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On Quantifying Local Geometric Structures of Fiber Tracts

  • Jian ChengEmail author
  • Tao Liu
  • Feng Shi
  • Ruiliang Bai
  • Jicong Zhang
  • Haogang Zhu
  • Dacheng Tao
  • Peter J. Basser
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11072)

Abstract

In diffusion MRI, fiber tracts, represented by densely distributed 3D curves, can be estimated from diffusion weighted images using tractography. The spatial geometric structure of white matter fiber tracts is known to be complex in human brain, but it carries intrinsic information of human brain. In this paper, inspired by studies of liquid crystals, we propose tract-based director field analysis (tDFA) with total six rotationally invariant scalar indices to quantify local geometric structures of fiber tracts. The contributions of tDFA include: (1) We propose orientational order (OO) and orientational dispersion (OD) indices to quantify the degree of alignment and dispersion of fiber tracts; (2) We define the local orthogonal frame for a set of unoriented curves, which is proved to be a generalization of the Frenet frame defined for a single oriented curve; (3) With the local orthogonal frame, we propose splay, bend, and twist indices to quantify three types of orientational distortion of local fiber tracts, and a total distortion index to describe distortions of all three types. The proposed tDFA for fiber tracts is a generalization of the voxel-based DFA (vDFA) which was recently proposed for a spherical function field (i.e., an ODF field). To our knowledge, this is the first work to quantify orientational distortion (splay, bend, twist, and total distortion) of fiber tracts. Experiments show that the proposed scalar indices are useful descriptors of local geometric structures to visualize and analyze fiber tracts.

Notes

Acknowledgement

This work was supported by Australian Research Council Projects FL-170100117, DP-180103424, LP-150100671, Intramural Research Program of NICHD (ZIA-HD000266), the National Key R&D Program of China (2016YFF0201002), and the Beijing Municipal Science and Technology Commission (BJMSJY-160153).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jian Cheng
    • 1
    • 4
    • 5
    Email author
  • Tao Liu
    • 1
  • Feng Shi
    • 2
  • Ruiliang Bai
    • 3
  • Jicong Zhang
    • 1
  • Haogang Zhu
    • 1
  • Dacheng Tao
    • 4
  • Peter J. Basser
    • 5
  1. 1.Beijing Advanced Innovation Center for Big Data-Based Precision MedicineBeihang UniversityBeijingChina
  2. 2.Shanghai United Imaging Intelligence Co., Ltd.ShanghaiChina
  3. 3.Interdisciplinary Institute of Neuroscience and TechnologyZhejiang UniversityHangzhouChina
  4. 4.UBTECH Sydney AI Centre, SIT, FEITUniversity of SydneySydneyAustralia
  5. 5.SQITS, NIBIB, NICHDNational Institutes of HealthBethesdaUSA

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