examine ASL signal stability. Using designed matched-phase RF, the longitudinal slice profile was sharpened without signal-to-noise ratio loss. In velocity-selective arterial spin labeling imaging, the temporal standard deviation of cerebral blood flow measurements was reduced from 48 mL/100 g/min to 32 mL/100 g/min by 33% using matched-phase RF pulses, and as a result, cerebral blood flow image quality improved. This study reports that near-contiguous multislice imaging can be achieved using matched-phase RF pulses without compromising signal-to-noise ratio and signal stability.

Designing adiabatic radio frequency pulses using the Shinnar–Le Roux algorithm

Adiabatic pulses are a special class of radio frequency (RF) pulses that may be used to achieve uniform flip angles in the presence of a nonuniform B(1) field. In this work, we present a new, systematic method for designing high-bandwidth (BW), low-peak-amplitude adiabatic RF pulses that utilizes the Shinnar-Le Roux (SLR) algorithm for pulse design. Currently, the SLR algorithm is extensively employed to design nonadiabatic pulses for use in magnetic resonance imaging and spectroscopy. We have adapted the SLR algorithm to create RF pulses that also satisfy the adiabatic condition. By overlaying sufficient quadratic phase across the spectral profile before the inverse SLR transform, we generate RF pulses that exhibit the required spectral characteristics and adiabatic behavior. Application of quadratic phase also distributes the RF energy more uniformly, making it possible to obtain the same spectral BW with lower RF peak amplitude. The method enables the pulse designer to specify spectral profile parameters and the degree of quadratic phase before pulse generation. Simulations and phantom experiments demonstrate that RF pulses designed using this new method behave adiabatically.

General parameter relations for the Shinnar-Le Roux pulse design algorithm

The magnetization ripple amplitudes from a pulse designed by the Shinnar-Le Roux algorithm are a non-linear function of the Shinnar-Le Roux A and B polynomial ripples. In this paper, the method of Pauly et al. [J. Pauly, P. Le Roux, D. Nishimura, A. Macovski, Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm, IEEE Transactions on Medical Imaging 10 (1991) 56–65.] has been extended to derive more general parameter relations. These relations can be used for cases outside the five classes considered by Pauly et al., in particular excitation pulses for flip angles that are not small or 90°. Use of the new relations, together with an iterative procedure to obtain polynomials with the specified ripples from the Parks–McClellan algorithm, are shown to give simulated slice profiles that have the desired ripple amplitudes.

Optimized outer volume suppression for single-shot fast spin-echo cardiac imaging.

Among the ultrafast MRI techniques, the single-shot fast spin-echo sequence offers a robust alternative to echo planar imaging, essentially because of a much reduced sensitivity to B0 inhomogeneity. This property is particularly appealing in situations in which B0 inhomogeneities can be severe and difficult to correct, such as in cardiac imaging. With single-shot cardiac imaging, however, achieving high resolution over the necessarily large field of views without introducing back-folding artifacts is problematic. One option is to use multishot sequences. However, then issues related to cardiac gating arise. Another solution is to use, optimized presaturation slabs with quadratic phase pulses generated by the Shinnar-LeRoux algorithm. These can be set to reduce the field of view in the phase-encoding direction, resulting in a reduction in the number of phase-encoding steps. For instance, for a 1 x 2-mm spatial resolution, over a rectangular, 250 x 125-mm field of view, and using a half Fourier acquisition, an echo-train length of only 40 is required. With a 4.5-msec echo spacing, the total imaging time is approximately 180 msec. The efficacy of this solution on phantoms and volunteers is demonstrated. Multislice short-axis examinations of the whole heart, realized within a single short breath-hold of approximately 10 seconds, are shown. The possibility of investigating not only cardiac anatomy but also both contractility and myocardial perfusion is discussed.

Improved water and lipid suppression for 3D PRESS CSI using RF band selective inversion with gradient dephasing (BASING).

A T1 insensitive solvent suppression technique-band selective inversion with gradient dephasing (BASING)-was developed to suppress water and lipids for 1H magnetic resonance spectroscopy (MRS). BASING, which consists of a frequency selective RF inversion pulse surrounded by spoiler gradient pulses of opposite signs, was used to dephase stopband resonances and minimally impact passband metabolites. Passband phase linearity was achieved with a dual BASING scheme. Using the Shinnar-Le Roux algorithm, a highpass filter was designed to suppress water and rephase the lactate methyl doublet independently of TE, and water/lipid bandstop filters were designed for the brain and prostate. Phantom and in vivo experimental 3D PRESS CSI data were acquired at 1.5 T to compare BASING with CHESS and STIR suppression. With BASING, the measured suppression factor was over 100 times higher than with CHESS or STIR causing baseline distortions to be removed. It was shown that BASING can be incorporated into a variety of sequences to offer improved suppression in the presence of B1 and T1 inhomogeneites.

An integrated program for amplitude-modulated RF pulse generation and re-mapping with shaped gradients

Efficient generation of amplitude modulated, frequency selective RF pulses has been demonstrated by the Shinnar-Le Roux (SLR) algorithm. In the present article, we provide an overview of a relatively comprehensive computer program that includes a version of the SLR algorithm and also incorporates an algorithm for re-mapping a selective RF pulse onto a new dwell time with modulated gradients. The re-mapping may be used to reduce SAR, or to shorten the RF pulse time by increasing the gradient and RF strength in regions where the original RF pulse amplitude was low. The program includes additional useful features including a Bloch equations algorithm, and pulse scaling, to enable examination of pulse profiles under a variety of conditions such as RF inhomogeneity and even nuclear relaxation. The program, MATPULSE, was developed with the MATLAB for Windows programming language and makes extensive use of the MATLAB graphical user interface (GUI) features to generate a userfriendly interface. A number of examples are provided to illustrate the capabilities of the MATPULSE program.