Quantitative MRI using T1ρ and T2 in human osteoarthritic cartilage specimens: correlation with biochemical measurements and histology

Purpose

A direct correlation between T_1ρ, T₂ and quantified proteoglycan and collagen contents in human osteoarthritic cartilage has yet to be documented. We aimed to investigate the orientation effect on T_1ρ and T₂ values in human osteoarthritic cartilage and to quantify the correlation between T_1ρ, T₂ vs. biochemical composition and histology in human osteoarthritic cartilage.

Materials and methods

Thirty-three cartilage specimens were collected from patients who underwent total knee arthroplasty due to severe osteoarthritis and scanned with a 3T MR scanner for T_1ρ and T₂ quantification. Nine specimens were scanned at three different orientations with respect to the B₀: 0°, 90° and 54.7°. Core punches were taken after MRI. Collagen and proteoglycan contents were quantified using biochemical assays. Histology sections were graded using Mankin scores. The correlation between imaging parameters, biochemical contents and histological scores were studied.

Results

Both mean T_1ρ and T₂ at 54.7° were significantly higher than those measured at 90° and 0°, with T_1ρ showing less increase compared to T₂. R_1ρ (1/T_1ρ) values had a significant but moderate correlation with proteoglycan contents (R=.45, P=.002), while R₂ (1/T₂) was not correlated with proteoglycan. No significant correlation was found between relaxation times (T_1ρ or T₂) and collagen contents. The T_1ρ values of specimen sections with high Mankin scores were significantly higher than those with low Mankin scores (P<.05).

Conclusions

Quantitative MRI has a great potential to provide noninvasive imaging biomarkers for cartilage degeneration in osteoarthritis.     

Determination of T1ρ values for head and neck tissues at 0.1 T: a comparison to T1 and T2 relaxation times

In order to optimize head and neck magnetic resonance (MR) imaging with the spin-lock (SL) technique, the T₁ρ relaxation times for normal tissues were determined. Furthermore, T₁ρ was compared to T₁ and T₂ relaxation times. Ten healthy volunteers were studied with a 0.1 T clinical MR imager. T₁ρ values were determined by first measuring the tissue signal intensities with different locking pulse durations (TL), and then by fitting the signal intensity values to the equation with the least-squares method. The T₁ρ relaxation times were shortest for the muscle and tongue, intermediate for lymphatic and parotid gland tissue and longest for fat. T₁ρ demonstrated statistically significant differences (p < 0.05) between all tissues, except between muscle and tongue. T₁ρ values measured at locking field strength (B1L) of 35 μT were close to T₂ values, the only exception being fat tissue, which showed T₁ρ values much longer than T₂ values. Determination of tissue relaxation times may be utilized to optimize image contrast, and also to achieve better tissue discrimination potential, by choosing appropriate imaging parameters for the head and neck spin-lock sequences.     

An average-magnetization analysis of R 1ρ relaxation outside of the fast exchange limit

Approximate expressions for the NMR spin relaxation rate constant in the rotating frame of reference R _1ρ are derived for two-site chemical exchange by consideration of the evolution of the average density operator using the stochastic Liouville equation. R _1ρ is obtained as a linearized approximation to the largest (least negative) eigenvalue of the matrix describing the evolution of the average density operator in the long-term limit. The expressions obtained are more accurate than existing expressions when exchange is not fast and the populations of the exchanging sites are close to equal. The new expressions for R _1ρ facilitate the interpretation of chemical exchange phenomena in proteins and other biological macromolecules.     

