Optimal control design of turbo spin-echo sequences with applications to parallel-transmit systems

Design of calibration-free RF pulses for T 2 $$ {}_2 $$ -weighted single-slab 3D turbo-spin-echo sequences at 7T utilizing parallel transmission

PURPOSE

T  2 $$ {}_2 $$ -weighted turbo-spin-echo (TSE) sequences are a fundamental technique in brain imaging but suffer from field inhomogeneities at ultra-high fields. Several methods have been proposed to mitigate the problem, but were limited so far to nonselective three-dimensional (3D) measurements, making short acquisitions difficult to achieve when targeting very high resolution images, or needed additional calibration procedures, thus complicating their application.

METHODS

Slab-selective excitation pulses were designed for flexible placement utilizing the concept of k  T $$ {}_T $$ -spokes. Phase-coherent refocusing universal pulses were subsequently optimized with the Gradient Ascent Pulse Engineering algorithm and tested in vivo for improved signal homogeneity.

RESULTS

Implemented within a 3D variable flip angle TSE sequence, these pulses led to a signal-to-noise ratio (SNR) improvement ranging from 10% to 30% compared to a two-dimensional (2D) T2w TSE sequence employingB 1 + $$ {\mathrm{B}}_1^{+} $$ -shimmed pulses.B 1 + $$ {\mathrm{B}}_1^{+} $$ field inhomogeneities could be mitigated and artifacts fromB 0 $$ {\mathrm{B}}_0 $$ deviations reduced. The concept of universal pulses was successfully applied.

CONCLUSION

We present a pulse design method which provides a set of calibration-free universal pulses (UPs) for slab-selective excitation and phase-coherent refocusing in slab-selective TSE sequences.

Parallel transmission 2D RARE imaging at 7T with transmit field inhomogeneity mitigation and local SAR control

PURPOSE

We develop and test a parallel transmit (pTx) pulse design framework to mitigate transmit field inhomogeneity with control of local specific absorption rate (SAR) in 2D rapid acquisition with relaxation enhancement (RARE) imaging at 7T.

METHODS

We design large flip angle RF pulses with explicit local SAR constraints by numerical simulation of the Bloch equations. Parallel computation and analytical expressions for the Jacobian and the Hessian matrices are employed to reduce pulse design time. The refocusing-excitation "spokes" pulse pairs are designed to satisfy the Carr-Purcell-Meiboom-Gill (CPMG) condition using a combined magnitude least squares-least squares approach.

RESULTS

In a simulated dataset, the proposed approach reduced peak local SAR by up to 56% for the same level of refocusing uniformity error and reduced refocusing uniformity error by up to 59% (from 32% to 7%) for the same level of peak local SAR compared to the circularly polarized birdcage mode of the pTx array. Using explicit local SAR constraints also reduced peak local SAR by up to 46% compared to an RF peak power constrained design. The excitation and refocusing uniformity error were reduced from 20%-33% to 4%-6% in single slice phantom experiments. Phantom experiments demonstrated good agreement between the simulated excitation and refocusing uniformity profiles and experimental image shading.

CONCLUSION

PTx-designed excitation and refocusing CPMG pulse pairs can mitigate transmit field inhomogeneity in the 2D RARE sequence. Moreover, local SAR can be decreased significantly using pTx, potentially leading to better slice coverage, enabling larger flip angles or faster imaging.

