Generalized Bloch model: A theory for pulsed magnetization transfer.

PURPOSE: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water. THEORY AND METHODS: Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. RESULTS: Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations smaller than 300 µs. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2 µs. CONCLUSION: The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for MT, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF-fields) and describes experimental data better than previous models.

Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences.

Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control­derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.

Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy.

In high sensitivity inductive electron spin resonance spectroscopy, superconducting microwave resonators with large quality factors are employed. While they enhance the sensitivity, they also distort considerably the shape of the applied rectangular microwave control pulses, which limits the degree of control over the spin ensemble. Here, we employ shaped microwave pulses compensating the signal distortion to drive the spins faster than the resonator bandwidth. This translates into a shorter echo, with enhanced signal-to-noise ratio. The shaped pulses are also useful to minimize the dead-time of our spectrometer, which allows to reduce the wait time between successive drive pulses.

Spin-Scenario: A flexible scripting environment for realistic MR simulations.

In this paper we present a new open source package, Spin-Scenario, aimed at developing an intuitive, flexible and unique scripting framework able to cover many aspects of simulations in both MR imaging and MR spectroscopy. For this purpose, we adopted the Liouville space model as the standard computing engine and let the consequent computational burden be afforded by parallel computing techniques. Benefitting from the powerful Lua scripting language, the pulse sequence programming syntax was specially designed to offer an extremely concise way of scripting. Moreover, the built-in dataflow graph based optimal control scheme enables an efficient optimization of shaped pulses or multiple cooperative pulses for real-life experiment evaluations. As the name states, the users are expected to be able to realize their creative ideas like a scenarist that creates a scenario script and looks at the spin actors acting accordingly. The validation of the framework was demonstrated with several examples within MR imaging and MR spectroscopy. Spin-Scenario is available for download at https://github.com/spin-scenario.

pH Dependence of T1 for 13 C-Labelled Small Molecules Commonly Used for Hyperpolarized Magnetic Resonance Imaging.

Hyperpolarization is a method to enhance the nuclear magnetic resonance signal by up to five orders of magnitude. However, the hyperpolarized (HP) state is transient and decays with the spin-lattice relaxation time (T1 ), which is on the order of a few tens of seconds. Here, we analyzed the pH-dependence of T1 for commonly used HP 13 C-labelled small molecules such as acetate, alanine, fumarate, lactate, pyruvate, urea and zymonic acid. For instance, the T1 of HP pyruvate is about 2.5 fold smaller at acidic pH (25 s, pH 1.7, B0 =1 T) compared to pH close to physiological conditions (66 s, pH 7.3, B0 =1 T). Our data shows that increasing hydronium ion concentrations shorten the T1 of protonated carboxylic acids of most of the analyzed molecules except lactate. Furthermore it suggests that intermolecular hydrogen bonding at low pH can contribute to this T1 shortening. In addition, enhanced proton exchange and chemical reactions at the pKa appear to be detrimental for the HP-state.

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 B 0 -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.

Simultaneous characterization of tumor cellularity and the Warburg effect with PET, MRI and hyperpolarized 13C-MRSI.

Modern oncology aims at patient-specific therapy approaches, which triggered the development of biomedical imaging techniques to synergistically address tumor biology at the cellular and molecular level. PET/MR is a new hybrid modality that allows acquisition of high-resolution anatomic images and quantification of functional and metabolic information at the same time. Key steps of the Warburg effect-one of the hallmarks of tumors-can be measured non-invasively with this emerging technique. The aim of this study was to quantify and compare simultaneously imaged augmented glucose uptake and LDH activity in a subcutaneous breast cancer model in rats (MAT-B-III) and to study the effect of varying tumor cellularity on image-derived metabolic information. Methods: For this purpose, we established and validated a multimodal imaging workflow for a clinical PET/MR system including proton magnetic resonance (MR) imaging to acquire accurate morphologic information and diffusion-weighted imaging (DWI) to address tumor cellularity. Metabolic data were measured with dynamic [18F]FDG-PET and hyperpolarized (HP) 13C-pyruvate MR spectroscopic imaging (MRSI). We applied our workflow in a longitudinal study and analyzed the effect of growth dependent variations of cellular density on glycolytic parameters. Results: Tumors of similar cellularity with similar apparent diffusion coefficients (ADC) showed a significant positive correlation of FDG uptake and pyruvate-to-lactate exchange. Longitudinal DWI data indicated a decreasing tumor cellularity with tumor growth, while ADCs exhibited a significant inverse correlation with PET standard uptake values (SUV). Similar but not significant trends were observed with HP-13C-MRSI, but we found that partial volume effects and point spread function artifacts are major confounders for the quantification of 13C-data when the spatial resolution is limited and major blood vessels are close to the tumor. Nevertheless, analysis of longitudinal data with varying tumor cellularity further detected a positive correlation between quantitative PET and 13C-data. Conclusions: Our workflow allows the quantification of simultaneously acquired PET, MRSI and DWI data in rodents on a clinical PET/MR scanner. The correlations and findings suggest that a major portion of consumed glucose is metabolized by aerobic glycolysis in the investigated tumor model. Furthermore, we conclude that variations in cell density affect PET and 13C-data in a similar manner and correlations of longitudinal metabolic data appear to reflect both biochemical processes and tumor cellularity.

