Anisotropy in tendon investigated in vivo by a portable NMR scanner, the NMR-MOUSE

Ordered tissue like tendon is known to exhibit the magic-angle phenomenon in magnetic resonance investigations. Due to the anisotropic structure the transverse relaxation time T(2) depends on the orientation of the tendon in the magnetic field. In medical imaging, relaxation measurements of tendon orientation are restricted by the size of the object and the space available in the magnet. For humans, tendon orientation can only be varied within small limits. As a consequence, the magic-angle phenomenon may lead to a misjudgement of tendon condition. It is demonstrated that the NMR-MOUSE (mobile universal surface explorer), a hand-held NMR sensor, can be employed to investigate the anisotropy of T(2) in Achilles tendon in vivo. The NMR-MOUSE provides a convenient tool for analyzing the correlation of T(2) and the physical condition of tendon.     

Thermo-oxidative aging of elastomers: a temperature control unit for operation with the NMR-MOUSE

Temperature-controlled measurements of the transverse relaxation time were conducted with the NMR-MOUSE (nuclear magnetic resonance mobile universal surface explorer) at 50°C to investigate the heterogeneity of rubber sheets induced by thermo-oxidative aging. With temperature stabilization the relative error ofT ₂ decreased by a factor of 4 on the short time scale. Without temperature stabilization it may reach 30% in the long-time range because of temperature changes in the laboratory. Two different types of mobile temperature control units operating with the NMR-MOUSE are described. These temperature control units are small and portable like the NMR-MOUSE.     

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG ¹H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T_2,short and 1/T_2,long were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T₁/T₂ ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T₂/T_2,eff is derived as a function of the T₁/T₂ ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T₁–T₂ correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T₁–T₂ experimental correlations maps were corrected for the T₁/T₂ effect using the derived T₂/T_2,eff correction factor.     

Multi-components of T2 relaxation in ex vivo cartilage and tendon

The multi-components of T₂ relaxation in cartilage and tendon were investigated by microscopic MRI (μMRI) at 13 and 26 μm transverse resolutions. Two imaging protocols were used to quantify T₂ relaxation in the specimens, a 5-point sampling and a 60-point sampling. Both multi-exponential and non-negative-least-square (NNLS) fitting methods were used to analyze the μMRI signal. When the imaging voxel size was 6.76 × 10⁻⁴ mm³ and within the limit of practical signal-to-noise ratio (SNR) in microscopic imaging experiments, we found that (1) canine tendon has multiple T₂ components; (2) bovine nasal cartilage has a single T₂ component; and (3) canine articular cartilage has a single T₂ component. The T₂ profiles from both 5-point and 60-point methods were found to be consistent in articular cartilage. In addition, the depletion of the glycosaminoglycan component in cartilage by the trypsin digestion method was found to result in a 9.81–20.52% increase in T₂ relaxation in articular cartilage, depending upon the angle at which the tissue specimen was oriented in the magnetic field.     

Effect of oxygen on the NMR relaxation properties of crude oils

Nuclear magnetic resonance relaxation measurements of bulk fluids provide a sensitive probe of the dynamics of molecular motion. Dissolved oxygen can interfere with this technique as its paramagnetic nature leads to a reduction of the paramagnetic relaxation times of the fluids. We studied this effect for the relaxation properties of crude oils that are in general characterized by a distribution of relaxation times. The samples were stock tank oils that have been exposed to air. We comparedT ₁ andT ₂ relaxation time distributions and their correlation functions of the initial (oxygenated) samples with those from the deoxygenated samples. Oxygen was removed from the oils with a freeze-thaw technique. As expected, the effect of oxygen is most apparent in oils with long relaxation times. In these oils the effect of oxygen can be described by an additional relaxation rate 1/T _1,2 ^ox to the transverse and longitudinal relaxation rates that is sample dependent but does not vary within the relaxation time distribution of the oil. Values of 1/T _1,2 ^ox for different crude oils were found to be in the range of 2.5 to 8.3 s. For crude oils that have components with relaxation times less than 100 ms, no significant oxygen effect is observed.     

Influence of magnetic impurities on proton spin relaxation of water in clay

The¹H nuclear magnetic spin relaxation of water in slurry of kaolin clay was investigated in the presence of magnetite (black iron oxide, Fe₃O₄) at 0.2 T and room temperature. The water spectra at high magnetite contents showed two different resonances, presumably from surface-associated water and free interstitial water. The difference in observed resonance frequencies increased as much as 200 ppm with increasing magnetite content. The apparent nuclear magnetic resonance intensity decreased biexponentially as a function of magnetite added. The observedT ₂^* values at low magnetite contents were in accordance with the predicted values from the resonance intensities and the estimated magnetic susceptibilities. TheT ₁ relaxation was multiexponential in character, so a uniform penalty program was used for the analysis of distribution. At 0.2 T for¹H, kaolin slurry containing less than 5.5 ppm magnetite did not differ significantly from magnetite-free clay in the longitudinal relaxation rates of water. However, higher concentrations of magnetite produced features in theT ₁ distribution significantly different from those of magnetite-free clay. TheT ₂ could be approximated by monoexponential relaxation, probably because the fast-decaying components relaxed before they could be recorded. The apparent transverse relaxation ratesR ₂ increased linearly as a function of magnetite content. On the basis of the comparison of spin-echo and Carr-Purcell-Meiboom-Gill data, an empirical relation was derived to describe the signal loss due to diffusion. It can be expressed by a power function of magnetite amount, which is multiplied by the sum of volume-dependent and volume-independent terms.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Characterization and Suppression Techniques for Degree of Radiation Damping in Inversion Recovery Measurements

