Transverse relaxation mechanisms in articular cartilage

Relaxation rates in the rotating frame (R1rho) and spin-spin relaxation rates (R2) were measured in articular cartilage at various orientations of cartilage layer to the static magnetic field (B0), at various spin locking field strengths and at two different static magnetic field strengths. It was found that R1rho in the deep radial zone depended on the orientation of specimens in the magnet and decreased with increasing the spin locking field strength. In contrast, R1rho values in the transitional zone were nearly independent of the specimen orientation and the spin locking field strength. Measurements of the same specimens at 2.95 and 7.05 T showed an increase of R1rho and most R2 values with increasing B0. The inverse B0 dependence of some R2 values was probably due to a multicomponent character of the transverse magnetization decay. The experiments revealed that the dominant T1rho and T2 relaxation mechanism at B0 < or = 3 T is a dipolar interaction due to slow anisotropic motion of water molecules in the collagen matrix. On average, the contribution of scalar relaxation due to rapid proton exchange in femoral head cartilage at 2.95 T is about 6% or less of the total R1rho at the spin locking field of 1000 Hz.     

Evaluation of water content by spatially resolved transverse relaxation times of human articular cartilage

Non-invasive assessment of cartilage properties, specifically water content, could prove helpful in the diagnosis of early degenerative joint diseases. Transverse relaxation times T(2) of human articular cartilage (34 cartilage slices of three donors) were measured on a pixel-by-pixel basis in a clinical whole body MR system in vitro. In vivo feasibility to measure quantitative T(2) maps was shown for human patellar cartilage. The relaxation times of cartilage with collagen in the radial zone oriented perpendicular to the magnetic field increased from approximately 10 ms near the bone to approximately 60 ms near the articular surface. Cartilage water content of the tibial plateau and femoral condyles could be determined from the correlation with T(2) (R(2) = 0.71) with an error of approximately 2 wt.%. In vivo, directional variation would need to be considered. If confirmed in vivo, T(2) measurements could potentially serve as a non-invasive tool for the evaluation of the status and distribution of water content in articular cartilage.     

Dynamics of the biopolymers in articular cartilage studied by magic angle spinning NMR

To understand the viscoelastic properties of cartilage tissue and for the development of tissue-engineered cartilage, we have studied the physicochemical properties of bovine nasal and pig articular cartilage by¹³C nuclear magnetic resonance (NMR) methods. The major macromolecular components of cartilage can be investigated individually by applying¹³C high-resolution (HR) NMR with scalar decoupling (for the polysaccharide component) and solid-state NMR with dipolar decoupling (for the collagen component). Partially resolved NMR spectra of the cartilage polysaccharides can be obtained by HR¹³C NMR indicating that these polysaccharides are highly mobile. Resonance lines have been assigned to chondroitin sulfate, the most mobile component of cartilage. To characterize time scales of molecular motions, we have measuredT ₁ andT ₂ relaxation times as a function of temperature and analyzed these data by means of a broad distribution of molecular correlation times. Typical correlation times for the large amplitude motions of chondroitin sulfate are of the order of 0.1–10 ns. For the detection and dynamical characterization of the cartilage collagen cross-polarization magic angle spinning (CP MAS) and high-power decoupling are indispensable.¹³C CP MAS spectra of cartilage are dominated by resonances from rigid collagen, while only low-intensity signals from the polysaccharides are observed. The good sensitivity at a magnetic field strength of 17.6 T allows the site-specific investigation of cartilage collagen dynamics by two-dimensional NMR methods. The cartilage collagen is essentially rigid with low-amplitude segmental motions on the fast time scale. Considering the high water content of cartilage and the almost isotropic mobility of the chondroitin sulfate molecules it is remarkable how little this affects the collagen dynamics. The dynamics of cartilage macromolecules is broadly distributed from almost completely rigid to highly mobile, which lends cartilage its mechanical strength and shock-absorbing properties.     