A Fetal Brain magnetic resonance Acquisition Numerical phantom (FaBiAN)

Accurate characterization of in utero human brain maturation is critical as it involves complex and interconnected structural and functional processes that may influence health later in life. Magnetic resonance imaging is a powerful tool to investigate equivocal neurological patterns during fetal development. However, the number of acquisitions of satisfactory quality available in this cohort of sensitive subjects remains scarce, thus hindering the validation of advanced image processing techniques. Numerical phantoms can mitigate these limitations by providing a controlled environment with a known ground truth. In this work, we present FaBiAN, an open-source Fetal Brain magnetic resonance Acquisition Numerical phantom that simulates clinical T2-weighted fast spin echo sequences of the fetal brain. This unique tool is based on a general, flexible and realistic setup that includes stochastic fetal movements, thus providing images of the fetal brain throughout maturation comparable to clinical acquisitions. We demonstrate its value to evaluate the robustness and optimize the accuracy of an algorithm for super-resolution fetal brain magnetic resonance imaging from simulated motion-corrupted 2D low-resolution series compared to a synthetic high-resolution reference volume. We also show that the images generated can complement clinical datasets to support data-intensive deep learning methods for fetal brain tissue segmentation.

Accuracy and performance analysis for Bloch and Bloch-McConnell simulation methods

PURPOSE

To introduce new solution methods for the Bloch and Bloch-McConnell equations and compare them quantitatively to different known approaches.

THEORY AND METHODS

A new exact solution per time step is derived by means of eigenvalues and generalized eigenvectors. Fast numerical solution methods based on asymmetric and symmetric operator splitting, which are already known for the Bloch equations, are extended to the Bloch-McConnell equations. Those methods are compared to other numerical methods including spin domain, one-step and multi-step methods, and matrix exponential. Error metrics are introduced based on the exact solution method, which allows to assess the accuracy of each solution method quantitatively for arbitrary example data.

RESULTS

Accuracy and performance properties for nine different solution methods are analyzed and compared in extensive numerical experiments including various examples for non-selective and slice-selective MR imaging applications. The accuracy of the methods heavily varies, in particular for short relaxation times and long pulse durations.

CONCLUSION

In absence of relaxation effects, the numerical results confirm the rotation matrices approach as accurate and computationally efficient Bloch solution method. Otherwise, as well as for the Bloch-McConnell equations, symmetric operator splitting methods are recommended due to their excellent numerical accuracy paired with efficient run time.

MRzero - Automated discovery of MRI sequences using supervised learning

PURPOSE

A supervised learning framework is proposed to automatically generate MR sequences and corresponding reconstruction based on the target contrast of interest. Combined with a flexible, task-driven cost function this allows for an efficient exploration of novel MR sequence strategies.

METHODS

The scanning and reconstruction process is simulated end-to-end in terms of RF events, gradient moment events in x and y, and delay times, acting on the input model spin system given in terms of proton density, T 1 and T 2 , and Δ B 0 . As a proof of concept, we use both conventional MR images and T 1 maps as targets and optimize from scratch using the loss defined by data fidelity, SAR penalty, and scan time.

RESULTS

In a first attempt, MRzero learns gradient and RF events from zero, and is able to generate a target image produced by a conventional gradient echo sequence. Using a neural network within the reconstruction module allows arbitrary targets to be learned successfully. Experiments could be translated to image acquisition at the real system (3T Siemens, PRISMA) and could be verified in the measurements of phantoms and a human brain in vivo.

CONCLUSIONS

Automated MR sequence generation is possible based on differentiable Bloch equation simulations and a supervised learning approach.

Real-time assessment of potential peak local specific absorption rate value without phase monitoring: Trigonometric maximization method for worst-case local specific absorption rate determination

Purpose

Multi‐transmit MRI systems are typically equipped with dedicated hardware to sample the reflected/lost power in the transmit channels. After extensive calibration, the amplitude and phase of the signal at the feed of each array element can be accurately determined. However, determining the phase is more difficult and monitoring errors can lead to a hazardous peak local specific absorption rate (pSAR_10g) underestimation. For this purpose, methods were published for online maximum potential pSAR_10g estimation without relying on phase monitoring, but these methods produce considerable overestimation. We present a trigonometric maximization method to determine the actual worst‐case pSAR_10g without any overestimation.

