Parsimonious Approximation of Streamline Trajectories in White Matter Fiber Bundles

Abstract

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.

Double Diffeomorphism: Combining Morphometry and Structural Connectivity Analysis

“…In order to deal with the considerable amount of streamlines resulting from tractography algorithms, we rely on the parsimonious representation, based on weighted prototypes, introduced in [30]. Both prototypes and streamlines are modelled as weighted currents [30].…”

“…Both prototypes and streamlines are modelled as weighted currents [30]. This model is well suited for any kind of fiber bundle, both sheet-like [31] and tubular [12].…”

“…When landmarks are not available, we propose to use two correspondence-free shape metrics: varifolds [32], for grey matter surfaces, and weighted currents [30], for white matter streamlines. In both frameworks, meshes are embedded into a infinite-dimensional Hilbert space where the union of surfaces or streamlines is equal to a sum of varifolds (V ) or weighted currents (C) respectively.…”

“…This can be achieved by tracing all streamlines of a bundle from one ROI (Region Of Interest) to another one, as it is the case in this paper. For more details, please see [30].…”

A General Framework for Curve and Surface Comparison and Registration with Oriented Varifolds

“…Later on, [11,10] introduced the alternative but orientation-invariant representation known as varifolds before the higher order model of normal cycles was recently investigated in [31]. Since then, all these different frameworks have found numerous applications to the morphological analysis of cortical surfaces [26,30], brain sulci [31], white matter fiber bundles [13,18] or registration of lung vessels [29]...…”