Orientation dependent proton transverse relaxation in 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 the 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 R and R were divided into isotropic R and anisotropic parts, R ∗ f(α,Φ - ε), with α denoting an open angle and ε an orientation (Φ) offset from DTI-derived primary diffusivity direction. The proposed framework (Fit A) was compared to prior models without ε 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 ε was in good agreement with calculated ε from directional diffusivities. Compared with those from healthy adult, the fitted R, R, and α from neonates were substantially reduced but ε increased, consistent with developing myelination. Significant positive (R) and negative (α and R) 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.