Theory and Method

The proposed method takes advantage of the sinusoidal relation between the SAR_10g in each voxel and the phases of input signals, to return the maximum achievable SAR_10g in a few iterations. The method is applied to determine the worst‐case pSAR_10g for three multi‐transmit array configurations at 7T: (1) body array with eight fractionated dipoles; (2) head array with eight fractionated dipoles; (3) head array with eight rectangular loops. The obtained worst‐case pSAR_10g values are compared with the pSAR_10g values determined with a commonly used method and with a more efficient method based on reference‐phases.

Results

For each voxel, the maximum achievable SAR_10g is determined in less than 0.1 ms. Compared to the reference‐phases‐based method, the proposed method reduces the mean overestimation of the actual pSAR_10g up to 52%, while never underestimating the true pSAR_10g.

Conclusion

The proposed method can widely improve the performance of parallel transmission MRI systems without phase monitoring.

Technical feasibility of magnetic resonance fingerprinting on a 1.5T MRI-linac

Hybrid MRI-linac (MRL) systems enable daily multiparametric quantitative MRI to assess tumor response to radiotherapy. Magnetic resonance fingerprinting (MRF) may provide time efficient means of rapid multiparametric quantitative MRI. The accuracy of MRF, however, relies on adequate control over system imperfections, such as eddy currents and [Formula: see text], which are different and not as well established on MRL systems compared to diagnostic systems. In this study we investigate the technical feasibility of gradient spoiled 2D MRF on a 1.5T MRL. We show with phantom experiments that the MRL generates reliable MRF signals that are temporally stable during the day and have good agreement with spin-echo reference measurements. Subsequent in-vivo MRF scans in healthy volunteers and a patient with a colorectal liver metastasis showed good image quality, where the quantitative values of selected organs corresponded with the values reported in literature. Therefore we conclude that gradient spoiled 2D MRF is feasible on a 1.5T MRL with similar performance as on a diagnostic system. The precision and accuracy of the parametric maps are sufficient for further investigation of the clinical utility of MRF for online quantitatively MRI-guided radiotherapy.

Conditional safety margins for less conservative peak local SAR assessment: A probabilistic approach

Purpose

The introduction of a linear safety factor to address peak local specific absorption rate (pSAR_10g) uncertainties (eg, intersubject variation, modeling inaccuracies) bears one considerable drawback: It often results in over‐conservative scanning constraints. We present a more efficient approach to define a variable safety margin based on the conditional probability density function of the effectively obtained pSAR_10g value, given the estimated pSAR_10g value.

Methods

The conditional probability density function can be estimated from previously simulated data. A representative set of true and estimated pSAR_10g samples was generated by means of our database of 23 subject‐specific models with an 8‐fractionated dipole array for prostate imaging at 7 T. The conditional probability density function was calculated for each possible estimated pSAR_10g value and used to determine the corresponding safety margin with an arbitrary low probability of underestimation. This approach was applied to five state‐of‐the‐art local SAR estimation methods, namely: (1) using just the generic body model “Duke”; (2) using our model library to assess the maximum pSAR_10g value over all models; (3) using the most representative “local SAR model”; (4) using the five most representative local SAR models; and (5) using a recently developed deep learning–based method.

Results

Compared with the more conventional safety factor, the conditional safety‐margin approach results in lower (up to 30%) mean overestimation for all investigated local SAR estimation methods.

Conclusion

The proposed probabilistic approach for pSAR_10g correction allows more accurate local SAR assessment with much lower overestimation, while a predefined level of underestimation is accepted (eg, 0.1%).

Computational MRI with Physics-based Constraints: Application to Multi-contrast and Quantitative Imaging

Compressed sensing takes advantage of low-dimensional signal structure to reduce sampling requirements far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transform, finite differences, and low rank extensions. Though powerful, these image priors are phenomenological in nature and do not account for the mechanism behind the image formation. On the other hand, MRI signal dynamics are governed by physical laws, which can be explicitly modeled and used as priors for reconstruction. These explicit and implicit signal priors can be synergistically combined in an inverse problem framework to recover sharp, multi-contrast images from highly accelerated scans. Furthermore, the physics-based constraints provide a recipe for recovering quantitative, bio-physical parameters from the data. This article introduces physics-based modeling constraints in MRI and shows how they can be used in conjunction with compressed sensing for image reconstruction and quantitative imaging. We describe model-based quantitative MRI, as well as its linear subspace approximation. We also discuss approaches to selecting user-controllable scan parameters given knowledge of the physical model. We present several MRI applications that take advantage of this framework for the purpose of multi-contrast imaging and quantitative mapping.