Investigation of laminar appearance of articular cartilage by means of magnetic resonance microscopy

Magnetic resonance (MR) images and relaxation and diffusion maps of articular cartilage were obtained to explain discrepancies in its MR appearance. Porcine specimens were studied only by MR microscopy. For human specimens a combination of MR microscopy and large-scale MR imaging was used. Common features in the laminar structures of human and porcine samples are described. It was found that the decay of transverse magnetization was nonexponential with a rapidly decaying component which prevented construction of reliable proton-density maps. Dependence of T₂ values on the orientation of specimens in the magnetic field as well as magnetization transfer experiments supported the previous suggestions about a significant role of dipolar interaction with protons of collagen in the laminar appearance of articular cartilage. The loss of the laminar structure induced by rotation of the human cartilage specimen around the axis normal to its surface demonstrated nonuniform angular distribution of the collagen fibers within the layer.     

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.     

Ultrasonic propagation properties of articular cartilage at 100 MHz

A pilot study on articular cartilage assessed the contributions of individual matrix components to ultrasound propagation. The influence of collagen fibril orientation and collagen cross linking was also assessed. Sections of adult bovine articular cartilage cut both parallel and perpendicular to the articular surface were examined using the scanning laser acoustic microscope (SLAM) operating at an ultrasonic frequency of 100 MHz. A set of samples was evaluated that had been sequentially treated by enzymes to (1) remove 85% of the chondroitin sulfate; (2) remove remaining glycosaminoglycans, glycoproteins, and other noncollagen proteins, leaving only the collagen fibril network; and (3) disrupt the collagen intermolecular cross links. Two striking observations were made: a profound effect of the "preferred" collagen fibril orientation on ultrasonic speed and a marked increase in attenuation coefficient when intermolecular cross links were broken in the collagen.     

Dependencies of multi-component T2 and T1ρ relaxation on the anisotropy of collagen fibrils in bovine nasal cartilage

Both NMR spectroscopy and MRI were used to investigate the dependencies of multi-component T2 and T1ρ relaxation on the anisotropy of bovine nasal cartilage (BNC). The non-negative least square (NNLS) method and the multi-exponential fitting method were used to analyze all experimental data. When the collagen fibrils in nasal cartilage were oriented at the magic angle (55°) to the magnetic field B0, both T2 and T1ρ were single component, regardless of the spin-lock field strength or the echo spacing time in the pulse sequences. When the collagen fibrils in nasal cartilage were oriented at 0° to B0, both T2 and T1ρ at a spin-lock field of 500 Hz had two components. When the spin-lock field was increased to 1000 Hz or higher, T1ρ relaxation in nasal cartilage became a single component, even when the specimen orientation was 0°. These results demonstrate that the specimen orientation must be considered for any multi-component analysis, even for nasal cartilage that is commonly considered homogenously structured. Since the rapidly and slowly relaxing components can be attributed to different portions of the water population in tissue, the ability to resolve different relaxation components could be used to quantitatively examine individual molecular components in connective tissues.     

Mechanism of disease in early osteoarthritis: application of modern MR imaging techniques — a technical report

The application of biomolecular magnetic resonance imaging becomes increasingly important in the context of early cartilage changes in degenerative and inflammatory joint disease before gross morphological changes become apparent. In this limited technical report, we investigate the correlation of MRI T1, T2 and T1ρ relaxation times with quantitative biochemical measurements of proteoglycan and collagen contents of cartilage in close synopsis with histologic morphology. A recently developed MRI sequence, T1ρ, was able to detect early intracartilaginous degeneration quantitatively and also qualitatively by color mapping demonstrating a higher sensitivity than standard T2-weighted sequences. The results correlated highly with reduced proteoglycan content and disrupted collagen architecture as measured by biochemistry and histology. The findings lend support to a clinical implementation that allows rapid visual capturing of pathology on a local, millimeter level. Further information about articular cartilage quality otherwise not detectable in vivo, via normal inspection, is needed for orthopedic treatment decisions in the present and future.     