Radiation damping is a phenomenon in which transverse nuclear magnetization couples with the current in a coil used in nuclear magnetic resonance experiments. This results in an additional magnetic field that increases the relaxation pathway for the magnetization, which then relaxes back to equilibrium more quickly. Radiation damping has been shown to affect longitudinal relaxation time (T₁) measurement in inversion recovery experiments. In this work, we demonstrate that the extent of radiation damping depends upon the T₁ of the sample. Radiation damping difference spectroscopy is used to characterize the severity of radiation damping, while gradient inversion recovery is used for radiation damping suppression in T₁ measurements. At field strength of 9.4 T, for the radiation damping characteristic time (T_rd) of 50 ms, these investigations show non-negligible radiation damping effects for T₁ values greater than T_rd, with severe distortions for T₁ longer than about 150 ms, showing reasonable agreement with the predicted T_rd. We also report a discrepancy between published expressions for the characteristic radiation damping time.     

An NMR thermometer for cryogenic magic-angle spinning NMR: the spin-lattice relaxation of (127)I in cesium iodide

The accurate temperature measurement of solid samples under magic-angle spinning (MAS) is difficult in the cryogenic regime. It has been demonstrated by Thurber et al. (J. Magn. Reson., 196 (2009) 84-87) [10] that the temperature dependent spin-lattice relaxation time constant of ⁷⁹Br in KBr powder can be useful for measuring sample temperature under MAS over a wide temperature range (20–296 K). However the value of T₁ exceeds 3 min at temperatures below 20 K, which is inconveniently long. In this communication, we show that the spin-lattice relaxation time constant of ¹²⁷I in CsI powder can be used to accurately measure sample temperature under MAS within a reasonable experimental time down to 10 K.     

Behavior of the glass transition and crystallization temperatures of the oxide glass MgO-Al2O3-SiO2 under external influences

The kinetics of the glass transition Tg and crystallization Tcr temperatures of the glass MgO-Al₂O₃-SiO₂ is studied under conditions of annealing in the glass transition interval and after treatment with a pulsed magnetic field (PMF). It is found that all the parameters studied exhibit nonmonotonic and intercorrelated variations in time. These temporal variations are due to structural relaxation (SR) in the glass. It is observed that a relative decrease of T _g and T _cr occurs in the annealed or PMF-treated glass. This effect is important from the standpoint of modern ideas about the mechanisms of structural relaxation and is due to the concentrational redistribution of chemical bonds. The condition for externally induced anomalous behavior of the temperatures investigated is determined. Zh. Tekh. Fiz. 67, 30–34 (October 1997)     

Spin physics in solid helium: Experimental results and applications

We have observed optical pumping signals from Cs atoms trapped in solid⁴He. While the longitudinal electronic spin relaxation timeT ₁ is found to be in the range of 1–2 s, the transverse relaxation timeT ₂, as inferred from magnetic resonance linewidths has a lower bound of 150 s, and is determined by magnetic field inhomogeneities. We present a quantitative discussion of how paramagnetic species trapped in solid He might be used in a highly sensitive search for permanent atomic electric dipole moments.     

Studies of magnetism by nuclear orientation and NMRON

Low temperature nuclear orientation (NO) and nuclear magnetic resonance on oriented nuclei (NMRON) are used to investigate the magnetic properties of solids, and are especially useful when high sensitivity is required, for example in the study of small or dilute systems. Measurement of the static hyperfine interaction and the nuclear spin-lattice and spin-spin relaxation times T ₁ and T ₂ yield information about the electronic magnetization and spin dynamics, respectively. A number of NMRON techniques are available and their application to the study of magnetism will be briefly discussed. In particular, the pulsed technique has been shown to be effective for studying insulators. Recent NO and NMRON measurements, primarily on insulating magnets and magnetic multilayers, will be reviewed. Spins of stable isotopes can also be investigated using NMR thermally detected by NO (NMR-TDNO), and this method, in combination with NMRON, has been recently applied in both metals and insulators to obtain information about nuclear spin-spin couplings, “frequency pulling” and nuclear magnons. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

On the possibility of studying crystal field levels and excitations by μ+SR spectroscopy

We point out that ⁺SR relaxation timesT ₁ andT ₂ measured in metallic magnetic materials can sometimes be expressed in terms of the spin-spin correlation functions of the magnetic ions. We calculate these functions in a random phase approximation and notice they can strongly depend on the crystal field levels and excitations of the magnetic ions. The shortcomings of this approximation are discussed.Part of this work was done at the French Atomic Commission at Grenoble.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.     

