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

Orientation-independent quantification of macromolecular proton fraction in tissues with suppression of residual dipolar coupling

Quantitative magnetization transfer (MT) imaging enables noninvasive characterization of the macromolecular environment of tissues. However, recent work has highlighted that the quantification of MT parameters using saturation radiofrequency (RF) pulses exhibits orientation dependence in ordered tissue structures, potentially confounding its clinical applications. Notably, in tissues with ordered structures, such as articular cartilage and myelin, the residual dipolar coupling (RDC) effect can arise owing to incomplete averaging of dipolar-dipolar interactions of water protons. In this study, we demonstrated the confounding effect of RDC on quantitative MT imaging in ordered tissues can be suppressed by using an emerging technique known as macromolecular proton fraction mapping based on spin-lock (MPF-SL). The off-resonance spin-lock RF pulse in MPF-SL could be designed to generate a strong effective spin-lock field to suppress RDC without violating the specific absorption rate and hardware limitations in clinical scans. Furthermore, suppressing the water pool contribution in MPF-SL enabled the application of a strong effective spin-lock field without confounding effects from direct water saturation. Our findings were experimentally validated using human knee specimens and healthy human cartilage. The results demonstrated that MPF-SL exhibits lower sensitivity to tissue orientation compared withR 2 $$ {R}_2 $$ ,R 1 ρ $$ {R}_{1\rho } $$ , and saturation-pulse-based MT imaging. Consequently, MPF-SL could serve as a valuable orientation-independent technique for the quantification of MPF.

Deciphering adiabatic rotating frame relaxometry in biological tissues

PURPOSE

This work aims to unravel the intricacies of adiabatic rotating frame relaxometry in biological tissues.

THEORY AND METHODS

The classical formalisms of dipolar relaxationR 1 ρ $$ {R}_{1\rho } $$ andR 2 ρ $$ {R}_{2\rho } $$ were systematically analyzed for water molecules reorienting on "fast" and "slow" timescales. These two timescales are, respectively, responsible for the absence and presence ofR 1 ρ $$ {R}_{1\rho } $$ dispersion. A time-averagedR 1 ρ $$ {R}_{1\rho } $$ orR 2 ρ $$ {R}_{2\rho } $$ over an adiabatic pulse duration was recast into a sum ofR 1 $$ {R}_1 $$ andR 2 $$ {R}_2 $$ , but with different weightings. These weightings depend on the specific modulations of adiabatic pulse waveforms. In this context, stretched hyperbolic secant (HSn $$ HSn $$ ) pulses were characterized. Previously publishedH S 1 $$ HS1 $$ R 1 ρ $$ {R}_{1\rho } $$ , continuous-wave (CW)R 1 ρ $$ {R}_{1\rho } $$ , andR 1 $$ {R}_1 $$ measures from 12 agarose phantoms were used to validate the theoretical predictions. A similar validation was also performed on previously publishedHSn $$ HSn $$ R 1 ρ $$ {R}_{1\rho } $$ (n $$ n $$ =1, 4, 8) andHS 1 $$ HS1 $$ R 2 ρ $$ {R}_{2\rho } $$ from bovine cartilage specimens.

RESULTS

Longitudinal relaxation weighting decreases forHSn $$ HSn $$ pulses asn $$ n $$ increases. Predicted CWR 1 ρ cal $$ {R}_{1\rho}^{cal} $$ values from agarose phantoms align well with the measured CWR 1 ρ exp $$ {R}_{1\rho}^{exp} $$ values, as indicated by a linear regression function:R 1 ρ cal = 1.04 * R 1 ρ exp - 1.96 $$ {R}_{1\rho}^{cal}={1.04}^{\ast }{R}_{1\rho}^{exp}-1.96 $$ . The predicted adiabaticR 1 ρ $$ {R}_{1\rho } $$ andR 2 ρ $$ {R}_{2\rho } $$ from cartilage specimens are consistent with those previously measured, as quantified by:R 1 ρ , 2 ρ cal = 1.10 * R 1 ρ , 2 ρ exp - 0.41 $$ {R}_{1\rho, 2\rho}^{cal}={1.10}^{\ast }{R}_{1\rho, 2\rho}^{exp}-0.41 $$ .

