Free Induction Decay Research Articles

Магнитный резонанс кольцевых спиновых кластеров

Using a quantum-based approach, we modeled the free induction decay signals for ring clusters of finite radius consisting of 6 and 8 particles with spin 1/2. In addition, we modeled a free induction decay signal for a spherical spin cluster by superimposing the ring signals. The current research uses two possible orientations of the spins. The ring plane was assumed to be only parallel or orthogonal to the external magnetic field. The free induction decays curves and their Fourier spectra were calculated both with and without the exchange interaction between the spins. The second and fourth moments of the magnetization response were evaluated by direct theoretical equations. The dependence of relaxation time on the ring radius was found. The exchange interaction was found to cause an increase in the relaxation time of a ring cluster when the exchange is positive, and a decrease in the time when it is negative. At the same time, the results obtained for the spherical cluster model do not show such an effect.

Effects of Microwave Gating on Nuclear Spin Echoes in Dynamic Nuclear Polarization.

Dipolar or quadrupolar echoes allow one to observe undistorted powder patterns, in contrast to simple Fourier transformations of free induction decays (FIDs). In this work, the buildup of proton polarization due to dynamic nuclear polarization (DNP) is monitored by observing echoes rather than FIDs. When the microwave irradiation is interrupted during the buildup of DNP, the electrons relax back to their Boltzmann distribution at high fields (B0 = 6.7 T) and low temperatures 1.2 < Tsample < 4.0 K, so that dipolar flip-flop-flip terms involving two electrons and one proton become largely ineffective as a mechanism of proton decoherence. This leads to a prolongation of the nuclear coherence lifetime T2'(1H). The increase in T2'(1H) leads to transient surges of the amplitudes of spin echoes. Conversely, transient slumps of spin echoes are observed when the microwave irradiation is switched back on, due to a shortening of nuclear coherence lifetimes.

Organic matter detection in shale reservoirs using a novel pulse sequence for T1-T2 relaxation maps at 2 MHz

Quantification of organic matter and fluids contained in oil source rocks from shale plays is a fundamental goal for the petrophysical and geochemical assessment of the production potential of a well. Laboratory 1H nuclear magnetic resonance (NMR) is a fast, reliable, and non-destructive method widely used in the oil industry. Measurement of T1-T2 correlation maps have been found to be critical for identifying the presence of solid organic matter, liquid hydrocarbons, and brine in these formations. However, the inherent long echo times associated with standard laboratory equipment for large sample volume challenge the detection of contribution from kerogen and viscous bitumen. In this work, we use a commercial low field NMR rock-core analyzer where a novel T1- T2*&T2 pulse sequence is implemented to enable the detection of solid organic matter by acquiring the free induction decay after the first excitation pulse. This acquisition is followed by a train of refocusing pulses that generate multiple echoes from which liquid components are detected. A set of outcrop and well samples from the Vaca Muerta Formation in Argentina, with a varying amount of total organic content, were measured. The signal intensity assigned to solid matter was correlated with RockEval 6 pyrolisis. The novel pulse sequence presented here can be implemented in any commercial apparatus without the need for hardware modifications.

Quantitative Evaluation of Phase Distribution in UHMWPE as Derived from a Combined Use of NMR FID Analysis and Monte Carlo Simulation

A new and robust statistical approach is explored with the objective to derive quantitative and reliable information on the molecular dynamics within distinct domains (crystalline, intermediate and amorphous domains) of ultra-high molecular weight polyethylene (UHMWPE). The method consists of a critical evaluation of the free induction decay (FID) model, which is used to generate synthetic FID with a predefined signal-to-noise ratio by Monte Carlo simulations. The application of the method is demonstrated for three UHMWPE samples. A subsequent model fitting of their synthetic FIDs revealed a unique correlation between the error, i.e., standard deviation, of the derived parameters and the FID signal-to-noise ratio (SNRFID). Moreover, it was found that the method can be used to estimate the minimum required sampling time to obtain reliable parameter estimation of the FID model to experimental data.

Spatially resolved free-induction decay spectroscopy using a 3D ultra-short echo time multi-echo imaging sequence with systematic echo shifting and compensation of B0 field drifts.

