The Annals of Applied Statistics

Local tests for identifying anisotropic diffusion areas in human brain with DTI

Tao Yu, Chunming Zhang, Andrew L. Alexander, and Richard J. Davidson

Full-text: Open access

Abstract

Diffusion tensor imaging (DTI) plays a key role in analyzing the physical structures of biological tissues, particularly in reconstructing fiber tracts of the human brain in vivo. On the one hand, eigenvalues of diffusion tensors (DTs) estimated from diffusion weighted imaging (DWI) data usually contain systematic bias, which subsequently biases the diffusivity measurements popularly adopted in fiber tracking algorithms. On the other hand, correctly accounting for the spatial information is important in the construction of these diffusivity measurements since the fiber tracts are typically spatially structured. This paper aims to establish test-based approaches to identify anisotropic water diffusion areas in the human brain. These areas in turn indicate the areas passed by fiber tracts. Our proposed test statistic not only takes into account the bias components in eigenvalue estimates, but also incorporates the spatial information of neighboring voxels. Under mild regularity conditions, we demonstrate that the proposed test statistic asymptotically follows a $\chi^{2}$ distribution under the null hypothesis. Simulation and real DTI data examples are provided to illustrate the efficacy of our proposed methods.

Article information

Source
Ann. Appl. Stat., Volume 7, Number 1 (2013), 201-225.

Dates
First available in Project Euclid: 9 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1365527196

Digital Object Identifier
doi:10.1214/12-AOAS573

Mathematical Reviews number (MathSciNet)
MR3086416

Zentralblatt MATH identifier
06171269

Keywords
Brain tissue diffusion tensor eigenvalue fiber tracts local test quantitative scalar

Citation

Yu, Tao; Zhang, Chunming; Alexander, Andrew L.; Davidson, Richard J. Local tests for identifying anisotropic diffusion areas in human brain with DTI. Ann. Appl. Stat. 7 (2013), no. 1, 201--225. doi:10.1214/12-AOAS573. https://projecteuclid.org/euclid.aoas/1365527196


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Supplemental materials

  • Supplementary material: Supplement to “Local tests for identifying anisotropic diffusion areas in human brain with DTI”. This file provides proofs for Theorems 1 and 2, a short summary of $\operatorname{FDR}_{L}$ procedure [Zhang, Fan and Yu (2011)], steps for constructing $\mathbb{K}$ based on DWI data and some more simulation results.