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Spin echo small angle neutron scattering using a continuously pumped 3He neutron polarisation analyser
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MR elastography of liver at 3 Tesla: comparison of gradient-recalled echo (GRE) and spin-echo (SE) echo-planar imaging (EPI) sequences and agreement across stiffness measurements
Purpose: To compare 2D gradient-recalled echo (GRE) and 2D spin-echo (SE) echo-planar imaging (EPI) MR elastography (MRE) for measurement of hepatic stiffness in adult patients with known or suspected liver disease at 3 Tesla. Materials and methods: Three hundred and eighty-seven consecutive patients underwent MRE of the liver at 3 Tesla with 2D-GRE and 2D-SE-EPI sequences. ‘Mean liver stiffness (LS)’ calculated by averaging 3 ROIs in the right lobe, ‘Maximum LS’ calculated by an ROI in the right lobe; and ‘Freehand LS’ calculated by an ROI in the entire liver were measured by two independent readers. Inter-observer and inter-class variability in stiffness measurements were assessed. Stiffness values were correlated with degree of liver fibrosis (METAVIR scores) in 97 patients who underwent biopsy. The diagnostic performance was compared by a receiver-operating characteristic analysis. Results: The technical failure rate was 2.8% for 2D-SE-EPI (11/387) and 4.1% for 2D-GRE (16/387, 9 had R{sub 2}* > 80 s{sup −1} indicating iron overload). There is high reproducibility for both GRE and SE-EPI variants (ICC = 0.84–0.94 for both GRE and SE-EPI MRE). The highest sensitivity, specificity, and accuracy of differentiating mild fibrosis (F0–F2) from advanced fibrosis (F3–F4) are 0.84 (GRE Freehand measurement), 0.92 (GRE Maximum stiffness measurement), and 0.88 (GRE Freehand measurement), respectively. Conclusions: High intra-class correlation and intra-reader correlation are seen on measured hepatic stiffness for both 2D-GRE and 2D-SE-EPI MRE. 2D-SE-EPI has lower failure rate. Diagnostic performance of both sequences is equivalent, with highest sensitivity for 2D-GRE Freehand stiffness measurement, and highest specificity 2D-GRE Maximum stiffness measurement.
Neutron Spin–Echo Studies of the Structural Relaxation of Network Liquid ZnCl 2 at the Structure Factor Primary Peak and Prepeak
Using neutron spin-echo spectroscopy, we studied the microscopic structural relaxation of a prototypical network ionic liquid ZnCl 2 at the structure factor primary peak and pre-peak. The results show that the relaxation at the primary peak is faster than the pre-peak and the activation energy is ≈33% higher. Stretched exponential relaxation is observed even at temperatures well above the melting point T m . Surprisingly, the stretching exponent shows a rapid increase upon cooling, especially at the primary peak, where it changes from stretched exponential to simple exponential on approaching T m . Furthermore, these results suggest that the appearance of glassy dynamics typical of the supercooled state even in the equilibrium liquid state of ZnCl 2 as well as the difference of activation energy at the two investigated length scales are related to the formation of network structure on cooling.
Bayesian Gaussian process inference for neutron spin echo measurement
Neutron spin echo (NSE) spectroscopy provides unique access to microscopic dynamics, but its application is often constrained by low neutron flux, long acquisition times, and significant noise. Here, we present a Bayesian inference approach based on Gaussian process regression (GPR) to reconstruct high-quality spin echo signals from sparse and noisy data by exploiting correlations in reciprocal space. Benchmarks on synthetic datasets and validation with experimental NSE measurements of dendrimers show that GPR suppresses noise, interpolates missing intensity values, and accommodates irregular observations. The method improves accuracy, shortens acquisition times, and enables high-throughput and real-time studies. Beyond NSE, the framework is broadly applicable to other low signal-to-noise ratio scattering techniques, thereby extending the scope of neutron spectroscopy.
Neutron spin-echo study of the critical dynamics of spin- 5 2 antiferromagnets in two and three dimensions
Here, we report a neutron spin-echo study of the critical dynamics in the S= 5 2 antiferromagnets MnF 2 and Rb 2 MnF 4 with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the Néel temperature, T N . By taking advantage of the μeV energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents z for both longitudinal and transverse fluctuations. In MnF 2 , both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents z in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb 2 MnF 4 , the critical dynamics crosses over from the expected 2D Heisenberg behavior for T » T N to a scaling regime with exponent z = 1.387(4), which has not been predicted by theory and may indicate the influence of long-range dipolar interactions.
