A unique anisotropic R2 of collagen degeneration (ARCADE) mapping as an efficient alternative to composite relaxation metric (R2 -R1 ρ ) in human knee cartilage study

Anisotropy of T2 and T1ρ relaxation time in articular cartilage at 3 T

PURPOSE

The anisotropy of R2 and R1ρ relaxation rates in articular cartilage contains information about the collagenous structure of the tissue. Here we determine and study the anisotropic and isotropic components of T2 and T1ρ relaxation parameters in articular cartilage with a clinical 3T MRI device. Furthermore, a visual representation of the topographical variation in anisotropy is given via anisotropy mapping.

METHODS

Eight bovine stifle joints were imaged at 22 orientations with respect to the main magnetic field using T2, continuous-wave (CW) T1ρ, and adiabatic T1ρ mapping sequences. Relaxation rates were separated into isotropic and anisotropic relaxation components using a previously established relaxation anisotropy model. Pixel-wise anisotropy values were determined from the relaxation-time maps using Michelson contrast.

RESULTS

The relaxation rates obtained from the samples displayed notable variation depending on the sample orientation, magnetization preparation, and cartilage layer. R2 demonstrated significant anisotropy, whereas CW-R1ρ (300 Hz) and CW-R1ρ (500 Hz) displayed a low degree of anisotropy. Adiabatic R1ρ was largely isotropic. In the deep cartilage regions, relaxation rates were generally faster and more anisotropic than in the cartilage closer to the tissue surface. The isotropic relaxation rate components were found to have similar values regardless of measurement sequence.

CONCLUSIONS

The fitted relaxation model for T2 and T1ρ demonstrated varying amounts anisotropy, depending on magnetization preparation, and studied the articular cartilage layer. Anisotropy mapping of full joints showed varying amounts of anisotropy depending on the quantitative MRI parameter and topographical location, and in the case of T2, showed systematic changes in anisotropy across cartilage depth.

Orientation dependent proton transverse relaxation in the human brain white matter: The magic angle effect on a cylindrical helix

PURPOSE

To overcome some limitations of previous proton orientation-dependent transverse relaxation formalisms in human brain white matter (WM) by a generalized magic angle effect function.

METHODS

A cylindrical helix model was developed embracing anisotropic rotational and translational diffusion of restricted molecules in WM, with the former characterized by an axially symmetric system. Transverse relaxation rates R₂ and R₂^∗ were divided into isotropic R₂ⁱ and anisotropic parts, R₂^a ∗ f(α,Φ - ε₀), with α denoting an open angle and ε₀ an orientation (Φ) offset from DTI-derived primary diffusivity direction. The proposed framework (Fit A) was compared to prior models without ε₀ on previously published water and methylene proton transverse relaxation rates from developing, healthy, and pathological WM at 3 T. Goodness of fit was represented by root-mean-square error (RMSE). F-test and linear correlation were used with statistical significance set to P ≤ 0.05.

RESULTS

Fit A significantly (P < 0.01) outperformed prior models as demonstrated by reduced RMSEs, e.g., 0.349 vs. 0.724 in myelin water. Fitted ε₀ was in good agreement with calculated ε₀ from directional diffusivities. Compared with those from healthy adult, the fitted R₂ⁱ, R₂^a, and α from neonates were substantially reduced but ε₀ increased, consistent with developing myelination. Significant positive (R₂ⁱ) and negative (α and R₂^a) correlations were found with aging (demyelination) in elderly.

CONCLUSION

The developed framework can better characterize orientation dependences from a wide range of proton transverse relaxation measurements in the human brain WM, thus shedding new light on myelin microstructural alterations at the molecular level.

