Longitudinal Magnetization Research Articles

Nutation-based longitudinal-sensing protocols for high-field NMR with nitrogen-vacancy centers in diamond

Nitrogen-vacancy (N-V) centers in diamond enable nuclear magnetic resonance (NMR) spectroscopy of samples at the nano- and microscale. However, at typical tesla-scale NMR magnetic field strengths, N-V–NMR protocols become difficult to implement due to the challenge of driving fast N-V pulse sequences sensitive to nuclear Larmor frequencies above a few megahertz. We perform simulations and theoretical analysis of the experimental viability of N-V NMR at tesla-scale magnetic fields using a measurement protocol called DRACAERIS (Double Rewound ACquisition Amplitude Encoded Radio Induced Signal). DRACAERIS detects the longitudinal magnetization of the NMR sample at a much lower driven Rabi frequency, more suitable technically for N-V detection. We discuss how pulse errors, finite pulse lengths, and nuclear spin-spin couplings affect the resulting NMR spectra. We find that DRACAERIS is less susceptible to pulse imperfections and off-resonance effects than previous protocols for longitudinal magnetization detection. We also identify reasonable parameters for experimental implementation. Published by the American Physical Society 2024

Study of magnetic phase transitions by helium-3 in DyF3 nanoparticles

The spin kinetics of liquid 3He in contact with a mixture of LaF3 (99.7 %) and DyF3 (0.3 %) powders at temperatures of 1.5–3 K was studied by pulsed nuclear magnetic resonance. DyF3 particles have ellipsoidal shape and average size 225 × 153 nm with the magnetic phase transition at temperature Tc = 2.45 K. The temperature dependence of the longitudinal and transverse magnetization relaxation rates of 3He nuclei with a mixture of LaF3 and DyF3 powders has a broad maximum near Tc, which is related to the magnetic phase transition. It is shown that the adsorbed layer of 3He is extremely sensitive to magnetic phase transitions. Preplating the particles surface with adsorbed nitrogen layers allowed to vary the distance from 3He nuclei to the surface of particles in a controlled way. Calculations of the nuclear magnetic relaxation rates with a change in the distance of helium-3 from the particle surface have been carried out, which is in good agreement with experimental data. It was shown that helium-3 is extremely sensitive to surface magnetism and can be used to study surface effects and surface magnetism.

Generalized inhomogeneity-resilient relaxation along a fictitious field (girRAFF) for improved robustness in rotating frame relaxometry at 3T.

To optimize Relaxation along a Fictitious Field (RAFF) pulses for rotating frame relaxometry with improved robustness in the presence of and field inhomogeneities. The resilience of RAFF pulses against and inhomogeneities was studied using Bloch simulations. A parameterized extension of the RAFF formulation was introduced and used to derive a generalized inhomogeneity-resilient RAFF (girRAFF) pulse. RAFF and girRAFF preparation efficiency, defined as the ratio of the longitudinal magnetization before and after the preparation ( ), were simulated and validated in phantom experiments. and parametric maps were acquired at 3T in phantom, the calf muscle, and the knee cartilage of healthy subjects. The relaxation time maps were analyzed for resilience against artificially induced field inhomogeneities and assessed in terms of in vivo reproducibility. Optimized girRAFF preparations yielded improved preparation efficiency (0.95/0.91 simulations/phantom) with respect to RAFF (0.36/0.67 simulations/phantom). preparations showed in phantom/calf 6.0/4.8 times higher resilience to inhomogeneities than RAFF, and a 4.7/5.3 improved resilience to inhomogeneities. In the knee cartilage, (53 14 ms) was higher than (42 11 ms). Moreover, girRAFF preparations yielded 7.6/4.9 times improved reproducibility across / inhomogeneity conditions, 1.9 times better reproducibility across subjects and 1.2 times across slices compared with RAFF. Dixon-based fat suppression led to a further 15-fold improvement in the robustness of girRAFF to inhomogeneities. RAFF pulses display residual sensitivity to off-resonance and pronounced sensitivity to inhomogeneities. Optimized girRAFF pulses provide increased robustness and may be an appealing alternative for applications where resilience against field inhomogeneities is required.

