Gradient coils are critical subsystems of magnetic resonance imaging (MRI) scanners, requiring tradeoffs among multiple performance metrics. Single-constraint target-field methods (TFMs) often fail to optimize these conflicting objectives simultaneously, and Tikhonov regularization relies on empirically selected coefficients and may lead to ill-conditioned problems as additional constraints are introduced. This study proposes a multi-constraint gradient coil design framework using an improved decomposition-based multi-objective evolutionary algorithm (MOEA/D). Shielding field, power dissipation, magnetic energy, winding smoothness, and Lorentz torque are incorporated as regularization constraints, with the corresponding seven regularization coefficients treated as decision variables. Target field inhomogeneity is enforced as a hard constraint, formulating the problem as a multi-objective minimization. To improve optimization efficiency, a Gaussian Process Regression (GPR) surrogate model is incorporated to reduce repeated electromagnetic evaluations. In addition, two problem specific strategies are developed to address the high-dimensional, strongly coupled nature of this problem: (1) an adaptive directional mutation strategy based on the correlation analysis between regularization coefficients and Lorentz torque performance, which guides a physics informed search toward the Lorentz torque objective; (2) an elite preservation and diversity injection mechanism that prioritizes field inhomogeneity to prevent premature convergence and the loss of feasible solutions. The method is validated by designing a three-axis asymmetric gradient coil for a 1.5T head-only MRI system developed by the Wuhan National High Magnetic Field Center (WHMFC). Compared with designs without multi-constraint optimization, the proposed approach reduces Z coil resistance and inductance by 35.1% and 56.1%, and X coil resistance, inductance, and torque by 53.4%, 41.2%, and 96.1%, respectively, while maintaining gradient inhomogeneity within ±5% over the designated spherical volume (DSV). Convergence analysis indicates that the improved MOEA/D exhibits superior stability relative to conventional MOEA/D and NSGA-II. Subsequent coil fabrication and volunteer brain imaging experiments confirm the engineering feasibility and practical utility of the proposed method.
High-field nuclear magnetic resonance spectroscopy is a powerful and highly reproducible platform for serum metabolomics, but its technical complexity and maintenance requirements have limited its implementation in routine clinical environments. Benchtop NMR spectrometers offer a simpler and more accessible alternative, although their lower magnetic field strength reduces spectral resolution and sensitivity. Here, we evaluated whether an 80 MHz Fourier benchtop NMR spectrometer can reproduce clinically relevant metabolic information obtained with a 600 MHz IVDr high-field platform. Serum samples from two independent cohorts were analyzed using both NMR platforms under comparable conditions. We compared platform-specific metabolic and lipoprotein signatures against a broad panel of non-invasive clinical biosensors. Despite yielding fewer quantified variables than the 600 MHz platform, the 80 MHz spectrometer captured a highly similar clinical association landscape, preserving both the direction and magnitude of most metabolite-biosensor relationships. Finally, an 80 MHz partial least-squares regression model accurately predicted the 600 MHz-derived MetSCORE, a continuous NMR-based metric of metabolic syndrome risk, achieving strong agreement between platforms. These findings demonstrate that benchtop NMR can preserve clinically meaningful metabolic information despite reduced spectral granularity, supporting its potential use as a scalable tool for translational metabolomics and clinical risk stratification.
Spin-lock preparations have been proposed to detect weak low-frequency magnetic fields, including neuronal magnetic fields, by magnetic resonance. Most current analytic models are limited to sinusoidal targets or long-time effective descriptions. They are therefore not directly suitable for reconstructing arbitrary time-varying waveforms. We formulate spin-lock detection as a finite-time perturbative observation problem. From the rotating-frame Bloch equation, we separate the weak target field from the reference spin-lock dynamics and apply a first-order Dyson expansion. For unmodulated spin-lock, the longitudinal-magnetization perturbation is a linear functional of the target waveform. Equivalently, it is a finite-time, convolution-like kernel response. We extend this approach to Spin-lock Phase-modulated Active Resonance eXcitation (SPARX). The modulation-induced pseudo-magnetic field is included in the reference dynamics, while only the weak target field is treated as the perturbation. Numerical Bloch simulations validate the first-order endpoint response for a Gaussian-envelope carrier, a Hann-windowed sinc-envelope carrier, and a waveform derived from an open rapid invisible frequency tagging magnetoencephalography dataset. We also compare full Bloch and first-order solutions over 0-3ω1 and for all three magnetization components. Amplitude sweeps identify the perturbative regime and the onset of higher-order effects. For SPARX, we compare an adjoint numerical kernel with a finite damped-trigonometric basis. We show that pseudo-field modulation shifts the response bands relative to unmodulated spin-lock. This forward model links spin-lock pulse design to time-series reconstruction of weak magnetic-field waveforms.