Neutron spin echo spectroscopy
Neutron spin echo (NSE) spectroscopy is a powerful technique used to probe the internal dynamics and diffusion processes within matter, allowing researchers to quantify how materials respond to changes in external conditions. To fully understand the bulk properties of a material, it is often crucial to investigate dynamic processes occurring on nanometre length scales and nanosecond timescales. NSE spectroscopy provides an exceptional capability to measure such dynamics across a broad spectrum of condensed matter systems, ranging from proteins and quantum magnets to catalysts. In this Primer, we present an overview of NSE spectroscopy, highlighting the instruments used, methods of data collection and representative applications in both soft-matter and hard-matter sciences.
Efficient data extraction from neutron time-of-flight spin-echo raw data
Neutron spin-echo spectrometers with a position-sensitive detector and operating with extended time-of-flight-tagged wavelength frames are able to collect a comprehensive set of data covering a large range of wavevector and Fourier time space with only a few instrumental settings in a quasi-continuous way. Extracting all the information contained in the raw data and mapping them to a suitable physical space in the most efficient way is a challenge. This article reports algorithms employed in dedicated software, DrSpine (data reduction for spin echo), that achieves this goal and yields reliable representations of the intermediate scattering function S(Q, t) independent of the selected `binning'.
Correcting aberrations of a transverse-field neutron resonance spin echo instrument
Neutron resonance spin echo (NRSE) technique has the potential to increase the Fourier time and energy resolution in neutron scattering by using radio frequency (rf) neutron spin-flippers. However, aberrations arising from variations in the neutron path length between the rf flippers reduce the polarization. Here, we develop and test a transverse static-field magnet, a series of which are placed between the rf flippers, to correct for these aberrations. The prototype correction magnet was both simulated in an NRSE beamline using McStas, a Monte Carlo neutron ray-tracing software package, and measured using neutrons. The results from the prototype demonstrate that this static-field design corrects for transverse-field NRSE aberrations.
Data Reproducibility of Spin-Echo Small-Angle Neutron Scattering Instruments
Spin-echo small-angle neutron scattering (SESANS) is a unique method to measure structures of materials in real space with length scales from ∼ 30 μm to ∼20 µm. As shown in Figure 1, the accessible length scale of SESANS is given by its ability to encode the momentum transfer into the Larmor phase, namely Φ = $\vec{𝛿}$ ⋅ $\vec{𝑄}$, where $\vec{𝑄}$ is the momentum transfer and $\vec{𝛿}$ is the encoding vector of the setup and its projection along Q (δQ) is called spin-echo length (SEL). The spin echo length, which is synonymous with the spatial correlation distance probed, is defined as the following 𝛿𝑄 ∝ 𝜆 2 𝐵𝐿cot𝜃 where 𝜆 is neutron wavelength, B is magnetic field, L is length of the parallelogram magnetic field region, and 𝜃 is the angle between the inclined magnetic field boundary and the beam direction, as shown in Figure 1. The result of the SESANS experiment is a Hankel transformation of the SANS scattering function I(Q), which yields the correlation function of the sample in real space.
NMR spin-echo amplitude estimation
Technologies applicable to NMR spin-echo amplitude estimation are disclosed. Example methods may calibrate for distortion of a shape and estimated amplitude of measured NMR spin or gradient echoes. NMR spin or gradient echo measurements may be performed on a sample. The measured NMR spin or gradient echoes may be used to calculate an echo-shape calibration factor. The echo-shape calibration factor may estimate an effect of echo shape on estimated spin or gradient echo amplitude(s) of the NMR spin or gradient echoes. The echo-shape calibration factor may be used to correct for underestimation or overestimation of the spin or gradient echo amplitude(s).
