Tract-based morphometry for white matter group analysis

Abstract

We introduce an automatic method that we call tract-based morphometry, or TBM, for measurement and analysis of diffusion MRI data along white matter fiber tracts. Using subject-specific tractography bundle segmentations, we generate an arc length parameterization of the bundle with point correspondences across all fibers and all subjects, allowing tract-based measurement and analysis. In this paper we present a quantitative comparison of fiber coordinate systems from the literature and we introduce an improved optimal match method that reduces spatial distortion and improves intra- and inter-subject variability of FA measurements. We propose a method for generating arc length correspondences across hemispheres, enabling a TBM study of interhemispheric diffusion asymmetries in the arcuate fasciculus (AF) and cingulum bundle (CB). The results of this study demonstrate that TBM can detect differences that may not be found by measuring means of scalar invariants in entire tracts, such as the mean diffusivity (MD) differences found in AF. We report TBM results of higher fractional anisotropy (FA) in the left hemisphere in AF (caused primarily by lower λ₃, the smallest eigenvalue of the diffusion tensor, in the left AF), and higher left hemisphere FA in CB (related to higher λ₁, the largest eigenvalue of the diffusion tensor, in the left CB). By mapping the significance levels onto the tractography trajectories for each structure, we demonstrate the anatomical locations of the interhemispheric differences. The TBM approach brings analysis of DTI data into the clinically and neuroanatomically relevant framework of the tract anatomy.

Introduction

By measuring water diffusion in the brain, diffusion tensor MRI (DTI) gives information about the orientation and integrity of fiber tracts, the major neural connections in the white matter. DTI tractography (Basser et al., 2000) follows directions of maximal water diffusion to estimate the trajectories of the fiber tracts. Clinical and neuroscientific questions regarding white matter pathways may be addressed by analyzing DTI data in regions of specific white matter tracts (Johansen-Berg and Behrens, 2006). Many tractography-based analyses (Pagani et al., 2005, Heiervang et al., 2006, Jones et al., 2006, Wakana et al., 2007) have calculated the mean in the entire tract of a scalar value such as the fractional anisotropy (FA) or the mean diffusivity (MD). Other studies have measured mean FA or other scalars in regions of interest (ROIs) within tracts (e.g. Pierpaoli et al., 1996, Kubicki et al., 2003). Due to anatomical factors such as crossing fibers or nearness to cerebrospinal fluid or gray matter, as well as tissue microstructural factors such as packing densities and axon diameters (Pierpaoli et al., 1996), FA and MD vary spatially along tract trajectories (Xue et al., 1999). Thus analysis of their mean values may not be optimal for localization of group differences in the white matter.

Therefore we propose to perform quantitative analysis of DTI data along the white matter tracts, an approach that we call tract-based morphometry (TBM). In this work we present an automatic TBM method for white matter analysis in groups. First DTI tractography from multiple subjects is analyzed to produce common arc length coordinates (point correspondences) across fibers from all subjects, then statistical analysis is performed in this tract-based coordinate system. Our inspiration for naming TBM was the analogy between the voxel-based morphometry method (Ashburner and Friston, 2000) in which local statistical analyses are performed on features derived from scalar MRI (gray and white matter concentrations), and our local statistical analyses of features derived from DTI. For simplicity, to develop the TBM method in this paper we focus only on measurements of white matter microstructural morphometry such as FA, however macroscopic morphological features regarding the entire tract may also be studied with the TBM method. This includes features measured for individual fibers, such as curvatures, as well as shape features (widths, volumes, areas) of the entire bundle.

Other groups have described methods for tract-based analysis of DTI. The methods differ in the coordinate system that is overlaid on the fiber tracts (voxel-based/fiber-based/skeleton-based), in whether they are able to handle data from multiple subjects, and in whether statistical results have been demonstrated in group data.

The first class of methods performs voxel-based measurements along tracts. These methods are limited to fiber tracts that are approximately perpendicular to the axial, sagittal, or coronal image planes. Several groups have quantified diffusion in this way, for example along the trajectory of the corticospinal tract on consecutive axial images (Reich et al., 2006, Lin et al., 2006, Wakana et al., 2007), or in the anterior thalamic radiation, inferior longitudinal fasciculus (Wakana et al., 2007), and cingulum bundle (Gong et al., 2005) using coronal images. In the slice-based measurement framework, the problem of registering the measured data across subjects has been addressed using anatomical landmarks along tracts (Wakana et al., 2007, Gong et al., 2005). Little statistical analysis has been performed along the fiber tracts, with the exception of the cingulum study of interhemispheric FA differences (Gong et al., 2005).

Another class of methods generates coordinate systems based on fibers, and thus is more able to handle arbitrarily shaped fiber tracts. These methods find trajectory correspondences along the length of the fibers. One approach for fiber tract parameterization by arc length employed human interaction to define a corresponding point on all fibers, then assumed point correspondences based on the distance along the fiber from the selected point (Corouge et al., 2006). Other work assumed endpoint correspondences were sufficient to align fibers, even across subjects (Batchelor et al., 2006). Another approach, demonstrated on the corona radiata and cingulum, estimated three level sets to produce a fiber coordinate system (Niethammer et al., 2006). A principled statistical bundle model with point correspondences along fibers was constructed using a unified method for fiber clustering and measurement (Maddah et al., 2008). These more advanced fiber coordinate system methods have so far been demonstrated on fibers from single subjects, but not extended to group data.

A different approach for statistical analysis of DTI uses spatial skeletons to define locations likely to correspond to central parts of fiber bundles. In the tract-based spatial statistics method, in each subject locally high FA values were aligned to a group FA skeleton and voxel-based morphometry was performed (Smith et al., 2006). However, by working in a voxel coordinate system the method could mix information from nearby but differently oriented tracts. Finally, a recent method that blended the spatial skeleton and fiber approaches performed group analysis of MD by sampling each subject's data using a medial model derived from tractography in atlas space (Yushkevich et al., 2008).

Inspired by the highly successful voxel-based morphometry method (Ashburner and Friston, 2000), we have coined the term tract-based morphometry (TBM) to describe the statistical analysis of medical image data in a white matter tract coordinate system. Our TBM method can be simply understood in terms of its inputs and outputs. The input to the method is a “bundle” of tractography data from all subjects to be studied. (We will refer to each trajectory as a “fiber” and to each anatomical structure as a “bundle”.) The output from the method includes a mean fiber trajectory for the bundle, as well as diffusion measurements and statistical analysis in the coordinate system of the mean fiber. In contrast with other methods for white matter analysis in groups, in which diffusion data is sampled in locations defined by an atlas (e.g. Smith et al., 2006, Yushkevich et al., 2008), in TBM we employ subject-specific tractography segmentations.

The methodological contributions of this work include: quantitative testing of tract-based coordinate systems from the literature, an improved optimal match method for arc length parameterization of fibers that reduces spatial distortion and variability of measured data, a method for generating arc length correspondences across hemispheres, and an investigation into the appropriate size scale for statistical analysis of diffusion data along tracts.

This paper is divided into two main sets of experiments. The first experiments are performed to optimize our TBM implementation. Then, using the final implementation, we demonstrate the TBM method using a study of hemispheric asymmetry of FA, MD, and the three eigenvalues of the diffusion tensor (λ₁ > = λ₂ > = λ₃) in the cingulum bundle (CB) and arcuate fasciculus (AF) of normal right-handed subjects. TBM results regarding FA in the cingulum replicate those measured manually in (Gong et al., 2005), while the other data are quantified for the first time along the AF and CB tracts.