Preparation-based B mapping in the heart using Bloch-Siegert shifts.

To develop and evaluate a robust cardiac mapping sequence at 3 T, using Bloch-Siegert shift (BSS)-based preparations. A longitudinal magnetization preparation module was designed to encode . After magnetization tip-down, off-resonant Fermi pulses, placed symmetrically around two refocusing pulses, induced BSS, followed by tipping back of the magnetization. Bloch simulations were used to optimize refocusing pulse parameters and to assess the mapping sensitivity. Relaxation-induced error was simulated for various / times. The effective mapping range was determined in phantom experiments, and maps were compared to the conventional BSS method and subadiabatic hyperbolic-secant 8 (HS8) pulse-sensitized method. Cardiac maps were acquired in healthy subjects, and evaluated for repeatability and imaging plane intersection consistency. The technique was modified for three-dimensional (3D) acquisition of the whole heart in a single breath-hold, and compared to two-dimensional (2D) acquisition. Simulations indicate that the proposed preparation can be tailored to achieve high mapping sensitivity across various ranges, with maximum sensitivity at the upper range. / -induced bias did not exceed 5.2 . Experimentally reproduced sensitization closely matched simulations for (mean difference 0.031 0.022, compared to 0.018 0.025 in the HS8-sensitized method), and showed 20-fold reduction in the standard deviation of repeated scans, compared with conventional BSS mapping, and an equivalent 2-fold reduction compared with HS8-sensitization. Robust cardiac map quality was obtained, with an average test-retest variability of 0.027 0.043 relative to normalized magnitude, and plane intersection bias of 0.052 0.031. 3D acquisitions showed good agreement with 2D scans (mean absolute deviation 0.055 0.061). BSS-based preparations enable robust and tailorable 2D/3D cardiac mapping at 3 T in a single breath-hold.

Cross-correlated relaxation in the NMR of near-equivalent spin pairs: Longitudinal relaxation and long-lived singlet order.

The evolution of nuclear spin state populations is investigated for the case of a 13C2-labeled triyne in solution, for which the near-equivalent coupled pairs of 13C nuclei experience cross-correlated relaxation mechanisms. Inversion-recovery experiments reveal different recovery curves for the main peak amplitudes, especially when the conversion of population imbalances to observable coherences is induced by a radio frequency pulse with a small flip angle. Measurements are performed over a range of magnetic fields by using a sample shuttle apparatus. In some cases, the time constant TS for decay of nuclear singlet order is more than 100 times larger than the time constant T1 for the equilibration of longitudinal magnetization. The results are interpreted by a theoretical model incorporating cross-correlated relaxation mechanisms, anisotropic rotational diffusion, and an external random magnetic field. A Lindbladian formalism is used to describe the dissipative dynamics of the spin system in an environment of finite temperature. Good agreement is achieved between theory and experiment.

Designing and fabricating a stationary magnetic particle system for Non-destructive testing

The bench unit, also known as the stationary magnetic particle system or the wet horizontal system, has been designed and fabricated to incorporate both circular and longitudinal magnetization techniques. Its primary purpose is to test machine parts commonly used in various industries, including aviation, automotive, and railway. The system comprises several key components: a transformer, a current control unit, a parameter display and adjustment circuit, a head shot, a coil, and wet magnetic irrigation device. This system is in compliance with international standards and is ready for implementation in companies that require it

Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network.

