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

Abstract

ABSTRACTPurposeTo overcome some limitations of prior orientation-dependent proton transverse relaxation formalisms in white matter (WM) with a novel framework based on generalized magic angle effect function.MethodsA cylindrical helix model was developed embracing anisotropic rotational and translational diffusion of restricted molecules in human brain WM, with the former characterized by an axially symmetric system. Transverse relaxation rates R2 and were divided into isotropic and anisotropic parts, , 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 with prior models without ε0 on previously published water and methylene proton transverse relaxation rates from developing, healthy, and pathological WM at 3T. 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 and α from neonates were substantially reduced but ε0 increased, consistent with incomplete myelination. Significant positive and negative (α and ) 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 human brain WM, shedding new light on myelin microstructural alterations at the molecular level.