Wavelength-independent constant period spin-echo modulated small angle neutron scattering
Spin-Echo Modulated Small Angle Neutron Scattering (SEMSANS) in Time-of-Flight (ToF) mode has been shown to be a promising technique for measuring (very) small angle neutron scattering (SANS) signals and performing quantitative Dark-Field Imaging (DFI), i.e., SANS with 2D spatial resolution. However, the wavelength dependence of the modulation period in the ToF spin-echo mode has so far limited the useful modulation periods to those resolvable with the limited spatial resolution of the detectors available. Here we present our results of an approach to keep the period of the induced modulation constant for the wavelengths utilised in ToF. This is achieved by ramping the magnetic fields in the coils responsible for creating the spatially modulated beam in synchronisation with the neutron pulse, thus keeping the modulation period constant for all wavelengths. Such a setup enables the decoupling of the spatial detector resolution from the resolution of the modulation period by the use of slits or gratings in analogy to the approach in grating-based neutron DFI.
Oak Ridge National Laboratory Neutron Spin Echo Beamline on NB-2
Neutron Spin Echo (NSE) spectroscopy uniquely measures the Q-dependence of slow relaxation dynamics, and having such a machine at HFIR will advance polarized neutron spectroscopy and promote the study of biophysical and energy materials using neutrons. The 2018 Instrument Advisory Board (IAB) advises Neutron Sciences Directorate, ORNL to upgrade the cold neutron delivery system at HFIR, addressing geometrical challenges in neutron transfer from the bright cold source. This is being optimized now: the entrance to the guide system is moving closer to the source, and more guides are being added. However, there are still significant challenges to making the cold flux at the sample world-class. With the proposed guide system, NB-2 can deliver more than 10 6 polarized neutrons per cm 2 /sec below 8Å, and probably 10Å with further optimization. With no potential for running user experiments with neutrons longer than 15Å, the utility of such a machine for biological studies is limited. However, there is a large demand for this class of spectrometer in materials science, chemical engineering, and nanotechnology. Workshops held over the past decade and the three-source vision have highlighted the community's need for a low-angle, high-energy resolution spectrometer at HFIR. A detailed design study of this spectrometer is needed, focusing on optimizing the neutron delivery system for SANS-type studies. This neutron spectrometer would complement studies already performed on both SNSNSE and BASIS by overlapping and extend the dynamic range accessible, while acknowledging the proposed machine, EXPANSE, at the Second Target Station. Two technologies currently exist for such a spectrometer: traditional DC solenoids like those on BL-15 at SNS and IN15 at the ILL, and RF-flipper-based machines similar to RESEDA at FRMII. Either instrument would satisfy the scientific justification. However, there are strong business and scientific cases to utilize the thermal flux, the resonant expertise developed at ORNL, and the potential to utilize an entangled beam of neutrons to probe quantum matter by adopting the neutron resonant spin-echo configuration.
Spin echo small-angle neutron scattering using superconducting magnetic Wollaston prisms
Here, we show the implementation of superconducting magnetic Wollaston prisms for spin echo small-angle neutron scattering. Two calibration methods for the spin echo length are presented: one utilizing spin echo modulated small-angle neutron scattering and the other based on the neutron refraction by quartz wedge crystals. Our experimental results with polystyrene nano-particle colloids showcase the system’s efficacy in measuring both dilute and concentrated colloidal systems. Additionally, investigations into the pore diameter and pitch of a nano-porous alumina membrane demonstrate its capability in analyzing nano-porous materials. Furthermore, we discuss potential optimizations to further extend the accessible spin echo length.