Background: The arterial input function (AIF) is vital for myocardial blood flow quantification in cardiac MRI to indicate the input time-concentration curve of a contrast agent. Inaccurate AIFs can significantly affect perfusion quantification. Purpose: When only saturated and biased AIFs are measured, this work investigates multiple ways of leveraging tissue curve information, including using AIF + tissue curves as inputs and optimizing the loss function for deep neural network training. Methods: Simulated data were generated using a 12-parameter AIF mathematical model for the AIF. Tissue curves were created from true AIFs combined with compartment-model parameters from a random distribution. Using Bloch simulations, a dictionary was constructed for a saturation-recovery 3D radial stack-of-stars sequence, accounting for deviations such as flip angle, T2* effects, and residual longitudinal magnetization after the saturation. A preliminary simulation study established the optimal tissue curve number using a bidirectional long short-term memory (Bi-LSTM) network with just AIF loss. Further optimization of the loss function involves comparing just AIF loss, AIF with compartment-model-based parameter loss, and AIF with compartment-model tissue loss. The optimized network was examined with both simulation and hybrid data, which included in vivo 3D stack-of-star datasets for testing. The AIF peak value accuracy and ktrans results were assessed. Results: Increasing the number of tissue curves can be beneficial when added tissue curves can provide extra information. Using just the AIF loss outperforms the other two proposed losses, including adding either a compartment-model-based tissue loss or a compartment-model parameter loss to the AIF loss. With the simulated data, the Bi-LSTM network reduced the AIF peak error from -23.6 ± 24.4% of the AIF using the dictionary method to 0.2 ± 7.2% (AIF input only) and 0.3 ± 2.5% (AIF + ten tissue curve inputs) of the network AIF. The corresponding ktrans error was reduced from -13.5 ± 8.8% to -0.6 ± 6.6% and 0.3 ± 2.1%. With the hybrid data (simulated data for training; in vivo data for testing), the AIF peak error was 15.0 ± 5.3% and the corresponding ktrans error was 20.7 ± 11.6% for the AIF using the dictionary method. The hybrid data revealed that using the AIF + tissue inputs reduced errors, with peak error (1.3 ± 11.1%) and ktrans error (-2.4 ± 6.7%). Conclusions: Integrating tissue curves with AIF curves into network inputs improves the precision of AI-driven AIF corrections. This result was seen both with simulated data and with applying the network trained only on simulated data to a limited in vivo test dataset.

Ab initio investigation of laser-induced ultrafast demagnetization of L10 FePt: Intensity dependence and importance of electron coherence

We theoretically investigate the optically induced demagnetization of ferromagnetic FePt using the time-dependent density functional theory (TDDFT). We compare the demagnetization mechanism in the perturbative and nonperturbative limits of light-matter interaction and show how the underlying mechanism of the ultrafast demagnetization depends on the driving laser intensity. Our calculations show that the femtosecond demagnetization in TDDFT is a longitudinal magnetization reduction and results from a nonlinear optomagnetic effect, akin to the inverse Faraday effect. The demagnetization scales quadratically with the electric field E in the perturbative limit, i.e., ΔMz∝E2. Moreover, the magnetization dynamics happens dominantly at even multiples nω0, (n=0,2,⋯) of the pump-laser frequency ω0, whereas odd multiples of ω0 do not contribute. We further investigate the demagnetization in conjunction to the optically induced change of electron occupations and electron correlations. Dynamical correlations within the Kohn-Sham local-density framework are shown to have an appreciable yet distinct effect on the amount of demagnetization depending on the laser intensity. Comparing the computed demagnetizations with those calculated from spin occupations, we show that electronic coherence plays a dominant role in the demagnetization process, whereas interpretations based on the time-dependent occupation numbers poorly describe the ultrafast demagnetization. Published by the American Physical Society 2024

Generation of a super-oscillation magnetization hotspot by reversing the electric dipole array radiation

We propose an all-optical approach to realize a super-oscillatory longitudinal magnetization hotspot with about 0.1λ in a 4π focusing system using time-reversed dipole radiation and vector diffraction theory calculations. Such a magnetization behavior is induced by focal fields of opposite polarities in the central and peripheral regions based on the inverse Faraday effect. By regulating the destructive interference in the central and peripheral regions of the focal field, a super-oscillating magnetization field is generated. Moreover, two important parameters affect the size of the magnetization field are also explored. Superoscillating magnetization hotspots in the focal region can be achieved by either increasing δ (the intensity of electric field) or reducing dn (the distance of electric field). The achieved ultrasmall magnetization spot shows great prospects in high-density magnetic recording, magnetic resonance imaging, and magnetic sensors.

