Accelerated radial diffusion spectrum imaging using a multi‐echo stimulated echo diffusion sequence

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Diffusion spectrum imaging (DSI) 1 provides us with robust non‐invasive renditions of the complex white matter tract architecture in the human brain 2. DSI achieves this by characterizing the three‐dimensional diffusion displacement of water molecules in the diffusion encoding space (also dubbed q‐space). Based on these diffusion weighted signal intensities, DSI enables model‐free, unbiased estimation of the orientation distribution function (ODF), a measure of complex distribution of intravoxel fiber orientations in each voxel. Resulting voxel‐wise ODF information is combined over the brain volume with tractography algorithms to generate estimates of brain connectivity. Although tractography continues to improve, the information it provides is already successfully used to depict changes in brain connectivity in brain research [e.g. Refs. 4] and pathologically relevant conditions 3.
DSI and other high angular resolution diffusion imaging 6 methods such as Q‐ball imaging 7 do not rely on prior assumptions about intravoxel fiber distributions in the human brain. Consequently, these methods are well suited to produce accurate depictions of two or more crossing fibers, combinations of dominant and minor fiber bundles, and “kissing” fibers found in each voxel in the human brain 6. These methods thus receive increasing attention over methods which assume single [diffusion tensor imaging, DTI, 9] or multiple 6 fiber bundles as promising tools for detailed visualizations of brain neural connectivity 2.
The crucial property of DSI in identifying intravoxel fiber crossings is the angular resolution, or the smallest crossing angle that can be resolved between two fibers 11. The obtained angular resolution depends on the sampling geometry of q‐space. In the traditional rectangular q‐space grid, increased angular resolution requires larger q‐space radii and a larger sampling matrix, resulting in a cubic increase both in the number of required samples and in acquisition time 13. As a result, for clinical applications using conventional MRI hardware (40–80 mT/m, 180 mT/m/ms gradients), the maximum angular resolution is a trade‐off between scan time and SNR with the optimum maximum q‐value limited by gradient performance 14. Even then, the large number of q‐space samples needed leads to long acquisition times 15. One approach to mitigating these limitations is the use of simultaneous multi‐slice or multiband techniques in which several slices are encoded at the same time 16. Here, we choose to explore a complementary approach to improve the time efficiency of DSI by acquiring full 2D k‐spaces for each of several q‐space samples per readout train.
A recently introduced improvement of DSI, Radial q‐space sampling for DSI [radial diffusion spectrum imaging (RDSI), 13], succeeds in improving angular resolution at moderately high b‐values (e.g. b = 4000 s/mm2). RDSI samples q‐space on a radial raster and analytically reconstructs the resulting q‐space directly (no interpolation) to provide estimates of the ODF at each angular direction via the Central Section Theorem (Fourier Slice Theorem). Not only does this make the nominal angular resolution primarily dependent on the number of radial lines Nl along which samples are acquired (i.e. a quadratic increase of samples with angular resolution instead of a cubic increase) 13; but it is also more robust against truncation effects due to Gibbs ringing artifacts 13. The latter can lead to unwanted spurious peaks 13. RDSI uses multiple shells in q‐space, similar to multi‐shell q‐ball imaging approaches 20. However, it is important to note that the RDSI reconstruction is an exact DSI‐reconstruction [i.e. a full Fourier Transform by way of the Fourier Slice Theorem (13)], rather than a fit of orthogonal basis functions on a sphere's surface as in q‐ball imaging.

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