Anomalous NMR relaxation in cartilage matrix components and native cartilage: fractional-order models

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T(1) and T(2)). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T(1) and T(2) relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T(2) relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T(1) was observed in BNC. In the single-component gels, for T(2) measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T(2) NMR relaxation processes in biological tissues.     

Compressed sensing sodium MRI of cartilage at 7T: preliminary study

Sodium MRI has been shown to be highly specific for glycosaminoglycan (GAG) content in articular cartilage, the loss of which is an early sign of osteoarthritis (OA). Quantitative sodium MRI techniques are therefore under development in order to detect and assess early biochemical degradation of cartilage, but due to low sodium NMR sensitivity and its low concentration, sodium images need long acquisition times (15-25 min) even at high magnetic fields and are typically of low resolution. In this preliminary study, we show that compressed sensing can be applied to reduce the acquisition time by a factor of 2 at 7 T without losing sodium quantification accuracy. Alternatively, the nonlinear reconstruction technique can be used to denoise fully-sampled images. We expect to even further reduce this acquisition time by using parallel imaging techniques combined with SNR-improved 3D sequences at 3T and 7 T.     

Quantitative and qualitative assessment of articular cartilage in the goat knee with magnetization transfer imaging

We investigated the role of collagen in the magnetization transfer (MT) effect in contrast to other macromolecules. By means of phantoms made of collagen, chondroitin sulfate (CS) and albumin, MR parameters have been optimized in order to reduce the acquisition time and improve the sensitivity, as well as to minimize the contributions from CS and albumin to the MT induced signal attenuation. The same method was used to study cartilage ex vivo (bovine articular and nasal cartilage plugs) and in vivo (goat knee femoral chondyle). In phantom samples, the MT signal attenuation depended on the collagen concentration while contributions from the other macromolecules were found to be minimal. In average, analysis of MT images revealed a 25%, 35% and 30% signal attenuation in 10% w/v type I collagen gels, cartilage plugs, and cartilage from the weight-bearing areas of the goat knee, respectively. Biochemical data revealed that treatment of cartilage plugs with bacterial collagenase led to collagen depletion and correspondingly to a decrease of the MT response. In contrast, trypsin-induced proteoglycan loss in cartilage plugs did not alter the MT effect. A significant correlation was observed between the collagen content in these plugs and their respective MT ratios and the rate constant k for the exchange process bound versus free water. Finally, data obtained from in vivo MT measurement of the goat knee demonstrated that intra-articular injection of papain might not only cause degradation of proteoglycans but also a change in collagen integrity in a dose-dependent manner. We conclude that in vivo measurement of MT ratios gives quantitative and qualitative information on the collagen status and may be applied for the routine evaluation of normal and abnormal articular cartilage.     

Sodium visibility and quantitation in intact bovine articular cartilage using high field (23)Na MRI and MRS

Noninvasive methods of detecting cartilage degeneration can have an impact on identifying the early stages of osteoarthritis. Accurate measurement of sodium concentrations within the cartilage matrix provides a means for analyzing tissue integrity. Here a method is described for quantitating sodium concentration and visibility in cartilage, with general applications to all tissue types. The sodium concentration in bovine patellar cartilage plugs was determined by three different methods: NMR spectroscopy of whole cartilage plugs, NMR spectroscopy of liquefied cartilage in concentrated HCl, and inductively coupled plasma emission spectroscopy. Whole bovine patellae were imaged with relaxation normalized calibration phantoms to ascertain sodium concentrations inside the articular cartilage. Sodium concentrations in intact articular cartilage were found to range from approximately 200 mM on the edges to approximately 390 mM in the center, with an average of approximately 320 mM in five separate bovine patellae studied. In essence, we have created sodium distribution maps of the cartilage, showing for the first time, spatial variations of sodium concentration in intact cartilage. This average concentration measurement correlates very well with the values obtained from the spectroscopic methods. Furthermore, sodium was found to be 100% NMR visible in cartilage plugs. Applications of this method in diagnosing and monitoring treatment of osteoarthritis are discussed.     