Using Phase Difference Information to Detect Errors in the Flip Angle Measured with Actual Flip Angle Imaging at 7T.

Flip angle (FA) measurements using the actual flip angle imaging (AFI) method may induce significant errors in ultrahigh fields. We aimed to develop a method for detecting errors in FA measurements using phase information at 7 tesla. We performed computer simulations to elucidate the relationship between the FA calculation errors and the phase difference between the two AFI source images. We then examined whether a method based on the phase difference could detect FA calculation errors and determine the prescribed nominal FA of the scanner for accurate measurements in phantoms and healthy volunteers. The simulations confirmed that the calculated FA values erroneously decreased when the longitudinal magnetization and phase in one of the source images were inverted. Tests on phantoms and human subjects demonstrated that the phase difference information between the source images with a cut-off of 90° could readily detect FA calculation errors in the AFI method.

Exploring weak ligand-protein interactions by relaxometry of long-lived spin order.

Relaxation times of nuclear spins often serve as a valuable source of information on the dynamics of various biochemical processes. Measuring relaxation as a function of the external magnetic field turned out to be extremely useful for the studies of weak ligand-protein interactions. We demonstrate that observing the relaxation of the long-lived spin order instead of longitudinal magnetization extends the capability of this approach. We studied the field-dependent relaxation of the longitudinal magnetization and the singlet order (SO) of methylene protons in alanine-glycine dipeptide and citrate in the presence of human serum albumin (HSA). As a result, SO relaxation proved to be more sensitive to ligand-protein interaction, providing higher relaxation contrast for various HSA concentrations. To assess the parameters of the binding process in more details, we utilized a simple analytical relaxation model to fit the experimental field dependences for both SO and T1 relaxation. We also tested the validity of our approach in the experiments with trimethylsilylpropanoic acid (TSP) used as a competitor in ligand binding with HSA.

Improving signal-to-noise ratio by maximal convolution of longitudinal and transverse magnetization components in MRI: application to the breast cancer detection.

The extraction of information from images provided by medical imaging systems may be employed to obtain the specific objectives in the various fields. The quantity of signal to noise ratio (SNR) plays a crucial role in displaying the image details. The higher the SNR value, the more the information is available. In this study, a new function has been formulated using the appropriate suggestions on convolutional combination of the longitudinal and transverse magnetization components related to the relaxation times of T1 and T2 in MRI, where by introducing the distinct index on the maximum value of this function, the new maps are constructed toward the best SNR. Proposed functions were analytically simulated using Matlab software and evaluated with respect to various relaxation times. This proposed method can be applied to any medical images. For instance, the T1- and T2-weighted images of the breast indicated in the reference [35] were selected for modelling and construction of the full width at x maximum (FWxM) map at the different values of x-parameter from 0.01 to 0.955 at 0.035 and 0.015 intervals. The range of x-parameter is between zero and one. To determine the maximum value of the derived SNR, these intervals have been first chosen arbitrarily. However, the smaller this interval, the more precise the value of the x-parameter at which the signal to noise is maximum. The results showed that at an index value of x = 0.325, the new map of FWxM (0.325) will be constructed with a maximum derived SNR of 22.7 compared to the SNR values of T1- and T2-maps by 14.53 and 17.47, respectively. By convolving two orthogonal magnetization vectors, the qualified images with higher new SNR were created, which included the image with the best SNR. In other words, to optimize the adoption of MRI technique and enable the possibility of wider use, an optimal and cost-effective examination has been suggested. Our proposal aims to shorten the MRI examination to further reduce interpretation times while maintaining primary sensitivity. Our findings may help to quantitatively identify the primary sources of each type of solid and sequential cancer.

