Robust conversion of singlet spin order in coupled spin-1/2 pairs by adiabatically ramped RF-fields

Robust parahydrogen-induced polarization at high concentrations

Parahydrogen-induced polarization (PHIP) is a potent technique for generating target molecules with high nuclear spin polarization. The PHIP process involves a chemical reaction between parahydrogen and a target molecule, followed by the transformation of nuclear singlet spin order into magnetization of a designated target nucleus through magnetic field manipulations. Although the singlet-to-magnetization polarization transfer process works effectively at moderate concentrations, it is observed to become much less efficient at high molar polarization, defined as the product of polarization and concentration. This strong dependence on the molar polarization is attributed to interference due to the field produced by the sample magnetization during polarization transfer, which leads to complex dynamics and can severely affect the scalability of the technique. We address this challenge with a pulse sequence that suppresses the influence of the distant dipolar field, while simultaneously achieving singlet-to-magnetization polarization transfer to the desired target spins, free from restrictions on the molar polarization.

Excitation of long-lived nuclear spin order using spin-locking: a geometrical formalism

Over the last two decades, numerous pulse sequences have been introduced for the excitation of long-lived spin order (LLS) in high fields. The long continuous wave (CW) or adiabatic pulses used in the SLIC and APSOC sequences should remind one of the spin-locking pulses that are used to induce cross-polarization (CP). Dynamics during these spin-lockings in CP experiments are explained through a geometrical formalism. However, the SLIC and APSOC sequences are described in terms of the energy-level picture or in the language of level anti-crossings. Motivated by this analogy, this work presents here a geometrical formalism for the LLS excitation by spin-locking pulses in weakly coupled systems. The formalism is similar to the one used for CP dynamics and reveals new pulse sequences involving CW or adiabatic locking. A similar formalism for the sustaining period of LLS is also provided, which reveals new features of the dynamics and suggests the usage of modulated spin-lockings for proper LLS sustaining. For strong and intermediate regimes, although a simple geometrical formalism seems infeasible, a new pulse sequence that employs a ramp-down adiabatic pulse for both LLS excitation and reconversion to observables in both these regimes is presented here. Given the similarities between LLS excitation and well-developed CP, it may be anticipated that this work would initiate the search for new LLS excitation methods and applications.

Hyperpolarisation criteria in magnetic resonance

Nuclear Magnetic Resonance (NMR) techniques display an inherently low sensitivity due to a small equilibrium magnetisation. Nowadays this issue is easily overcome through the use of hyperpolarisation methods. This however raises the question as to what precisely do we mean by "hyperpolarisation". Recently a formal definition of hyperpolarisation has been given based on the von Neumann entropy of a system. Ideally this definition should conform with the general usage in the magnetic resonance community, where hyperpolarisation is often used synonymously with "larger" NMR signals. Within this article I show that an entropy-based hyperpolarisation criterion does not always conform with the general usage. Based on this observation I introduce an alternative hyperpolarisation criterion utilising the concept of latent polarisation, where latent polarisation is a measure of the highest possible amount of polarisation that may be extracted from a system. I show that a hyperpolarisation criterion based on latent polarisation correlates more strongly with the general usage within the magnetic resonance community. Ultimately however our results show that there are several possible notions of hyperpolarisation, and the choice depends upon the questions of interest.

In Situ Hyperpolarization Enables 15N and 13C Benchtop NMR at Natural Isotopic Abundance

Without employing isotopic labeling, we demonstrate the generation of 15N and 13C NMR signals for molecules containing -NH2 motifs using benchtop NMR spectrometers (1-1.4 T). Specifically, high-SNR (>50) detection of ammonia, 4-aminopyridine, benzylamine, and phenethylamine dissolved in methanol or dichloromethane is demonstrated after only 10 s of parahydrogen bubbling using signal amplification by reversible exchange and applying a pulse sequence based on spin-lock-induced crossing. Optimization of the sequence parameters allows us to achieve up to 12% 15N and 0.4% 13C polarization in situ without the need for the sample transfer typically employed in other hyperpolarization methods. Moreover, hyperpolarization is generated continuously without having to stop the parahydrogen bubbling to reset magnetization, paving the way toward fast 2D spectroscopic methods and relaxometry. The provided methodology may find application for the identification of diluted chemicals relevant to industry and research with the aid of affordable benchtop NMR spectrometers.

Selective filtration of NMR signals arising from weakly- and strongly-coupled spin systems

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing chemical and biological systems. However, in complex solutions with similar molecular components, NMR signals can overlap, making it challenging to distinguish and quantify individual species. In this paper, we introduce new spectral editing sequences that exploit the differences in nuclear spin interactions (J-couplings) between weakly- and strongly-coupled two-spin systems. These sequences selectively attenuate or nullify undesired spin magnetization while they preserve the desired signals, resulting in simplified NMR spectra and potentially facilitating single-species imaging applications. We demonstrate the effectiveness of our approach using a 31P spectral filtration method on a model system of nicotinamide dinucleotide (NAD), which exists in oxidized (NAD+) and reduced (NADH) forms. The presented sequences are robust to field inhomogeneity, do not require additional sub-spectra, and retain a significant portion of the original signal.