Comparison of agarose and cross-linked protein gels as magnetic resonance imaging phantoms

Measurements of the magnetic field dependence of spin-lattice relaxation rates and the response of the water-proton signal intensity to off-resonance radio frequency fields show that the commonly used agarose phantom provides a less faithful representation for the magnetic response of tissue than does a cross-linked protein system. The origin of these differences lies in the structure and intramolecular dynamics of the macromolecular system used to make the gel. These distinctions will also cause differences in the magnetic response of the water spin system when paramagnetic relaxation agents or contrast agents are incorporated. Use of a thermally cross-linked bovine serum albumin phantom is suggested.     

Influence of topological transitions in a quantizing magnetic field and anisotropy of current carrier scattering by acoustic phonons on the longitudinal electrical conductivity of layered crystals with open fermi surfaces

It is demonstrated that the dependence of Fermi’s energy on the magnetic field causes a set of the Shubnikov – de Haas (SDH) oscillation frequencies to change, and their relative contribution to the total longitudinal conductivity of layered crystals depends on whether the scattering of current carriers is isotropic or anisotropic. Owing to the topological transition in a strong magnetic field, Fermi’s surface (FS) is transformed from open into closed one and is compressed in the magnetic field direction. Therefore, in an ultraquantum limit, disregarding the Dingle factor, the longitudinal electrical conductivity of the layered crystal tends to zero as a reciprocal square of the magnetic field for the isotropic scattering and as a reciprocal cube of the magnetic field for the anisotropic scattering. All calculations are performed in the approximation of relaxation time considered to be constant versus the quantum numbers for the isotropic scattering and proportional to the longitudinal velocity of current carriers for the anisotropic scattering.     

A quantitative analysis of recombination data in high magnetic fields

Magnetic field effects on the hydrogen abstraction reaction of 4-methoxybenzophenone with thiophenol in several solvents of different viscosity have been reported, and the observed magnetic field dependence was explained as caused by the Δg and a polarized initial triplet radical pair state. The present work reports a quantitative analysis of the data based on a recently derived general analytical formula. It is found that the observed magnetic field dependence can be explained as originating from an unpolarized triplet state, if both the coherent mixing caused by different g values of the two radicals and the incoherent mixing due to spin relaxation are included. Several different expressions for the magnetic field dependence of the longitudinal and transverse relaxation rates were applied. Rather surprisingly, the different models gave almost identical fits. However, the values obtained of the microscopic parameters depended significantly on the model. Physically sensible parameter values were obtained only when the complete magnetic field dependence of the two relaxation times were used. For this model it was found that both the anisotropy factor of the g tensors and the diffusion coefficient agreed with expectations.     

Raman analysis of proteoglycans simultaneously in bone and cartilage

Bone and cartilage are connective tissues with distinct organic matrix (collagen and non‐collagenous proteins) composition facilitating their biological function. Proteoglycans (PGs), a member of the non‐collagenous proteins fulfill functions that are determined by both their core protein and their glycosaminoglycan chains. The purpose of the present study was to identify Raman bands that are representative of PG concentration and may be used in both bone and cartilage tissues. To achieve this goal, we analyzed a series of reference PGs and collagens, as well as turkey leg tendon to verify the laser polarization independency of the identified bands. Additionally, the applicability of these bands in both cartilage and bone tissue simultaneously was tested in a healthy femoral head by Raman imaging and hierarchical cluster analysis to describe the distribution of PGs at the micron level from articular cartilage to subchondral bone. The results of the study show that the Raman band ~1375 cm⁻¹ can be used as a PGs marker band in both cartilage and bone. Moreover, articular cartilage has a lower content of organic matrix (mostly type II collagen), while the middle and deep transitional zone haves a higher concentration of PGs. The calcified cartilage is characterized by a lower content of PGs and total organic matrix (estimated from the integrated area of the amide III band). Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of a longitudinal magnetic field on spin injection and detection in InAs/GaAs quantum dot structures

