AnatomiCuts: Hierarchical clustering of tractography streamlines based on anatomical similarity

Abstract

Diffusion MRI tractography produces massive sets of streamlines that contain a wealth of information on brain connections. The size of these datasets creates a need for automated clustering methods to group the streamlines into meaningful bundles. Conventional clustering techniques group streamlines based on their spatial coordinates. Neuroanatomists, however, define white-matter bundles based on the anatomical structures that they go through or next to, rather than their spatial coordinates. Thus we propose a similarity measure for clustering streamlines based on their position relative to cortical and subcortical brain regions. We incorporate this measure into a hierarchical clustering algorithm and compare it to a measure that relies on Euclidean distance, using data from the Human Connectome Project. We show that the anatomical similarity measure leads to a 20% improvement in the overlap of clusters with manually labeled tracts. Importantly, this is achieved without introducing any prior information from a tract atlas into the clustering algorithm, therefore without imposing the existence of any named tracts.

Keywords: Diffusion MRI; Hierarchical clustering; Normalized cuts; Tractography.

Figure 1:

Directions in which nearest neighboring segmentation labels are found, for a streamline point that lies in the center of the cube. Red directions belong to the 6, 14 and 26-element neighborhoods. Blue directions belong to the 14 and 26-element neighborhoods. Green directions belong only to the 26-element neighborhood.

Figure 2:

Example of the anatomical neighborhood of a point in the corticospinal tract. Neighboring FreeSurfer segmentation labels in the L-R and I-S directions are shown in the table.

Figure 3:

Sagittal (a) and axial (b) view of the 18 manually labeled bundles that we use for comparison to the unsupervised clustering results, shown in a randomly selected subject.

Figure 4:

(a) Dice coefficient between the manually labeled WM bundles and the streamline clusters obtained with each of the two similarity measures, averaged over all 18 bundles and 32 subjects, as a function of the total number of clusters. (b) Average Dice coefficient over all subjects by tract, when the total number of clusters is 200.

Figure 5:

Population averages of the manually labeled bundles and the streamline clusters that contain more than 5% streamlines overlapping with the corresponding manually labeled bundle. Each color represents a different WM pathway. The population averages across all subjects are shown as isosurfaces in axial and sagittal views.

Figure 6:

Population averages of the manually labeled bundles and the streamline clusters that contain more than 5% streamlines overlapping with the corresponding manually labeled bundle (continued from Fig. 5). Each color represents a different WM pathway. The population averages across all subjects are shown as isosurfaces in axial and sagittal views.

Figure 7:

Homogeneity (a) and completeness (b) of unsupervised clustering, averaged over 18 WM bundles and 32 subjects, as a function of the number of clusters.

Figure 8:

Euclidean similarity measure w_E (a), anatomical similarity measure w_A (b), and mean closest-point distance w_Cp (c), for streamlines clustered together either by the Euclidean or the anatomical similarity measure (w_E-optimal vs. w_A-optimal). All measures are plotted as a function of the number of clusters, averaged over all subjects.

Figure 9:

Clusters from a single subject, obtained with each of the two similarity measures. Clusters were selected so that at least 5% of the streamlines in a cluster pass through a pair of anatomical segmentation labels: (a) precentral and brainstem, (b) superior parietal and brainstem, (c) superior temporal and precentral, (d) isthmus cingulate and rostral anterior cingulate.

Figure 10:

Example of an original (left) and perturbed (right) indivudual anatomical segmentation used to evaluate robustness to segmentation errors.

Figure 11:

Dice coefficient with respect to manually labeled bundles (a), homogeneity (b), and completeness (c) of unsupervised clustering with our anatomical similarity measure, when the subjects’ original and perturbed anatomical segmentations are used.

Figure 12:

Mean closest-point distance between automatically segmented and manually labeled brain structures that are included in the FreeSurfer subcortical segmentation.

Figure 13:

Top: Tree representation of the hierarchical cuts performed on a subject’s whole-brain tractography data using our anatomical similarity measure. Bottom: Clusters associated with the tree nodes labeled (a)-(i).