Bundle-Specific Axon Diameter Index as a New Contrast to Differentiate White Matter Tracts

Abstract

In the central nervous system of primates, several pathways are characterized by different spectra of axon diameters. In vivo methods, based on diffusion-weighted magnetic resonance imaging, can provide axon diameter index estimates non-invasively. However, such methods report voxel-wise estimates, which vary from voxel-to-voxel for the same white matter bundle due to partial volume contributions from other pathways having different microstructure properties. Here, we propose a novel microstructure-informed tractography approach, COMMIT_AxSize, to resolve axon diameter index estimates at the streamline level, thus making the estimates invariant along trajectories. Compared to previously proposed voxel-wise methods, our formulation allows the estimation of a distinct axon diameter index value for each streamline, directly, furnishing a complementary measure to the existing calculation of the mean value along the bundle. We demonstrate the favourable performance of our approach comparing our estimates with existing histologically-derived measurements performed in the corpus callosum and the posterior limb of the internal capsule. Overall, our method provides a more robust estimation of the axon diameter index of pathways by jointly estimating the microstructure properties of the tissue and the macroscopic organisation of the white matter connectivity.

Keywords: diffusion MRI; human brain; microstructure; microstructure informed tractography; tractography; white-matter axon signature.

Figure 1

Voxel-wise vs. bundle-specific axon diameter estimation. (A) Schematic illustration of two crossing fiber populations characterized by different compositions: the green bundle contains larger axons than the blue. (B) Axon diameter estimation using a voxel-wise approach; for simplicity, we report the estimated mean diameters. The arrow points to the crossing region where such methods are known to especially suffer from overestimation. (C) Characterization of the axon diameter of a white matter bundle is typically done by averaging, along its entire course, the values previously estimated in every voxel; this indirect procedure is affected by such overestimated voxels and leads to biased results. (D) Estimation of bundle-specific axon diameter.

Figure 2

How to enable estimation of bundle-specific axon diameter index. (A) Simple crossing configuration of two fiber populations with different axon compositions, i.e., the vertical one is composed of larger axons than the horizontal, to illustrate the construction of the proposed formulation. (B) Corresponding DW-MRI signal in four representative voxels. (C) Example of two possible streamlines reconstructed with tractography. (D) Visual representation of the response functions in the Cylinder-Zeppelin-Ball forward model for each compartment. (E) The vector y contains a concatenation of the DW-MRI signal acquired in all voxels, while the matrix A is constructed by combining the response functions with the local orientations of the streamlines in each voxel.

Figure 3

Topology of fibers in the Corpus Callosum (CC) and posterior limb of the internal capsule (PIC), reconstructed with DW-MRI tractography of a single healthy volunteer. (A) Subdivision of the mid-sagittal section of the CC in 11 sectors (corresponding to ROIs), see Supplementary Figure 9. (B,C) Streamlines colored according to the corresponding ROIs (medial and lateral views of the hemisphere). (D) Projection of the streamlines onto the pial surface. (E) Subdivision of PIC in 6 sectors (ROIs). (F,G) Streamlines colored according to the corresponding ROIs (medial and lateral view of the hemisphere). (H) Projection of the streamlines onto the pial surface.

Figure 4

Axon diameter indexes (ADI) estimated on the 45-degrees crossing synthetic phantom. The figures show the bundle-specific ADI estimated using the COMMIT_AxSize method (top row) and the voxel-wise ADI estimated using the ActiveAx_AMICO method (bottom row). The boxplots show the results 50 different Rician noise realisations for COMMIT_AxSize and 100 voxels sampled in each single bundle areas and in the crossing area, for the ActiveAx_AMICO method. The mean ground truth cylinder diameter of the green and blue bundles are 4.0 μm, and 2.7 μm, respectively (colored dashed line). The first boxplot column show the estimated ADI at various SNR, the second column using various number of columns in matrix A to compute the ADI and the last column shows the estimates for data with various levels of dispersion.

Figure 5

Streamline Axon Diameter Index (sADI) in the Corpus Callosum (CC) and posterior limb of the internal capsule (PIC) of a single healthy volunteer. (A,C) show streamlines colored according to their sADI. (B,D) show the projection of streamlines'sADI onto the pial surface; colors correspond to the sADI averaged across streamlines. Abbreviations: ces, central sulcus; ifs, inferior frontal sulcus; ips, interparietal sulcus; prs, precentral sulcus; sfs, superior frontal sulcus. Numbers correspond to Brodman areas.

Figure 6

DW-MRI cylinder diameter distribution of CC and PIC sectors compared to histological mean volume-weighted axon diameter from human (CC) and monkey (PIC) histology. Star markers represent the means of volume weighted histological distributions; hexagon markers represent the means of volume weighted cylinder distributions in the range 2.0μm to 6.5μm.