Bi-phase age-related brain gray matter magnetic resonance T1ρ relaxation time change in adults

ObjectivesTo investigate normative value and age-related change of brain magnetic resonance T1ρ relaxation at 1.5 T.MethodsThis study was approved by the local ethical committee with participants' written consent obtained. There were 42 adults healthy volunteers, including 20 males (age: 41 ± 16 (mean ± standard deviation) years, range: 22–68 years,) and 22 females (age: 39 ± 15 years, range: 21–62 years). MRI was performed at 1.5 T using 3D fluid suppressed turbo spin echo sequence. Regions-of-interests (ROIs) were obtained by atlas-based tissue segmentation and T1ρ was calculated by fitting the mean value to mono-exponential model. Correlation between T1ρ relaxation of brain gray matter regions and age was investigated.ResultsA regional difference among individual gray matter areas was noted; the highest values were observed in the hippocampus (98.37 ± 5.37 ms, median: 97.88 ms) and amygdala (94.95 ± 4.34 ms, median: 94.73 ms), while the lowest values were observed in the pallidum (83.81 ± 5.49 ms, median: 83.77 ms) and putamen (83.93 ± 4.76 ms, median: 83.99 ms). Gray matter T1ρ values decreased slowly (mean slope: − 0.256) and significantly (p < 0.05) with age in gray matter for subjects younger than 40 years old, while for subjects older than 40 years old there was no apparent correlation between T1ρ relaxation and age. Global white matter measured T1ρ value of 88.65 ± 3.47 ms (median: 87.86 ms), and the correlation with age was not significant (p = 0.18).ConclusionGray matter T1ρ relaxation demonstrates a bi-phase change with age in adults of 22–68 years.     

Rapid acquisition strategy for functional T1ρ mapping of the brain

Functional T1ρ mapping has been proposed as a method to assess pH and metabolism dynamics in the brain with high spatial and temporal resolution. The purpose of this work is to describe and evaluate a variant of the spin-locked echo-planar imaging sequence for functional T1ρ mapping at 3 T. The proposed sequence rapidly acquires a time series of T1ρ maps with 4.0 second temporal resolution and 10 slices of volumetric coverage. Simulation, phantom, and in vivo experiments are used to evaluate many aspects of the sequence and its implementation including fidelity of measured T1ρ dynamics, potential confounds to the T1ρ response, imaging parameter tradeoffs, time series analysis approaches, and differences compared to blood oxygen level dependent functional magnetic resonance imaging. It is shown that the high temporal resolution and volumetric coverage of the sequence are obtained with some expense including underestimation of the T1ρ response, sensitivity to T1 dynamics, and reduced signal-to-noise ratio. In vivo studies using a flashing checkerboard functional magnetic resonance imaging paradigm suggest differences between T1ρ and blood oxygen level dependent activation patterns. Possible sources of the functional T1ρ response and potential sequence improvements are discussed. The capability of T1ρ to map whole-brain pH and metabolism dynamics with high temporal and spatial resolution is potentially unique and warrants further investigation and development.     

Investigation of the parametric excitation and relaxation of phonons in antiferromagnetic α-Fe2O3

Parametric excitation of magnetoelastic waves was investigated in the easy-plane antiferromagnet α-Fe₂O₃ by parallel and perpendicular microwave pumping over a wide range of frequencies, magnetic fields, and temperatures, and the parametric resonance thresholds were measured. The frequencies of the natural magnetoelastic vibrations of the sample were investigated as a function of the magnetic field and temperature. The results of the measurements were used to calculate the parameters of the magnetoelastic wave spectrum and the rate of relaxation of the excited quasi-phonons. Possible mechanisms for quasi-phonon damping were analyzed.     

Transport properties and the anisotropy of Ba1 − x K x Fe2As2 single crystals in normal and superconducting states

The transport and superconducting properties of Ba_{1 ? x} K _x Fe₂As₂ single crystals with T _c ≈ 31 K were studied. Both in-plane and out-of-plane resistivity was measured by a modified Montgomery method. The in-plane resistivity is almost the same for all studied samples, unlike the out-of-plane resistivity, which differs considerably. We have found that the resistivity anisotropy γ = ρ _c /ρ _ab is almost independent of temperature and lies in the range 10–30 for the studied samples. This indicates the extrinsic nature of high out-of-plane resistivity, which may be due to the presence of flat defects along Fe-As layers in the samples. This statement is supported by comparatively small effective mass anisotropy, obtained from the upper critical field measurements, and from the observation of the so-called “Friedel transition,” which indicates the existence of some disorder in the samples in the c-direction.     