Biologically interesting signals can exhibit fast transverse relaxation and frequency shifts compared to free water. For spectral assignment, a ultra-short echo time (UTE) imaging sequence was modified to provide pixel-wise free-induction decay (FID) acquisition. The UTE-FID approach presented relies on a multi-echo 3D spiral UTE sequence with six echoes per radiofrequency (RF) excitation (TEmin 0.05ms, echo spacing 3ms). A complex pixel-wise raw data set for FID spectroscopy is obtained by several multi-echo UTE measurements with systematic shifting of the readout by 0.25 or 0.5ms, until the time domain is filled for 18 or 45ms. B0 drifts are compensated by mapping and according phase correction. Autoregressive extrapolation of the signal is performed before Gaussian filtering. This method was applied to a phantom containing collagen-water solutions of different concentrations. To calculate the collagen content, a 19-peak collagen model was extracted from a non-selective FID spectrum (50% collagen solution). Proton-density-collagen-fraction (PDCF) was calculated for 10 collagen solutions (2%-50%). Furthermore, an in vivo UTE-FID spectrum of adipose tissue was recorded. UTE-FID signal patterns agreed well with the non-spatially selective pulse-acquire FID spectrum from a sphere filled with 50% collagen. Differentiation of collagen solution from distilled water in the PDCF map was possible from 4% collagen concentration for a UTE-FID sequence with 128 × 128 × 64 matrix (voxel size 1 × 1 × 2.85mm3 ). The mean values of the PDCF correlate linearly with collagen concentration. The presented UTE-FID approach allows pixel-wise raw data acquisition similar to non-spatially selective pulse-acquire spectroscopy. Spatially resolved applications for assessment of spectra of rapidly decaying signals seem feasible.

Improvement of simulated nuclear quadrupole resonance signals from explosive detection via a Red-Pitaya board

In Nuclear quadrupole resonance (NQR), the interaction of the nuclear magnetic moments of quadrupolar nuclei (spin greater than 1/2) with the electric field gradient of the surrounding molecular orbitals produces an energy splitting. Because the resonant frequency is very specific to the molecular structure, the NQR can be used to detect explosive materials very accurately and it is extremely useful for detecting modern bombs whose containers made from plastics and wood instead of metals. However, NQR signals are generally very weak so they are difficult to be detected. Recently, Red-Pitaya boards, a Field Programmable Gate Array (FPGA) on Single Board Computers, have been being utilized in many electronic applications due to their small size and low cost. Since the boards can generate and acquire radio frequency signals, they can be taken as the console of portable bomb detectors. In this work, we study an improvement of the NQR signals of an explosive, ammonium nitrate with a resonant frequency of 423.6 kHz, acquired by using a Red-Pitaya board (STEMlab 125-14). To construct the NQR signals, we simulate free induction decay (FID) signals (exponential decay of sinusoidal functions) and add real measured noises from an input port of the Red-Pitaya board. To mimic real situations, the FID amplitude is varied, frequency fluctuations and phase shifts are added. The results show that averaging of signals from repeat measurements can improve the signals in all cases. To distinguish the signals from the noises, a minimal number of measurements is required. This necessary number of repeat measurements increases with frequency fluctuations and phase shifts but decreases when the FID amplitude grows.

JOM-4S Overhauser Magnetometer and Sensitivity Estimation.

