FRATS: Functional Regression Analysis of DTI Tract Statistics

Abstract

Diffusion tensor imaging (DTI) provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. This paper presents a functional regression framework, called FRATS, for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest, such as age, diagnostic status and gender, in real applications. The functional regression framework consists of four integrated components: the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles, a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates, a global test statistic for testing hypotheses of interest, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy, mean diffusivity, and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. Significant age and gestational age effects on the five diffusion properties were found in both tracts. The resulting analysis pipeline can be used for understanding normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles.

Along-tract statistics allow for enhanced tractography analysis

“…However, since the sample locations along the streamlines are still given by a continuous arc length variable (albeit now a standardized arc length) there is a remaining correspondence issue since there is not a one-to-one mapping of vertices across streamlines and subjects. One progressive approach to circumvent this challenge has been to model the underlying continuous biological variation in FA directly though a higher dimensional framework for statistical inference called functional data analysis (Goodlett et al, 2008, 2009; Zhu et al, 2010, 2011). A simpler general approach, which has also been successful, only considers a more proximal set of vertices that have arc-length positional correspondence across all streamlines.…”

“…One natural option, which we use to address this issue here, is to use cubic B-splines to re-parameterize the polylines as curves (a schematic is shown in Fig. 3A,B) (Corouge et al, 2006; O’Donnell et al, 2009; Zhu et al, 2010). Fig.…”

“…While previous work has included efforts to examine DTI metrics along tract lengths (Corouge et al, 2006; Goodlett et al, 2008, 2009; Jones et al, 2005; O’Donnell et al, 2009; Zhu et al, 2010), as well as more generic within-tract methods that can accommodate variability along even more dimensions within tracts (Yushkevich et al, 2008; Zhang et al, 2010), it has typically been focused on individual aspects of the along-tract workflow or specific customized applications. It remains true that the large majority of streamline tractography analyses still rely on a simpler tract-averaged methodology.…”

Cook’s Distance Measures for Varying Coefficient Models With Functional Responses

“…To apply our diagnostic measures to a real example, we analyze a diffusion tensor imaging (DTI) tract data which was reported in Zhu et al (2010) and Zhu et al (2011). Since diffusion tensor imaging (DTI) can track the effective diffusion of water in the human brain in vivo, it can map the structure and orientation of the white matter fiber tracts of the brain.…”

“…The gestational ages at MR scanning were 298 ± 17.>6 (Mean±Std) days and their range was 262-433. For details about statistical results and imaging processing procedure, see Zhu et al (2010) and Zhu et al (2011).…”