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

Abstract

PurposeTo 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. MethodsA 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, R2a ∗ 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. ResultsFit 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, R2a, and α from neonates were substantially reduced but ε0 increased, consistent with developing myelination. Significant positive (R2i) and negative (α and R2a) correlations were found with aging (demyelination) in elderly. ConclusionThe 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.