  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.
