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

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.