We investigate the spin interaction mechanisms in a Rb-Xe vapor cell containing both 129Xe and 131Xe. The Xe polarization is quantitatively related to the Rb polarization through the Fermi-contact interaction between Rb Xe. By selectively suppressing the Xe polarization using a strong resonant radio-frequency (RF) field, it is demonstrated that the RF field itself does not induce measurable shifts in the Xe resonance frequency. Furthermore, measurements of the longitudinal relaxation times show that cross relaxation between the two Xe isotopes is negligible under the present experimental conditions. The remaining frequency shifts, observed at the milliHertz level, are consistent with a mean-field interaction arising from the macroscopic magnetization of polarized Xe nuclei. These results provide a clear understanding of spin interactions in multi-isotope Xe vapor cells and are relevant for high-precision NMR measurements and NMR-based gyroscopes.
Hyperpolarization by signal amplification by reversible exchange (SABRE) is a promising route toward fast, low-cost, and repeatable sensitivity enhancement for nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI). Because dimethyl sulfoxide (DMSO) is biocompatible and dissolves a broad range of organic and biological substrates, performing SABRE directly in DMSO could substantially widen the scope of parahydrogen-based hyperpolarization toward biomedical applications. To date, however, DMSO has been regarded as an inefficient SABRE medium for the conventional [Ir(IMes)(COD)Cl] catalyst, which provides only modest enhancements relative to methanol. Here we report two new iridium N-heterocyclic carbene (NHC) catalysts-the [Ir(COD)Cl] complexes of 1,3-dibenzylimidazol-2-ylidene (Ir-Imid) and 1,3-dibenzylbenzimidazol-2-ylidene (Ir-Benzimid)-that deliver the highest 1H SABRE enhancements reported in DMSO to date. Across five representative substrates, the new catalyst improves the enhancement factor for protons at the same position by about 1.23 to 3.24 times compared to Ir-IMes. Density functional theory (DFT) calculations of the catalyst-substrate-parahydrogen complexes relate these trends to the average axial and equatorial Ir-ligand bond lengths and provide rational design guidance for further development of SABRE catalysts that operate efficiently in DMSO.
Nuclear magnetic resonance (NMR) relaxation data are typically analyzed by different methods from simple multi-exponential nonlinear fitting to ill-posed linear inversion. However, linear sampling with a constant echo spacing captures signals from short T2 components only in the first few echoes when measuring samples containing very short T2 components such as organic matter or bitumen. Consequently, fast decay of short relaxation signals leads to incompleteness of short T2 components in two-dimensional Laplace inversion. Based on the conversion of multi-exponential nonlinear fitting to a linear inversion problem, this study further converts the linear inversion problem into a deconvolution problem. A uniform logarithmic fitting and regularized deconvolution (LFD) algorithm is proposed, effectively addressing the incomplete and inaccurate recovery of short T2 components in traditional T1-T2 inversion algorithms. Specifically, the uniform logarithmic fitting method is employed to reconstruct both echo data and the inversion kernel function, which mitigates the ill-conditioned nature of the conventional inversion and improves computational efficiency. Numerical simulations and core experiments indicate that the proposed method significantly improves the accuracy of short T2 component inversion in T1-T2 maps: for the shale model example, the relative error for kerogen saturation decreases from 20.20% to 2.60%, for bitumen from 14.97% to 1.90%, and for clay bound water saturation from 5.85% to 0.90%. Applicable conditions are also discussed.
The coordination environments of Cu2+ in a copper-doped 2D ZnO-stearic acid (SA) nanocomposite were investigated by Electron Paramagnetic Resonance (EPR) spectroscopy. The material, Zn₀.₉₅Cu₀.₀₅O-(SA)0.13, synthesized following a previously reported procedure, was studied using continuous-wave (CW) EPR at X- and Q-band over the temperature range 30-300 K, together with pulsed EPR at X-band at 15 K. An important part in the analysis of these spectra is the simulation of distributions (strains) of Zeeman- and hyperfine coupling tensor parameters, whose anisotropies are anti-correlated. A significant fraction of the Cu2+ ions is incorporated into the ordered layered structure, where slow thermally activated motions lead to progressive spectral broadening with increasing temperature. These results provide a detailed microscopic picture of the distribution, local symmetry, and dynamics of Cu2+ sites in Zn₀.₉₅Cu₀.₀₅O-(SA)0.13, highlighting the role of structural heterogeneity in shaping their magnetic resonance signatures. Overall, this work develops a general strategy of using paramagnetic probes to investigate structural complexity in similar layered and organic-inorganic materials.
