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

Purpose: To overcome limitations of prior orientation-dependent R2 and R2* formalisms in white matter (WM) with a novel framework based on magic angle effect. Methods: A cylindrical helix model was developed embracing both anisotropic rotational and translational diffusions of ordered water in WM, with the former characterized by an axially symmetric system. Both R2 and R2* were divided into isotropic (R2i) and anisotropic parts, R2a*f(ε-ε0,α), with α denoting a funnel opening angle and ε0 an orientation (ε) offset relative to DTI-derived primary diffusivity direction. The proposed framework (Fit A) was compared with prior model without ε0 (Fit B) and applied to published R2 and R2* in WM of underdeveloped, healthy, and diseased conditions. Goodness of fit was characterized by root-mean-square error (RMSE). F-test and Pearson correlation coefficient (PCC) were used with statistical significance set to P ≤ .05. Results: Fit A significantly outperformed Fit B as demonstrated by reduced RMSEs in myelin water (i.e., 0.349 vs. 0.724). The fitted ε0 was in good agreement with the calculated ε0 from DTI directional diffusivities. Significant positive (R2i) and negative (α and R2a) correlations were found with aging (demyelination) in adults while ε0 showed a weak positive correction (PCC=0.11, P= .28). Compared to those from healthy adult WM, the fits of R2i, R2a, and α from neonates were considerably reduced but ε0 increased, consistent with limited myelination. Conclusion: The developed framework can better characterize anisotropic transverse relaxation in WM, shedding new light on myelin microstructural alterations at the molecular level.