Enabling constrained spherical deconvolution and diffusional variance decomposition with tensor-valued diffusion MRI

Diffusion tensor imaging (DTI) is widely used to extract valuable tissue measurements and white matter (WM) fiber orientations, even though its lack of specificity is now well-known, especially for WM fiber crossings. Models such as constrained spherical deconvolution (CSD) take advantage of high angular resolution diffusion imaging (HARDI) data to compute fiber orientation distribution functions (fODF) and tackle the orientational part of the DTI limitations. Furthermore, the recent introduction of tensor-valued diffusion MRI allows for diffusional variance decomposition (DIVIDE), opening the door to the computation of measures more specific to microstructure than DTI measures, such as microscopic fractional anisotropy (FA). However, tensor-valued diffusion MRI data is not mathematically compatible with latest versions of CSD and the impacts of such atypical data on fODF reconstruction with CSD are yet to be studied. In this work, we lay down the mathematical and computational foundations of a tensor-valued CSD and use simulated data to explore the effects of various combinations of diffusion encodings on the angular resolution of extracted fOFDs. We also compare the combinations with regards to their performance at producing accurate and precise FA with DIVIDE, and present an optimised protocol for both methods. We show that our proposed protocol enables the reconstruction of both fODFs and FA on in vivo data.