Singlet-assisted diffusion-NMR (SAD-NMR): extending the scope of diffusion tensor imaging via singlet NMR

In this study, long-lived nuclear singlet order methods are combined with diffusion tensor imaging with the purpose of characterizing the full diffusion tensor of molecules diffusing freely in large pores of up to a millimeter in size. Such sizes are out of reach in conventional diffusion tensor imaging because of the limitations imposed by the relaxation decay constant of the longitudinal magnetization. A singlet-assisted diffusion tensor imaging methodology able to circumvent such limitations is discussed, and the new possibilities that it offers are demonstrated through simulation and experiments on plastic phantoms containing cylindrical channels of 1 mm in diameter.

A dual-core NMR system for field-cycling singlet assisted diffusion NMR

Long-lived singlet spin order offers the possibility to extend the spin memory by more than an order of magnitude. This enhancement can be used, among other applications, to assist NMR diffusion experiments in porous media where the extended lifetime of singlet spin order can be used to gain information about structural features of the medium as well as the dynamics of the imbibed phase. Other than offering the possibility to explore longer diffusion times of the order of many minutes that, for example, gives unprecedented access to tortuosity in structures with interconnected pores, singlet order has the important advantage to be immune to the internal field gradients generated by magnetic susceptibility inhomogeneities. These inhomogeneities, however, are responsible for very short T₂ decay constants in high magnetic field and this precludes access to the singlet order in the first instance. To overcome this difficulty and take advantage of singlet order in diffusion experiments in porous media, we have here developed a dual-core system with radiofrequency and 3-axis pulsed field gradients facilities in low magnetic field, for preparation and manipulation of singlet order and a probe, in high magnetic field, for polarisation and detection. The system operates in field-cycling and can be used for a variety of NMR experiments including diffusion tensor imaging (both singlet assisted and not). In this paper we present and discuss the new hardware and its calibration, and demonstrate its capabilities through a variety of examples.

Long-lived states of methylene protons in achiral molecules

In nuclear magnetic resonance (NMR), the lifetimes of long-lived states (LLSs) are exquisitely sensitive to their environment. However, the number of molecules where such states can be excited has hitherto been rather limited. Here, it is shown that LLSs can be readily excited in many common molecules that contain two or more neighboring CH2 groups. Accessing such LLSs does not require any isotopic enrichment, nor does it require any stereogenic centers to lift the chemical equivalence of CH2 protons. LLSs were excited in a variety of metabolites, neurotransmitters, vitamins, amino acids, and other molecules. One can excite LLSs in several different molecules simultaneously. In combination with magnetic resonance imaging, LLSs can reveal a contrast upon noncovalent binding of ligands to macromolecules. This suggests new perspectives to achieve high-throughput parallel drug screening by NMR.

A flow electrochemistry-enabled synthesis of 2-substituted N-(methyl-d)piperidines

A synthesis of N-monodeuteriomethyl-2-substituted piperidines is described. An efficient and readily scalable anodic methoxylation of N-formylpiperidine in an undivided microfluidic electrolysis cell delivers methoxylated piperidine 3, which is a precursor to a N-formyliminium ion and enables C-nucleophiles to be introduced at the 2-position. The isotopically labelled N-deuteriomethyl group is installed using the Eschweiler-Clarke reaction with formic acid-d₂ and unlabelled formaldehyde. Monodeuterated N-methyl groups in these molecular systems possess small isotropic proton chemical shift differences important in the investigation of molecules that are able to support long-lived nuclear spin states in solution nuclear magnetic resonance.

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.

Theory and Simulation Framework for the Relaxation of Nuclear Spin Order in Porous Media

The theory of nuclear spin relaxation in a liquid permeating a solid structure of irregular geometry is examined. The effects of restricted diffusion and the demagnetizing field generated by an inhomogeneous distribution of magnetic susceptibility in the system are explored. A framework comprising Brownian Dynamics, average Hamiltonian theory, and Liouville-space spin dynamics is proposed for simulating nuclear spin relaxation in 3D models of random structures obtained from CT scans of actual samples. Simulations results are compared with experimental data. An analytical solution valid within approximation is also reported.

Prediction of 1H Singlet Relaxation via Intermolecular Dipolar Couplings Using the Molecular Dynamics Method

Dissolution dynamic nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tagging to probe slow dynamic processes, and detection of ligand-protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular dipolar, intermolecular dipolar between solvent and solute, chemical shift anisotropy, and spin-rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

Nuclear singlet relaxation by chemical exchange

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C₂ squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH^-) and squaric acid (SqH₂) characterized by the dissociation constants pK₁ = 1.5 and pK₂ = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants T_S when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the T_S behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.

Centralizer theory for long-lived spin states

Nuclear long-lived spin states represent spin density operator configurations that are exceptionally well protected against spin relaxation phenomena. Their long-lived character is exploited in a variety of Nuclear Magnetic Resonance (NMR) techniques. Despite the growing importance of long-lived spin states in modern NMR, strategies for their identification have changed little over the last decade. The standard approach heavily relies on a chain of group theoretical arguments. In this paper, we present a more streamlined method for the calculation of such configurations. Instead of focusing on the symmetry properties of the relaxation superoperator, we focus on its corresponding relaxation algebra. This enables us to analyze long-lived spin states with Lie algebraic methods rather than group theoretical arguments. We show that the centralizer of the relaxation algebra forms a basis for the set of long-lived spin states. The characterization of the centralizer, on the other hand, does not rely on any special symmetry arguments, and its calculation is straightforward. We outline a basic algorithm and illustrate advantages by considering long-lived spin states for some spin-1/2 pairs and rapidly rotating methyl groups.

Nuclear Spin Relaxation of Longitudinal and Singlet Order in Liquid-CO2 Solutions

Hyperpolarization techniques can enormously enhance the NMR signal thus allowing the exploitation of hyperpolarized substrates for in-vivo MRI applications. The short lifetime of hyperpolarized spin order poses significant limitations in such applications. Spin order storage can be prolonged through the use of long-lived spin states. Additionally, the storage of spin polarization-either in the form of longitudinal or singlet order-can be prolonged in low viscosity solutions. Here, we report the use of low viscosity liquid-CO₂ solutions to store nuclear spin polarization in the form of longitudinal and singlet order for extended periods. Our results demonstrate that this storage time can be considerably sustained in liquid-CO₂ solutions in comparison to other low viscosity solvents, opening up the possibility of new, exciting storage experiments in the future.

Single-scan measurements of nuclear spin singlet order decay rates

Measurements of singlet spin order decay rates are time consuming due to the long-lived nature of this form of order and the typical pseudo-2D mode of acquisition. Additionally, this acquisition modality is not ideal for experiments run on hyperpolarized order because of the single-shot nature of hyperpolarization techniques. We present a methodology based on spatial encoding that not only significantly reduces the duration of these experiments but also confers compatibility using spin hyperpolarization techniques. The method condenses in a single shot the variable delay array used to measure decay rates in conventional pseudo-2D relaxation experiments. This results in a substantial time saving factor and, more importantly, makes the experiment compatible with hyperpolarization techniques since only a single hyperpolarized sample is required. Furthermore, the presented method, besides offering savings on time and costs, avoids reproducibility concerns associated with repetition in the hyperpolarization procedure. The method accelerates the measurement and characterization of singlet order decay times, and, when coupled with hyperpolarization techniques, can facilitate the quest for systems with very long decay times.

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.

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.

Assessment of heteronuclear long-lived states at ultralow magnetic fields

A study of long-lived spin states in hetero-nuclear spin systems is presented.