Thermal expansion anisotropy of β-TlInS2 crystals in the course of phase transitions

Basing on the thermal expansion studies performed for β-TlInS₂ crystals in the course of their phase transitions, we have found that the crystals aged for one year are composed from at least two polytypes, which undergo phase transitions at different temperatures. The detailed analysis of anisotropy of the thermal expansion demonstrates that all of the diagonal components of the thermal expansion tensor associated with the eigensystem have almost the same modules but differ by their signs. This leads to appearance of an elliptical conical surface of zero thermal expansion. The orientation of this surface does not depend on the temperature in the temperature interval under study. We have also found that the thermal expansion coefficients along the crystallographic a and b axes are close to zero.     

Effect of excitation intensity and electric field on the photoconductivity relaxation in CdxHg1−x Te/GaAs polycrystalline layers

The photoconductivity relaxation and the stationary photoconductivity in the n-Cd_0.8Hg_0.2Te compensated polycrystalline layers at T=300 K have been investigated as a function of the light intensity and the strength of applied electric field E. It is demonstrated that, at low excitation intensities, the saturation of stationary photoconductivity and a decrease in the relaxation time with an increase in E are caused by the minority carrier extraction. The effect of minority carrier extraction is analyzed with due regard for the internal electric field of potential barriers in intergranular layers. It is assumed that the features of nonequilibrium-carrier recombination, which proceeds through several channels and depends on the excitation intensity and extraction electric field strength, can stem from the polycrystalline structure of the Cd_0.8Hg_0.2Te layers.     

The low-temperature 13C and 2H spectra and relaxation rates of methyl groups depend on the azimuth of B0 in the molecular frame. Those of 1H do not. Why?

It is shown that the answer to the question asked in the title is: Because the axial symmetry axes of the H-H dipolar coupling tensors in a -CH3 group are perpendicular to the (assumed) threefold axis of the group. By contrast, those of the 13C-H dipolar and 2H quadrupolar coupling tensors are not. The use of "symmetry adapted" spin functions and of a symmetry adapted form of the (dipolar) coupling Hamiltonian greatly simplifies the analysis.     

Effect of relaxation rate on population distribution, EIT and refraction in Λ and V systems

In the three-level Λ-type and V-type systems, we find that the same pump-effect parameter R\left(=\dfrac{2|V_{c}|^{2}γ}{(ω_{ac}-ω_{c})^{2}+γ^{2}}\right) determines the population distributions, while the probe field leads to population fluctuations near the absorption peaks. With the increasing of the relaxation rate γ, the population distributions are shifted and their fluctuation amplitudes decrease. At the same time the electromagnetically induced transparency window becomes a broadened absorption peak, and the dispersion at the zero probe detuning changes from positive to negative. Large population fluctuation and non-fluctuation observed in different systems are attributed to the different relaxation rates.     

The effect of frenkel defects on the electronic structure of 1T−TiSe2

Using a tight binding formalism the wave vector resolved electronic density of states has been calculated in the coherent potential approximation for an 1 T–TiSe₂ crystal containing Frenkel defects. Additional structure originating from disorder is discussed. An extra peak in the A direction at 1.5 eV binding energy can be traced back to a resonance caused by titanium vacancies.     

Bilaminar pattern of tibial condyle cartilage layer on the fat-suppressed 3D gradient echo images: artifact or structural and biochemical difference in composition of cartilage?