Multiple Stroboscopic Detection of Long-Lived Nuclear Magnetization for Glutathione Oxidation Kinetics

Imaging the molecular kinetics of antioxidants by magnetic resonance can contribute to the mechanistic understanding of therapeutic approaches. Magnetic resonance detection of the response to flashes of oxidative stress requires sequential spectroscopy on the same time scale on which reactive oxygen species are generated. To this effect, we propose a single-polarization multiple-detection stroboscopic experiment. We demonstrate this experiment for the follow-up of glutathione oxidation kinetics. On-the-fly stroboscopic detection minimizes the durations necessary for single acquisitions yet necessitates sustaining of magnetization lifetimes. Long-lived proton spin states (LLS) in the cysteine and glycine residues of glutathione with T_LLS up to 16 s are reached. Based on ¹H LLS, we followed fast oxidation kinetics in the glutathione redox pair GSH/GSSG. This new detection method allows sampling of long-lived spin order multiple times via small flip-angle excitations. This establishes the ground for the follow-up of redox processes detecting GSH/GSSG kinetics as magnetic-resonance biomarker of FLASH oxidative processes on time scales of tens of seconds.

Distinguishing glutamate and glutamine in in vivo 1 H MRS based on nuclear spin singlet order filtering

PURPOSE

The signals of glutamate (Glu) and glutamine (Gln) are often significantly overlapped in routine ¹ H-MR spectra of human brain in vivo. Selectively probing the signals of Glu and Gln in vivo is very important for the study of the metabolisms in which Glu and Gln are involved.

METHODS

The Glu-/Gln- targeted pulse sequences are developed to selectively probe the signals of Glu and Gln. The core part of the Glu-/Gln- targeted pulse sequences lies on the preparation of the nuclear spin singlet orders (SSOs) of the five-spin systems of Glu and Gln. The optimal control method is used to prepare the SSOs of Glu and Gln with high efficiency.

RESULTS

The Glu-/Gln- targeted pulse sequences have been applied on phantoms to selectively probe the signals of Glu and Gln. Moreover, in the in vivo experiments, the signals of Glu and Gln in human brains of healthy subjects have been successfully probed separately.

CONCLUSION

The developed Glu-/Gln- targeted pulse sequences can be used to distinguish the ¹ H-MR signals of Glu and Gln in human brains in vivo. The optimal control method provides an effective way to prepare the SSO of a specific spin system with high efficiency and in turn selectively probe the signals of a targeted molecule.

In vivo singlet state filtered nuclear magnetic resonance: towards monitoring toxic responses inside living organisms

In line with recent paradigm shifts in toxicity testing, in vivo nuclear magnetic resonance (NMR) is a powerful tool for studying the biological impacts and perturbations caused by toxicants in living organisms. However, despite the excellent molecular insights that can be obtained through this technique, in vivo NMR applications are hampered by considerable experimental challenges such as poor line shape and spectral overlap. Here, we demonstrate the application of singlet-filtered NMR to target specific metabolites and facilitate the study of metabolite fluxes in living Daphnia magna, an aquatic keystone species and model organism. Informed by mathematical simulations and experiments on ex vivo organisms, singlet state NMR is used to monitor the flux of metabolites such as d-glucose and serine in living D. magna, during the environmentally relevant processes of anoxic stress and reduced food availability. Overall, singlet state NMR is shown to have significant future potential for studying metabolic processes in vivo.

Using optimal controlled singlet spin order to accurately target molecular signal in MRI and MRS

Magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) have made great successes in clinical diagnosis, medical research, and neurological science. MRI provides high resolution anatomical images of tissues/organs, and MRS provides information of the functional molecules related to a specific tissue/organ. However, it is difficult for classic MRI/MRS to selectively image/probe a specific metabolite molecule other than the water or fat in tissues/organs. This greatly limits their applications on the study of the molecular mechanism(s) of metabolism and disease. Herein, we report a series of molecularly targeted MRI/MRS methods to target specific molecules. The optimal control method was used to efficiently prepare the singlet spin orders of varied multi-spin systems and in turn greatly expand the choice of the targeted molecules in the molecularly targeted MRI/MRS. Several molecules, such as N-acetyl-L-aspartic acid (NAA), dopamine (DA), and a tripeptide (alanine-glycine-glycine, AGG), have been used as targeted molecules for molecularly targeted MRI and MRS. We show in vivo NAA-targeted ¹H MRS spectrum of a human brain. The high-resolution signal of NAA suggests a promising way to study important issues in molecular biology at the molecular level, e.g., measuring the local pH value of tissue in vivo, demonstrating the high potential of such methods in medicine.

