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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Pseudo Steady-State Free Precession for MR-Fingerprinting.

PURPOSE: This article discusses the signal behavior in the case the flip angle in steady-state free precession sequences is continuously varied as suggested for MR-fingerprinting sequences. Flip angle variations prevent the establishment of a steady state and introduce instabilities regarding to magnetic field inhomogeneities and intravoxel dephasing. We show how a pseudo steady state can be achieved, which restores the spin echo nature of steady-state free precession. METHODS: Based on geometrical considerations, relationships between the flip angle, repetition and echo time are derived that suffice to the establishment of a pseudo steady state. The theory is tested with Bloch simulations as well as phantom and in vivo experiments. RESULTS: A typical steady-state free precession passband can be restored with the proposed conditions. The stability of the pseudo steady state is demonstrated by comparing the evolution of the signal of a single isochromat to one resulting from a spin ensemble. As confirmed by experiments, magnetization in a pseudo steady state can be described with fewer degrees of freedom compared to the original fingerprinting and the pseudo steady state results in more reliable parameter maps. CONCLUSION: The proposed conditions restore the spin-echo-like signal behavior typical for steady-state free precession in fingerprinting sequences, making this approach more robust to B0 variations. Magn Reson Med 77:1151-1161, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

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.

Spin echoes in the regime of weak dephasing.

PURPOSE: This article analyzes possibilities and limits of spin echoes beyond Hahn's theory. The regime of weak dephasing is explored with the purpose of combining the enhanced signal and reduced artifacts of spin echoes with the speed and flexibility of the fast low angle shot sequence. METHODS: In the regime of weak dephasing, an upper boundary of the echo time is derived analytically. This limit is verified with optimal control pulses, which are also used to heuristically examine the transition to Hahn's regime of complete dephasing. The potential of the proposed pulses is demonstrated in proof-of-concept spin echo fast low angle shot images of a volunteer's lung and head. RESULTS: It was found that the time between the end of the pulse and the spin echo can exceed the duration of the composite radio frequency-pulse, which stands in contrast to Hahn echoes where those measures are at most equal. The maximum echo time was found to mainly depend on the total amount of dephasing. In vivo spin echo fast low angle shot images show an increased pulmonary signal as well as reduced artifacts in areas affected by susceptibility differences. CONCLUSION: The spin dynamics in the regime of weak dephasing was investigated and the feasibility of spin echo fast low angle shot imaging was demonstrated in vivo.

Multiparametric human hepatocellular carcinoma characterization and therapy response evaluation by hyperpolarized (13) C MRSI.

Individual tumor characterization and treatment response monitoring based on current medical imaging methods remain challenging. This work investigates hyperpolarized (13) C compounds in an orthotopic rat hepatocellular carcinoma (HCC) model system before and after transcatheter arterial embolization (TAE). HCC ranks amongst the top six most common cancer types in humans and accounts for one-third of cancer-related deaths worldwide. Early therapy response monitoring could aid in the development of personalized therapy approaches and novel therapeutic concepts. Measurements with selectively (13) C-labeled and hyperpolarized urea, pyruvate and fumarate were performed in tumor-bearing rats before and after TAE. Two-dimensional, slice-selective MRSI was used to obtain spatially resolved maps of tumor perfusion, cell energy metabolic conversion rates and necrosis, which were additionally correlated with immunohistochemistry. All three injected compounds, taken together with their respective metabolites, exhibited similar signal distributions. TAE induced a decrease in blood flow into the tumor and thus a decrease in tumor to muscle and tumor to liver ratios of urea, pyruvate and its metabolites, alanine and lactate, whereas conversion rates remained stable or increased on TAE in tumor, muscle and liver tissue. Conversion from fumarate to malate successfully indicated individual levels of necrosis, and global malate signals after TAE suggested the washout of fumarase or malate itself on necrosis. This study presents a combination of three (13) C compounds as novel candidate biomarkers for a comprehensive characterization of genetically and molecularly diverse HCC using hyperpolarized MRSI, enabling the simultaneous detection of differences in tumor perfusion, metabolism and necrosis. If, as in this study, bolus dynamics are not required and qualitative perfusion information is sufficient, the desired information could be extracted from hyperpolarized fumarate and pyruvate alone, acquired at higher fields with better spectral separation. Copyright © 2016 John Wiley & Sons, Ltd.

Observation of Time-Invariant Coherence in a Nuclear Magnetic Resonance Quantum Simulator.

The ability to live in coherent superpositions is a signature trait of quantum systems and constitutes an irreplaceable resource for quantum-enhanced technologies. However, decoherence effects usually destroy quantum superpositions. It was recently predicted that, in a composite quantum system exposed to dephasing noise, quantum coherence in a transversal reference basis can stay protected for an indefinite time. This can occur for a class of quantum states independently of the measure used to quantify coherence, and it requires no control on the system during the dynamics. Here, such an invariant coherence phenomenon is observed experimentally in two different setups based on nuclear magnetic resonance at room temperature, realizing an effective quantum simulator of two- and four-qubit spin systems. Our study further reveals a novel interplay between coherence and various forms of correlations, and it highlights the natural resilience of quantum effects in complex systems.

Engineering of an all-heteronuclear 5-qubit NMR quantum computer.

The realization of an all-heteronuclear 5-qubit nuclear magnetic resonance quantum computer is reported, from the design and synthesis of a suitable molecule through the engineering of a prototype 6-channel probe head. Full control over the quantum computer is shown by a benchmark experiment.