The purpose of this study was to examine if an unusual bilaminar pattern of lateral tibial condyle cartilage layer on the fat-suppressed three-dimensional (3D) spoiled gradient echo sequence is artifactual or correlates with structural and/or biochemical composition of cartilage. The laminar appearance of the lateral tibial condyle cartilage layer was studied on fat-suppressed 3D spoiled gradient echo MR images of the knee joint in 67 patients (mean age: 28y) performed at 1.0 Tesla. After i.v. administration of gadopentetate dimeglumine, diffusion of the contrast media into cartilage layer was qualitatively analysed over time on inversion recovery spin echo images of knee joints of five asymptomatic volunteers (mean age: 25y). In a patient with osteosarcoma and total knee replacement, MR examination of cartilage layer of lateral tibial plateau was compared with histologic specimens stained with Safranin-O, demonstrating proteoglycan distribution in cartilage. The retrospective analysis of 67 knee joints revealed a bilaminar appearance of lateral tibial condyle cartilage layer in the gradient echo images in the majority of cases (81%) with a statistically significant tendency to a trilaminar pattern in patients older than 20 years. With i.v. contrast administration, the contrast enhancement was only observed in the superficial zone of tibial cartilage layer. Histologic specimens in one patient demonstrated a good correlation between thickness of proteoglycan-free and proteoglycan-rich laminae of lateral tibial condyle on Safranin-O staining with hyperintense and hypointense zones, respectively, on corresponding fat-suppressed 3D spoiled gradient echo images (correlation coefficient of 0.87). Bilaminar pattern of tibial condyle cartilage layer on fat-suppressed 3D spoiled gradient echo images in younger subjects is not an artifact or an intrachondral lesion, but it may represent a regional difference in composition of extracellular cartilage matrix possibly produced by a highly-oriented collagen fiber structure associated with a high concentration of proteoglycans in the middle and deep portion of the cartilage layer.     

Influence of solvent and intramolecular relaxation on dynamics of luminescence spectra in donor–acceptor complexes

The oscillator strengths for Rydberg states of a NaHe molecule are calculated using a semianalytic procedure with the l-coupling effect taken into account (due to the dipole potential of a core). This effect gives rise to nonzero oscillator strengths for transitions forbidden in the atomic model of molecular Rydberg states. The difference between calculations in terms of the atomic model and calculations with consideration of the dipole moment of a core is shown for allowed transitions.     

Low temperature vibrational relaxation of OD in the A2Σ, state

The vibrational relaxation of the A ²Σ state of OD has been studied in the low translational temperature environment of an argon free-jet (T_trans near 5 K). Using laser induced fluorescence (LIF), the absolute vibrational relaxation rate coefficients were measured for OD A²Σ (ν′) to be 7.1 ± 2.6 × 10^?11, 5.9 ± 1.4 × 10^?11, and 2.7 ± 1.1 × 10^?11 cm³ s^?1 for the ν = 3, 2 and 1 states, respectively. State-to-state relaxation rate coefficients were also obtained for the ν= 1, ? = 1 level going to ν= 0, ? levels in the A²Σ manifold. The rotational relaxation rate coefficient for ν= 1, ?= 1 in the A state of OD was found to be 9.6 ± 1.0 × 10^?11cm³s^?1. These values are consistent with values measured for OH A²Σ, and the total loss rates are near the capture rate coefficient value. The vibrational relaxation rate coefficients k_ν appear to be governed by the vibrational energy of the molecule rather then by interaction with nearby dissociative states such as the a⁴Σ state. The relative Einstein A factors for the A²σ (ν = 3) state of OD were determined and compared with the available calculated value.     

Depth and orientational dependencies of MRI T(2) and T(1ρ) sensitivities towards trypsin degradation and Gd-DTPA(2-) presence in articular cartilage at microscopic resolution

Depth and orientational dependencies of microscopic magnetic resonance imaging (MRI) T(2) and T(1ρ) sensitivities were studied in native and trypsin-degraded articular cartilage before and after being soaked in 1 mM Gd-DTPA(2-) solution. When the cartilage surface was perpendicular to B(0), a typical laminar appearance was visible in T(2)-weighted images but not in T(1ρ)-weighted images, especially when the spin-lock field was high (2 kHz). At the magic angle (55°) orientation, neither T(2)- nor T(1ρ)-weighted image had a laminar appearance. Trypsin degradation caused a depth- and orientational-dependent T(2) increase (4%-64%) and a more uniform T(1ρ) increase at a sufficiently high spin-lock field (55%-81%). The presence of the Gd ions caused both T(2) and T(1ρ) to decrease significantly in the degraded tissue (6%-38% and 44%-49%, respectively) but less notably in the native tissue (5%-10% and 16%-28%, respectively). A quantity Sensitivity was introduced that combined both the percentage change and the absolute change in the relaxation analysis. An MRI experimental protocol based on two T(1ρ) measurements (without and with the presence of the Gd ions) was proposed to be a new imaging marker for cartilage degradation.     

