Synopsis

The effective transverse relaxation rate (R₂^*) is increasingly used in quantitative MRI, and its dependence on the orientation of white matter fibers in the brain has received significant attention. In this contribution, we assess the effect of the flip angle of a multi-echo gradient-echo sequence on the orientation dependence of the derived R₂^* map and suggest a simplified explanation to the observed R₂^*(θ; FA) behavior.

Introduction

Material and Methods

Six subjects (three female; age 22—29, median age 25) were examined using a 3T MRI system with 64-channel head Tx/Rx coil.

Data acquisition

R₂^* decays were investigated by using a 3D multi-echo GRE (ME-GRE) imaging sequence, which was repeated four times with different flip angles (FA = 6°, 17°, 35° and 60°) but otherwise identical acquisition parameters (TR = 37 ms, TE_1-5 = 8.12/13.19/19.26/24.33/29.4 ms, monopolar readout, bandwidth = 280 Hz/px, voxel size = 1 mm × 1 mm × 1 mm). The orientation of WM fiber bundles was assessed from two diffusion-weighted acquisitions (voxel size = 1.5 mm×1.5 mm× 1.5 mm; TR = 3300 ms, TE = 84 ms) with reversed PE polarities and multi-shell diffusion scheme (16, 32, 64, and 96 directions with b-values of 0, 835, 1665 and 2500 s/mm², respectively).

Data processing

Diffusion acquisitions were combined, distortion-corrected via FSL^5,6 and linearly registered to the GRE data (@FA=17°). The predominant fiber orientation was determined in each voxel using constrained spherical deconvolution⁷. Fiber orientation was computed as the angle θ between the first ODF peak and the B₀ direction. R₂^* maps were calculated from each of the four ME-GRE acquisition via monoexponential fit with the ARLO algorithm⁸. Further analysis was performed for voxels whose second peak of the ODF was smaller than 50% compared to the first peak. Voxels were grouped by the angle θ in 5°-wide bins for each flip angle independently. Bin-averaged R₂^* values were fitted to $$$R_2^* = a_0 + a_1\cos 2\theta + a_2\cos 4\theta $$$ (eq. 1)⁹.

Results

The four R₂^* maps derived from the acquisitions with different flip angle demonstrate different contrast in white matter, particularly in areas with one single predominant orientation of the fibers (see Fig. 1).

Figure 2 shows the orientation dependence of the binned R₂^* data for the four flip angles in one volunteer (left). Higher apparent R₂^* values were extracted from the measurements with higher flip angles. The orientation dependence of the apparent R₂^* appears stronger with higher flip angle.

The fit of the model to the data is also shown in Fig. 2 (right). In agreement with previously published results^9,10, the orientation dependence of R₂^* follows closely the functional dependence given in eq. 1.

Box-plots of the fitted coefficients to eq. 1 are displayed in Fig. 3. The values for the coefficients agree reasonably well with previously published results¹⁰ and are discussed below.

Discussion

The results in Fig. 3 can be interpreted when considering WM consisting of two compartments with the following properties: predominantly axonal/extracellular water with longer T₁ and T₂^* values and mostly isotropic magnetic susceptibility (compartment 1); small fraction of myelin water with shorter T₁ and T₂^* and anisotropic susceptibility (compartment 2).

1. The increase of a₀ with flip angle is known and explained by the increasing saturation of compartment 1.
2. Following He and Yablonski¹¹, the $$$\cos 2 \theta$$$ term is associated with a contribution from water in parallel oriented structures, which can be ascribed to the axonal water compartment given its prevalence. Interestingly, a₁ exhibits non-monotonic dependence on the flip angle, reaching its smallest absolute value around the Ernst angle of compartment 1.
3. As proposed by Lee et al.⁹, the $$$\cos 4\theta$$$ contribution can be associated with a compartment with anisotropic susceptibility, which is believed to be myelin water. This explains increasing a₂, as the predominant axonal compartment is increasingly saturated with higher flip angles.

Conclusion

Care must be taken when comparing models of orientation dependency of R₂^* derived from acquisitions with different flip angles.

Sensitivity of R₂^* to tissue architecture or its susceptibility anisotropy can be to some extend affected by adjusting the flip angle of the acquisition.

Acknowledgements

References

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