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 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 were divided into isotropic and anisotropic parts, , 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 in WM of underdeveloped, healthy, and diseased conditions. Goodness of fit was characterized by rootmean-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 and negative (α and ) 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 , 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.