Convexity-constrained and nonnegativity-constrained spherical factorization in diffusion-weighted imaging.

Diffusion-weighted imaging (DWI) facilitates probing neural tissue structure non-invasively by measuring its hindrance to water diffusion. Analysis of DWI is typically based on generative signal models for given tissue geometry and microstructural properties. In this work, we generalize multi-tissue spherical deconvolution to a blind source separation problem under convexity and nonnegativity constraints. This spherical factorization approach decomposes multi-shell DWI data, represented in the basis of spherical harmonics, into tissue-specific orientation distribution functions and corresponding response functions, without assuming the latter as known thus fully unsupervised. In healthy human brain data, the resulting components are associated with white matter fibres, grey matter, and cerebrospinal fluid. The factorization results are on par with state-of-the-art supervised methods, as demonstrated also in Monte-Carlo simulations evaluating accuracy and precision of the estimated response functions and orientation distribution functions of each component. In animal data and in the presence of oedema, the proposed factorization is able to recover unseen tissue structure, solely relying on DWI. As such, our method broadens the applicability of spherical deconvolution techniques to exploratory analysis of tissue structure in data where priors are uncertain or hard to define.

Global tractography of multi-shell diffusion-weighted imaging data using a multi-tissue model.

Diffusion-weighted imaging and tractography provide a unique, non-invasive technique to study the macroscopic structure and connectivity of brain white matter in vivo. Global tractography methods aim at reconstructing the full-brain fiber configuration that best explains the measured data, based on a generative signal model. In this work, we incorporate a multi-shell multi-tissue model based on spherical convolution, into a global tractography framework, which allows to deal with partial volume effects. The required tissue response functions can be estimated from and hence calibrated to the data. The resulting track reconstruction is quantitatively related to the apparent fiber density in the data. In addition, the fiber orientation distribution for white matter and the volume fractions of gray matter and cerebrospinal fluid are produced as ancillary results. Validation results on simulated data demonstrate that this data-driven approach improves over state-of-the-art streamline and global tracking methods, particularly in the valid connection rate. Results in human brain data correspond to known white matter anatomy and show improved modeling of partial voluming. This work is an important step toward detecting and quantifying white matter changes and connectivity in healthy subjects and patients.