Phase-shifted transverse relaxation orientation dependences in human brain white matter

This work aimed to demonstrate an essential phase shift ε 0 $$ {\varepsilon}_0 $$ for better quantifying R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ in human brain white matter (WM), and to further elucidate its origin related to the directional diffusivities from standard diffusion tensor imaging (DTI). ε 0 $$ {\varepsilon}_0 $$ was integrated into a proposed generalized transverse relaxation model for characterizing previously published R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ orientation dependence profiles in brain WM, and then comparisons were made with those without ε 0 $$ {\varepsilon}_0 $$ . It was theorized that anisotropic diffusivity direction ε $$ \varepsilon $$ was collinear with an axon fiber subject to all eigenvalues and eigenvectors from an apparent diffusion tensor. To corroborate the origin of ε 0 $$ {\varepsilon}_0 $$ , R 2 $$ {R}_2 $$ orientation dependences referenced by ε $$ \varepsilon $$ were compared with those referenced by the standard principal diffusivity direction Φ $$ \Phi $$ at b-values of 1000 and 2500 (s/mm² ). These R 2 $$ {R}_2 $$ orientation dependences were obtained from T 2 $$ {T}_2 $$ -weighted images (b = 0) of ultrahigh-resolution Connectome DTI datasets in the public domain. A normalized root-mean-square error ( NRMSE % $$ NRMSE\% $$ ) and an F $$ F $$ -test were used for evaluating curve-fittings, and statistical significance was considered to be a p of 0.05 or less. A phase-shifted model resulted in significantly reduced NRMSE % $$ NRMSE\% $$ compared with that without ε 0 $$ {\varepsilon}_0 $$ in quantifying various R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ profiles, both in vivo and ex vivo at multiple B 0 $$ {B}_0 $$ fields. The R 2 $$ {R}_2 $$ profiles based on Φ $$ \Phi $$ manifested a right-shifted phase ( ε 0 > 0 $$ {\varepsilon}_0>0 $$ ) at two b-values, while those based on ε $$ \varepsilon $$ became free from ε 0 $$ {\varepsilon}_0 $$ . For all phase-shifted R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ profiles, ε 0 $$ {\varepsilon}_0 $$ generally depended on the directional diffusivities by tan - 1 D ⊥ / D ∥ $$ {\tan}^{-1}\left({D}_{\perp }/{D}_{\parallel}\right) $$ , as predicted. In summary, a ubiquitous phase shift ε 0 $$ {\varepsilon}_0 $$ has been demonstrated as a prerequisite for better quantifying transverse relaxation orientation dependences in human brain WM. Furthermore, the origin of ε 0 $$ {\varepsilon}_0 $$ associated with the directional diffusivities from DTI has been elucidated. These findings could have a significant impact on interpretations of prior R 2 $$ {R}_2 $$ and R 2 * $$ {R}_2^{\ast } $$ datasets and on future research.

Adiabatically prepared spin-lock could reduce the R1ρ dispersion

Background

R_1ρ (or spin-lock) imaging is prone to artifacts arising from field inhomogeneities that may impact the R_1ρ quantification. Previous research has proposed two types of method to manage the artifacts in continuous-wave constant amplitude spin-lock, one is based on the composite block pulses to compensate for the field imperfections, another category uses adiabatic pulses in the R_1ρ pre-pulse to excite and reverse the magnetization (named adiabatic prepared approach). Although both methods have proved their efficiency in alleviating artifacts, we observed that the adiabatic pulse approach could produce much lower R_1ρ dispersion in human knee cartilage than the block pulse method (characterized by the R_1ρ difference ∆R_1ρ =11.4 Hz (from spin-lock field 50 to 500 Hz) for the block pulse method vs. ∆R_1ρ =4.5 Hz for the adiabatic pulse approach). Prompted by this observation, the purpose of this study was to investigate the underlying factors that may affect the R_1ρ dispersion through numerical simulations based on the two-pool exchanging Bloch-McConnell equations.

Methods

The effects of free water pool size P_a (from 0.80 to 0.95), chemical exchange rate k_b (from the bound to free water pool, ranged from 500 to 3,000 Hz), adiabatic pulse duration T_p (from 5.0 to 25 ms), and the chemical shift of the bound pool ppm_b (from 1.0 to 5.0 ppm) were examined on the degree of the R_1ρ dispersion for the two R_1ρ imaging methods.

Results

In general, the greater the ppm_b, k_b, T_p, and the smaller P_a, the more significant difference in R_1ρ dispersion between the block and adiabatic approaches, with the dispersion curve of the adiabatic method becoming flatter.