Spin Hyperpolarization in Modern Magnetic Resonance

Magnetic resonance techniques are successfully utilized in a broad range of scientific disciplines and in various practical applications, with medical magnetic resonance imaging being the most widely known example. Currently, both fundamental and applied magnetic resonance are enjoying a major boost owing to the rapidly developing field of spin hyperpolarization. Hyperpolarization techniques are able to enhance signal intensities in magnetic resonance by several orders of magnitude, and thus to largely overcome its major disadvantage of relatively low sensitivity. This provides new impetus for existing applications of magnetic resonance and opens the gates to exciting new possibilities. In this review, we provide a unified picture of the many methods and techniques that fall under the umbrella term "hyperpolarization" but are currently seldom perceived as integral parts of the same field. Specifically, before delving into the individual techniques, we provide a detailed analysis of the underlying principles of spin hyperpolarization. We attempt to uncover and classify the origins of hyperpolarization, to establish its sources and the specific mechanisms that enable the flow of polarization from a source to the target spins. We then give a more detailed analysis of individual hyperpolarization techniques: the mechanisms by which they work, fundamental and technical requirements, characteristic applications, unresolved issues, and possible future directions. We are seeing a continuous growth of activity in the field of spin hyperpolarization, and we expect the field to flourish as new and improved hyperpolarization techniques are implemented. Some key areas for development are in prolonging polarization lifetimes, making hyperpolarization techniques more generally applicable to chemical/biological systems, reducing the technical and equipment requirements, and creating more efficient excitation and detection schemes. We hope this review will facilitate the sharing of knowledge between subfields within the broad topic of hyperpolarization, to help overcome existing challenges in magnetic resonance and enable novel applications.

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Description of interacting spin systems relies on understanding the spectral properties of the corresponding spin Hamiltonians. However, the eigenvalue problems arising here lead to algebraic problems too complex to be analytically tractable. This is already the case for the simplest nontrivial (Kmax−1) block for an isotropic hyperfine Hamiltonian for a radical with spin-12 nuclei, where n nuclei produce an n-th order algebraic equation with n independent parameters. Systems described by such blocks are now physically realizable, e.g., as radicals or radical pairs with polarized nuclear spins, appear as closed subensembles in more general radical settings, and have numerous counterparts in related central spin problems. We provide a simple geometrization of energy levels in this case: given n spin-12 nuclei with arbitrary positive couplings ai, take an n-dimensional hyper-ellipsoid with semiaxes ai, stretch it by a factor of n+1 along the spatial diagonal (1, 1, …, 1), read off the semiaxes of thus produced new hyper-ellipsoid qi, augment the set {qi} with q0=0, and obtain the sought n+1 energies as Ek=−12qk2+14∑iai. This procedure provides a way of seeing things that can only be solved numerically, giving a useful tool to gain insights that complement the numeric simulations usually inevitable here, and shows an intriguing connection to discrete Fourier transform and spectral properties of standard graphs.

Parahydrogen-induced polarization and spin order transfer in ethyl pyruvate at high magnetic fields

Nuclear magnetic resonance has experienced great advances in developing and translating hyperpolarization methods into procedures for fundamental and clinical studies. Here, we propose the use of a wide-bore NMR for large-scale (volume- and concentration-wise) production of hyperpolarized media using parahydrogen-induced polarization. We discuss the benefits of radio frequency-induced parahydrogen spin order transfer, we show that 100% polarization is theoretically expected for homogeneous B₀ and B₁ magnetic fields for a three-spin system. Moreover, we estimated that the efficiency of spin order transfer is not significantly reduced when the B₁ inhomogeneity is below ± 5%; recommendations for the sample size and RF coils are also given. With the latest breakthrough in the high-yield synthesis of 1-¹³C-vinyl pyruvate and its deuterated isotopologues, the high-field PHIP-SAH will gain increased attention. Some remaining challenges will be addressed shortly.

Polychromatic Excitation of Delocalized Long-Lived Proton Spin States in Aliphatic Chains

Long-lived states (LLS) involving pairs of magnetically inequivalent but chemically equivalent proton spins in aliphatic (CH_{2})_{n} chains can be excited by simultaneous application of weak selective radio frequency fields at n chemical shifts by polychromatic spin-lock induced crossing. The LLS are delocalized throughout the aliphatic chains by mixing of intrapair singlet states and by excitation of LLS comprising products of four and six spin operators. The measured lifetimes T_{LLS} in a model compound are about 5 times longer than T_{1} and are strongly affected by interactions with macromolecules.

Analytical solution for the inverting pulses with constant adiabaticity

The exact solution was found for inverting pulses with constant adiabaticity for spin ½. The analytical relationship between the time-varying frequency of the microwave resonant field (or RF field in the case of NMR) and its amplitude time dependence such that the adiabaticity parameter remains constant for the single isochromat throughout the pulse is found. Comparison with EPR (hyperbolic tangent)-(hyperbolic secant) pulse method was carried out. On the basis of the analytical solution the pulses with different dependences of the microwave field amplitude conserving the constant adiabaticity have been constructed. The pulses exhibit rather sharp inversion selectivity that can be used in the field of EPR, NMR and MRI.