A deep learning method for image-based subject-specific local SAR assessment

Purpose

Local specific absorption rate (SAR) cannot be measured and is usually evaluated by offline numerical simulations using generic body models that of course will differ from the patient's anatomy. An additional safety margin is needed to include this intersubject variability. In this work, we present a deep learning–based method for image‐based subject‐specific local SAR assessment. We propose to train a convolutional neural network to learn a “surrogate SAR model” to map the relation between subject‐specific B1+ maps and the corresponding local SAR.

Method

Our database of 23 subject‐specific models with an 8–transmit channel body array for prostate imaging at 7 T was used to build 5750 training samples. These synthetic complex B1+ maps and local SAR distributions were used to train a conditional generative adversarial network. Extra penalization for local SAR underestimation errors was included in the loss function. In silico and in vivo validation were performed.

Results

In silico cross‐validation shows a good qualitative and quantitative match between predicted and ground‐truth local SAR distributions. The peak local SAR estimation error distribution shows a mean overestimation error of 15% with 13% probability of underestimation. The higher accuracy of the proposed method allows the use of less conservative safety factors compared with standard procedures. In vivo validation shows that the method is applicable with realistic measurement data with impressively good qualitative and quantitative agreement to simulations.

Conclusion

The proposed deep learning method allows online image‐based subject‐specific local SAR assessment. It greatly reduces the uncertainty in current state‐of‐the‐art SAR assessment methods, reducing the time in the examination protocol by almost 25%.

Parallel Transmission for Ultrahigh Field MRI

Magnetic resonance imaging (MRI) has been driven toward ultrahigh magnetic fields (UHF) in order to benefit from correspondingly higher signal-to-noise ratio and spectral resolution. Technological challenges associated with UHF, such as increased radiofrequency (RF) energy deposition and RF excitation inhomogeneity, limit realization of the full potential of these benefits. Parallel RF transmission (pTx) enables decreases in the inhomogeneity of RF excitations and in RF energy deposition by using multiple-transmit RF coils driven independently and operating simultaneously. pTx plays a fundamental role in UHF MRI by bringing the potential applications of UHF into reality. In this review article, we review the recent developments in pTx pulse design and RF safety in pTx. Simultaneous multislice imaging and inner volume imaging using pTx are reviewed with a focus on UHF applications. Emerging pTx design approaches using improved pTx design frameworks and calibrations are reviewed together with calibration-free approaches that remove the necessity of time-consuming calibrations necessary for successful pTx. Lastly, we focus on the safety of pTx that is improved by using intersubject variability analysis, proactively managing pTx and temperature-based pTx approaches.

Pros and cons of ultra-high-field MRI/MRS for human application

Magnetic resonance imaging and spectroscopic techniques are widely used in humans both for clinical diagnostic applications and in basic research areas such as cognitive neuroimaging. In recent years, new human MR systems have become available operating at static magnetic fields of 7 T or higher (≥300 MHz proton frequency). Imaging human-sized objects at such high frequencies presents several challenges including non-uniform radiofrequency fields, enhanced susceptibility artifacts, and higher radiofrequency energy deposition in the tissue. On the other side of the scale are gains in signal-to-noise or contrast-to-noise ratio that allow finer structures to be visualized and smaller physiological effects to be detected. This review presents an overview of some of the latest methodological developments in human ultra-high field MRI/MRS as well as associated clinical and scientific applications. Emphasis is given to techniques that particularly benefit from the changing physical characteristics at high magnetic fields, including susceptibility-weighted imaging and phase-contrast techniques, imaging with X-nuclei, MR spectroscopy, CEST imaging, as well as functional MRI. In addition, more general methodological developments such as parallel transmission and motion correction will be discussed that are required to leverage the full potential of higher magnetic fields, and an overview of relevant physiological considerations of human high magnetic field exposure is provided.