Conclusions

The adiabatic prepared approach may compromise the R_1ρ dispersion, the effect is determined by the combination of the tissue and radiofrequency (RF) pulse properties. It is suggested that care should be taken when using the adiabatically prepared approach to study R_1ρ dispersion.

Hydrated Collagen: Where Physical Chemistry, Medical Imaging, and Bioengineering Meet

It is well-known that collagen is the most abundant protein in the human body; however, what is not often appreciated is its fascinating physical chemistry and molecular physics. In this Perspective, we aim to expose some of the physicochemical phenomena associated with the hydration of collagen and to examine the role collagen's hydration water plays in determining its biological function as well as applications ranging from radiology to bioengineering. The main focus is on the Magic-Angle Effect, a phenomenon observed in Nuclear Magnetic Resonance (NMR) spectroscopy and Magnetic Resonance Imaging (MRI) of anisotropic collagenous tissues such as articular cartilage and tendon. While the effect has been known in NMR and MRI for decades, its exact molecular mechanism remains a topic of debate and continuing research in scientific literature. We survey some of the latest research aiming to develop a comprehensive molecular-level model of the Magic-Angle Effect. We also touch on other fields where understanding of collagen hydration is important, particularly nanomechanics and mechanobiology, biomaterials, and piezoelectric sensors.

A self-compensated spin-locking scheme for quantitative R1ρ dispersion MR imaging in ordered tissues

PURPOSE

To propose a self-compensated spin-locking (SL) method for quantitative R_1ρ dispersion imaging in ordered tissues.

METHODS

Two pairs of antiphase rotary-echo SL pulses were proposed in a new scheme with each pairs sandwiching one refocusing RF pulse. This proposed SL method was evaluated by Bloch simulations and experimental studies relative to three prior schemes. Quantitative R_1ρR dispersion imaging studies with constant SL duration (TSL = 40 ms) were carried out on an agarose (1-4% w/v) phantom and one in vivo human knee at 3 T, using six SL RF strengths ranging from 50 to 1000 Hz. The performances of these SL schemes were characterized with an average coefficient of variation (CV) of the signal intensities in agarose gels and the sum of squared errors (SSE) for quantifying in vivo R_1ρ dispersion of the femoral and tibial cartilage.

RESULTS

The simulations demonstrate that the proposed SL scheme was less prone to B₀ and B₁ field inhomogeneities. This theoretical prediction was supported by fewer image banding artifacts and less signal fluctuation signified by a reduced CV (%) on the phantom without R_1ρ dispersion (i.e., 4.04 ± 1.36 vs. 18.87 ± 4.46 or 6.66 ± 2.92 or 5.71 ± 2.05 for others), and further by mostly decreased SSE (*10^-3) for characterizing R_1ρ dispersion of the femoral (i.e., 0.3 vs. 1.2 or 0.4 or 0.1) and tibial (i.e., 0.4 vs. 7.2 or 3.2 or 2.8) cartilage.

CONCLUSION

The proposed SL scheme is less sensitive to B₀ and B₁ field artifacts for a wide range of SL RF strengths and thus more suitable for quantitative R_1ρ dispersion imaging in ordered tissues.

Characterization of anisotropic T2W signals from human knee femoral cartilage: The magic angle effect on a spherical surface

The aim of the current study was to propose a generalized magic angle effect (gMAE) function for characterizing anisotropic T2W signals of human knee femoral cartilage with a spherical surface in clinical studies. A gMAE model function f(α, ε) was formulated for an orientation-dependent (ε) transverse T₂ (i.e., 1/R₂ ) relaxation in cartilage assuming an axially symmetric distribution (α) of collagen fibers. T2W sagittal images were acquired on an adult volunteer's healthy knee at 3 T, and ROI-based average signals S(ε) were extracted from angularly and radially segmented femoral cartilage. Compared with the standard MAE (sMAE) functions in the deep (DZ, α = 0°) and in the superficial (SZ, α = 90°) zones, a general form of R₂ orientation-dependent function f(α, ε) was fitted to S(ε), including an isotropic R₂ contribution (internal reference [REF]). Goodness of fit was evaluated by root-mean-square deviations (RMSDs). An F-test and a paired t-test were respectively used to assess significant differences between the observed variances and means, with statistical significance set to p less than .05. As a symmetric orientation-dependence function with a varying dynamic range, the proposed gMAE model outperformed the previous sMAE functions manifested by significantly reduced RMSDs in the DZ (0.239 ± 0.122 vs. 0.267 ± 0.097, p = .014) and in the SZ (0.183 ± 0.081 vs. 0.254 ± 0.085, p < .001). The fitted average angle α (38.5 ± 34.6° vs. 45.1 ± 30.1°, p < .43) and REF (5.092 ± 0.369 vs. 5.305 ± 0.440, p < .001) were smaller in the DZ than those in SZ, in good agreement with the reported collagen fibril microstructural configurations and the nonbound water contribution to R₂ in articular cartilage. In conclusion, a general form of the magic angle effect function was proposed and demonstrated for better characterizing anisotropic T2W signals from human knee femoral cartilage at 3 T in clinical studies.