31P spin-lattice and singlet order relaxation mechanisms in pyrophosphate studied by isotopic substitution, field shuttling NMR, and molecular dynamics simulation

Nuclear spin relaxation mechanisms are often difficult to isolate and identify, especially in molecules with internal flexibility. Here we combine experimental work with computation in order to determine the major mechanisms responsible for ³¹P spin-lattice and singlet order (SO) relaxation in pyrophosphate, a physiologically relevant molecule. Using field-shuttling relaxation measurements (from 2 μT to 9.4 T) and rates calculated from molecular dynamics (MD) trajectories, we identified chemical shift anisotropy (CSA) and spin-rotation as the major mechanisms, with minor contributions from intra- and intermolecular coupling. The significant spin-rotation interaction is a consequence of the relatively rapid rotation of the -PO₃^2- entities around the bridging P-O bonds, and is treated by a combination of MD simulations and quantum chemistry calculations. Spin-lattice relaxation was predicted well without adjustable parameters, and for SO relaxation one parameter was extracted from the comparison between experiment and computation (a correlation coefficient between the rotational motion of the groups).

Selective Excitation of Long-Lived Nuclear Spin States

Nuclear magnetization storage, once limited by longitudinal and transverse relaxation lifetimes, T₁ and T₂, can be prolonged by symmetry-adapted nuclear spin order, i.e. long-lived states (LLS) and long-lived coherences (LLC), which have significantly extended relaxation time constants compared to T₁ and T₂, respectively. Excitation and/or detection of LLS currently involves pulses covering wide frequency ranges in high-magnetic-field spectrometers. This leads to excitation of unwanted signals that may overlap and interfere with the resonances of interest. Herein, we present a new pulse sequence that converts longitudinal magnetization to LLS and further to detectable magnetization using only frequency-selective pulses. We demonstrate the suitability of this sequence for different J-coupled spin pairs in dipeptide AlaGly and protein Ubiquitin. The newly developed method is adapted for investigations of LLS in complex systems such as proteins and mixtures of metabolites where selected molecular groups are to be investigated separately.

Symmetry Constraints on Spin Order Transfer in Parahydrogen-Induced Polarization (PHIP)

It is well known that the association of parahydrogen (pH2) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed for converting pH2-derived nuclear spin order to the observable magnetization of protons or other nuclei of interest, usually 13C or 15N. Here, we analyze the constraints imposed by the topological symmetry of the spin systems on the amplitude of transferred polarization. We find that in asymmetric systems, heteronuclei can be polarized to 100%. However, the amplitude drops to 75% in A2BX systems and further to 50% in A3B2X systems. The latter case is of primary importance for biological applications of PHIP using sidearm hydrogenation (PHIP-SAH). If the polarization is transferred to the same type of nuclei, i.e., 1H, symmetry constraints impose significant boundaries on the spin-order distribution. For AB, A2B, A3B, A2B2, AA’(AA’) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH2). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27 and can exceed 2 in the absence of symmetry constraints (where is the number of spins). We also discuss the effect of dipole–dipole-induced pH2 spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis.

Frequency-Selective Manipulations of Spins allow Effective and Robust Transfer of Spin Order from Parahydrogen to Heteronuclei in Weakly-Coupled Spin Systems

We present a selectively pulsed (SP) generation of sequences to transfer the spin order of parahydrogen (pH₂) to heteronuclei in weakly coupled spin systems. We analyze and discuss the mechanism and efficiency of SP spin order transfer (SOT) and derive sequence parameters. These new sequences are most promising for the hyperpolarization of molecules at high magnetic fields. SP‐SOT is effective and robust despite the symmetry of the ¹H‐¹³C J‐couplings even when precursor molecules are not completely labeled with deuterium. As only one broadband ¹H pulse is needed per sequence, which can be replaced for instance by a frequency‐modulated pulse, lower radiofrequency (RF) power is required. This development will be useful to hyperpolarize (new) agents and to perform the hyperpolarization within the bore of an MRI system, where the limited RF power has been a persistent problem.