Elasticity of the B2 phase and the effect of the B1–B2 phase transition on the elasticity of MgO

A study of the high-pressure anisotropy of MgO was conducted using first-principles calculations based on density functional theory within the generalized gradient approximations. The pressure dependence of the elastic stiffness coefficients and the anisotropy parameters, in both B1 and B2 phases, shows that for high-hydrostatic compression the easiest deformation is the shear along (100) plane and the the material's response to deformation and to shearing strains is quite the same. According to the calculations of the velocities of propagation of elastic waves, we deduced that MgO develop an elastic anisotropy, especially, in the B1 phase. We present the B2 phase elastic properties which are not already studied under high pressure.     

The dependence of interfacial properties on the layer number in 1T′/2H-MoS2 van der Waals heterostructures

Metallic 1T′-MoS₂ monolayers are predicted to be efficient hole injection contacts for nanoelectronic devices composed of 2H-MoS₂ monolayers. The layer number can affect the physical properties of two-dimensional materials. In this paper, the dependence of the interfacial properties of 1T′/2H-MoS₂ van der Waals (vdW) heterojunctions on the layer number was studied using density functional theory. The calculation results show that 1T′-MoS₂ forms p-type contacts with 2H-MoS₂, and the p-type Schottky barrier height (SBH) is between -75 and 30 meV and depends on the number of 1T′-/2H-MoS₂ layers. Thus, the efficiency of 1T′-MoS₂ as a hole injection contact for 2H-MoS₂ can be tuned by the layer number. This work provides a method for tuning the contact-resistance in nanodevices composed of 2H-MoS₂.     

Comparison of dynamic mechanical and dielectric loss data on the β relaxation process in poly(ethylene terephthalate)

The dynamic mechanical and dielectric β loss peaks in poly(ethylene tereph-thalate) are shown not to be comparable. Only the dielectric data are internally consistent, and these are used to infer which conformational changes occur during commercial processing.     

MR T1ρ quantification of cartilage focal lesions in acutely injured knees: correlation with arthroscopic evaluation

Objective

Quantitative T₁ρ MRI has been suggested as a promising tool to detect changes in cartilage composition that are characteristic of cartilage damage and degeneration. The objective of this study was to evaluate the capability of MR T₁ρ to detect cartilage lesions as evaluated by arthroscopy in acutely ACL-injured knees and to compare with the Whole-Organ Magnetic Resonance Imaging Score (WORMS) using clinical standard MRI.

Method

Ten healthy controls (mean age 35) with no ACL injury or history of osteoarthritis (OA) and 10 patients with acute ACL injuries (mean age 39) were scanned at 3 Tesla (3 T). ACL patients underwent ACL reconstruction, where focal lesions were graded according to an Outerbridge grading system during arthroscopic evaluation. Normalized MR T₁ρ values (T₁ρ z-scores normalized to control values in matched regions) in full thickness, and superficial and deep layers of cartilage were compared between defined sub-compartments with and without focal lesions. Intraclass (ICC) correlation and the root mean square coefficient of variation (RMS-CV) were performed to evaluate the inter-observer reproducibility of T₁ρ quantification. Sub-compartments of cartilage were also evaluated using WORMS scoring and compared to their Outerbridge score respectively.

Results

The inter-observer ICC and the RMS-CV of the sub-compartment T₁ρ quantification were 0.961 and 3.9%, respectively. The average T₁ρ z-scores were significantly increased in sub-compartments with focal lesions compared to those without focal lesions and to the control cohort (p < 0.05).

Conclusion

Our results indicate that T₁ρ provided a better diagnostic capability than clinical standard MRI grading in detecting focal cartilage abnormalities after acute injuries. Quantitative MRI may have great potential in detecting cartilage abnormalities and degeneration non-invasively, which are occult with standard morphological MRI.