A Statistical Model of White Matter Fiber Bundles Based on Currents

Abstract

Abstract. The purpose of this paper is to measure the variability of a population of white matter fiber bundles without imposing unrealistic geometrical priors. In this respect, modeling fiber bundles as currents seems particularly relevant, as it gives a metric between bundles which relies neither on point nor on fiber correspondences and which is robust to fiber interruption. First, this metric is included in a diffeomorphic registration scheme which consistently aligns sets of fiber bundles. In particular, we show that aligning directly fiber bundles may solve the aperture problem which appears when fiber mappings are constrained by tensors only. Second, the measure of variability of a population of fiber bundles is based on a statistical model which considers every bundle as a random diffeomorphic deformation of a common template plus a random non-diffeomorphic perturbation. Thus, the variability is decomposed into a geometrical part and a "texture" part. Our results on real data show that both parts may contain interesting anatomical features.

Fiberprint: A subject fingerprint based on sparse code pooling for white matter fiber analysis

“…Multi-step or multi-level approaches have also been proposed to segment fiber trajectories, for example, by combining both voxel and fiber trajectory groupings [12], fusing labels from multiple handlabeled atlases [13], using a white matter voxel-space atlas and a bundle representation based on maximum density paths [15], or using Gaussian processes 100 [53]. A few studies have also investigated the representation of specific fiber trajectory bundles using different techniques such as gamma mixture models [54], hierarchical Dirichlet processes [55], and the computational model of rectifiable currents [56,57].…”

Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents

“…As preliminarily shown in Durrleman et al (2009a), the metric based on currents seems to be particularly well suited for this purpose. It has been introduced in field of medical imaging in Vaillant & Glaunès (2005); Glaunès (2005); Glaunès et al (2008) to avoid the need to find point correspondences in feature-based registration as in Chen & Medioni (1991); Besl & McKay (1992); Joshi & Miller (2000) for instance.…”

Double Diffeomorphism: Combining Morphometry and Structural Connectivity Analysis

“…The second deformation φ All deforms both the resulting white matter φ W (T W ) and T G . This formulation derives from the forward model [35], [38], [39] where we assume that all elements belong to an algebraic structure where addition is defined. It results:…”

“…B). Two curves are considered similar if their pathways are alike, as in usual currents [39], but also if their endpoints are close to each other. The inner product is parametrised by three user-defined bandwidths: λ g , λ a , λ b .…”