Generation of sub-wavelength longitudinal magnetization needle and multiple longitudinal spots using circularly polarized beam through an annular walsh function filter

Generation of sub-wavelength longitudinal magnetization needle and multiple longitudinal spots using circularly polarized beam through an annular walsh function filter

Ex vivo imaging of subacute myocardial ischemia with ultra-short echo time 3-D quantitative T1-mapping MRI in mice

Abstract Introduction Cardiac magnetic resonance (CMR) is important tool for assessment of structure and function of the myocardium in various cardiac conditions, such as after myocardial infarction (MI). CMR methods rely solely on multi-slice 2-D imaging, which tends to be slow, since every slice is imaged separately with the >3 min scan time. Furthermore, multi-slice methods are somewhat approximate, due to the slice thickness, which is usually around 1 mm for mice and 8 mm for humans. Therefore, 3-D CMR imaging methods with isotropic resolution are urgently needed. In this study, we present quantitative, ultra-short echo time 3-D Look-Locker T1[1] Multi-Band SWeep Imaging with Fourier Transform[2] and Compressed Sensing[3] (LL MB-SWIFT-CS) technique for imaging in MI mice hearts ex vivo. Purpose To develop an ultra-short echo time 3-D CMR method for imaging subacute myocardial ischemia quantitatively and in an accelerated way. Materials and Methods Hearts were collected 7 days after Left Anterior Descending (LAD) Coronary Artery was ligated in C57BL mice, fixated in 4% PFA in PBS and imaged with LL MB-SWIFT-CS MRI. The heart was scanned in 3-D with a total acquisition time of 3.25 min with resolution of 256³. For T1 determination, saturation recovery (SR) of the longitudinal magnetization was measured with following parameters: TR=3 ms, FA=4º, FOV=25 mm³, total number of unique spokes acquired=16384 and spokes per LL curve=1024, filling the 3-D data space homogeneously 16 times during the recovery. Total scan time was 52 min. After imaging, the SR LL curve was reconstructed into 32 images with CS reconstruction. For comparison, we imaged the hearts with 2-D MRI TRAFF2-mapping method[4] and histology. For regions of interests (ROIs) analysis, the damaged and remote ROI areas were observed from 2-D MR images and drawn to corresponding anatomical 3-D images. The same ROIs were then used to collect the T1 relaxation time data. For histology, standard paraffin embedding, and tissue processing protocols were used. 4 μm thick sections were cut and stained with Hematoxylin Eosin and Sirius Red staining. Results and Discussion The T1 relaxation time values were elevated in the damaged areas (p<0.005) (Fig. 1), as shown earlier[5,6]. The T1 values in the ischemic and remote myocardium were 0.76±0.03s and 0.70±0.02s, respectively. Ischemic areas can also be observed visually in the T1- and 2D TRAFF2-maps (Fig. 2). Sirius Red staining showed increased collagen formation in the ischemic myocardium, supporting the CMR findings. Moreover, hematoxylin-eosin staining showed loss of cardiomyocytes and coronary capillaries, and infiltration of inflammatory cells, like macrophages and lymphocytes. Conclusion With this method, we were able to detect the statistically significant differences between damaged and remote tissue based on the T1-relaxation times within the myocardium, allowing isotropic quantitative 3-D assessment of the entire myocardium.T1 values for MB-SWIFT-CSVisual validation of MB-SWIFT-CS

Magic angle spinning effects on longitudinal NMR relaxation: 15N in L-histidine

Solid-state magnetic resonance is a unique technique that can reveal the dynamics of complex biological systems with atomic resolution. Longitudinal relaxation is a mechanism that returns longitudinal nuclear magnetization to its thermal equilibrium by incoherent processes. The measured longitudinal relaxation rate constant however represents the combination of both incoherent and coherent contributions to the change of nuclear magnetization. This work demonstrates the effect of magic angle spinning rate on the longitudinal relaxation rate constant in two model compounds: L-histidine hydrochloride monohydrate and glycine serving as proxies for isotopically-enriched biological materials. Most notably, it is demonstrated that the longitudinal N15 relaxation of the two nitrogen nuclei in the imidazole ring in histidine is reduced by almost three orders of magnitude at the condition of rotational resonance with the amine, while the amine relaxation rate constant is increased at these conditions. The observed phenomenon may have radical implications for the solid-state magnetic resonance in biophysics and materials, especially in the proper measurement of dynamics and as a selective serial transfer step in dynamic nuclear polarization.