CONCLUSION

This work has theoretically and experimentally demonstrated that adiabaticR 1 ρ $$ {R}_{1\rho } $$ andR 2 ρ $$ {R}_{2\rho } $$ can be recast into a sum ofR 1 $$ {R}_1 $$ andR 2 $$ {R}_2 $$ , with varying weightings. Therefore, any suggestions that adiabatic rotating frame relaxometry in biological tissues could provide more information than the standardR 1 $$ {R}_1 $$ andR 2 $$ {R}_2 $$ warrant closer scrutiny.

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.

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.

Magnetization-prepared spoiled gradient-echo snapshot imaging for efficient measurement of R2 -R1ρ in knee cartilage

PURPOSE

To validate the potential of quantifying R₂ -R_1ρ using one pair of signals with T_1ρ preparation and T₂ preparation incorporated to magnetization-prepared angle-modulated partitioned k-space spoiled gradient-echo snapshots (MAPSS) acquisition and to find an optimal preparation time (T_prep ) for in vivo knee MRI.

METHODS

Bloch equation simulations were first performed to assess the accuracy of quantifying R₂ -R_1ρ using T_1ρ - and T₂ -prepared signals with an equivalent T_prep . For validation of this technique in comparison to the conventional approach that calculates R₂ -R_1ρ after estimating both T₂ and T_1ρ , phantom experiments and in vivo validation with five healthy subjects and five osteoarthritis patients were performed at a clinical 3T scanner.

RESULTS

Bloch equation simulations demonstrated that the accuracy of this efficient R₂ -R_1ρ quantification method and the optimal T_prep can be affected by image signal-to-noise ratio (SNR) and tissue relaxation times, but quantification can be closest to the reference with an around 25 ms T_prep for knee cartilage. Phantom experiments demonstrated that the proposed method can depict R₂ -R_1ρ changes with agarose gel concentration. With in vivo data, significant correlation was observed between cartilage R₂ -R_1ρ measured from the conventional and the proposed methods, and a T_prep of 25.6 ms provided the most agreement by Bland-Altman analysis. R₂ -R_1ρ was significantly lower in patients than in healthy subjects for most cartilage compartments.

CONCLUSION

As a potential biomarker to indicate cartilage degeneration, R₂ -R_1ρ can be efficiently measured using one pair of T_1ρ -prepared and T₂ -prepared signals with an optimal T_prep considering cartilage relaxation times and image SNR.

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.

Magic angle effect on adiabatic T1ρ imaging of the Achilles tendon using 3D ultrashort echo time cones trajectory

The protons in collagen-rich musculoskeletal (MSK) tissues such as the Achilles tendon are subject to strong dipolar interactions which are modulated by the term (3cos² θ-1) where θ is the angle between the fiber orientation and the static magnetic field B₀ . The purpose of this study was to investigate the magic angle effect in three-dimensional ultrashort echo time Cones Adiabatic T_1ρ (3D UTE Cones-AdiabT_1ρ ) imaging of the Achilles tendon using a clinical 3 T scanner. The magic angle effect was investigated by Cones-AdiabT_1ρ imaging of five cadaveric human Achilles tendon samples at five angular orientations ranging from 0° to 90° relative to the B₀ field. Conventional Cones continuous wave T_1ρ (Cones-CW-T_1ρ ) and Cones T₂ * (Cones-T₂ *) sequences were also applied for comparison. On average, Cones-AdiabT_1ρ increased 3.6-fold from 13.6 ± 1.5 ms at 0° to 48.4 ± 5.4 ms at 55°, Cones-CW-T_1ρ increased 6.1-fold from 7.0 ± 1.1 ms at 0° to 42.6 ± 5.2 ms at 55°, and Cones-T2* increased 12.3-fold from 2.9 ± 0.5 ms at 0° to 35.8 ± 6.4 ms at 55°. Although Cones-AdiabT_1ρ is still subject to significant angular dependence, it shows a much-reduced magic angle effect compared to Cones-CW-T_1ρ and Cones-T₂ *, and may be used as a novel and potentially more effective approach for quantitative evaluation of the Achilles tendon and other MSK tissues.