Forkhead box O (FOXO) transcription factors regulate metabolism, DNA damage repair, cell cycle, and apoptosis. FOXO4 contains ΦXXΦΦ motifs in its intrinsically disordered conserved regions (CR2C and CR3) that mediate interactions with the KIX domain of CREB-binding protein (CBP), a transcriptional coactivator and histone acetyltransferase. While FOXO3a binds to CBP KIX through both CR2C and CR3, the interaction between FOXO4 CR2C and CBP KIX has remained uncharacterized, despite FOXO4 CR2C uniquely carrying four consecutive prolines immediately following its ΦXXΦΦ motif. Here, we characterize this interaction by solution NMR spectroscopy. Chemical-shift perturbation identifies the binding interfaces on both proteins and reveals splitting of several amide cross-peaks in CR2C into two sets. Systematic proline mutagenesis and truncation support the presence of distinct conformational subpopulations, for which apparent Kd values were estimated independently. Circular dichroism analysis shows that CR2C remains disordered upon binding, and docking models suggest that FOXO4 CR2C binds in multiple disordered conformations on the KIX MLL site. These results illustrate how an adjacent poly-proline tract modulates the KIX binding behavior of CR2C through conformational heterogeneity.
Establishing carbon-carbon connectivities by NMR at natural isotope abundance is intrinsically challenging due to the low sensitivity of 13C-13C correlation experiments. Conventional strategies rely on polarization transfer from light nuclei, i.e. 1H or 19F, to enhance sensitivity, rendering systems devoid of such nuclei particularly difficult to study. We recently developed an NMR-optimized Overhauser-effect dynamic nuclear polarization (OE-DNP) setup that provides signal enhancements of up to two orders of magnitude for carbons which are chlorinated or iodinated, but lack 1H and 19F, in small organic molecules dissolved in organic solvent. Here, we demonstrate that in such systems, hyperpolarization can be coherently transferred between 13C nuclei using 1D and pseudo-2D isotropic mixing (IM) experiments. This allows 13C-13C satellite signals to be detected, at natural isotopic abundance, from which one-bond carbon-carbon scalar coupling (1JCC) constants can be read off. These OE-DNP-enhanced IM experiments are shown to even outperform conventional 1D INADEQUATE experiments in these challenging systems. Furthermore, we demonstrate that IM can be used as a preparatory block in OE-DNP-enhanced multiple pulse NMR experiments, as exemplified by a 2D OE-DNP-IM-HETCOR sequence. Finally, the transfer of polarization in hyperpolarized systems is described using both an approximate analytical treatment, based on the product operator formalism, and numerical simulations employing an effective Hamiltonian theory.
To address the issue of conventional passive shimming (PS) occupying the internal space of Halbach magnets, this study explores a PS method that improves magnetic-field homogeneity by controlling the axial displacement of the magnet blocks composing the Halbach magnet. Based on the spherical harmonic decomposition method (SHDM), the Axial-Moving Array of Magnetic Blocks configurations (AAMBs) capable of generating the corresponding spherical harmonic terms (SHs) is constructed. By optimizing the movement step size of each AAMBs, the inhomogeneous magnetic-field components of the Halbach magnet are compensated. The method is experimentally validated on a home-built 90 mT dual-layer Halbach magnet. The results show a 17-fold improvement in field homogeneity and significant suppression of SHs. The proposed approach offers simple operation and high PS efficiency, making it suitable for the design of high-homogeneity Halbach magnets for portable and miniaturized MR instruments. This work provides a structurally integrated solution to the longstanding trade-off between magnet compactness and field homogeneity. Moreover, it has potential for future extension to high-field, high-homogeneity Halbach designs for benchtop NMR spectrometers.