Ab Initio Simulation of pH-Sensitive Biomarkers in Magnetic Resonance Imaging.

An ab initio simulation scheme is introduced as a theoretical prescreening approach to facilitate and enhance the research for pH-sensitive biomarkers. The proton 1H and carbon 13C nuclear magnetic resonance (NMR) chemical shifts of the recently published marker for extracellular pH, [1,5-13C2]zymonic acid (ZA), and the as yet unpublished ( Z)-4-methyl-2-oxopent-3-enedioic acid (OMPD) were calculated with ab initio methods as a function of the pH. The influence of the aqueous solvent was taken into account either by an implicit solvent model or by explicit water molecules, where the latter improved the accuracy of the calculated chemical shifts considerably. The theoretically predicted chemical shifts allowed for a reliable NMR peak assignment. The p Ka value of the first deprotonation of ZA and OMPD was simulated successfully whereas the parametrization of the implicit solvent model does not allow for an accurate description of the second p Ka. The theoretical models reproduce the pH-induced chemical shift changes and the first p Ka with sufficient accuracy to establish the ab initio prescreening approach as a valuable support to guide the experimental search for pH-sensitive biomarkers.

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.

Overcoming Volume Selectivity of Dipolar Recoupling in Biological Solid-State NMR Spectroscopy.

Dipolar recoupling in solid-state NMR is an essential method for establishing correlations between nuclei that are close in space. In applications on protein samples, the traditional experiments like ramped and adiabatic DCP suffer from the fact that dipolar recoupling occurs only within a limited volume of the sample. This selection is dictated by the radiofrequency (rf) field inhomogeneity profile of the excitation solenoidal coil. We employ optimal control strategies to design dipolar recoupling sequences with substantially larger responsive volume and increased sensitivity. We show that it is essential to compensate for additional temporal modulations induced by sample rotation in a spatially inhomogeneous rf field. Such modulations interfere with the pulse sequence and decrease its performance. Using large-scale optimizations we developed pulse schemes for magnetization transfer from amide nitrogen to carbonyl (NCO) as well as aliphatic carbons (NCA). Our experiments yield a signal intensity increased by a factor of 1.5 and 2.0 for NCA and NCO transfers, respectively, compared to conventional ramped DCP sequences. Consistent results were obtained using several biological samples and NMR instruments.

Multi-step phase-cycling in a free-electron laser-powered pulsed electron paramagnetic resonance spectrometer.

Electron paramagnetic resonance (EPR) is a powerful tool for research in chemistry, biology, physics and materials science, which can benefit significantly from moving to frequencies above 100 GHz. In pulsed EPR spectrometers driven by powerful sub-THz oscillators, such as the free electron laser (FEL)-powered EPR spectrometer at UCSB, control of the duration, power and relative phases of the pulses in a sequence must be performed at the frequency and power level of the oscillator. Here we report on the implementation of an all-quasioptical four-step phase cycling procedure carried out directly at the kW power level of the 240 GHz pulses used in the FEL-powered EPR spectrometer. Phase shifts are introduced by modifying the optical path length of a 240 GHz pulse with precision-machined dielectric plates in a procedure we call phase cycling with optomechanical phase shifters (POPS), while numerical receiver phase cycling is implemented in post-processing. The POPS scheme was successfully used to reduce experimental dead times, enabling pulsed EPR of fast-relaxing spin systems such as gadolinium complexes at temperatures above 190 K. Coherence transfer pathway selection with POPS was used to perform spin echo relaxation experiments to measure the phase memory time of P1 centers in diamond in the presence of a strong unwanted FID signal in the background. The large excitation bandwidth of FEL-EPR, together with phase cycling, enabled the quantitative measurement of instantaneous electron spectral diffusion, from which the P1 center concentration was estimated to within 10%. Finally, phase cycling enabled saturation-recovery measurements of T1 in a trityl-water solution at room temperature - the first FEL-EPR measurement of electron T1.