A simplified framework to optimize MRI contrast preparation

PURPOSE

This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences.

METHODS

Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution.

RESULTS

The proposed approach reduces the computation time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:math> -robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. The chosen parameterization allows to formulate the total preparation duration as a constraint, which improves the overall compromise between contrast performance and preparation time. Simulation, in vitro and in vivo results validate this improvement, illustrate the straightforward applicability of the proposed approach, and point out its flexibility in terms of achievable contrasts. Major improvement is especially achieved for short-T₂ enhancement, as shown by the acquisition of a non-trivial contrast on a rat brain, where a short-T₂ white matter structure (corpus callosum) is enhanced compared to surrounding gray matter tissues (hippocampus and neocortex).

CONCLUSIONS

This approach proposes key advances for the design of optimal contrast preparation sequences, that emphasize their ability to generate non-standard contrasts, their potential benefit in a clinical context, and their straightforward applicability on any MR system.

Constant gradient elastography with optimal control RF pulses

This article presents a new motion encoding strategy to perform magnetic resonance elastography (MRE). Instead of using standard motion encoding gradients, a tailored RF pulse is designed to simultaneously perform selective excitation and motion encoding in presence of a constant gradient. The RF pulse is designed with a numerical optimal control algorithm, in order to obtain a magnetization phase distribution that depends on the displacement characteristics inside each voxel. As a consequence, no post-excitation encoding gradients are required. This offers numerous advantages, such as reducing eddy current artifacts, and relaxing the constraint on the gradients maximum switch rate. It also allows to perform MRE with ultra-short TE acquisition schemes, which limits T₂ decay and optimizes signal-to-noise ratio. The pulse design strategy is developed and analytically analyzed to clarify the encoding mechanism. Finally, simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved when compared to standard MRE encoding strategies.

Whole-brain 3D FLAIR at 7T using direct signal control

Purpose

Image quality obtained for brain imaging at 7T can be hampered by inhomogeneities in the static magnetic field, B₀, and the RF electromagnetic field, B₁. In imaging sequences such as fluid‐attenuated inversion recovery (FLAIR), which is used to assess neurological disorders, these inhomogeneities cause spatial variations in signal that can reduce clinical efficacy. In this work, we aim to correct for signal inhomogeneities to ensure whole‐brain coverage with 3D FLAIR at 7T.

Methods

The direct signal control (DSC) framework was used to optimize channel weightings applied to the 8 transmit channels used in this work on a pulse‐by‐pulse basis through the echo train in the FLAIR sequences. 3D FLAIR brain images were acquired on 5 different subjects and compared with imaging using a quadrature‐like mode of the transmit array. Precomputed “universal” DSC solutions calculated from a separate set of 5 subjects were also explored.

Results

DSC consistently enabled improved imaging across all subjects, with no dropouts in signal seen over the entire brain volume, which contrasted with imaging in quadrature mode. Further, the universal DSC solutions also consistently improved imaging despite not being optimized specifically for the subject being imaged.

Conclusion

3D FLAIR brain imaging at 7T is substantially improved using DSC and is able to recover regions of low signal without increasing imaging time or interecho spacing.

Extended phase graph formalism for systems with magnetization transfer and exchange

Purpose

An extended phase graph framework (EPG‐X) for modeling systems with exchange or magnetization transfer (MT) is proposed.

Theory

EPG‐X models coupled two‐compartment systems by describing each compartment with separate phase graphs that exchange during evolution periods. There are two variants: EPG‐X(BM) for systems governed by the Bloch‐McConnell equations, and EPG‐X(MT) for the pulsed MT formalism. For the MT case, the “bound” protons have no transverse components, so their phase graph consists of only longitudinal states.