For small molecules in isotropic liquid relaxation typically has little impact on the efficiency of coherent polarization transfer. However, in the presence of sources that induce rapid nuclear relaxation, it can become significant, leading to nuclear enhancements far from theoretical maximum. Examples of such sources include paramagnetic metals and organic radicals used in dynamic nuclear polarization (DNP) experiments. Here, we examined the role of relaxation in the classical refocused insensitive nuclei enhanced by polarization transfer (INEPT) experiment, in the presence of stable organic radicals. Despite the plethora of literature on relaxation, disagreement has arisen in recent literature regarding the mechanism responsible for the loss of magnetization during the INEPT experiment, prompting us to revisit this topic. In the present work, it is reestablished that for heteronuclear scalar-coupled spin-½ systems, transverse magnetization decays at an average rate of the in-phase and antiphase coherences - analogous to the homonuclear case - and in line with literary precedent. A variety of spin-locking experiments are used to validate the derived theory, and which are found to be in close agreement. Details and practical considerations are provided on the use of spin-locking experiments in the particular context of liquid-state Overhauser DNP (ODNP), as well as the use of sapphire NMR tubes in this.
Nuclear magnetic relaxation dispersion (NMRD) measurements report on molecular dynamics via the field-dependence of longitudinal (R1) and transverse (R2) relaxation rates. Commercial fast-field-cycling (FFC) relaxometers cover the kHz to MHz regime using large electromagnets, but show reduced sensitivity at lower frequencies. Optically pumped magnetometer based ultra-low-field (ULF) methods are highly sensitive to low frequencies (Hz to kHz), making them sensitive to slow molecular dynamics, but are restricted to the sub-kilohertz band. In this work, we introduce a compact shuttle-based relaxometry system that combines high-field prepolarization with programmable relaxation fields from nanotesla to tesla, and uses a set of multi-channel optically pumped magnetometers for arrayed detection. To benchmark the system's sensitivity and reproducibility we performed initial experiments on water samples, and then studied the field-dependent relaxivity of Gd-DTPA. These results agree quantitatively with a commercial FFC relaxometer across the accessible frequency range of three orders of magnitude (10 kHz to 20 MHz), and our setup extended the measurement range to eight orders of magnitude (Hz to 100 MHz). We also performed measurements on aqueous metal-organic framework solutions, highlighting the ability of ULF detection to mitigate susceptibility-induced internal field gradients. This platform enables wide-range, quantitative relaxometry, naturally interfaces with low-field hyperpolarization and supports applications in biomedical sensing of contrast agents and metabolites, porous-media and materials studies, and on-site chemical screening.
With the ongoing miniaturization of nuclear magnetic resonance (NMR) instruments, smaller and smaller devices are being developed. Tabletop relaxometers first emerged in the early 1970's, and mobile stray-field relaxometers were introduced in 1980 for well logging and subsequently for nondestructive materials testing. Portable center-field NMR relaxometers are still in development stage. The performance of a commercial, miniature, center-field relaxometer was field-tested by comparing transverse 1H water relaxation decays from a variety of sources in Rome. With attention to reproducibility of measurements, the transverse 1H NMR relaxation times at a 20 MHz Larmor frequency were measured locally right after sampling in Rome, Italy, and later under controlled laboratory conditions in Davis, California, USA. Although functional, the reproducibility of the miniature relaxometer is highly temperature-dependent and requires well-controlled environmental conditions.
SABRE-SHEATH (Signal Amplification by Reversible Exchange in SHield Enables Alignment Transfer to Heteronuclei) is a parahydrogen-based hyperpolarization technique increasingly used for metabolic sensing. Typically limited to 5-mm NMR tube reactors (0.5-1 mL volumes) and requiring manual sample transfer for quantification, SABRE remains constrained by its throughput. Here, we describe a new low-field magnetic resonance system that enables in-situ polarimetry of hyperpolarized [1-13C]pyruvate. This setup utilizes a mu-metal shielded solenoid magnet, performing hyperpolarization at 0.4 μT (SABRE-SHEATH) and in-situ NMR sensing at 140 μT (1.6 kHz 13C frequency), which eliminates the need for sample transfer. We demonstrate that a surface-coil detection design accommodates diverse sample geometries, including 15-mm ID HPLC columns. By increasing the parahydrogen flow rate 12-fold, we successfully scaled the production of [1-13C]pyruvate to a 10-mL volume, achieving a 7% polarization level-comparable to that of smaller 0.8-mL samples. Furthermore, the integration of automated fluidics and a saddle-shaped RF excitation coil enables both SABRE-SHEATH and Spin-Lock Induced Crossing (SLIC)-SABRE protocols. Notably, we demonstrate the utility of this in-situ detection for optimizing SABRE conditions, including the screening of DMSO concentrations. Finally, the ability to operate with diverse solvent systems and scalable volumes lays the foundation for producing biocompatible hyperpolarized formulations, broadening the potential for metabolic research. These advances establish a scalable, automated framework for producing larger, biocompatible volumes of hyperpolarized molecular probes.
