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.     

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Spin relaxation is a sensitive probe of molecular structure and dynamics. Correlation of relaxation time constants, such as T₁ and T₂, conceptually similar to the conventional multidimensional spectroscopy, have been difficult to determine primarily due to the absense of an efficient multidimensional Laplace inversion program. We demonstrate the use of a novel computer algorithm for fast two-dimensional inverse Laplace transformation to obtain T₁–T₂ correlation functions. The algorithm efficiently performs a least-squares fit on two-dimensional data with a nonnegativity constraint. We use a regularization method to find a balance between the residual fitting errors and the known noise amplitude, thus producing a result that is found to be stable in the presence of noise. This algorithm can be extended to include functional forms other than exponential kernels. We demonstrate the performance of the algorithm at different signal-to-noise ratios and with different T₁–T₂ spectral characteristics using several brine-saturated rock samples.     

In vivo NMR T2 relaxation of experimental brain tumors in the cat: A multiparameter tissue characterization

Experimental gliomas (F98) were inoculated in cat brain for the systematic study of their in vivo T₂ relaxation time behavior. With a CPMG multi-echo imaging sequence, a train of 16 echoes was evaluated to obtain the transverse relaxation time and the magnetization M(0) at time t = 0. The magnetization decay curves were analyzed for biexponentiality. All tissues showed monoexponential T₂, only that of the ventricular fluid and part of the vital tumor tissue were biexponential. Based on these NMR relaxation parameters the tissues were characterized, their correct assignment being assured by comparison with histological slices. T₂ of normal grey and white matter was 74 ± 6 and 72 ± 6 msec, respectively. These two tissue types were distinguished through M(0) which for white matter was only 0.88 of the intensity of grey matter in full agreement with water content, determined from tissue specimens. At the time of maximal tumor growth and edema spread a tissue differentiation was possible in NMR relaxation parameter images. Separation of the three tissue groups of normal tissue, tumor and edema was based on T₂ with T_2(normal) < T_2(tumor) < T_2(edema). Using M(0) as a second parameter the differentiation was supported, in particular between white matter and tumor or edema. Animals were studied at 1–4 wk after tumor implantation to study tumor development. The magnetization M(0) of both tumor and peritumoral edema went through a maximum between the second and third week of tumor growth. T₂ of edema was maximal at the same time with 133 ± 4 msec, while the relaxation time of tumor continued to increase during the whole growth period, reaching values of 114 ± 12 msec at the fourth week. Thus, a complete characterization of pathological tissues with NMR relaxometry must include a detailed study of the developmental changes of these tissues to assure correct experimental conditions for the goal of optimal contrast between normal and pathological regions in the NMR images.     

Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 2: Application to Human Brain Images

Owing to the heterogeneity of living tissues, it is challenging to quantify tissue properties using magnetic resonance imaging. Within a single voxel, contributions to the signal may result from several types of¹H nuclei with varied chemical (e.g., −CH₂−, −OH) and physical environments (e.g., tissue density, compartmentalization). Therefore, mixtures of¹H environments are prevalent. Furthermore, each unique type of¹H environment may possess a unique and characteristic spin–lattice relaxation time (T₁) and spin–spin relaxation time (T₂). A method for resolving these unique exponentials is introduced in a separate paper (Part 1. Algorithm and Model System) and uses the direct exponential curve resolution algorithm (DECRA). We present results from an analysis of images of the human head comprising brain tissues.     

A rapid measurement of : The DECPMG sequence

The Driven-Equilibrium Carr–Purcell Meiboom–Gill (DECPMG) pulse sequence is a rapid method for obtaining the average ratio of longitudinal to transverse relaxation times T₁/T₂ as a function of T₂. Since this is a one-dimensional experiment, the T₁/T_2T2 ratio can be acquired, potentially, in just two scans; the second scan being a reference CPMG measurement. Conventionally, T₁/T₂ is determined from a two-dimensional T₁-T₂ relaxation correlation experiment. The method described here offers a significant reduction in experimental time without a reduction in signal-to-noise. The T₁/T₂ ratio is useful for comparing the behaviour of liquids in porous media. Here we demonstrate the application of the DECPMG sequence to the study of oil-bearing rocks by differentiating oil or water saturated rock cores, and by observing the relative strengths of surface interaction for water in two types of rock by measuring T₁/T₂ as a function of magnetic field strength.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