Effects of a longitudinal magnetic field on optical spin injection and detection in InAs/GaAs quantum dot (QD) structures are investigated by optical orientation spectroscopy. An increase in the optical and spin polarization of the QDs is observed with increasing magnetic field in the range 0-2?T, and is attributed to suppression of exciton spin depolarization within the QDs that is promoted by the hyperfine interaction and anisotropic electron-hole exchange interaction. This leads to a corresponding enhancement in spin detection efficiency of the QDs by a factor of up to 2.5. At higher magnetic fields, when these spin depolarization processes are quenched, the electron spin polarization in anisotropic QD structures (such as double QDs that are preferably aligned along a specific crystallographic axis) still exhibits a rather strong field dependence under non-resonant excitation. In contrast, such a field dependence is practically absent in more 'isotropic' QD structures (e.g.?single QDs). We attribute the observed effect to stronger electron spin relaxation in the spin injectors (i.e.?wetting layer and GaAs barriers) of the lower-symmetry QD structures, which also explains the lower spin injection efficiency observed in these structures.     

Dynamics of nuclear polarization in InGaAs quantum dots in a transverse magnetic field

The time-resolved Hanle effect is examined for negatively charged InGaAs/GaAs quantum dots. Experimental data are analyzed by using an original approach to separate behavior of the longitudinal and transverse components of nuclear polarization. This made it possible to determine the rise and decay times of each component of nuclear polarization and their dependence on transverse magnetic field strength. The rise and decay times of the longitudinal component of nuclear polarization (parallel to the applied field) were found to be almost equal (approximately 5 ms). An analysis of the transverse component of nuclear polarization shows that the corresponding rise and decay times differ widely and strongly depend on magnetic field strength, increasing from a few to tens of milliseconds with an applied field between 20 and 100 mT. Current phenomenological models fail to explain the observed behavior of nuclear polarization. To find an explanation, an adequate theory of spin dynamics should be developed for the nuclear spin system of a quantum dot under conditions of strong quadrupole splitting.     

关节软骨内胶原纤维各向异性的红外光谱学显微成像研究

福尔马林溶液对于固化关节软骨组织、防止在长时间测量过程中组织的分解退化起到很好的作用,但对福尔马林溶液浸泡后软骨组织的结构变化(固化)过程及其胶原纤维各向异性的改变却鲜有研究。采用傅里叶变换红外光谱显微成像技术与偏振技术相结合的方法,通过关节软骨内胶原纤维(蛋白)的红外光谱特征吸收峰(Amide Ⅰ,Amide Ⅱ带)的吸光度随福尔马林溶液浸泡时间及偏光角度的变化来研究福尔马林溶液对软骨组织结构即胶原纤维各向异性的影响,并利用与各向异性方程拟合得到的决定系数(R2)对胶原蛋白纤维各向异性程度进行表征。研究发现,关节软骨Amide Ⅰ和Amide Ⅱ带的各向异性随着福尔马林浸泡时间的增长而愈加明显(Amide Ⅰ带变化尤为明显),说明福尔马林溶液中甲醛分子诱发了胶原蛋白分子新的交联,最终获得较好的固化效果,有利于关节软骨的各向异性分析。本研究将为今后关节软骨样本的制备、储存及各向异性研究提供参考。     

Anisotropy of spin splitting and spin relaxation in lateral quantum dots

Inelastic spin relaxation and spin splitting epsilon(s) in lateral quantum dots are studied in the regime of strong in-plane magnetic field. Because of both the g-factor energy dependence and spin-orbit coupling, epsilon(s) demonstrates a substantial nonlinear magnetic field dependence similar to that observed by Hanson et al. [Phys. Rev. Lett. 91, 196802 (2003)]. It also varies with the in-plane orientation of the magnetic field due to crystalline anisotropy of the spin-orbit coupling. The spin relaxation rate is also anisotropic, the anisotropy increasing with the field. When the magnetic length is less than the "thickness" of the GaAs dot, the relaxation can be an order of magnitude faster for B ||[100] than for B || [110].