The Overhauser magnetometer is a scalar quantum magnetometer based on the dynamic nuclear polarization (DNP) effect in the Earth’s magnetic field. Sensitivity is a key technical specification reflecting the ability of instruments to sense small variations of the Earth’s magnetic field and is closely related to the signal-to-noise ratio (SNR) of the free induction decay (FID) signal. In this study, deuterated 15N TEMPONE radical is used in our sensor to obtain high DNP enhancement. The measured SNR of the FID signal is approximately 63/1, and the transverse relaxation time T2 is 2.68 s. The direct measurement method with a single instrument and the synchronous measurement method with two instruments are discussed for sensitivity estimation in time and frequency domains under different electromagnetic interference (EMI) environments and different time periods. For the first time, the correlation coefficient of the magnetic field measured by the two instruments is used to judge the degree of the influence of the environmental noise on the sensitivity estimation. The sensitivity evaluation in the field environment is successfully realized without electrical and magnetic shields. The direct measurement method is susceptible to EMI and cannot work in general electromagnetic environments, except it is sufficiently quiet. The synchronous measurement method has an excellent ability to remove most natural and artificial EMIs and can be used under noisy environments. Direct and synchronous experimental results show that the estimated sensitivity of the JOM-4S magnetometer is approximately 0.01 nT in time domain and approximately 0.01 nT/ in frequency domain at a 3 s cycling time. This study provides a low-cost, simple, and effective sensitivity estimation method, which is especially suitable for developers and users to estimate the performance of the instrument.

Abstract 12812: Creatine Chemical Exchange Transfer MRI Demonstrates Abnormal Calf Muscle Energetics in Peripheral Arterial Disease

Introduction: Creatine chemical exchange saturation transfer (CrCEST) is a novel MRI technique utilizing radiofrequency pulses to monitor creatine concentrations at high spatial resolution. The study utilized CrCEST kinetics to compare post-exercise creatine decay in peripheral arterial disease (PAD) patients to normal subjects and to validate against phosphocreatine (PCr) recovery by 31 phosphorus (P) MR spectroscopy (MRS). Methods: 23 subjects with PAD (claudication and ankle-brachial index&lt;0.9) and 28 healthy subjects were enrolled. All underwent 3T MRI (Siemens Prisma) using a knee coil around the calf. Pre- and post-exercise images were obtained around plantar flexion ergometry (Ergospect) until exhaustion. Regions of interests were drawn around major muscle groups. Creatine decay times were obtained by fitting an exponential curve to the CrCEST values. 31 P spectra were obtained 20 minutes later at peak exercise using a surface-coil localized, free induction decay acquisition with 25 signal averages at a repetition time of 550s with calculation of PCr recovery time constant. Results: 23 PAD subjects (mean ABI 0.66 ± 0.11, age 64 ± 8, 17% females) had prolonged median overall calf muscle creatine decay time of 286 seconds (s) (Interquartile Range (IQR) 134 to 370) versus 152 s (IQR 114 to 193) in controls (age 63 ± 9, 70% females), p = 0.009. The gastrocnemius muscle demonstrated a creatine decay time of 316 s in PAD (IQR 189 to 510) versus 181 s in controls (IQR 102 to 236), p = 0.003 and the posterior tibialis muscle, 186 s (IQR 119 to 653) versus 125 s (IQR 72 to 221), p = 0.013. 8 PAD patients and 6 controls underwent CrCEST and 31 P MRS which were compared over the entire calf. Bland-Altman analysis (Figure 1B) yielded a mean difference of 71s (SD 109). Conclusions: Imaging with CrCEST demonstrates prolonged creatine kinetics in PAD patients compared to normal subjects with high spatial resolution and good agreement with 31 P MRS, although PCr recovery appears faster.

Peculiarities of Rabi oscillations and free induction decay in two-component nuclear spin systems with Ising nuclei interactions

Nuclear spin systems in manganites, having separation of ferromagnetic and antiferromagnetic phases, which are manifested as two lines in the NMR spectrum, are studied. Taking into account the Ising nuclear interaction, we obtain an analytical description of Rabi oscillations and free induction decay in two-component nuclear spin systems when a radio-frequency pulse non-resonantly excites the nuclei of one magnetic phase and resonantly the nuclei of the other phase. It is revealed that the nonlinearity of interaction between the nuclei of these phases results in additional harmonics in the Rabi oscillations of the non-resonantly excited subsystem. We also show that the Ising interaction inside this subsystem forms multiple echoes in the free induction decay, whereas their non-monotonic damping and amplitude modulation is caused by the spin coupling between the subsystems.

