Automatic clustering of white matter fibers in brain diffusion MRI with an application to genetics

Highlights

• Developed a workflow to extract fiber tracts through whole-brain tractography

• Extended the label fusion scheme to fiber clustering

• Designed a pointwise fiber matching algorithm to facilitate population studies

• Demonstrated a heritability population study with the proposed workflow

• Provided a practical tool for future population studies (ex. Alzheimer's disease)

Abstract

To understand factors that affect brain connectivity and integrity, it is beneficial to automatically cluster white matter (WM) fibers into anatomically recognizable tracts. Whole brain tractography, based on diffusion-weighted MRI, generates vast sets of fibers throughout the brain; clustering them into consistent and recognizable bundles can be difficult as there are wide individual variations in the trajectory and shape of WM pathways. Here we introduce a novel automated tract clustering algorithm based on label fusion – a concept from traditional intensity-based segmentation. Streamline tractography generates many incorrect fibers, so our top-down approach extracts tracts consistent with known anatomy, by mapping multiple hand-labeled atlases into a new dataset. We fuse clustering results from different atlases, using a mean distance fusion scheme. We reliably extracted the major tracts from 105-gradient high angular resolution diffusion images (HARDI) of 198 young normal twins. To compute population statistics, we use a pointwise correspondence method to match, compare, and average WM tracts across subjects. We illustrate our method in a genetic study of white matter tract heritability in twins.

Introduction

Diffusion-weighted magnetic resonance imaging (DT-MRI) (Basser et al., 1994) is a powerful non-invasive brain imaging technique introduced in LeBihan et al. (1986), Merboldt et al. (1985), Taylor and Bushell (1985). DT-MRI measures water diffusion in tissues, and provides biologically and clinically relevant information on white matter (WM) integrity and connectivity not available from other imaging modalities. It is increasingly used to study pathology and connectivity of WM pathways in the living brain (Daianu et al., 2013, Jahanshad et al., 2012, Thomason and Thompson, 2011).

Recently, diffusion MRI has been extended to more sophisticated models of local diffusion, such as high angular resolution diffusion imaging (HARDI) (Tuch, 2004), diffusion spectrum imaging (Wedeen et al., 2005), or even hybrid imaging where large numbers of angular samples are collected at several diffusion weightings (Zhan et al., 2011). With these imaging protocols, we can more accurately reconstruct fibers that mix and cross.

Tractography is a method to reconstruct the pathways of major WM fiber bundles, by fitting a curved path through the directional diffusion data at each voxel. Deterministic tractography (Basser et al., 2000, Conturo et al., 1999, Mori et al., 1999) recovers fibers emanating from a seed voxel by following the principal direction of the diffusion tensor or the dominant direction of the diffusion orientation distribution function (ODF). However, deterministic tractography has limitations: it depends on the choice of initial seed points and can be sensitive to the estimated principal directions. To overcome those drawbacks, probabilistic tractography methods have been proposed (Aganj et al., 2011, Behrens et al., 2003, Parker and Alexander, 2003). They can be computationally more intensive but can be more robust to partial volume averaging effects and uncertainties in the underlying fiber direction, which are inevitable due to imaging noise.

Several approaches have been developed to study brain connectivity using whole-brain tractography. Jahanshad et al. (2011) computed a whole-brain connectivity matrix based on streamline tractography and anatomical parcellation. Network-based analysis of this matrix can identify factors that affect the interconnectedness of regions in the brain. For example, Ingalhalikar et al. (2014) revealed connectivity pattern differences between males and females. Prasad et al. (2011) applied a probabilistic WM atlas to extract major fiber bundles and represented them by using a “maximum density” path. A mean curve was used to represent each bundle in each subject. Fractional anisotropy (FA) values, and other indices of diffusion, can be compared along this path across a population, using ‘along-tract’ statistics (Colby et al., 2011, Corouge et al., 2006).

Obviously it is important to accurately identify WM structures and fibers from whole-brain tractography. If fibers are grouped into bundles, the results can offer valuable insight on how disease affects the integrity of particular WM tracts (Price et al., 2007, Price et al., 2008). Clustering methods can group fibers obtained from tractography into organized bundles or tracts, enabling large population studies of disease and genetic effects on tract integrity, or even tract shapes. One simple yet practical strategy selects anatomically well-known WM tracts that interconnect anatomical regions of interest (ROI) (Wakana et al., 2007, Zhang et al., 2010). 3D models of tracts can facilitate large-scale population studies (Brouwer et al., 2010, Yushkevich et al., 2008). Even so, the final results often need substantial manual intervention to help screen out false positive fibers.