The structure of polyacrylamide gels was studied using proton spin–lattice relaxation and PFG diffusion methods. Polyacrylamide gels, with total polymer concentrations ranging from 0.25 to 0.35 g/ml and crosslinker concentrations from 0 to 10% by weight, were studied. The data showed no effect of the crosslinker concentration on the diffusion of water molecules. The Ogston–Morris and Mackie–Meares models fit the general trends observed for water diffusion in gels. The diffusion coefficients from the volume averaging method also fit the data, and this theory was able to account for the effects of water-gel interactions that are not accounted for in the other two theories. The averaging theory also did not require the physically unrealistic assumption, required in the other two theories, that the acrylamide fibers are of similar size to water molecules. Contrary to the diffusion data,T₁relaxation measurements showed a significant effect of crosslinker concentration on the relaxation of water in gels. The model developed using the Bloch equations and the volume averaging method described the effects of water adsorption on the gel medium on both the diffusion coefficients and the relaxation measurements. In the proposed model the gel medium was assumed to consist of three phases (i.e., bulk water, uncrosslinked acrylamide fibers, and a bisacrylamide crosslinker phase). The effects of the crosslinker concentration were accounted for by introducing the proton partition coefficient,K^eq, between the bulk water and crosslinker phase. The derived relaxation equations were successful in fitting the experimental data. The partition coefficient,K^eq, decreased significantly as the crosslinker concentration increased from 5 to 10% by weight. This trend is consistent with the idea that bisacrylamide tends to form hydrophobic regions with increasing crosslinker concentration.     

Feasibility of similarity coefficient map in improving morphological evaluation of T2* weighted MRI for renal cancer

The purpose of this paper is to investigate the feasibility of similarity coefficient map (SCM) in improving morphological evaluation of T₂^* weighted (T₂^*W) magnatic resonance imaging (MRI) for renal cancer. Simulation studies and in vivo 12-echo T₂^*W experiments for renal cancers were performed for this purpose. The results of the first simulation study suggest that SCM can reveal small structures which are hard to be distinguished from the background tissue in T₂^*W images and the corresponding T₂^* map. The capability of improving morphological evaluation is likely due to the improvement in signal to noise ratio (SNR) and carrier to noise ratio (CNR) by SCM technique. Compared with T₂^*W images, SCM can improve SNR by a factor ranging from 1.87 to 2.47. Compared with T₂^* maps, SCM can improve SNR by a factor ranging from 3.85 to 33.31. Compared with T₂^*W images, SCM can improve CNR by a factor raging from 2.09 to 2.43. Compared with T₂^* maps SCM can improve CNR by a factor raging from 1.94 to 8.14. For a given noise level, the improvements of SNR and CNR depend mainly on the original SNRs and CNRs in T₂^*W images, respectively. In vivo experiments confirmed the results of the first simulation study. The results of the second simulation study suggest that more echoes are used to generate SCM, and higher SNR and CNR can be achieved in SCM. In conclusion, SCM can provide improved morphological evaluation of T₂^*W MR images for renal cancer by unveiling fine structures which are ambiguous or invisible in the corresponding T₂^*W MR images and T₂^* maps. What is more, in practical application, for a fixed total sampling time, one should increase the number of echoes as much as possible to achieve SCMs with better SNR and CNR.     

Effects of L-spin longitudinal quadrupolar relaxation in heteronuclear recoupling and S-spin magic-angle spinning NMR

In experiments on S–L heteronuclear spin systems with evolution of the S-spin magnetization under the influence of a quadrupolar nucleus (L-spin), effects of longitudinal quadrupolar (T_1Q) relaxation of the L-spin coherence on the sub-millisecond time scale have been documented and explored, and methods for minimizing their effect have been demonstrated. The longitudinal relaxation results in heteronuclear dephasing even in the reference signal S₀ of S{L} REDOR, REAPDOR, RIDER, or SPIDER experiments, due to T_1Q-relaxation of the transiently generated S_yL_z coherence, reducing or even eliminating the observable dephasing ΔS. Pulse sequences for measuring an improved reference signal S₀₀ with minimal heteronuclear recoupling but the same number of pulses as for S₀ and S have been demonstrated. From the observed intensity ΔS₀ = S₀₀ − S₀ and the SPIDER signal ΔS/S₀, T_1Q can be estimated. Accelerated decays analogous to the dipolar S₀ curves will occur in T₂ measurements for J-coupled S–L spin pairs. Even in the absence of recoupling pulses, fast T_1Q relaxation of the unobserved nucleus shortens the transverse relaxation time T_2S,MAS of the observed nucleus, in particular at low spinning frequencies, due to unavoidable heteronuclear dipolar evolution during a rotation period. The observed spinning-frequency dependence of T_2S,MAS matches the theoretical prediction and may be used to estimate T_1Q. The effects are demonstrated on several ¹³C{¹⁴N} spin systems, including an arginine derivative, the natural N-acetylated polysaccharide chitin, and a model peptide, (POG)₁₀.     