Estimation of Radiation Damping Rates Using 133Cs, 7Li and 31P Solution NMR Spectroscopy and a Theoretical NMR RASER Model

Radio amplification using stimulated emission of radiation (RASER) effects in the NMR can increase NMR signals over time due to a feedback loop between the sample magnetization and the probe coil coupled with radiation damping (RD). Previously, RD rates had been directly observed only for the 1H, 3He, 17O and 129Xe nuclei. We report that experimental direct measurements of an NMR RASER to determine RD time constants for the three heteronuclei (133Cs (I = 7/2), 7Li (I = 3/2) and 31P (I = 1/2)) in a highly concentrated solution from the NMR RASER emissions using a conventional NMR probe. Under conditions where the RD rate exceeds the transverse relaxation rate (i.e., the NMR RASER condition is fulfilled), we recorded both the transverse NMR RASER response to imperfect inversion and the recovery of longitudinal magnetization. The data were directly evaluated based on the well-known Bloom model as estimated RD rate constants of 8.0, 1.8 and 25 Hz for 133Cs, 7Li and 31P, respectively. The proposed method can be applied to observe RD rate constants for the other nuclei as well.

What can we gain from subpopulation universal pulses? A simulation-based study.

The aim of the study was to explore a novel methodology for designing universal pulses (UPs) that balances the benefits of a calibration-free approach with subject-specific online pulse design. The proposed method involves segmenting the population into subpopulations with variability in anatomical shapes and positions reduced to 75%, 50%, and 25% of their original values while keeping the mean values unchanged. An additional 25% extreme case with a large volume of interest and shifted position was included. For each group, a 5kT-points universal inversion pulse was designed and assessed by the normalized root mean square error (NRMSE) on the target longitudinal magnetization profile. The performance was compared to the conventional one-size-fits-all approach. A total of 132 electromagnetic simulations were executed to generate representative anatomies and specific absorption rate (SAR) distributions in a three-dimensional parameter space comprised of head breadth, head length, and Y-shift. The 99.9th percentile on the peak local SAR distribution was utilized to establish an intersubject variability safety margin. UPs designed for subpopulations with decreased head shape and position variability reduced the anatomical safety margin by up to 20%. Furthermore, when a head was significantly different to the average case, the proposed approach improved the inversion homogeneity by up to 24%, compared to the conventional one-size-fits-all approach. Subpopulation UPs present an opportunity to improve the homogeneity and reduce anatomical SAR safety margins at 7T without additional acquisition time for calibration.

A revisit to the Ising model in a transverse and random magnetic field

In this article we consider a Hamiltonian representing the Ising model in a random transverse magnetic field (RTIM). We use mean field theory via Bogoliubov’s inequality to calculate the Gibbs free energy and the longitudinal (mz) and transverse (mx) magnetizations. We show a quantum phase transition at zero temperature, i.e. the magnetization mz goes to zero only due to the transverse magnetic field. The temperature behavior as a function of the transverse magnetic field is also shown for different values of the anisotropy parameter p, where no tricritical behavior is observed. The behavior of mz and mx as a function of temperature and transverse magnetic field have been plotted, showing that there is no tricritical behavior.

Magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π focusing system.

This paper explored the optically induced magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π high numerical aperture (NA) focusing system, which is based on the vector diffraction theory and the inverse Faraday effect. The results show that in the case of radial modulation parameter L=0, one longitudinal magnetization chain with adjustable length can be obtained by modulating the truncation parameter β. When the radial modulation parameter L=1.3, two magnetization chains can be obtained by modulating the truncation parameter β. By modulating the radial modulation parameter L, two magnetization chains along the optical axis can be generated, each with four dark magnetic traps; meanwhile, the spacing between two magnetization chains can be adjusted. These results may be helpful in high-density all-optical magnetic recording, atom capture, and magnetic resonance microscopy.

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.