A critical evaluation of heteronuclear TOCSY (HEHAHA) experiments for 1H,6Li spin pairs.

Heteronuclear TOCSY (HEHAHA) experiments for (1) H,(6) Li spin pairs in organolithium compounds with adjacent strongly coupled (1) H,(1) H spin systems showed unexpected cross peak behaviour: for n-butyllithium (1) H,(6) Li cross peaks were completely missing, whereas for the dimer of (Z)-2-lithio-1-(o-lithiophenyl)ethane, a cross peak for remote protons was observed even at very short mixing times. It was assumed that strong magnetization transfer within the proton spin systems was responsible for these results, which prevented unambiguous chemical shift assignments. Selective experiments with the (6) Li,(1) H-HET-PLUSH-TACSY sequence then showed the expected (6) Li,(1) H cross peaks for the transfer via the directly coupled (1) H and (6) Li nuclei. For n-butyllithium transfer to H(Cα) via an unresolved heteronuclear coupling constant below 0.1 Hz is unambiguously observed. Cross peaks in the 2D (6) Li,(1) H-HET-PLUSH-TACSY spectra for the dimer of (Z)-2-lithio-1-(o-lithiophenyl)ethane are readily explained by the measured coupling network and the corresponding active mixing conditions.

Next-generation heteronuclear decoupling for high-field biomolecular NMR spectroscopy.

Ultra-high-field NMR spectroscopy requires an increased bandwidth for heteronuclear decoupling, especially in biomolecular NMR applications. Composite pulse decoupling cannot provide sufficient bandwidth at practical power levels, and adiabatic pulse decoupling with sufficient bandwidth is compromised by sideband artifacts. A novel low-power, broadband heteronuclear decoupling pulse is presented that generates minimal, ultra-low sidebands. The pulse was derived using optimal control theory and represents a new generation of decoupling pulses free from the constraints of periodic and cyclic sequences. In comparison to currently available state-of-the-art methods this novel pulse provides greatly improved decoupling performance that satisfies the demands of high-field biomolecular NMR spectroscopy.

Chemical shift correlations from hyperpolarized NMR using a single SHOT.

A significant challenge in realizing the promise of the dissolution dynamic nuclear polarization technique for signal enhancement in high-resolution NMR lies in the nonrenewability of the hyperpolarized spin state. This property prevents the application of traditional two-dimensional correlation spectroscopy, which relies on regeneration of spin polarization before each successive increment of the indirect dimension. Since correlation spectroscopy is one of the most important approaches for the identification and structural characterization of molecules by NMR, it is important to find easily applicable methods that circumvent this problem. Here, we introduce the application of scaling of heteronuclear couplings by optimal tracking (SHOT) to achieve this goal. SHOT decoupling pulses have been numerically optimized on the basis of optimal control algorithms to obtain chemical shift correlations in C-H groups, either by acquiring a single one-dimensional (13)C spectrum with (1)H off-resonance decoupling or vice versa. Vanillin, which contains a number of functional groups, was used as a test molecule, allowing the demonstration of SHOT decoupling tailored toward simplified and accurate data analysis. This strategy was demonstrated for two cases: First, a linear response to chemical shift offset in the correlated dimension was optimized. Second, a pulse with alternating linear responses in the correlated dimension was chosen as a goal to increase the sensitivity of the decoupling response to the chemical shift offset. In these measurements, error ranges of ±0.03 ppm for the indirectly determined (1)H chemical shifts and of ±0.4 ppm for the indirectly determined (13)C chemical shifts were found. In all cases, we show that chemical shift correlations can be obtained from information contained in a single scan, which maximizes the ratio of signal to stochastic noise. Furthermore, a comprehensive discussion of the robustness of the method toward nonideal conditions is included based on experimental and simulated data. Unique features of this technique include the abilities to control the accuracy of chemical shift determination in spectral regions of interest and to acquire such chemical shift correlations rapidly-the latter being of interest for potential application in real-time spectroscopy.

Saturation-recovery metabolic-exchange rate imaging with hyperpolarized [1-13C] pyruvate using spectral-spatial excitation.

Within the last decade hyperpolarized [1-13C] pyruvate chemical-shift imaging has demonstrated impressive potential for metabolic MR imaging for a wide range of applications in oncology, cardiology, and neurology. In this work, a highly efficient pulse sequence is described for time-resolved, multislice chemical shift imaging of the injected substrate and obtained downstream metabolites. Using spectral-spatial excitation in combination with single-shot spiral data acquisition, the overall encoding is evenly distributed between excitation and signal reception, allowing the encoding of one full two-dimensional metabolite image per excitation. The signal-to-noise ratio can be flexibly adjusted and optimized using lower flip angles for the pyruvate substrate and larger ones for the downstream metabolites. Selectively adjusting the excitation of the down-stream metabolites to 90° leads to a so-called "saturation-recovery" scheme with the detected signal content being determined by forward conversion of the available pyruvate. In case of repetitive excitations, the polarization is preserved using smaller flip angles for pyruvate. Metabolic exchange rates are determined spatially resolved from the metabolite images using a simplified two-site exchange model. This novel contrast is an important step toward more quantitative metabolic imaging. Goal of this work was to derive, analyze, and implement this "saturation-recovery metabolic exchange rate imaging" and demonstrate its capabilities in four rats bearing subcutaneous tumors.