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.     

What causes the hyperintense T2-weighting and increased short T2 signal in the corticospinal tract?

The corticospinal tract (CST) appears hyperintense on both T₂-weighted images and myelin water maps. Here, an extended multiecho T₂ relaxation sequence with echoes out to 1120 ms was used to characterize the longer T₂ times present in the CST. The T₂ distribution from the CST was compared to other white matter structures in 14 healthy subjects. The intra-/extracellular T₂ peak of the CST was broadened relative to other white matter structures and often split into two distinct peaks. In the CST, it appeared that the intracellular and extracellular water environments had unique T₂ times, causing the intracellular water peak to be pushed down into the myelin water T₂ regime and the extracellular peak to be pushed up to longer T₂ times. The conventional myelin water T₂ limits of 5-40 ms resulted in an artificial increase in myelin water fraction (MWF), causing the CST to be bright on myelin water images. When the upper limit for MWF was decreased to 25 ms, the CST regions exhibited MWF values similar to those found for adjacent anterior and posterior regions. The CST has unique magnetic resonance characteristics, which should be taken into consideration when being examined, especially when compared to pathological tissue.     

Directional behavior of nuclear quadrupole resonance in YBa2Cu3O6

Powder samples of YBa₂Cu₃O₆ were magnetically aligned and the anisotropies in the systems were studied by means of Cu(1) nuclear quadrupole resonance (NQR) in the absence of external magnetic fields. Our room temperature measurements of the NQR lineshapes and the spin–lattice and spin–spin relaxation times as a function of the aligning magnetic field indicate that full microscopic alignment can be achieved by using a magnetic field of about 4.7 T, for which doublet line patterns arising from a hyperfine splitting were observed.     

Changes in Porcine Muscle Water Characteristics during Growth—An in Vitro Low-Field NMR Relaxation Study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field ¹H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T₂ relaxation data imparted the existence of three distinct water populations, T_2b, T₂₁, and T₂₂, with relaxation times of approximately 1–10, 45–120, and 200–500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T₂₁. It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T₂₁, during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T₂₁ time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

Methods for correlating T1ρ and FID components in wideline H NMR studies of motionally heterogeneous polymer systems

We address the problem of correlating the observed FID and T_1ρ components in wideline ¹H relaxation measurements of motionally heterogeneous polymers, and show that different methods of data treatment can highlight different aspects of the correlations present. For a sample of polypropylene we find that the T_1ρ relaxation behaviour is driven by relaxation associated with the intermediate FID component, which strongly suggests a motionally inhomogeneous amorphous region in the sample.     

Flip-back, an old trick to face highly contrasted relaxation times: application in the characterization of pharmaceutical mixtures by CPMAS NMR

The ¹³C–¹H CPMAS with flip-back pulse NMR experiment is revisited in view of applications to pharmaceutical mixtures. The analysis of the kinetics of relaxation and CP transfer with and without the flip-back pulse shows that a significant gain in ¹³C signal can be expected (thus in experimental time) from the flip-back pulse for protons with long T₁. The gain is of the order of T₁ of the protons expressed in seconds. The experiment is applied on samples with highly contrasted spin-lattice relaxation times T₁ for protons, situation encountered in pharmaceutical mixtures. The application of the flip-back increases significantly the relative signal intensity of the component with the longer T₁, making this component detectable even after using short recycle delays. Therefore, this CPMAS with flip-back experiment could be used routinely to get ¹³C CPMAS NMR spectra of mixtures in constant experimental time and signal-to-noise ratio without the need for optimization of the recycle delays, and for whatever may be the degree of crystallinity of the active principal ingredient (API) and/or excipients.     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

Magnetotransport and magnetotunneling in single-layer, two-layer, and three-layer Bi2Sr2Can−1CunOz (n=1,2,3) single crystals