Photochemical and photocatalytic reactions studied by NMR spectroscopy require efficient and uniform sample illumination that is effective for optically dense samples and, ideally, is compatible with high-throughput workflows. Here we systematically investigate bottom-illumination strategies for light-coupled NMR experiments using cryogenically cooled probeheads (CRPs), examining how light propagation pathways, sample tube geometry, surface treatments, and fibre positioning influence illumination intensity and uniformity. Using photo-chemically induced dynamic nuclear polarization (photo-CIDNP) as a quantitative, spatially resolved measure of local light intensity, we identify three principal illumination pathways: direct axial transmission through the sample, propagation and scattering within the tube walls, and light transport with scattering in the annular gap between the sample tube and the probehead bore. We show that direct axial illumination in light-absorbing samples produces severe intensity gradients, whereas delivering light through the annular gap and scattering it into the sample from the sides markedly improves illumination uniformity. We demonstrate that combining flat-bottom sample tubes with engineered wall etching and optimised fibre-tube separation can redistribute light among these pathways, yielding near-uniform illumination over the NMR-active volume, with high overall light intensity. The results establish practical design principles for uniform, strong and automation-compatible sample illumination in NMR probeheads that permit axial light delivery from below the sample, opening an avenue for high-throughput studies of a wide range of light-driven systems.
Biomolecular dynamics on the microsecond-to-millisecond (μs-ms) timescale are intimately linked to a wide range of biological functions. In solution-state NMR, Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments are widely employed to probe such motions, providing detailed kinetic, thermodynamic, and mechanistic insights at the atomic level. For studies of protein conformational dynamics, 15N spin probes in backbone amide groups are most commonly used due to the simplicity of the 15N spin system and the ease of sample preparation. Among various 15N CPMG methodologies, in-phase CPMG (ip-CPMG) scheme generally outperforms relaxation-compensated CPMG (rc-CPMG) approach owing to the more favorable relaxation property. However, this experiment typically requires strong radiofrequency (RF) field for 1H decoupling (≥15 kHz), which can be problematic for studying high-salt samples due to increased pulse width on cryogenic probes. Moreover, the strong RF field can induce substantial sample heating effects, potentially perturbing μs-ms timescale dynamics under investigation. In this work we present a new 15N ip-CPMG scheme that enables efficient 1H decoupling with substantially lower RF field strength (∼6 kHz). In addition, an optimized 15N rc-CPMG scheme that yields comparable relaxation dispersion profiles and exchange parameters is also introduced. These new approaches significantly reduce sample heating effects associated with 1H decoupling and are therefore better suited for studying protein samples under high-salt conditions that mimic physiological ionic strengths, enabling more reliable and comprehensive characterization of μs-ms timescale biomolecular dynamics.
Despite the growing demand for compact and cost-effective low-field NMR systems, their broader use remains limited by low sensitivity and reduced spectral resolution. One important approach for addressing these limitations is the integration of parahydrogen-based hyperpolarization with benchtop NMR. Because this hyperpolarization approach can be implemented using relatively simple and low-cost equipment, experimental setups originally developed for high-field NMR can be readily adapted to benchtop systems. Such compatibility makes the parahydrogen-induced polarization (PHIP) and Signal Amplification by Reversible Exchange (SABRE) strategies particularly attractive for expanding the analytical capabilities of benchtop NMR. Herein, we review the principles and experimental requirements of PHIP- and SABRE-based hyperpolarization for benchtop NMR, followed by a discussion of their recent applications, current challenges, and future opportunities for chemical, biological, and biomedical analysis.
Accurate quantification of binding affinities for intrinsically disordered regions (IDRs) is challenged by their flexibility and propensity for aggregation, often requiring cross-validation across distinct biophysical methods. Here, we investigated the interaction between interacting domains of karyopherin β1 (KapN) and Nup153 (Nup153 3-2), a highly aggregation-prone IDR fragment of nucleoporin 153. To circumvent experimental time constraints imposed by rapid sample aggregation, we employed a suite of short-timescale methodologies: NMR chemical shift perturbations (CSPs), lineshape analysis, 15N-edited diffusion NMR, and isothermal titration calorimetry (ITC). Remarkably, despite relying on fundamentally different physical principles, all four methods yielded apparent dissociation constants (Kd) in the low-micromolar range, with lineshape analysis, diffusion NMR, and ITC converging closely (2-3 μM) while CSP gave a modestly lower value (1.18 μM). These findings demonstrate that cross-validating short-timescale methodologies can reveal and account for method-specific biases, providing a robust strategy for characterizing aggregation-prone biomolecular systems.