An efficient R1ρ dispersion imaging method for human knee cartilage using constant magnetization prepared turbo-FLASH

This work aimed to develop an efficient R_1ρ dispersion imaging method for clinical studies of human knee cartilage at 3 T. Eight constant magnetizations (M_prep ) were prepared by tailoring both the duration and amplitude (ω₁ ) of a fully refocused spin-lock preparation pulse. The limited M_prep dynamic range was expanded by the measure, equivalent to that with ω₁  = ∞, from the magic angle location in the deep femoral cartilage. The developed protocol with M_prep  = 60% was demonstrated on one subject's bilateral and two subjects' unilateral asymptomatic knees. The repeatability of the proposed protocol was estimated by two repeated scans with a three-month gap for the last two subjects. The synthetic R_1ρ and R₂ derived from R_1ρ dispersions were compared with the published references using state-of-the-art R_1ρ and R₂ mapping (MAPSS). The proposed protocol demonstrated good (<5%) repeatability quantified by the intra- and intersubject coefficients of variation in the femoral and tibial cartilage. The synthetic R_1ρ (1/s) and the references were comparable in the femoral (23.0 ± 5.3 versus 24.1 ± 3.8, P = 0.67) and the tibial (29.1 ± 8.8 versus 27.1 ± 5.1, P = 0.62), but not the patellar (16.5 ± 4.9 versus 22.7 ± 1.6, P < 0.01) cartilage. The same trends were also observed for the current and the previous R₂ . In conclusion, the developed R_1ρ dispersion imaging scheme has been revealed to be not only efficient but also robust for clinical studies of human knee cartilage at 3 T.

An order parameter without magic angle effect (OPTIMA) derived from R 1 ρ dispersion in ordered tissue

PURPOSE

MR R₂ imaging of ordered tissue exhibits the magic angle effect, potentially masking subtle pathological changes in cartilage. This work aimed to develop an orientation-independent order parameter (S) exclusively sensitive to collagen degeneration.

METHODS

A theory was developed based on R 1 ρ dispersion coupled with a simplified molecular motion model in which anisotropic R 2 a ( θ ) became directly proportional to correlation time τ b θ and S could be derived. This new parameter was validated with ex vivo R 1 ρ dispersion reported on orientated (n = 4), enzymatically depleted bovine cartilage (n = 6), and osteoarthritic human knee specimens (n = 14) at 9.4 Tesla, which was further demonstrated on 1 healthy human knee in vivo at 3 Tesla.

RESULTS

τ b θ from orientation-dependent R 1 ρ dispersion revealed a significantly high average correlation (r = 0.89 ± 0.05, P < 0.05) with R 2 a (θ) on cartilage samples and a moderate correlation (r = 0.48, P < 0.001) for the human knee in vivo. The derived S (10^-3 ) significantly decreased in advanced osteoarthritis (1.64 ± 0.03 vs. 2.30 ± 0.11, P < 0.001) and collagen-depleted samples (1.30 ± 0.11 vs. 2.12 ± 0.12, P < 0.001) when compared with early osteoarthritis and the control, respectively.

CONCLUSION

The proposed order parameter could be a potentially useful orientation-independent MR biomarker for collagen alterations in cartilage and other highly structured tissues.