Introduction

Subcortical structures are a group of interconnected gray matter structures lying deep beneath the white matter and include the diencephalon, pituitary gland, limbic structures, and the basal ganglia^1,2. These structures are involved in complex processes such as cognition, movement, memory, learning, emotion, and homeostasis. Accurate parcellation of the brain subcortex facilitates the investigation of the contributions of subcortical nuclei to human cognitive skills and social behaviors. Subcortical parcellation can be based on the connectivity profiles of subcortical voxels in relation to cortical gray matter, often determined using diffusion tractography^3–6. However, annotation inaccuracy of the cortex or the fiber tracts can affect subcortical parcellation. To overcome this limitation, we propose a data-driven approach for subject-specific subcortical parcellation without relying on cortical or tract annotations.

Materials and Methods

We utilized the anatomical and diffusion MRI data of 12 subjects from the Human Connectome Project Young Adult (HCP-YA) study⁷. The subjects were scanned between 24 and 34 years ($$$30.5 \pm 3.23$$$) of age using a Siemens 3T Prisma MRI scanner. Diffusion-weighted images were acquired with $$$(1.25 ~mm)^3$$$ isotropic voxel resolution along 270 noncollinear gradient directions with $$$b=1000,2000,3000 ~s/mm^2$$$. The data were minimally preprocessed with the standard HCP processing pipeline⁸.

Our approach for population subcortical parcellation involves (i) streamline clustering⁹; (ii) voxel annotation based on streamline clusters; and (iii) sparse non-negative matrix factorization (NMF) for subcortical parcellation³.

We start with whole-brain tractography using asymmetric fiber orientation distribution functions (AFODFs) to better capture complex axonal configurations (e.g., bending, fanning, and crossing) and to mitigate gyral bias for better cortico-cortical connectivity^10,11. Fiber streamlines are generated by successively following the local directions determined from the AFODFs¹². Whole-brain tractography is performed with 64 random seeds per voxel, resulting in approximately 100 million streamlines, but only streamlines that traverse subcortical regions are retained.

$$$\textbf{Unsupervised Bilateral Fiber Clustering.}$$$ We warp a random subset of the fiber streamlines of each subject to the MNI atlas space with affine and non-linear transforms estimated between the subject anatomical scan and the atlas. Spatially normalized streamlines of all subjects are combined for population-level fiber clustering using an automated unsupervised fiber clustering method. The streamlines are mapped to a Hilbert space via parameterization as coefficients of a cosine series¹³ and then grouped into $$$K$$$ clusters via $$$K$$$-medoids clustering⁹. Streamlines in both cerebral hemispheres are clustered bilaterally for consistency and robustness.

$$$\textbf{Voxel Annotation with Streamline Clusters.}$$$ We encode the relationship between the $$$K$$$ streamline clusters and the $$$N$$$ voxels using a matrix $$$C=(c_{ki})$$$, where $$$c_{ki}=1$$$ if more than 2 streamlines in cluster $$$k$$$ traverse voxel $$$i$$$, otherwise $$$c_{ki}=0$$$.

$$$\textbf{Sparse NMF parcellation.}$$$ Sparse NMF has been successfully applied for whole-brain parcellation³. The non-negativity constraint in NMF improves interpretability and robustness¹⁴. We decompose the encoding matrix as above into $$$M$$$ components using sparse NMF, resulting in a component matrix $$$H$$$ and the respective component coefficients. Each voxel is assigned to the component corresponding to the largest coefficient in the coefficient vector of the voxel, resulting in an initial parcellation map $$$S$$$ with $$$M$$$ parcels. Finally, We correct for isolated voxels by incorporating information from neighboring voxels by updating $$$S$$$ using constraints from adjacency voxels³.

We evaluated our parcellation method using a specificity score that characterizes the distance between the parcels. For each $$$M$$$, we encode in matrix $$$Q$$$ the cosine distances between component kernels. The specificity score is then defined as $$$\frac{D}{M}$$$, where $$$D$$$ is the principal component eigenvalue computed using singular value decomposition. A lower score indicates higher specificity, signifying better parcellation.

Results

We evaluated the parcels specificity of streamline clustering with different numbers of clusters. We found that $$$K=500$$$ is sufficient for capturing better specificity (Fig. 1). Subcortical parcellation results shown in Fig. 2 indicate great consistency with existing studies.

Acknowledgements

This work was supported in part by the United States National Institutes of Health (NIH) through grants MH125479, EB008374, and EB006733.

References

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