On the use of nuclear magnetic resonance spectroscopy in music composition- principles, practice and possibilities

Nuclear Magnetic Resonance (NMR) spectroscopy is an analytical technique commonly used across the natural sciences that works upon the detection of magnetically spin-aligned atomic nuclei resonating with an externally applied radio source. This work presents an overview of music created using NMR data and outlines principles for its use in composition. Methods for the sonification and musical interpretation of NMR spectra are demonstrated and opportunities for its development as a musical technique are identified. Abbreviations: 12-TET: Twelve-Tone Equal Temperament; ADC: Analogue to Digital Converter; COSY: Correlation Spectroscopy; FID: Free Induction Decay; FT: Fourier Transform; NMR: Nuclear Magnetic Resonance; PCM: Pulse Code Modulation; PPM: Parts per million; SNR: Signal-to-noise ratio; TMS: Tetramethylsilane

Floquet Prethermalization with Lifetime Exceeding 90s in a Bulk Hyperpolarized Solid.

We report the observation of long-lived Floquet prethermal states in a bulk solid composed of dipolar-coupled ^{13}C nuclei in diamond at room temperature. For precessing nuclear spins prepared in an initial transverse state, we demonstrate pulsed spin-lock Floquet control that prevents their decay over multiple-minute-long periods. We observe Floquet prethermal lifetimes T_{2}^{'}≈90.9 s, extended >60 000-fold over the nuclear free induction decay times. The spins themselves are continuously interrogated for ∼10 min, corresponding to the application of ≈5.8×10^{6} control pulses. The ^{13}C nuclei are optically hyperpolarized by lattice nitrogen vacancy centers; the combination of hyperpolarization and continuous spin readout yields significant signal-to-noise ratio in the measurements. This allows probing the Floquet thermalization dynamics with unprecedented clarity. We identify four characteristic regimes of the thermalization process, discerning short-time transient processes leading to the prethermal plateau and long-time system heating toward infinite temperature. This Letter points to new opportunities possible via Floquet control in networks of dilute, randomly distributed, low-sensitivity nuclei. In particular, the combination of minutes-long prethermal lifetimes and continuous spin interrogation opens avenues for quantum sensors constructed from hyperpolarized Floquet prethermal nuclei.

Insight into the Partitioning and Clustering Mechanism of Rare-Earth Cations in Alkali Aluminoborosilicate Glasses

Rare-earth (RE) containing alkali aluminoborosilicate glasses find increasingly broad technological applications, with their further development only impeded by yet-poor understanding of coordination environment and structural role of RE ions in glasses. In this work we combine free induction decay (FID)-detected electron paramagnetic resonance (EPR), electron spin echo envelope modulation (ESEEM), and MAS NMR spectroscopies, to examine the coordination environment and the clustering tendencies of RE3+ in a series of peralkaline aluminoborosilicate glasses co-doped with Nd2O3 (0.001-0.1 mol%) and 5 mol% La2O3. Quantitative EPR spectral analysis reveals three different Nd3+ forms coexisting in the glasses: isolated Nd3+ centers, dipole-coupled Nd clusters (Nd-O-X-O-Nd, where X = Si/B/Al), and spin-exchange-coupled Nd clusters, (Nd-O-Nd) and (Nd-O-La-O-Nd). Extensive RE clustering is observed at high RE2O3 concentrations, with more than 90% REs converting to dipole- and exchange-coupled Nd clusters already at [RE2O3] = 0.01 mol%. ESEEM analysis of the EPR-detectable Nd centers indicates a Na/Si-rich environment (four Na+ per Nd3+) for the isolated Nd3+ centers and the Na/Si/B-rich environment (2-3 Na+ and 1-2 boron per each Nd3+) for the dipole-coupled Nd clusters, while the EPR-undetectable exchanged-coupled RE clusters are predicted to exist in a Na/B-rich environment. The RE clustering induces nano-scale glass phase separation, while the Na/B-rich environment of the RE clusters implies a depletion of the same elements from the remaining host glass. Based on our results, we develop a mechanistic model that explains the high tendency of RE3+ to form clusters in alkali aluminoborosilicate glasses.

Spin echo formation in muscle tissue.

