Parameterization of White Matter Manifold-Like Structures Using Principal Surfaces

Abstract

In this manuscript, we are concerned with data generated from a diffusion tensor imaging (DTI) experiment. The goal is to parameterize manifold-like white matter tracts, such as the corpus callosum, using principal surfaces. The problem is approached by finding a geometrically motivated surface-based representation of the corpus callosum and visualized fractional anisotropy (FA) values projected onto the surface. The method also applies to any other diffusion summary. An algorithm is proposed that 1) constructs the principal surface of a corpus callosum; 2) flattens the surface into a parametric 2D map; 3) projects associated FA values on the map. The algorithm is applied to a longitudinal study containing 466 diffusion tensor images of 176 multiple sclerosis (MS) patients observed at multiple visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 20,000 voxels. Extensive simulation studies demonstrate fast convergence and robust performance of the algorithm under a variety of challenging scenarios.

Principal Manifold Estimation Via Model Complexity Selection

“…One approach to addressing computational burden is subsampling, for example, Yue et al. (2016). While leading to faster computation, subsampling may result in removing important sections of a given data set.…”

“…For ( d = 2, D = 3), we compare PME to two methods: (i) the principal surface (PS) algorithm introduced by Yue et al. (2016), where the optimal number of basis functions in PS is obtained by the new cross‐validation method proposed by Yue et al. (2016), using the R function for PS provided by the first author of Yue et al.…”

“…(2016), where the optimal number of basis functions in PS is obtained by the new cross‐validation method proposed by Yue et al. (2016), using the R function for PS provided by the first author of Yue et al. (2016); (ii) ISOMAP: Conducted as described above for its counterpart with d = 1, except we apply thin plate splines to achieve the corresponding minimizer (Duchon, 1977).…”

“…In turn, projecting data to the image of an embedding map results in a parameterization (e.g. Yue et al., 2016). In this paper, we propose a framework and estimation approach combining these two components.…”

Tract-Based Spatial Statistics and Other Approaches for Cross-Subject Comparison of Local Diffusion MRI Parameters

“…High reproducibility of tensor-derived parameters (FA, MD, eigenvalues), parameterized as a function of distance along the tract, is shown. Similarly, in Yue et al (2013), a related approach is taken; tracts are modeled as 'principal surfaces' using a combination of principal component analysis and thin-plate splines, and FA is then parameterized within the locally 2D tract-center representation. A cross-subject average of all subjects' tensor images is created in standard space.…”