March 2024 Estimating fiber orientation distribution with application to study brain lateralization using HCP D-MRI data
Seungyong Hwang, Thomas C. M. Lee, Debashis Paul, Jie Peng
Author Affiliations +
Ann. Appl. Stat. 18(1): 100-124 (March 2024). DOI: 10.1214/23-AOAS1781


Diffusion-weighted magnetic resonance imaging (D-MRI) is an in vivo and noninvasive imaging technology for characterizing tissue microstructure in biological samples. A major application of D-MRI is for white matter fiber tract reconstruction in brains. It begins by estimating the water molecule movements (serving as proxies for fiber directions) in the brain voxels and then combines the results to form fiber tracts. The voxel-level fiber direction information can be modeled by a fiber orientation distribution (FOD) function, and in this paper, we propose a computationally scalable FOD estimator, the blockwise James–Stein (BJS) estimator. We then apply BJS to the D-MRI data from the Human Connectome Project (HCP) to study brain lateralization, an important topic in neuroscience. Specifically, we focus on the association between lateralization of the superior longitudinal fasciculus (SLF)—a major association tract and handedness. For each subject from the HCP data, we extract voxel-level directional information by BJS and then reconstruct the SLF in each brain hemisphere through a tractography algorithm. Finally, we derive a lateralization score that quantifies hemispheric asymmetry of the reconstructed SLF. We then relate this lateralization score to gender and handedness through an ANOVA model, where significant handedness effects are found. The results indicate that the SLF lateralization is likely to be different in right-handed and left-handed individuals. Codes and example scripts for both synthetic experiments and HCP data application can be found at

Funding Statement

This research is supported by the following grants: NSF DMS-1713120 (D.P.), DMS-1811405(T.L., D.P.), DMS-1811661(T.L.), DMS-1915894(S.H., D.P., J.P.), DMS-1916125 (S.H., T.L.), and NIH 1R01EB021707(D.P., J.P.).


The authors would like to thank Hao Yan, Jilei Yang, and Raymond Wong for sharing codes for peak detection, fiber tracking, and generating synthetic D-MRI data. Data used in the real application were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research and by the McDonnell Center for Systems Neuroscience at Washington University.

Seungyong Hwang is also affiliated with Department of Genetics, Stanford University.


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Seungyong Hwang. Thomas C. M. Lee. Debashis Paul. Jie Peng. "Estimating fiber orientation distribution with application to study brain lateralization using HCP D-MRI data." Ann. Appl. Stat. 18 (1) 100 - 124, March 2024.


Received: 1 April 2022; Revised: 1 May 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1781

Keywords: James–Stein estimator , neuroimaging , spherical convolution , tractography

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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