TU-EF-BRA-03: Free Induction Decay (without the Decay) and Spin-Echo Imaging
NMR, and Proton Density MRI of the 1D Patient - Anthony Wolbarst Net Voxel Magnetization, m(x,t). T1-MRI; The MRI Device - Lisa Lemen ‘Classical’ NMR; FID Imaging in 1D via k-Space - Nathan Yanasak Spin-Echo; S-E/Spin Warp in a 2D Slice - Ronald Price Magnetic resonance imaging not only reveals the structural, anatomic details of the body, as does CT, but also it can provide information on the physiological status and pathologies of its tissues, like nuclear medicine. It can display high-quality slice and 3D images of organs and vessels viewed from any perspective, with resolution better than 1 mm. MRI is perhaps most extraordinary and notable for the plethora of ways in which it can create unique forms of image contrast, reflective of fundamentally different biophysical phenomena. As with ultrasound, there is no risk from ionizing radiation to the patient or staff, since no X-rays or radioactive nuclei are involved. Instead, MRI harnesses magnetic fields and radio waves to probe the stable nuclei of the ordinary hydrogen atoms (isolated protons) occurring in water and lipid molecules within and around cells. MRI consists, in essence, of creating spatial maps of the electromagnetic environments around these hydrogen nuclei. Spatial variations in the proton milieus can be related to clinical differences in the biochemical and physiological properties and conditions of the associated tissues. Imaging of proton density (PD), and of the tissue proton spin relaxation times known as T1 and T2, all can reveal important clinical information, but they do so with approaches so dissimilar from one another that each is chosen for only certain clinical situations. T1 and T2 in a voxel are determined by different aspects of the rotations and other motions of the water and lipid molecules involved, as constrained by the local biophysical surroundings within and between its cells – and they, in turn, depend on the type of tissue and its state of health. Three other common applications of MRI exploit its capability to detect and image distinct movements of fluids: MR angiography (MRA), which rivals CT angiography but often requires no contrast medium, monitors the bulk flow of blood; functional MRI ( f MRI), distinguishes the perfusion of oxygenated blood from that of de-oxygenated, and lights up parts of the brain that are activated by a stimulus, rather like PET; and diffusion tensor imaging (DTI) indicates the diffusion of free water along tracts of axons, thereby bringing nerve trunks into view. There are variants on all of these themes, and on others as well. Magnetic Resonance Spectroscopy (MRS), for example, can perform non-invasive ‘virtual biopsies’ that allow identification of certain cancers and other lesions. And an MRI-guided needle biopsy can sample brain tissue from a region only millimeters in dimensions. MRI, however, involves deeper and more complex aspects of physics, technology, and biology than do most other imaging modalities, and it is widely considered to be correspondingly more difficult to learn. We could probably cover all of this rather comprehensively if we had 50 hours available rather than 2 ̶ but, to paraphrase a former Secretary of Defense, you tell your story in the time you have allotted. The four presenters and another physicist, Kevin King from GE, have combined their efforts to co-author a single slide show that describes essentials of MRI as simply as possible. It is obviously far from thorough, but hopefully it will succeed in explaining some of the basics in a simplified but still valid fashion; in providing a taste of the numerous capabilities and complexities of the modality; and in whetting your appetite to learn more. Part I. NMR, and Proton Density MRI of the 1D Patient (Wolbarst), begins with an introductory case study that illustrates a half dozen ways in which MRI provides valuable clinical information. It then explores the nuclear magnetic resonance (NMR) phenomenon, which underlies MRI. NMR can be introduced with either of two approaches. In the first, one thinks (loosely) of the nuclei of hydrogen atoms as (rotating and charged and therefore) magnetic objects, whose spin-axes tend to align in a strong external magnetic field, much like a compass needle. As with the Bohr atom, this spin-up/spin-down picture is a highly abridged version of the full quantum mechanical treatment, but still it leads to some useful, legitimate pictures of the NMR process occurring within a voxel: When RF photons of the correct (Larmor) frequency elevate protons in a fixed magnetic field out of their lower-energy spin state into the upper, the NMR phenomenon is indicated by the detectable absorption of RF power. With the addition of a linear gradient field along a multi-voxel, one-dimensional patient/phantom, as well, we can determine the water content of each compartment – an example of a real MRI study, albeit in 1D. Part I concludes with a discussion of the net magnetization at position x, m0(x), under conditions of dynamic thermal equilibrium, which leads into: Part II. Net Voxel Magnetization, m(x,t); T1-MRI; The MRI Device (Lemen), investigates the biophysics of the form of proton spin relaxation process characterized by the time T1. It then moves on to the creation of an MR image that displays the spatial variation in the values of this clinically relevant parameter, again in 1D. Finally, the design and workings of a clinical MRI machine are sketched, in preparation for: Part III. ‘Classical’ NMR; FID Imaging in 1D via k-Space (Yanasak) presents the second standard