Determination of the spin echo signal evolution and of transverse relaxation rates is of high importance for microstructural modeling of muscle tissue in magnetic resonance imaging. So far, numerically exact solutions for the NMR signal dynamics in muscle tissue models have been reported only for the gradient echo free induction decay, with spin echo problems usually solved by approximate methods. In this work, we modeled the spin echo signal numerically exact by discretizing the radial dimension of the Bloch-Torrey equation and expanding the angular dependency in terms of even Chebyshev polynomials. This allows us to express the time dependence of the local magnetization as a closed-form matrix expression. Using this method, we were able to accurately capture the spin echo local and total magnetization dynamics. The obtained transverse relaxation rates showed a high concordance with random walker and finite-element simulations. We could demonstrate that in cases of smaller diffusion coefficients, the commonly used strong collision approximation significantly underestimates the true value considerably. Instead, the limiting behavior in this regime is correctly described either by the full solution or by the slow diffusion approximation. Experimentally measured transverse relaxation rates of a mouse limb muscle showed an angular dependence in accordance with the theoretical prediction.

Technical Note: Effects of rotating gantry on magnetic field and eddy currents in 0.35 T MRI-guided radiotherapy (MR-IGRT) system.

The purpose of this study was to identify the cause of severe image artifacts that occurred during gantry rotation in a 0.35 T MRI-Linac by comparing measurements of eddy currents, center frequency, and field inhomogeneities made with the gantry in motion and stationary. Gradient and B0 eddy currents were calculated from the free induction decays (FIDs) resulting from selective excitation at a temporal resolution of 200ms/measurement. B0 eddy currents were also calculated from FIDs acquired with nonselective excitation at a temporal resolution of 100ms/measurement. Center frequencies and B0 inhomogeneities were measured by acquiring FIDs with a repetition time (TR) of 290ms. Cartesian and radial 2D true fast imaging with steady-state precession (TrueFISP) pulse sequences used in real-time MRI-guided radiation therapy (MR-IGRT) were acquired. To assess artifact severity, the normalized root mean square error (nRMSE) was calculated between a reference MRI (static gantry) and MRIs acquired during gantry rotation for each serial acquisition. Image artifacts were qualitatively graded as nominal, minor, or severe. Measurements were conducted while the gantry was rotated through its entire range for both clockwise and counterclockwise. Measurements during gantry rotation were compared to measurements with a stationary gantry (every 30°). Severe image artifacts were observed 22-35% of the time while the gantry was rotating. Short time constant eddy currents were not affected by gantry rotation. The peak to peak center frequency and FWHM rose by factors of 13.2-14.5 and 1.1-1.6, respectively, for the rotating versus stationary gantry. The magnitude of the center frequency offset and field inhomogeneities depended on the direction of the gantry rotation. Image artifacts during gantry rotation were primarily caused by center frequency variations and field inhomogeneities. Therefore, dynamic B0 compensation techniques should be able to reduce artifacts during gantry rotation.

Controlling the collective radiative decay of molecular ions in strong laser fields

Molecular ions, produced via ultrafast ionization, can be quantum emitters with the aid of resonant electronic couplings, which makes them the ideal candidates to study strong-field quantum optics. In this work, we experimentally and numerically investigate the necessary condition for observing a collective emission arising from macroscopic quantum polarization in a population-inverted N 2 + gain system, uncovering how the individual ionic emitters proceed into a coherent collection within hundreds of femtoseconds. Our results show that for a relatively high-gain case, the collective emission behaviors can be readily initiated for all the employed triggering pulse area. However, for a low-gain case, the superradiant amplification is quenched since the building time of macroscopic interionic quantum coherence exceeds the dipole dephasing time, in which situation the seed amplification and free induction decay play an essential role. These findings not only clarify the contentious key issue regarding to the amplification mechanism of N 2 + lasing but also show the unique characteristics of ultrashort laser-induced amplification in a molecular ion system where both the microscopic and macroscopic quantum coherence might be present.

