YUXI PANG^{1}

^{1}Department of Radiology, University of Michigan, Ann Arbor, MI, United States

An angle offset has been identified in proton magnetic resonance transverse relaxation orientation dependencies in the human brain WM in vivo when DTI primary diffusivity direction was used as an internal reference. This angle offset has not yet been accounted for in previous studies. The present work demonstrates that the observed angle offset can be removed using an angle derived from the perpendicular and parallel diffusivities of an axially symmetric diffusion tensor regardless of axon fiber orientations. The finding from this study clearly suggests that the diffusion tensor principal diffusivity direction deviates from an axon fiber orientation in WM.

$$lnSO/TE=(lnS_0⁄TE-R_2^i)-R_2^a*f(α,Φ-ε_0 ) (3)$$ Note, $$$S_0$$$ is SO when TE=0 and the term $$$(lnS_0⁄TE-R_2^i)$$$ can be treated as a constant $$$C_0$$$ to be fitted. $$$Φ$$$ was determined from the primary eigenvector $$$\overrightarrow{e_{1}}$$$ by the relationship of $$$cosΦ=(\overrightarrow{e_{1}}\cdot{B_{0}})⁄(\mid\overrightarrow{e_{1}}\mid\cdot\mid{B_{0}}\mid)$$$. The measured SO (in a logarithmic scale) of specific voxels from the whole brain either with linear (i.e., 0.5<FA<0.9 and 0.5<MO<1.0) or planar (i.e., 0.3<FA<0.6 and -1.0<MO<-0.5) diffusion anisotropy were sorted and then averaged into 180 different bins of fiber orientations ranging from 0° to 90°. The fit using Eq. 3 was labeled respectively as “Fit A” with $$$ε_0$$$ or “Fit B” without $$$ε_0$$$. Goodness of fit was characterized by root-mean-square error (RMSE) and

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FIG. 1. Schematics of an axially symmetric diffusion tensor (1A) decomposed into
isotropic (1B) and anisotropic components (1C). The primary diffusion direction ($$$D_∥$$$) deviates from the direction ($$$\overrightarrow{n}$$$) of a resultant anisotropic diffusion by an
angle offset $$$ε_0$$$ (1D). The directions of diffusion tensor eigenvectors are
defined with respect to $$$B_0$$$ (+Z) in the
laboratory reference frame.

FIG. 2. An illustrative image of anisotropic $$$R_2$$$ (2A), principal diffusivity orientation $$$Φ=ε+ε_0$$$ (2B), and mode of diffusion (MO) anisotropy (2C); an example of the measured and fitted anisotropic $$$R_2$$$ profiles (2E) from voxels with restricted linear diffusion anisotropies as highlighted (black box) in a 2D histogram (2D), and orientation-dependent offset angles $$$ε_0$$$ (2F).

FIG. 3. Orientation-dependent angle offsets $$$ε_0$$$ from voxels with different linear anisotropies are plotted in Fig. 3A, with MO restricted to [0.4, 0.6] (red), [0.6, 0.8] (green), and [0.8, 1.0] (blue). Fig. 3B and 3C display, respectively, the measured (mean ± SD, colored shades) and fitted (thick solid lines) $$$R_2$$$ profiles with Fit A and Fit B after the corresponding orientation-dependent $$$ε_0$$$ removed. The distribution of voxels with different fiber orientations is presented in Fig. 3D.

FIG. 4. Measured (mean ± SD, colored shades) and fitted (Fit B, thick solid lines) $$$R_2$$$ profiles after removing orientation-dependent $$$ε_0$$$ from voxels with planar (-1.0<MO<-0.5) anisotropic diffusion where FA was limited to either [0.3, 0.5] (4A and 4C) or [0.4, 0.6] (4B and 4D). The fitted residue is depicted by thin blue lines and an offset angle $$$ε_0$$$ was calculated based on either planar (4A and 4B) or linear (4C and 4D) anisotropic case.

DOI: https://doi.org/10.58530/2022/0648