approach to NMR and MRI, the classical model. It focuses on the time dependence of the net nuclear magnetization, m(x,t), the overall magnetic field generated by the cohort of protons in the voxel at position x. Quite remarkably, this nuclear net magnetization itself acts in a strong magnetic field like a gyroscope in a gravitational field. This tack is better for explaining Free Induction Decay (FID), which involves a brief introduction to the Fourier transform and k-space. This leads to conventional Spin-Echo (S-E) reconstruction techniques for creating clinical images from raw data, and sets the stage for: Part IV. Spin-Echo; S-E / Spin Warp in a 2D Slice (Price) discusses application of the S- E sequence of radiofrequency pulses and gradient magnetic fields to the 1D patient. T2 is introduced but not explained. This Part also considers how to manipulate the image acquisition parameters so as to generate clinical pictures with contrast dominated by spatial variations in PD, T1, or T2. We conclude by demonstrating the spin-warp approach to imaging in 2D with a simple 2×2, 4-voxel example. Much of this material is presented in more detail in the chapter “MRI of the One-dimensional Patient, Part I”, in Advances in Medical Physics, Vol 5 (2014). Copies are on display at the Medical Physics Publishing booth. Learning Objectives: The participant will learn about the processes of NMR and T1 spin relaxation in a tissue voxel in a uniform magnetic field. The participant will learn about combining spin-up/spin-down NMR and T1 processes with a linear gradient to effect frequency-encoding of voxel spatial position. This approach can be used to create proton density and T1 MRI maps, respectively, of the contents of multi-voxel 1D phantoms. The participant will learn about how the ‘classical’ model of NMR it can generate Free Induction Decay (FID) images of 1D phantoms, which involves the use of the Fourier transform in k-space. This can lead simply into standard Spin-Echo images. The participant will learn about extending Spin-Echo imaging into 2 and more dimensions.
Quantum and classical correlations in electron-nuclear spin echo
The quantum properties of dynamic correlations in a system of an electron spin surrounded by nuclear spins under the conditions of free induction decay and electron spin echo have been studied. Analytical results for the time evolution of mutual information, classical part of correlations, and quantum part characterized by quantum discord have been obtained within the central-spin model in the high-temperature approximation. The same formulas describe discord in both free induction decay and spin echo although the time and magnetic field dependences are different because of difference in the parameters entering into the formulas. Changes in discord in the presence of the nuclear polarization β{sub I} in addition to the electron polarization β{sub S} have been calculated. It has been shown that the method of reduction of the density matrix to a two-spin electron-nuclear system provides a qualitatively correct description of pair correlations playing the main role at β{sub S} ≈ β{sub I} and small times. At large times, such correlations decay and multispin correlations ensuring nonzero mutual information and zero quantum discord become dominant.
Neutron resonance spin-echo upgrade at the three-axis spectrometer FLEXX
We describe the upgrade of the neutron resonance spin-echo setup at the cold neutron triple-axis spectrometer FLEXX at the BER II neutron source at the Helmholtz-Zentrum Berlin. The parameters of redesigned key components are discussed, including the radio frequency (RF) spin-flip coils, the magnetic shield, and the zero field coupling coils. The RF-flippers with larger beam windows allow for an improved neutron flux transfer from the source to the sample and further to the analyzer. The larger beam cross sections permit higher coil inclination angles and enable measurements on dispersive excitations with a larger slope of the dispersion. Due to the compact design of the spin-echo units in combination with the increased coil tilt angles, the accessible momentum-range in the Larmor diffraction mode is substantially enlarged. In combination with the redesigned components of the FLEXX spectrometer, including the guide, the S-bender polarizer, the double focusing monochromator, and a Heusler crystal analyzer, the count rate increased by a factor of 15.5, and the neutron beam polarization is enhanced. The improved performance extends the range of feasible experiments, both for inelastic scattering on excitation lifetimes in single crystals, and for high-resolution Larmor diffraction. The experimental characterization of the instrument components demonstrates the reliable performance of the new neutron resonance spin-echo option, now available for the scientific community at FLEXX.
Decoherence and spin echo in biological systems
The spin-echo approach is extended to include biocomplexes for which the interaction with dynamical noise, produced by the protein environment, is strong. Significant restoration of the free induction decay signal due to homogeneous (decoherence) and inhomogeneous (dephasing) broadening is demonstrated analytically and numerically for both an individual dimer of interacting chlorophylls and for an ensemble of dimers. Here, our approach does not require the use of small interaction constants between the electron states and the protein fluctuations. It is based on an exact and closed system of ordinary differential equations that can be easily solved for a wide range of parameters that are relevant for bioapplications.