Methods

The EPG‐X model was validated against steady‐state solutions and isochromat‐based simulation of gradient‐echo sequences. Three additional test cases were investigated: (i) MT effects in multislice turbo spin‐echo; (ii) variable flip angle gradient‐echo imaging of the type used for MR fingerprinting; and (iii) water exchange in multi‐echo spin‐echo T₂ relaxometry.

Results

EPG‐X was validated successfully against isochromat based transient simulations and known steady‐state solutions. EPG‐X(MT) simulations matched in‐vivo measurements of signal attenuation in white matter in multislice turbo spin‐echo images. Magnetic resonance fingerprinting–style experiments with a bovine serum albumin (MT) phantom showed that the data were not consistent with a single‐pool model, but EPG‐X(MT) could be used to fit the data well. The EPG‐X(BM) simulations of multi‐echo spin‐echo T₂ relaxometry suggest that exchange could lead to an underestimation of the myelin‐water fraction.

Conclusions

The EPG‐X framework can be used for modeling both steady‐state and transient signal response of systems exhibiting exchange or MT. This may be particularly beneficial for relaxometry approaches that rely on characterizing transient rather than steady‐state sequences. Magn Reson Med 80:767–779, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Design of universal parallel-transmit refocusing kT -point pulses and application to 3D T2 -weighted imaging at 7T

PURPOSE

T₂ -weighted sequences are particularly sensitive to the radiofrequency (RF) field inhomogeneity problem at ultra-high-field because of the errors accumulated by the imperfections of the train of refocusing pulses. As parallel transmission (pTx) has proved particularly useful to counteract RF heterogeneities, universal pulses were recently demonstrated to save precious time and computational efforts by skipping B₁ calibration and online RF pulse tailoring. Here, we report a universal RF pulse design for non-selective refocusing pulses to mitigate the RF inhomogeneity problem at 7T in turbo spin-echo sequences with variable flip angles.

METHOD

Average Hamiltonian theory was used to synthetize a single non-selective refocusing pulse with pTx while optimizing its scaling properties in the presence of static field offsets. The design was performed under explicit power and specific absorption rate constraints on a database of 10 subjects using a 8Tx-32Rx commercial coil at 7T. To validate the proposed design, the RF pulses were tested in simulation and applied in vivo on 5 additional test subjects.

RESULTS

The root-mean-square rotation angle error (RA-NRMSE) evaluation and experimental data demonstrated great improvement with the proposed universal pulses (RA-NRMSE ∼8%) compared to the standard circularly polarized mode of excitation (RA-NRMSE ∼26%).

CONCLUSION

This work further completes the spectrum of 3D universal pulses to mitigate RF field inhomogeneity throughout all 3D MRI sequences without any pTx calibration. The approach returns a single pulse that can be scaled to match the desired flip angle train, thereby increasing the modularity of the proposed plug and play approach. Magn Reson Med 80:53-65, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Active control of the spatial MRI phase distribution with optimal control theory

This paper investigates the use of Optimal Control (OC) theory to design Radio-Frequency (RF) pulses that actively control the spatial distribution of the MRI magnetization phase. The RF pulses are generated through the application of the Pontryagin Maximum Principle and optimized so that the resulting transverse magnetization reproduces various non-trivial and spatial phase patterns. Two different phase patterns are defined and the resulting optimal pulses are tested both numerically with the ODIN MRI simulator and experimentally with an agar gel phantom on a 4.7T small-animal MR scanner. Phase images obtained in simulations and experiments are both consistent with the defined phase patterns. A practical application of phase control with OC-designed pulses is also presented, with the generation of RF pulses adapted for a Magnetic Resonance Elastography experiment. This study demonstrates the possibility to use OC-designed RF pulses to encode information in the magnetization phase and could have applications in MRI sequences using phase images.