Bimodal fluorescence/magnetic resonance molecular probes with extended spin lifetimes

Bimodal molecular probes combining nuclear magnetic resonance (NMR) and fluorescence have been widely studied in basic science, as well as clinical research. The investigation of spin phenomena holds promise to broaden the scope of available probes allowing deeper insights into physiological processes. Herein, a class of molecules with a bimodal character with respect to fluorescence and nuclear spin singlet states is introduced. Singlet states are NMR silent but can be probed indirectly. Symmetric, perdeuterated molecules, in which the singlet states can be populated by vanishingly small electron‐mediated couplings (below 1 Hz) are reported. The lifetimes of these states are an order of magnitude longer than the longitudinal relaxation times and up to four minutes at 7 T. Moreover, these molecules show either aggregation induced emission (AIE) or aggregation caused quenching (ACQ) with respect to their fluorescence. In the latter case, the existence of excited dimers, which are proposed to use in a switchable manner in combination with the quenching of nuclear spin singlet states, is observed

NMR of 31P nuclear spin singlet states in organic diphosphates

³¹P NMR and MRI are commonly used to study organophosphates that are central to cellular energy metabolism. In some molecules of interest, such as adenosine diphosphate (ADP) and nicotinamide adenine dinucleotide (NAD), pairs of coupled ³¹P nuclei in the diphosphate moiety should enable the creation of nuclear spin singlet states, which may be long-lived and can be selectively detected via quantum filters. Here, we show that ³¹P singlet states can be created on ADP and NAD, but their lifetimes are shorter than T₁ and are strongly sensitive to pH. Nevertheless, the singlet states were used with a quantum filter to successfully isolate the ³¹P NMR spectra of those molecules from the adenosine triphosphate (ATP) background signal.

31P nuclear spin singlet lifetimes in a system with switchable magnetic inequivalence: experiment and simulation

³¹P NMR spectroscopy and the study of nuclear spin singlet relaxation phenomena are of interest in particular due to the importance of phosphorus-containing compounds in physiology. We report the generation and measurement of relaxation of ³¹P singlet order in a chemically equivalent but magnetically inequivalent case. Nuclear magnetic resonance singlet state lifetimes of ³¹P pairs have heretofore not been reported. Couplings between ¹H and ³¹P nuclei lead to magnetic inequivalence and serve as a mechanism of singlet state population conversion within this molecule. We show that in this molecule singlet relaxation occurs at a rate significantly faster than spin-lattice relaxation, and that anticorrelated chemical shift anisotropy can account for this observation. Calculations of this mechanism, with the help of molecular dynamics simulations and ab initio calculations, provide excellent agreement with the experimental findings. This study could provide guidance for the study of ³¹P singlets within other compounds, including biomolecules.

Constant-adiabaticity pulse schemes for manipulating singlet order in 3-spin systems with weak magnetic non-equivalence

Parahydrogen-induced polarization (PHIP) is a source of nuclear spin hyperpolarization, and this technique allows for the preparation of biomolecules for in vivo metabolic imaging. PHIP delivers hyperpolarization in the form of proton singlet order to a molecule, but most applications require that a heteronuclear (e.g. ¹³C or ¹⁵N) spin in the molecule is hyperpolarized. Here we present high field pulse methods to manipulate proton singlet order in the [1-¹³C]fumarate, and in particular to transfer the proton singlet order into ¹³C magnetization. We exploit adiabatic pulses, i.e., pulses with slowly ramped amplitude, and use constant-adiabaticity variants: the spin Hamiltonian is varied in such a way that the generalized adiabaticity parameter is time-independent. This allows for faster polarization transfer, and we achieve 96.2% transfer efficiency in thermal equilibrium experiments. We demonstrate this in experiments using hyperpolarization, and obtain 6.8% ¹³C polarization. This work paves the way for efficient hyperpolarization of nuclear spins in a variety of biomolecules, since the high-field pulse sequences allow individual spins to be addressed.

Symmetry versus entropy: Long-lived states and coherences

In recent years, new molecular symmetry-based approaches for magnetic resonance have been invented. The implications of these discoveries will be significant for molecular imaging via magnetic resonance, in vitro as well as in vivo, for quantum computing and for other fields. Since the initial observation in 2004 in Southampton that effective spin symmetry can be instilled in a molecule during magnetic resonance experiments, spin states that are resilient to relaxation mechanisms have been increasingly used. Most of these states are related to the nuclear singlet in a pair of J-coupled spins. Tailored relaxation rate constants for magnetization became available in molecules of different sizes and structures, as experimental developments broadened the scope of symmetry-adapted spin states. The ensuing access to timescales longer than the classically-attained ones by circa one order of magnitude allows the study of processes such as slow diffusion or slow exchange that were previously beyond reach. Long-lived states formed by differences between populations of singlets and triplets have overcome the limitations imposed by longitudinal relaxation times (T₁) by factors up to 40. Long-lived coherences formed by superpositions of singlets and triplets have overcome the limit of classical transverse coherence (T₂) by a factor 9. We present here an overview of the development and applications of long-lived states (LLS) and long-lived coherences (LLC's) and considerations on future perspectives.

