Dynamic nuclear polarization and optimal control spatial-selective 13C MRI and MRS

Optimal control gradient precision trade-offs: Application to fast generation of DeepControl libraries for MRI

We have recently demonstrated supervised deep learning methods for rapid generation of radiofrequency pulses in magnetic resonance imaging (https://doi.org/10.1002/mrm.27740, https://doi.org/10.1002/mrm.28667). Unlike the previous iterative optimization approaches, deep learning methods generate a pulse using a fixed number of floating-point operations - this is important in MRI, where patient-specific pulses preferably must be produced in real time. However, deep learning requires vast training libraries, which must be generated using the traditional methods, e.g., iterative quantum optimal control methods. Those methods are usually variations of gradient descent, and the calculation of the gradient of the performance metric with respect to the pulse waveform can be the most numerically intensive step. In this communication, we explore various ways in which the calculation of gradients in quantum optimal control theory may be accelerated. Four optimization avenues are explored: truncated commutator series expansions at zeroth and first order, a novel midpoint truncation scheme at first order, and the exact complex-step method. For the spin systems relevant to MRI, the first-order midpoint truncation is found to be sufficiently accurate, but also significantly faster than the machine precision gradient. This makes the generation of training databases for the machine learning methods considerably more realistic.

Rapid, B 1 -insensitive, dual-band quasi-adiabatic saturation transfer with optimal control for complete quantification of myocardial ATP flux

PURPOSE

Phosphorus saturation-transfer experiments can quantify metabolic fluxes noninvasively. Typically, the forward flux through the creatine kinase reaction is investigated by observing the decrease in phosphocreatine (PCr) after saturation of γ-ATP. The quantification of total ATP utilization is currently underexplored, as it requires simultaneous saturation of inorganic phosphate ( P i ) and PCr. This is challenging, as currently available saturation pulses reduce the already-low γ-ATP signal present.

METHODS

Using a hybrid optimal-control and Shinnar-Le Roux method, a quasi-adiabatic RF pulse was designed for the dual saturation of PCr and P i to enable determination of total ATP utilization. The pulses were evaluated in Bloch equation simulations, compared with a conventional hard-cosine DANTE saturation sequence, before being applied to perfused rat hearts at 11.7 T.

RESULTS

The quasi-adiabatic pulse was insensitive to a >2.5-fold variation in B 1 , producing equivalent saturation with a 53% reduction in delivered pulse power and a 33-fold reduction in spillover at the minimum effective B 1 . This enabled the complete quantification of the synthesis and degradation fluxes for ATP in 30-45 minutes in the perfused rat heart. While the net synthesis flux (4.24 ± 0.8 mM/s, SEM) was not significantly different from degradation flux (6.88 ± 2 mM/s, P = .06) and both measures are consistent with prior work, nonlinear error analysis highlights uncertainties in the P_i -to-ATP measurement that may explain a trend suggesting a possible imbalance.

CONCLUSIONS

This work demonstrates a novel quasi-adiabatic dual-saturation RF pulse with significantly improved performance that can be used to measure ATP turnover in the heart in vivo.

DeepControl: 2DRF pulses facilitating B 1 + inhomogeneity and B0 off-resonance compensation in vivo at 7 T

PURPOSE

Rapid 2DRF pulse design with subject-specific B 1 + inhomogeneity and B₀ off-resonance compensation at 7 T predicted from convolutional neural networks is presented.

METHODS

The convolution neural network was trained on half a million single-channel transmit 2DRF pulses optimized with an optimal control method using artificial 2D targets, B 1 + and B₀ maps. Predicted pulses were tested in a phantom and in vivo at 7 T with measured B 1 + and B₀ maps from a high-resolution gradient echo sequence.

RESULTS

Pulse prediction by the trained convolutional neural network was done on the fly during the MR session in approximately 9 ms for multiple hand-drawn regions of interest and the measured B 1 + and B₀ maps. Compensation of B 1 + inhomogeneity and B₀ off-resonances has been confirmed in the phantom and in vivo experiments. The reconstructed image data agree well with the simulations using the acquired B 1 + and B₀ maps, and the 2DRF pulse predicted by the convolutional neural networks is as good as the conventional RF pulse obtained by optimal control.