Automatic fiber clustering would accelerate and empower population studies, so long as the results are accurate and reliable. A typical framework for fiber clustering defines a pairwise similarity/distance between each pair of fibers in a large set of candidate fibers, to group them into separate and distinct tracts. Many different fiber similarity metrics have been proposed, such as the mean vector and the covariance matrix of fiber points (Brun et al., 2004), the number of points shared within the same voxel (Jonasson et al., 2004), an associativity vector (Wang et al., 2012), the average mean distance (Gerig et al., 2004, O'Donnell et al., 2006, Xia et al., 2005), Hausdorff distance (Gerig et al., 2004, Xia et al., 2005), and Mahalanobis distance (Maddah et al., 2008). Also, various clustering algorithms have been advocated, such as hierarchical clustering (Gerig et al., 2004, Visser et al., 2011, Xia et al., 2005), expectation-maximization (Wang et al., 2012), fuzzy c-means (Li et al., 2010), k-nearest neighbors (Ding et al., 2003), normalized cuts (Brun et al., 2004), dual rooted graphs (Tsai et al., 2007), and spectral clustering (O'Donnell and Westin, 2007, Wassermann et al., 2008).

If clustering algorithms have no anatomical information to guide them, tracts may not correspond to any anatomically familiar subdivisions. There is also no guarantee that the same basic sets of bundles will be generated again in datasets from new subjects, making it hard to compare results from one study to the next. Also, a user typically needs to specify the number of clusters or a threshold to decide when to stop merging or splitting clusters. Clustering results can vary drastically when different numbers of clusters are specified. “Bottom-up” methods cluster fibers into larger groups until major tracts are aggregated, but they may not efficiently filter out erroneous fibers buried in the large number of streamlines (100,000–1,000,000) generated by whole-brain tractography.

Recent hybrid approaches extract the well-known WM tracts by using a combination of prior information from an anatomically-labeled atlas and similarity-based clustering. Wassermann et al. (2010) proposed a Gaussian process framework to generate a fiber ‘dendrogram’ and selected which ones to merge through a query system based on parcellated volumetric information. Li et al. (2010) clustered tracts via anatomical ROI guidance, and then passed them through similarity-based fuzzy c-means clustering. Guevara et al. (2012) implemented a two-level (intra-subject and inter-subject) centroid-based average-link hierarchical clustering. The resulting clusters were manually labeled to form a multi-subject WM atlas. A new tractography data set was similarly segmented and the clusters were labeled using a supervised classification based on the atlas.

The large number of false positive fibers produced by streamline-based tractography hinders large population studies. An atlas-based top-down clustering method resolves this, by requiring that all subjects' WM tracts fall within a pre-defined set of shapes or regions. Even so, an atlas based on one individual subject's anatomy is not sufficient to capture the variability of individual WM tracts. One classical solution is called multi-atlas labeling or label fusion. This has commonly been applied to label brain structures on standard anatomical MRI (Chou et al., 2007, Chou et al., 2008, Chou et al., 2009, Heckemann et al., 2006, Lötjönen et al., 2010, Rohlfing et al., 2004, Sabuncu et al., 2010).

In traditional image segmentation, a deformable atlas may be used, in which an atlas is non-rigidly registered to the image to be labeled. The resulting deformation may then be used to map the training labels onto the new image. Multiple atlases and registrations may also be used to transfer multiple training labels to the new subject's space. The final labeling can be obtained by applying a weighting approach to the labels transferred from different atlases. Label fusion has two advantages: 1) it is easier to accommodate large individual variations in anatomy if one does not have to rely on a single atlas; 2) multiple registrations improve robustness against occasional registration failures and non-global minima of the registration cost function. The same idea can also improve voxel-based or tensor-based morphometry (Leporé et al., 2008).

Here we extend label fusion to fiber clustering and introduce a multi-atlas framework to automatically extract anatomically meaningful WM tracts. Based on the ROIs from a publicly available parcellated WM atlas (Oishi et al., 2009), we first manually construct a number of WM fiber tract atlases, consisting of several major WM tracts. In contrast to prior “bottom-up” methods, we use the WM tracts in multiple hand-labeled atlases as prior anatomical information. Our “top-down” approach transfers tract labels by selecting only fibers similar to the corresponding tracts in the atlases, based on a similarity measure. This eliminates many false positive fibers hidden in the ~ 1,000,000 fibers per subject produced by streamline tractography. Multiple atlases adapt to the variability of tract shapes in new subjects. This reduces the number of outliers and picks fibers that can be incorrectly omitted when registering a single atlas to the whole-brain tractography in a new subject. Finally, we use label fusion to combine the clustered results from individual atlases.

In the second part of the paper, we illustrate our method to study tract heritability based on the clustering results from our algorithm. Voxel-wise genetic analyses of DT-MRI show that many diffusivity measures, including FA, are heritable (Chiang et al., 2011, Jahanshad et al., 2013, Jahanshad et al., in press, Kochunov et al., 2011, Lee et al., 2010), but it is not yet well-understood which tracts are genetically influenced.

As individual WM fiber tracts are highly variable in shape, it can be difficult to find corresponding fibers that belong to the same tract across a population. Recent studies examined the skeleton of tracts, with methods such as tract-based spatial statistics (TBSS) (Bodini et al., 2009, Smith et al., 2007) or the average fiber tracts (Brouwer et al., 2010, Prasad et al., 2011) to perform statistical analyses of diffusion parameters in a large population. Nevertheless, these approaches do not always retain the full 3D profile of information from the tracts. To address this, we use a pointwise tract correspondence method to study clustered tract parameters in 3D. Finally, we calculate heritability statistics from corresponding tract points to understand genetic influences on the brain's tracts, and to demonstrate a practical use of our entire workflow.