Localized singlet-filtered MRS in vivo

MR is a prominent technology to investigate diseases, with millions of clinical procedures performed every year. Metabolic dysfunction is one common aspect associated with many diseases. Thus, understanding and monitoring metabolic changes is essential to develop cures for many illnesses, including for example cancer and neurodegeneration. MR methodologies are especially suited to study endogenous metabolites and processes within an organism in vivo, which has led to many insights about physiological functions. Advancing metabolic MR techniques is therefore key to further understand physiological processes. Here, we introduce an approach based on nuclear spin singlet states to specifically filter metabolic signals and particularly show that singlet-filtered glutamate can be observed distinctly in the hippocampus of a living mouse in vivo. This development opens opportunities to make use of the singlet spin phenomenon in vivo and besides its use as a filter to provide scope for new contrast agents.

Representation of population exchange at level anti-crossings

A theoretical framework is proposed to describe the spin dynamics driven by coherent spin mixing at level anti-crossings (LACs). We briefly introduce the LAC concept and propose to describe the spin dynamics using a vector of populations of the diabatic eigenstates. In this description, each LAC gives rise to a pairwise redistribution of eigenstate populations, allowing one to construct the total evolution operator of the spin system. Additionally, we take into account that in the course of spin evolution a "rotation" of the eigenstate basis case take place. The approach is illustrated by a number of examples, dealing with magnetic field inversion, cross-polarization, singlet-state nuclear magnetic resonance and parahydrogen-induced polarization.

Robust transformation of singlet order into heteronuclear magnetisation over an extended coupling range

Several important NMR procedures involve the conversion of nuclear singlet order into heteronuclear magnetisation, including some experiments involving long-lived spin states and parahydrogen-induced hyperpolarisation. However most existing sequences suffer from a limited range of validity or a lack of robustness against experimental imperfections. We present a new radio-frequency scheme for the transformation of the singlet order of a chemically-equivalent homonuclear spin pair into the magnetisation of a heteronuclear coupling partner. The proposed radio-frequency (RF) scheme is called gS2hM (generalized singlet-to-heteronuclear magnetisation) and has good compensation for common experimental errors such as RF and static field inhomogeneities. The sequence retains its robustness for homonuclear spin pairs in the intermediate coupling regime, characterised by the in-pair coupling being of the same order of magnitude as the difference between the out-of-pair couplings. This is a substantial improvement to the validity range of existing sequences. Analytical solutions for the pulse sequence parameters are provided. Experimental results are shown for two test cases.

In vitro singlet state and zero-quantum encoded magnetic resonance spectroscopy: Illustration with N-acetyl-aspartate

Magnetic resonance spectroscopy (MRS) allows the analysis of biochemical processes non-invasively and in vivo. Still, its application in clinical diagnostics is rare. Routine MRS is limited to spatial, chemical and temporal resolutions of cubic centimetres, mM and minutes. In fact, the signal of many metabolites is strong enough for detection, but the resonances significantly overlap, exacerbating identification and quantification. Besides, the signals of water and lipids are much stronger and dominate the entire spectrum. To suppress the background and isolate selected signals, usually, relaxation times, J-coupling and chemical shifts are used. Here, we propose methods to isolate the signals of selected molecular groups within endogenous metabolites by using long-lived spin states (LLS). We exemplify the method by preparing the LLSs of coupled protons in the endogenous molecules N-acetyl-L-aspartic acid (NAA). First, we store polarization in long-lived, double spin states, followed by saturation pulses before the spin order is converted back to observable magnetization or double quantum filters to suppress background signals. We show that LLS and zero-quantum coherences can be used to selectively prepare and measure the signals of chosen metabolites or drugs in the presence of water, inhomogeneous field and highly concentrated fatty solutions. The strong suppression of unwanted signals achieved allowed us to measure pH as a function of chemical shift difference.

Generalised magnetisation-to-singlet-order transfer in nuclear magnetic resonance

A variety of pulse sequences have been described for converting nuclear spin magnetisation into long-lived singlet order for nuclear spin-1/2 pairs. Existing sequences operate well in two extreme parameter regimes. The magnetisation-to-singlet (M2S) pulse sequence performs a robust conversion of nuclear spin magnetisation into singlet order in the near-equivalent limit, meaning that the difference in chemical shift frequencies of the two spins is much smaller than the spin-spin coupling. Other pulse sequences operate in the strong-inequivalence regime, where the shift difference is much larger than the spin-spin coupling. However both sets of pulse sequences fail in the intermediate regime, where the chemical shift difference and the spin-spin coupling are roughly equal in magnitude. We describe a generalised version of M2S, called gM2S, which achieves robust singlet order excitation for spin systems ranging from the near-equivalence limit well into the intermediate regime. This closes an important gap left by existing pulse sequences. The efficiency of the gM2S sequence is demonstrated numerically and experimentally for near-equivalent and intermediate-regime cases.

Algorithmic cooling of nuclear spins using long-lived singlet order

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent ¹³C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.