CONCLUSION

The proposed convolutional neural network-based 2DRF pulse design method predicts 2DRF pulses with an excellent excitation pattern and compensated B 1 + and B₀ variations at 7 T. The rapid 2DRF pulse prediction (9 ms) enables subject-specific high-quality 2DRF pulses without the need to run lengthy optimizations.

Hyperpolarized Carbon (13C) MRI of the Kidney: Experimental Protocol

Alterations in renal metabolism are associated with both physiological and pathophysiologic events. The existing noninvasive analytic tools including medical imaging have limited capability for investigating these processes, which potentially limits current understanding of kidney disease and the precision of its clinical diagnosis. Hyperpolarized 13C MRI is a new medical imaging modality that can capture changes in the metabolic processing of certain rapidly metabolized substrates, as well as changes in kidney function. Here we describe experimental protocols for renal metabolic [1-13C]pyruvate and functional 13C-urea imaging step-by-step. These methods and protocols are useful for investigating renal blood flow and function as well as the renal metabolic status of rodents in vivo under various experimental (patho)physiological conditions.This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers. This experimental protocol is complemented by two separate chapters describing the basic concept and data analysis.

Assessing spatial resolution, acquisition time and signal-to-noise ratio for commercial microimaging systems at 14.1, 17.6 and 22.3 T

This work provides a systematic comparison of the signal-to-noise ratio (SNR), spatial resolution, acquisition time and metabolite limits-of-detection for magnetic resonance microscopy and spectroscopy at three different magnetic field strengths of 14.1 T, 17.6 T and 22.3 T (the highest currently available for imaging), utilizing commercially available hardware. We find an SNR increase of a factor 5.9 going from 14.1 T to 22.3 T using 5 mm radiofrequency (saddle and birdcage) coils, which results in a 24-fold acceleration in acquisition time and deviates from the theoretically expected increase of factor 2.2 due to differences in hardware. This underlines the importance of not only the magnetic field strengths but also hardware optimization. In addition, using a home-built 1.5 mm solenoid coil, we can achieve an isotropic resolution of (5.5 µm)³ over a field-of-view of 1.58 mm × 1.05 mm × 1.05 mm with an SNR of 12:1 using 44 signal averages in 58 h 34 min acquisition time at 22.3 T. In light of these results, we discuss future perspectives for ultra-high field Magnetic Resonance Microscopy and Spectroscopy.

Hyperpolarized 13C MRI: A novel approach for probing cerebral metabolism in health and neurological disease

Cerebral metabolism is tightly regulated and fundamental for healthy neurological function. There is increasing evidence that alterations in this metabolism may be a precursor and early biomarker of later stage disease processes. Proton magnetic resonance spectroscopy (1H-MRS) is a powerful tool to non-invasively assess tissue metabolites and has many applications for studying the normal and diseased brain. However, the technique has limitations including low spatial and temporal resolution, difficulties in discriminating overlapping peaks, and challenges in assessing metabolic flux rather than steady-state concentrations. Hyperpolarized carbon-13 magnetic resonance imaging is an emerging clinical technique that may overcome some of these spatial and temporal limitations, providing novel insights into neurometabolism in both health and in pathological processes such as glioma, stroke and multiple sclerosis. This review will explore the growing body of pre-clinical data that demonstrates a potential role for the technique in assessing metabolism in the central nervous system. There are now a number of clinical studies being undertaken in this area and this review will present the emerging clinical data as well as the potential future applications of hyperpolarized 13C magnetic resonance imaging in the brain, in both clinical and pre-clinical studies.

High Intrarenal Lactate Production Inhibits the Renal Pseudohypoxic Response to Acutely Induced Hypoxia in Diabetes