In continuous magnetic fields H up to 28 T, we have studied the out-of-plane transport properties and tunneling characteristics of high-quality nondoped single crystals of the Bi-cuprate family: Bi₂Sr₂CuO_6+δ (Bi2201), Bi₂Sr₂CaCu₂O_8+δ (Bi2212) and Bi₂Sr₂Ca₂Cu₃O_10+δ (Bi2223) grown by an identical method. For all compounds the out-of-plane magnetotransport ρ_c(H) is negative in the temperature region where ρ_c(T) shows in the normal state a semiconducting-like temperature dependence. The negative magnetoresistance of ρ_c corresponds to the suppression of the semiconducting temperature dependence of ρ_c(T) which is found to be isotropic. For the Bi2201 compound, where the normal state can be reached in the available magnetic fields (28 T), a nearly complete suppression of the low-temperature upturn in ρ_c(T) is observed in the highest magnetic fields with a tendency towards a metallic behavior down to the lowest temperatures (0.4 K). Using the break-junction technique, especially for the Bi2212 and Bi2232 compounds, a clear superconducting gap structure can be observed. Both for temperatures above the critical temperature and for magnetic fields above the upper critical field, a pseudogap structure remains present in the tunneling spectra. The applied magnetic fields yield a stronger suppression of the superconducting state compared to that of the normal-state gap structures as manifested in ρ_c(T) transport and tunneling.     

Regional variations in MR relaxation of hip joint cartilage in subjects with and without femoralacetabular impingement

The objective of this study was to analyze regional variations of magnetic resonance (MR) relaxation times (T_1ρ and T₂) in hip joint cartilage of healthy volunteers and subjects with femoral acetabular impingement (FAI). Morphological and quantitative images of the hip joints of 12 healthy volunteers and 9 FAI patients were obtained using a 3 T MR scanner. Both femoral and acetabular cartilage layers in each joint were semi-automatically segmented on sagittal 3D high-resolution spoiled gradient echo (SPGR) images. These segmented regions of interest (ROIs) were automatically divided radially into twelve equal sub-regions (30⁰ intervals) based on the fitted center of the femur head. The mean value of T_1ρ/T₂ was calculated in each sub-region after superimposing the divided cartilage contours on the MR relaxation (T_1ρ/T₂) maps to quantify the relaxation times. T_1ρ and T₂ relaxation times of the femoral cartilage were significantly higher in FAI subjects compared to healthy controls (39.9 ± 3.3 msec in FAI vs. 35.4 ± 2.3 msec in controls for T_1ρ (P = 0.0020); 33.9 ± 3.1 msec in FAI vs. 31.1 ± 1.7 msec in controls for T₂ (P = 0.0160)). Sub-regional analysis showed significantly different T_1ρ and T₂ relaxation times in the anterior-superior region (R9) of the hip joint cartilage between subjects with FAI and healthy subjects, suggesting possible regional differences in cartilage matrix composition between these two groups. Receiver operating characteristic (ROC) analysis showed that sub-regional analysis in femoral cartilage was more sensitive in discriminating FAI joint cartilage from that of healthy joints than global analysis of the whole region (T_1ρ: area under the curve (AUC) = 0.981, P = 0.0001 for R9 sub-region; AUC = 0.901, P = 0.002 for whole region; T₂: AUC = 0.976, P = 0.0005 for R9 sub-region; AUC = 0.808, P = 0.0124 for whole region). The results of this study demonstrated regional variations in hip cartilage composition using MR relaxation times (T_1ρ and T₂) and suggested that analysis based on local regions was more sensitive than global measures in subjects with and without FAI.     

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.     

Use of NMR Relaxometry to identify frankfurters of different meat sources

ABSTRACT

Frankfurters are categorised as ready to eat meat products and are prepared by using different meat sources including beef, chicken, turkey or pork or mixtures of them. Due to cost and feasibility, it is very common to adulterate beef-, chicken- and turkey-based frankfurters with pork meat. Since pork is not consumed by some part of the population due to religion, it is important to identify pork frankfurters based on easy quality control methods. In this study, NMR Relaxometry was used to differentiate four different frankfurter types based on their relaxation times. Relaxation measurements were conducted on three permanent field benchtop NMR spectrometers (13.52/20.34/22.35?MHz) and also using an FFC Relaxometer at a frequency range of 40?kHz–8.86?MHz. Physical properties of frankfurters such as moisture and solid fat contents, water activity (a_w) and hardness values were also measured. Results showed that among the permanent field systems, 22.34?MHz was the best to differentiate frankfurters based on both T₁ and T₂ relaxation times. FFC experiments also showed that the dependence of T₁ with respect to frequency follows a well fitted power law behaviour throughout the whole frequency range (R²?>?0.97) and the highest difference on T₁ was observed at the lowest frequency of 40?kHz. Thus the results of the study showed that NMR Relaxometry has the potential to discriminate frankfurters of different meat origin. Further studies are needed to detect the authenticity of the type of mixture in frankfurters.