Submillimeter-resolution magnetic field imaging with digital micromirror device and atomic vapor cell

Magnetic field source localization and imaging happen at different scales. The sensing baseline ranges from meter scale, such as magnetic anomaly detection, to centimeter scale, such as brain field imaging, to nanometer scale, such as the imaging of a magnetic skyrmion and single cell. Here, we show how an atomic vapor cell can be used to realize a baseline of 109.6 μm with a magnetic sensitivity of 10 pT/Hz1/2 @0.6–100 Hz and a dynamic range of 2062–4124 nT. We used a free induction decay (FID) scheme to suppress low-frequency noise and avoid scale factor variation for different domains due to light non-uniformity. The measurement domains are scanned by a digital micromirror device. The currents of 22, 30, 38, and 44 mA are applied in the coils to generate different fields along the pumping axis, which are measured respectively by fitting the FID signals of the probe light. The residual fields of every domain are obtained from the intercept of linearly fitting of the measurement data corresponding to these four currents. The coil-generated fields are calculated by deducting the residual fields from the total fields. The results demonstrate that the hole of shield affects both the residual and the coil-generated field distribution. The potential impact of field distribution measurement with outstanding comprehensive properties of spatial resolution, sensitivity, and dynamic range is far-reaching. It could lead to capability of 3D magnetography for small things and/or organs in millimeter or even smaller scale.

Solid-State NMR Free Induction Decay, Simulated by the System of Classical Magnetic Moments and Quantum Correlations

Solid-State NMR Free Induction Decay, Simulated by the System of Classical Magnetic Moments and Quantum Correlations

Measurement of a129Xe transverse relaxation rate without the influence of Rb polarization-induced magnetic gradient.

We demonstrate the measurement of the transverse spin relaxation rate of Xe without the influence of the Rb polarization-induced magnetic field gradient. The optical pumping beam and probe beam turn on and off repeatedly during the measurement to reduce the relaxation originating from the Rb polarization-induced magnetic field gradient. During the absence of the optical pumping beam, the nuclear spin of the noble gas atom does not experience the alkali-polarization-induced magnetic field gradient so that the transverse spin relaxation rate (1/T2) decreases. When the duty cycle reaches zero, the measured transverse relaxation time T2 approaches the longitudinal spin relaxation time T1. Our method helps in roughly estimating the longitudinal spin relaxation time with a single measurement of the free induction decay.

Efficient numerical Bloch solutions for multipulse surface NMR

SUMMARY Simplified solutions of the Bloch equation can lead to inaccurate estimates of hydrogeological parameters from surface nuclear magnetic resonance measurements. Even for single pulse measurements, using simplified forward models is common practice because of the computational intensity of obtaining the full-Bloch solution. These challenges are exacerbated for multipulse sequences. We show parallelizing the full-Bloch solver on a Graphics Processing Unit reduces the solve time by three orders of magnitude. Further optimizations by numerical, analytical and hybrid solutions yield an additional 3× speed up. We simulate the full-Bloch physics for free-induction decay, spin-echo and pseudo-saturation recovery excitation schemes for an unprecedented range of physical scenarios. We explore the time-dependence and relaxation time sensitivity in these solution spaces. Characterizing the solution spaces with polynomials of the relaxation times, the solutions can be rapidly reproduced; a technique known as fast-mapping. By fitting these higher dimensional solution ensembles with polynomials, the original fast-mapping technique is extended to include T1 at arbitrary times. Accuracy of the 7th order polynomial is such that a minimum 96 per cent of the models are within a ±3 per cent relative error. This permits the rapid reproduction of full-Bloch solutions with a matrix multiplication and opens up surface NMR to time-series based inversion of single and multipulse data.

Coherent dynamics of Floquet-Bloch states in monolayer WS2 reveals fast adiabatic switching

Floquet engineering offers a path to optically-controlled materials, but experimental implementations have frequently relied on femtosecond pulses to achieve the high peak fields required to maximise interactions and obtain a measurable response. The Floquet formalism, however, is based on a continuous, periodic drive. Here we use femtosecond laser pulses to drive the optical Stark effect, a simple realization of Floquet engineering, in monolayer WS2. By monitoring the coherent evolution of the free-induction decay, we show that the system evolves adiabatically, and that the finite duration of the pulses does not introduce any effects beyond Floquet theory. Furthermore, we demonstrate that the induced energy shift follows a linear dependence on instantaneous intensity, even for ultrafast driving fields of fewer than 15 optical cycles.