Intrarenal hypoxia develops within a few days after the onset of insulinopenic diabetes in an experimental animal model (ie, a model of type-1 diabetes). Although diabetes-induced hypoxia results in increased renal lactate formation, mitochondrial function is well maintained, a condition commonly referred to as pseudohypoxia. However, the metabolic effects of significantly elevated lactate levels remain unclear. We therefore investigated in diabetic animals the response to acute intrarenal hypoxia in the presence of high renal lactate formation to delineate mechanistic pathways and compare these findings to healthy control animals. Hyperpolarized ¹³C-MRI and blood oxygenation level–dependent ¹H-MRI was used to investigate the renal metabolism of [1-¹³C]pyruvate and oxygenation following acutely altered oxygen content in the breathing gas in a streptozotocin rat model of type-1 diabetes with and without insulin treatment and compared with healthy control rats. The lactate signal in the diabetic kidney was reduced by 12%–16% during hypoxia in diabetic rats irrespective of insulin supplementation. In contrast, healthy controls displayed the well-known Pasteur effect manifested as a 10% increased lactate signal following reduction of oxygen in the inspired air. Reduced expression of the monocarboxyl transporter-4 may account for altered response to hypoxia in diabetes with a high intrarenal pyruvate-to-lactate conversion. Reduced intrarenal lactate formation in response to hypoxia in diabetes shows the existence of a different metabolic phenotype, which is independent of insulin, as insulin supplementation was unable to affect the pyruvate-to-lactate conversion in the diabetic kidney.

Evaluation of Active Brown Adipose Tissue by the Use of Hyperpolarized [1-13C]Pyruvate MRI in Mice

The capacity to increase energy expenditure makes brown adipose tissue (BAT) a putative target for treatment of metabolic diseases such as obesity. Presently, investigation of BAT in vivo is mainly performed by fluoro-d-glucose positron emission tomography (FDG PET)/CT. However, non-radioactive methods that add information on, for example, substrate metabolism are warranted. Thus, the aim of this study was to evaluate the potential of hyperpolarized [1-¹³C]pyruvate Magnetic Resonance Imaging (HP-MRI) to determine BAT activity in mice following chronic cold exposure. Cold (6 °C) and thermo-neutral (30 °C) acclimated mice were scanned with HP-MRI for assessment of the interscapular BAT (iBAT) activity. Comparable mice were scanned with the conventional method FDG PET/MRI. Finally, iBAT was evaluated for gene expression and protein levels of the specific thermogenic marker, uncoupling protein 1 (UCP1). Cold exposure increased the thermogenic capacity 3–4 fold (p < 0.05) as measured by UCP1 gene and protein analysis. Furthermore, cold exposure as compared with thermo-neutrality increased iBAT pyruvate metabolism by 5.5-fold determined by HP-MRI which is in good agreement with the 5-fold increment in FDG uptake (p < 0.05) measured by FDG PET/MRI. iBAT activity is detectable in mice using HP-MRI in which potential changes in intracellular metabolism may add useful information to the conventional FDG PET studies. HP-MRI may also be a promising radiation-free tool for repetitive BAT studies in humans.

Anisotropic diffusion phantoms based on microcapillaries

Diffusion MRI is an efficient and widely used technique for the investigation of tissue structure and organisation in vivo. Multiple phenomenological and biophysical diffusion models are intensively exploited for the analysis of the diffusion experiments. However, the verification of the applied diffusion models remains challenging. In order to provide a "gold standard" and to assess the accuracy of the derived parameters and the limitations of the diffusion models, anisotropic diffusion phantoms with well known architecture are demanded. In the present work we built four anisotropic diffusion phantoms consisting of hollow microcapillaries with very small inner diameters of 5, 10 and 20μm and outer diameters of 90 and 150μm. For testing the suitability of these phantoms, we performed diffusion measurements on all of them and evaluated the resulting data with a set of popular diffusion models, such as diffusion tensor and diffusion kurtosis imaging, a two compartment model with intra- and extra-capillary water spaces using bi-exponential fitting, and time-dependent diffusion coefficients in Mitra's limit. The perspectives and limitations of these diffusion phantoms are presented and discussed.

Comparative analysis of isotropic diffusion weighted imaging sequences

Visualisation of living tissue structure and function is a challenging problem of modern imaging techniques. Diffusion MRI allows one to probe in vivo structures on a micrometer scale. However, conventional diffusion measurements are time-consuming procedures, because they require several measurements with different gradient directions. Considerable time savings are therefore possible by measurement schemes that generate an isotropic diffusion weighting in a single shot. Multiple approaches for generating isotropic diffusion weighting are known and have become very popular as useful tools in clinical research. Thus, there is a strong need for a comprehensive comparison of different isotropic weighting approaches. In the present work we introduce two new sequences based on simple (co)sine modulations and compare their performance to established q-space magic-angle spinning sequences and conventional DTI, using a diffusion phantom assembled from microcapillaries and in vivo experiments at 7T. The advantages and disadvantages of all compared schemes are demonstrated and discussed.

Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points

PURPOSE

To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses.

THEORY AND METHODS

The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4.

RESULTS

The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4.

CONCLUSION

A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.

Application of the limited-memory quasi-Newton algorithm for multi-dimensional, large flip-angle RF pulses at 7T

OBJECTIVE

Ultrahigh field MRI provides great opportunities for medical diagnostics and research. However, ultrahigh field MRI also brings challenges, such as larger magnetic susceptibility induced field changes. Parallel-transmit radio-frequency pulses can ameliorate these complications while performing advanced tasks in routine applications. To address one class of such pulses, we propose an optimal-control algorithm as a tool for designing advanced multi-dimensional, large flip-angle, radio-frequency pulses. We contrast initial conditions, constraints, and field correction abilities against increasing pulse trajectory acceleration factors.

MATERIALS AND METHODS

On an 8-channel 7T system, we demonstrate the quasi-Newton algorithm with pulse designs for reduced field-of-view imaging with an oil phantom and in vivo with scans of the human brain stem. We used echo-planar imaging with 2D spatial-selective pulses. Pulses are computed sufficiently rapid for routine applications.

RESULTS

Our dataset was quantitatively analyzed with the conventional mean-square-error metric and the structural-similarity index from image processing. Analysis of both full and reduced field-of-view scans benefit from utilizing both complementary measures.

CONCLUSION

We obtained excellent outer-volume suppression with our proposed method, thus enabling reduced field-of-view imaging using pulse trajectory acceleration factors up to 4.

Facing and Overcoming Sensitivity Challenges in Biomolecular NMR Spectroscopy

In the Spring of 2013, NMR spectroscopists convened at the Weizmann Institute in Israel to brainstorm on approaches to improve the sensitivity of NMR experiments, particularly when applied in biomolecular settings. This multi-author interdisciplinary Review presents a state-of-the-art description of the primary approaches that were considered. Topics discussed included the future of ultrahigh-field NMR systems, emerging NMR detection technologies, new approaches to nuclear hyperpolarization, and progress in sample preparation. All of these are orthogonal efforts, whose gains could multiply and thereby enhance the sensitivity of solid- and liquid-state experiments. While substantial advances have been made in all these areas, numerous challenges remain in the quest of endowing NMR spectroscopy with the sensitivity that has characterized forms of spectroscopies based on electrical or optical measurements. These challenges, and the ways by which scientists and engineers are striving to solve them, are also addressed.

A 2DRF pulse sequence for bolus tracking in hyperpolarized 13C imaging

PURPOSE

A novel application of two-dimensional (2D) spatially selective radiofrequency (2DRF) excitation pulses in hyperpolarized 13C imaging is proposed for monitoring the bolus injection with highly efficient sampling of the initially polarized substrate, thus leaving more polarization available for detection of the subsequently generated metabolic products.

METHODS

A 2DRF pulse was designed with a spiral trajectory and conventional clinical gradient performance. To demonstrate the ability of our 2DRF bolus tracking pulse sequence, hyperpolarized [1-(13)ruvate in vivo imaging experiments were performed in normal rats, with a comparison to 1DRF excitation pulses.

RESULTS

Our designed 2DRF pulse was able to rapidly and efficiently monitor the injected bolus dynamics in vivo, with an 8-fold enhanced time resolution in comparison with 1DRF in our experimental settings. When applied at the pyruvate frequency for bolus tracking, our 2DRF pulse demonstrated reduced saturation of the hyperpolarization for the substrate and metabolic products compared to a 1DRF pulse, while being immune to ±0.5 ppm magnetic field inhomogeneity at 3T.

CONCLUSION

2DRF pulses in hyperpolarized 13C imaging can be used to efficiently monitor the bolus injection with reduced hyperpolarization saturation compared to 1DRF pulses. The parameters of our design are based on clinical scanner limits, which allows for rapid translation to human studies.

Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community.

Computer-intensive simulation of solid-state NMR experiments using SIMPSON

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations.