Surface-based Tracking of U-fibers in the Superficial White Matter

Abstract

The superficial white matter (SWM) lies directly underneath the cortical ribbon and contains the short association fibers, or U-fibers, that connect neighboring gyri. Connectivity of these U-fibers is important for various neuroscientific research from the development to the aging of the brain. Nonetheless, conventional tractography methods can only provide a partial representation of these connections. Moreover, previous studies on U-fibers mainly extract tracts based on their shape characteristics without imposing the biologically critical condition that they should tightly follow the cortical surface. In this work we leverage the high resolution diffusion imaging data from the Human Connectome Project (HCP), and develop a novel surface-based framework for reconstructing the U-fibers. Guided by the projected fiber orientation distributions (FODs) on cortical surfaces, our method tracks the U-fibers from sulcal seed regions to neighboring gyrus on the triangular mesh representation of the cortex. Compared to volume-based tractography, the main advantage of our method is that it is intrinsic to the cortical geometry. More specifically, we define a novel approach for measuring the change of angles on the tangent space of the surface and use them to determine the U-fiber passing through a sulcal seed point. In experimental results, we compare our surface-based method with state-of-the-art FOD-based tractography from MRtrix on a large-scale dataset of 484 HCP subjects, and demonstrate that our method clearly achieves superior performance on the reconstruction of U-fibers between the precentral and postcentral gyrus.

Fig. 1.

Surface-based reconstruction of U-fibers from FODs. (A) FODs computed from diffusion MRI data. (B) A zoomed view of the ROI (dashed box) in (A) including the superficial white matter (SWM) along the precentral and postcentral cortex. (C) The projection of FOD directions onto the tangent space of the white matter surface in the boxed region. For each vertex, the two fiber directions with the largest magnitudes are plotted. All FODs are color-coded by directions (red: left-right, green: anterior-posterior, blue: inferior-superior). FODs in the SWM show the fiber directions of the U-fiber (yellow curve) along the tangent space of the cortex.

Fig. 2.

Algorithmic details of surface-based tracking of U-fibers between the precentral and postcentral cortex. (A) The gyral skeletons (green) and seed sulcal regions (red) are generated from preprocessing steps. A zoomed view of the boxed region is shown in (B) and (C). (B) A streamline from a seed point (red dot) to the postcentral gyrus is first established. From all the possible fiber directions (brown arrows) at the seed point, a streamline with the minimum average deviation angle is selected. (C) With the predetermined fiber direction (brown arrow), which is opposite to the selected direction in (B) at the seed point, another streamline to the other gyrus (precentral) is generated. (D) A demonstration of the common procedure that controls the smoothness of the pathways within a triangle T_i by the deviation angle θ_in, and at the crossing to a neighboring triangle T_j by the deviation angle θ_xing.

Fig. 3.

An example of U-fiber reconstruction for one subject (101006) using our surface-based method (A, B) and MRtrix (C, D). (A, C) The streamlines superimposed on the WM surface with the same color scheme as in Fig. 1. (B, D) The same streamlines plotted without the meshes in three different views by slightly rotating about the z-axis, where the blue ones (valid U-fibers) meet both the sides of the precentral and postcentral gyrus, but the green ones do not.

Fig. 4.

Four representative examples of U-fiber reconstruction using our surface-based method (A) and MRtrix (B). Each column corresponds to the same HCP subject.

Fig. 5.

Quantitative comparisons of the surface-based method and MRtrix using the large-scale datasets of 484 HCP subjects. (A) Box plots of the ‘well-connected’ measure (number of streamlines successfully connecting the precentral and postcentral gyrus out of the total 2000 streamlines generated by each method). (B) Histogram of the ‘well-U-shaped’ measures from all the generated streamlines. (C) Box plots of the ‘well-distributed’ measure (number of the gyral sections hit by the streamlines from each method).