Ultrashort Broadband Cooperative Pulses for Multidimensional Biomolecular NMR Experiments.

NMR spectroscopy at ultra-high magnetic fields requires improved radiofrequency (rf) pulses to cover the increased spectral bandwidth. Optimized 90° pulse pairs were introduced as Ramsey-type cooperative (Ram-COOP) pulses for biomolecular NMR applications. The Ram-COOP element provides broadband excitation with enhanced sensitivity and reduced artifacts even at magnetic fields >1.0 GHz 1 H Larmor frequency (23 T). A pair of 30 µs Ram-COOP pulses achieves an excitation bandwidth of 100 kHz with a maximum rf field of 20 kHz, more than three-fold improved compared to excitation by rectangular pulses. Ram-COOP pulses exhibit little offset-dependent phase errors and are robust to rf inhomogeneity. The performance of the Ram-COOP element is experimentally confirmed with heteronuclear multidimensional NMR experiments, applied to proteins and nucleic acids. Ram-COOP provides broadband excitation at low rf field strength suitable for application at current magnetic fields and beyond 23 T.

Hyperpolarized Amino Acid Derivatives as Multivalent Magnetic Resonance pH Sensor Molecules.

pH is a tightly regulated physiological parameter that is often altered in diseased states like cancer. The development of biosensors that can be used to non-invasively image pH with hyperpolarized (HP) magnetic resonance spectroscopic imaging has therefore recently gained tremendous interest. However, most of the known HP-sensors have only individually and not comprehensively been analyzed for their biocompatibility, their pH sensitivity under physiological conditions, and the effects of chemical derivatization on their logarithmic acid dissociation constant (pKa). Proteinogenic amino acids are biocompatible, can be hyperpolarized and have at least two pH sensitive moieties. However, they do not exhibit a pH sensitivity in the physiologically relevant pH range. Here, we developed a systematic approach to tailor the pKa of molecules using modifications of carbon chain length and derivatization rendering these molecules interesting for pH biosensing. Notably, we identified several derivatives such as [1-13C]serine amide and [1-13C]-2,3-diaminopropionic acid as novel pH sensors. They bear several spin-1/2 nuclei (13C, 15N, 31P) with high sensitivity up to 4.8 ppm/pH and we show that 13C spins can be hyperpolarized with dissolution dynamic polarization (DNP). Our findings elucidate the molecular mechanisms of chemical shift pH sensors that might help to design tailored probes for specific pH in vivo imaging applications.

Application of spin echoes in the regime of weak dephasing to T1 -mapping of the lung.

PURPOSE: This work presents an approach to mapping the entire lung's proton density and T1 within a single breath-hold and analyzes the apparent T1 when exciting with a spin echo generating pulse in comparison to a standard gradient echo acquisition. METHODS: An inversion-recovery SNAPSHOT-FLASH sequence with a stack-of-stars k-space readout with a golden angle increment was modified to use a spin echo generating radiofrequency-pulse for excitation. Data of five volunteers were acquired on a 3T scanner and image reconstruction was performed by an iterative algorithm adopted from MR-Fingerprinting. RESULTS: The feasibility of acquiring quantitative maps of the entire lung with a resolution of 5 × 5 × 10 mm within 7.5 s is demonstrated. It is shown that the proposed spin echo forming radiofrequency-pulse increases the apparent proton density compared to a rectangular pulse. Further, the apparent T1 is reduced in the spin echo case compared to the gradient echo sequence. CONCLUSION: The proposed spin echo based method results in T1 maps that are comparable to the ones that were acquired with ultra-short echo time sequences elsewhere. The T1 shortening is believed to originate from increased signal contributions of the extra vascular compartment, which has a short T2∗ and T1 . Magn Reson Med 79:960-967, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Cooperative broadband spin echoes through optimal control.

The Hahn echo sequence is one of the most common building blocks in magnetic resonance, consisting of an excitation pulse and a refocusing pulse. Conventional approaches to improve the performance of echo experiments focused on the optimization of individual pulses, compensating their own imperfections. Here we present an approach to concurrently design both pulses such that they also compensate each others imperfections. The fact that for such cooperative pulses the individual pulses do not need to be perfect provides additional degrees of freedom, resulting in improved overall Hahn echo performance. Single-scan cooperative pulses are compared to conventional approaches by simulations as well as experiments.

Radiofrequency fields in MAS solid state NMR probes.

We present a detailed analysis of the radiofrequency (RF) field over full volume of a rotor that is generated in a solenoid coil. On top of the usually considered static distribution of amplitudes along the coil axis we describe dynamic radial RF inhomogeneities induced by sample rotation. During magic angle spinning (MAS), the mechanical rotation of the sample about the magic angle, a spin packet travels through areas of different RF fields and experiences periodical modulations of both the RF amplitude and the phase. These modulations become particularly severe at the end regions of the coil where the relative RF amplitude varies up to ±25% and the RF phase changes within ±30°. Using extensive numerical simulations we demonstrate effects of RF inhomogeneity on pulse calibration and for the ramped CP experiment performed at a wide range of MAS rates. In addition, we review various methods to map RF fields using a B0 gradient along the sample (rotor axis) for imaging purposes. Under such a gradient, a nutation experiment provides directly the RF amplitude distribution, a cross polarization experiment images the correlation of the RF fields on the two channels according to the Hartmann-Hahn matching condition, while a spin-lock experiment allows to calibrate the RF amplitude employing the rotary resonance recoupling condition. Knowledge of the RF field distribution in a coil provides key to understand its effects on performance of a pulse sequence at the spectrometer and enables to set robustness requirements in the experimental design.

Exact broadband excitation of two-level systems by mapping spins to springs.

Designing accurate and high-fidelity broadband pulses is an essential component in conducting quantum experiments across fields from protein spectroscopy to quantum optics. However, constructing exact and analytic broadband pulses remains unsolved due to the nonlinearity and complexity of the underlying spin system dynamics. Here, we present a nontrivial dynamic connection between nonlinear spin and linear spring systems and show the surprising result that such nonlinear and complex pulse design problems are equivalent to designing controls to steer linear harmonic oscillators under optimal forcing. We derive analytic broadband π/2 and π pulses that perform exact, or asymptotically exact, excitation and inversion over a defined bandwidth, and also with bounded amplitude. This development opens up avenues for pulse sequence design and lays a foundation for understanding the control of two-level systems.Coherent control of two-level systems is crucial for achieving fidelity in spectroscopy and quantum computing, but inherent nonlinearities and parameter variation have, to date, required an approximate, numerical approach. Here, Li et al. show how to map a spin ensemble to a spring model so analytic pulses can be designed using linear methods.

An optimal control approach to design entire relaxation dispersion experiments.

A general approach is introduced to optimize experiments for the analysis of spin systems in the presence of chemical exchange. Rather than optimizing individual pulse sequence elements, such as refocusing pulses, entire relaxation dispersion sequences are optimized in the form of a single shaped pulse. This is achieved by defining a performance index that is only based on the remaining signal after the relaxation dispersion sequence for a range of exchange, relaxation, offset, and rf inhomogeneity parameters. The approach is demonstrated by optimizing energy-limited broadband relaxation dispersion sequences that closely approach the overall effect of ideal CPMG sequences. As illustrated both theoretically and experimentally, significant improvements are found compared to standard amplitude or energy-limited CPMG sequences.

Deuteration of Hyperpolarized 13 C-Labeled Zymonic Acid Enables Sensitivity-Enhanced Dynamic MRI of pH.

Aberrant pH is characteristic of many pathologies such as ischemia, inflammation or cancer. Therefore, a non-invasive and spatially resolved pH determination is valuable for disease diagnosis, characterization of response to treatment and the design of pH-sensitive drug-delivery systems. We recently introduced hyperpolarized [1,5-13 C2 ]zymonic acid (ZA) as a novel MRI probe of extracellular pH utilizing dissolution dynamic polarization (DNP) for a more than 10000-fold signal enhancement of the MRI signal. Here we present a strategy to enhance the sensitivity of this approach by deuteration of ZA yielding [1,5-13 C2 , 3,6,6,6-D4 ]zymonic acid (ZAd ), which prolongs the liquid state spin lattice relaxation time (T1 ) by up to 39 % in vitro. Measurements with ZA and ZAd on subcutaneous MAT B III adenocarcinoma in rats show that deuteration increases the signal-to-noise ratio (SNR) by up to 46 % in vivo. Furthermore, we demonstrate a proof of concept for real-time imaging of dynamic pH changes in vitro using ZAd , potentially allowing for the characterization of rapid acidification/basification processes in vivo.