Joint Morphometry of Fiber Tracts and Gray Matter Structures Using Double Diffeomorphisms

Double Diffeomorphism: Combining Morphometry and Structural Connectivity Analysis

The brain is composed of several neural circuits which may be seen as anatomical complexes composed of grey matter structures interconnected by white matter tracts. Grey and white matter components may be modeled as 3-D surfaces and curves, respectively. Neurodevelopmental disorders involve morphological and organizational alterations which cannot be jointly captured by usual shape analysis techniques based on single diffeomorphisms. We propose a new deformation scheme, called double diffeomorphism, which is a combination of two diffeomorphisms. The first one captures changes in structural connectivity, whereas the second one recovers the global morphological variations of both grey and white matter structures. This deformation model is integrated into a Bayesian framework for atlas construction. We evaluate it on a data-set of 3-D structures representing the neural circuits of patients with Gilles de la Tourette syndrome (GTS). We show that this approach makes it possible to localise, quantify, and easily visualise the pathological anomalies altering the morphology and organization of the neural circuits. Furthermore, results also indicate that the proposed deformation model better discriminates between controls and GTS patients than a single diffeomorphism.

Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles

Fiber bundles stemming from tractography algorithms contain many streamlines. They require therefore a great amount of computer memory and computational resources to be stored, visualised and processed. We propose an approximation scheme for fiber bundles which results in a parsimonious representation of weighted prototypes. Prototypes are chosen among the streamlines and they represent groups of similar streamlines. Their weight is related to the number of approximated streamlines. Both streamlines and prototypes are modelled as weighted currents. This computational model does not need point-to-point correspondences and two streamlines are considered similar if their endpoints are close to each other and if their pathways follow similar trajectories. Moreover, the space of weighted currents is a vector space with a closed-form metric. This permits easy computation of the approximation error and the selection of the prototypes is based on the minimisation of this error. We propose an iterative algorithm which approximates independently and simultaneously all the fascicles of the bundle in a fast and accurate way. We show that the resulting representation preserves the shape of the bundle and it can be used to accurately reconstruct the original structural connectivity. We evaluate our algorithm on bundles obtained from both deterministic and probabilistic tractography algorithms. The resulting approximations use on average only 2% of the original streamlines as prototypes. This drastically reduces the computational burden of the processes where the geometry of the streamlines is considered. We demonstrate its effectiveness using as example the registration between two fiber bundles.

A Hybrid Multishape Learning Framework for Longitudinal Prediction of Cortical Surfaces and Fiber Tracts Using Neonatal Data

Dramatic changes of the human brain during the first year of postnatal development are poorly understood due to their multifold complexity. In this paper, we present the first attempt to jointly predict, using neonatal data, the dynamic growth pattern of brain cortical surfaces (collection of 3D triangular faces) and fiber tracts (collection of 3D lines). These two entities are modeled jointly as a multishape (a set of interlinked shapes). We propose a hybrid learning-based multishape prediction framework that captures both the diffeomorphic evolution of the cortical surfaces and the non-diffeomorphic growth of fiber tracts. In particular, we learn a set of geometric and dynamic cortical features and fiber connectivity features that characterize the relationships between cortical surfaces and fibers at different timepoints (0, 3, 6, and 9 months of age). Given a new neonatal multishape at 0 month of age, we hierarchically predict, at 3, 6 and 9 months, the postnatal cortical surfaces vertex-by-vertex along with fibers connected to adjacent faces to these vertices. This is achieved using a new fiber-to-face metric that quantifies the similarity between multishapes. For validation, we propose several evaluation metrics to thoroughly assess the performance of our framework. The results confirm that our framework yields good prediction accuracy of complex neonatal multishape development within a few seconds.