Singlet-filtered NMR spectroscopy

Selectively studying parts of proteins and metabolites in tissue with nuclear magnetic resonance promises new insights into molecular structures or diagnostic approaches. Nuclear spin singlet states allow the selection of signals from chemical moieties of interest in proteins or metabolites while suppressing background signal. This selection process is based on the electron-mediated coupling between two nuclear spins and their difference in resonance frequency. We introduce a generalized and versatile pulsed NMR experiment that allows populating singlet states on a broad scale of coupling patterns. This approach allowed us to filter signals from proton pairs in the Alzheimer's disease-related b-amyloid 40 peptide and in metabolites in brain matter. In particular, for glutamine/glutamate, we have discovered a long-lived state in tissue without the typically required singlet sustaining by radiofrequency irradiation. We believe that these findings will open up new opportunities to study metabolites with a view on future in vivo applications.

Generating and sustaining long-lived spin states in 15N,15N'-azobenzene

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-¹⁵N,¹⁵N′-azobenzene. The singlet state of the ¹⁵N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the ¹⁵N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of ¹⁵N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization.

Long live the singlet state!

The field of long-lived states in NMR is reviewed. The relationship of long-lived-state phenomena to those associated with spin isomerism is discussed. A brief overview is given of key developments in the field of long-lived states, including chemical symmetry-switching, the role of magnetic equivalence and magnetic inequivalence, long-lived coherences, hyperpolarized NMR involving long-lived states, quantum-rotor-induced polarization, and parahydrogen-induced hyperpolarization. Current application areas of long-lived states are reviewed, and a peer into the crystal ball reveals future developments in the field.

Proton Relaxometry of Long-Lived Spin Order

A study of long-lived spin order in chlorothiophene carboxylates at both high and low magnetic fields is presented. Careful sample preparation (removal of dissolved oxygen in solution, chelating of paramagnetic impurities, reduction of convection) allows one to obtain very long-lived singlet order of the two coupled protons in chlorothiophene derivatives, having lifetimes of about 130 s in D₂ O and 240 s in deuterated methanol, which are much longer than the T₁ -relaxation times (18 and 30 s, respectively, at a field B 0 =9.4 T). In protonated solvents the relaxation times become shorter, but the lifetime is still substantially longer than T 1 . In addition, long-lived coherences are shown to have lifetimes as long as 30 s. Thiophene derivatives can be used as molecular tags to study slow transport, slow dynamics and slow chemical processes, as has been shown in recent years.

Transport of hyperpolarized samples in dissolution-DNP experiments

The magnetic field strength during sample transfer in dissolution dynamic nuclear polarization influences the resulting spectra.

Experimental evidence for the role of paramagnetic oxygen concentration on the decay of long-lived nuclear spin order

The sensitivity of longitudinal magnetization and singlet order to relaxation from dissolved paramagnetic oxygen sources in solution is investigated experimentally.

Singlet excitation in the intermediate magnetic equivalence regime and field-dependent study of singlet–triplet leakage

Measuring field-dependence of singlet lifetimes in the intermediate magnetic equivalence regime.

OnlyParahydrogen SpectrosopY (OPSY) pulse sequences - One does not fit all

The hyperpolarization of nuclear spins using parahydrogen is an interesting effect that allows to increase the magnetic resonance signal by several orders of magnitude. Known as ParaHydrogen And Synthesis Allow Dramatically Enhanced Nuclear Alignment (PASADENA) and ParaHydrogen Induced Polarization (PHIP), the method was successfully used for in vitro analysis and in vivo imaging. In this contribution, we investigated four known and four new variants of Only Parahydrogen SpectroscopY (OPSY) sequences (Aguilar et al., 2007) with respect to the selective preparation of hyperpolarized NMR signal and background suppression. Depending on the method chosen, either anti-phase, in-phase or a mixture of both signals are obtained: anti-phase signals are beneficial to identify hyperpolarized signals and the structure or J-coupling constants; in-phase signals are useful for imaging applications or when the lines are broad. This comprehensive overview of sequences new and old facilitates selecting the right sequence for the task at hand.

Using optimal control methods with constraints to generate singlet states in NMR

A method is proposed for optimizing the performance of the APSOC (Adiabatic-Passage Spin Order Conversion) technique, which can be exploited in NMR experiments with singlet spin states. In this technique magnetization-to-singlet conversion (and singlet-to-magnetization conversion) is performed by using adiabatically ramped RF-fields. Optimization utilizes the GRAPE (Gradient Ascent Pulse Engineering) approach, in which for a fixed search area we assume monotonicity to the envelope of the RF-field. Such an approach allows one to achieve much better performance for APSOC; consequently, the efficiency of magnetization-to-singlet conversion is greatly improved as compared to simple model RF-ramps, e.g., linear ramps. We also demonstrate that the optimization method is reasonably robust to possible inaccuracies in determining NMR parameters of the spin system under study and also in setting the RF-field parameters. The present approach can be exploited in other NMR and EPR applications using adiabatic switching of spin Hamiltonians.

cis Versus trans-Azobenzene: Precise Determination of NMR Parameters and Analysis of Long-Lived States of 15N Spin Pairs