Multi-dimensional 1H NMR nuclear Overhauser spectroscopy under magic angle spinning: theory and application to elastomers

The process of cross-relaxation between different protons (nuclear Overhauser effect) is investigated in soft solids by 2- and 3-dimensional NMR under the conditions of fast magic-angle spinning. The cross-relaxation rates are found to depend weakly on fast motions in the Larmor frequency range and strongly on slow motions of the order of the spinning frequency W _R. Explicit expressions for the W _R dependent cross-relaxation rates are derived for different motional models. These findings were tested experimentally on elastomers, i.e., on a cross-linking series of styrene-butadiene rubbers where the cross-relaxation was studied as a function of W _R. Short mixing times as are required for extracting the relaxation rates could be realized conveniently using a pulsed magnetic-field gradient for coherence pathway selection. As in solution NMR, relative couplings between chemically resolved spins can be determined from the peak intensities. By combining cross-relaxation measurements with T ₁ measurements, the distribution of correlation times can be probed for slow and fast timescales, respectively. Only the former were found to depend on the crosslink density.     

Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 1: Algorithm and Model Study

Antalek and Windig recently presented a fast method to resolve a series of NMR mixture spectra, where the contribution of the components varies with a decaying exponential [B. Antalek and W. Windig,J. Am. Chem. Soc.118, 10,331–10,332 (1996); W. Windig and B. Antalek,Chemom. Intell. Lab. Syst.37, 241–254 (1997)]. The method was called DECRA (direct exponential curve resolution algorithm). In this paper DECRA will be applied to two series of magnetic resonance images. The signal of one series is based uponT₂relaxation, and the other is based uponT₁relaxation. In order to evaluate the technique, the magnetic resonance images of a phantom where used. A transformation is introduced to enable the application of DECRA to aT₁series of magnetic resonance images. A separate paper in this issue will describe the application of the techniques to magnetic resonance images of the human brain.     

Emulation of petroleum well-logging D-T2 correlations on a standard benchtop spectrometer

An experimental protocol is described that allows two-dimensional (2D) nuclear magnetic resonance (NMR) correlations of apparent diffusion coefficient D_app and effective transverse relaxation time T_2,eff to be acquired on a bench-top spectrometer using pulsed field gradients (PFG) in such a manner as to emulate D_app − T_2,eff correlations acquired using a well-logging tool with a fixed field gradient (FFG). This technique allows laboratory-scale NMR measurements of liquid-saturated cored rock to be compared directly to logging data obtained from the well by virtue of providing a comparable acquisition protocol and data format, and hence consistent data processing. This direct comparison supports the interpretation of the well-logging data, including a quantitative determination of the oil/brine saturation. The D − T₂ pulse sequence described here uses two spin echoes (2SE) with a variable echo time to encode for diffusion. The diffusion and relaxation contributions to the signal decay are then deconvolved using a 2D numerical inversion. This measurement allows shorter relaxation time components to be probed than in conventional diffusion measurements. A brief discussion of the numerical inversion algorithms available for inverting these non-rectangular data is included. The PFG-2SE sequence described is well suited to laboratory-scale studies of porous media and short T₂ samples in general.     

NMR relaxation study of avocado quality

Four nuclear magnetic resonance relaxation protocols are investigated as potential candidates for off-line and on-line determination of avocado maturity. Two-dimensionalT ₁-T ₂ andT ₂-D correlation spectroscopy provides the most information but is only suitable for off-line quality control. The CPMGT ₂ spectrum gives avocado oil content but requires intensive data processing. Suppression of the tissue water signal byT ₁-Null methods is shown to be unreliable but a new, single-shot pulse sequence which uses diffusive attenuation to suppress the tissue water is shown to give a good correlation with oil content and is suitable for both off-line and on-line implementation.     

Muon-spin-relaxation investigation of EuMn<Subscript>2</Subscript>O<Subscript>5</Subscript>

The magnetic properties of the EuMn₂O₅ multiferroic (samples consisting of single crystals and ceramic samples) have been investigated by the muon-spin-relaxation (μSR) method in the temperature range of 10–300 K. Below the magnetic ordering temperature T _N = 40 K, the loss of the polarization of muons and the effect of the external magnetic field have been observed. Both phenomena can be explained by an additional channel of the depolarization of muons owing to the appearance of muons in a medium with a low electron density due to the charge separation process (the redistribution of the electron density in the phase transition process). The “memory” phenomenon has been revealed in a sample in the external magnetic field; the memory relaxation time depends on the size of the structure units of the samples (single crystals or ceramic grains).