We provide a detailed evaluation of nuclear magnetic resonance (NMR) parameters of the cis- and trans-isomers of azobenzene (AB). For determining the NMR parameters, such as proton-proton and proton-nitrogen J-couplings and chemical shifts, we compared NMR spectra of three different isotopomers of AB: the doubly ¹⁵N labeled azobenzene, ¹⁵N,¹⁵N'-AB, and two partially deuterated AB isotopomers with a single ¹⁵N atom. For the total lineshape analysis of NMR spectra, we used the recently developed ANATOLIA software package. The determined NMR parameters allowed us to optimize experiments for investigating singlet long-lived spin states (LLSs) of ¹⁵N spin pairs and to measure LLS lifetimes in cis-AB and trans-AB. Magnetization-to-singlet-to-magnetization conversion has been performed using the SLIC and APSOC techniques, providing a degree of conversion up to 17 and 24% of the initial magnetization, respectively. Our approach is useful for optimizing the performance of experiments with singlet LLSs; such LLSs can be exploited for preserving spin hyperpolarization, for probing slow molecular dynamics, slow chemical processes and also slow transport processes.

Effect of convection and B1 inhomogeneity on singlet relaxation experiments

Nuclear spin singlet lifetimes can often exceed the T₁ length scales by a large factor. This property makes them suitable for polarization storage. The measurement of such long lifetimes itself can become challenging due to the influence of even very weak relaxation mechanisms. Here we show that a judicious choice of the singlet-to-triplet conversion method is highly important in order to achieve reliable singlet relaxation measurements. In particular, we identify thermal convection, in connection with B₁ field gradients, asa significant apparent decay mechanism, which limits the ability to measure the true singlet state lifetimes. Highly B₁-compensated broadband singlet excitation/detection sequences are shown to minimize the influence of macroscopic molecular motion and B₁ inhomogeneity.

Coherent evolution of singlet spin states in PHOTO-PHIP and M2S experiments

A consistent theoretical description of the spin dynamics underlying photo-PHIP (para-hydrogen induced polarization) experiments is given and validated experimentally: spectra from zero-quantum coherence (ZQC) "in-phase" and "out-of-phase" were obtained and evolution of ZQCs and the population of singlet spin state was tracked and modeled. Data from recent literature [O. Torres et al., J. Am. Chem. Soc., 2014] are reinterpreted. Advantages of using M2S sequences such as APSOC for detecting photo-PHIP are demonstrated. A sequence for 2D ZQ spectroscopy based on APSOC is proposed and the fundamental principles of ZQ spectroscopy are formulated. This investigation opens a new way to obtain information on the sign of J-couplings using ZQ spectroscopy. The proposed method is also useful to track the redistribution of the singlet spin population in various PHIP related experiments, which is essential for efficient polarization transfer to target nuclei.

NMR Spin-Lock Induced Crossing (SLIC) dispersion and long-lived spin states of gaseous propane at low magnetic field (0.05T)

When parahydrogen reacts with propylene in low magnetic fields (e.g., 0.05T), the reaction product propane develops an overpopulation of pseudo-singlet nuclear spin states. We studied how the Spin-Lock Induced Crossing (SLIC) technique can be used to convert these pseudo-singlet spin states of hyperpolarized gaseous propane into observable magnetization and to detect ¹H NMR signal directly at 0.05T. The theoretical simulation and experimental study of the NMR signal dependence on B₁ power (SLIC amplitude) exhibits a well-resolved dispersion, which is induced by the spin-spin couplings in the eight-proton spin system of propane. We also measured the exponential decay time constants (T_LLSS or T_S) of these pseudo-singlet long-lived spin states (LLSS) by varying the time between hyperpolarized propane production and SLIC detection. We have found that, on average, T_S is approximately 3 times longer than the corresponding T₁ value under the same conditions in the range of pressures studied (up to 7.6atm). Moreover, T_S may exceed 13s at pressures above 7atm in the gas phase. These results are in agreement with the previous reports, and they corroborate a great potential of long-lived hyperpolarized propane as an inhalable gaseous contrast agent for lung imaging and as a molecular tracer to study porous media using low-field NMR and MRI.

Singlet order conversion and parahydrogen-induced hyperpolarization of 13C nuclei in near-equivalent spin systems

We have demonstrated two radiofrequency pulse methods which convert the nuclear singlet order of proton spin pairs into the magnetisation of nearby ¹³C nuclei. These irradiation schemes work well in the near-equivalence regime of the three-spin system, which applies when the difference in the two ¹H-¹³C couplings is much smaller than the ¹H-¹H coupling. We use pulse sequences to generate thermally polarized singlet states in a reproducible manner, and study the singlet-to-magnetisation transfer step. Preliminary results demonstrate a parahydrogen-enhanced ¹³C polarization level of at least 9%, providing a signal enhancement factor of more than 9000, using 50% enriched parahydrogen.