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Diffusion tensor imaging (DTI) plays a key role in analyzing the physicalstructures of biological tissues, particularly in reconstructing fiber tractsof the human brain in vivo. On the one hand, eigenvalues of diffusion tensors(DTs) estimated from diffusion weighted imaging (DWI) data usually containsystematic bias, which subsequently biases the diffusivity measurementspopularly adopted in fiber tracking algorithms. On the other hand, correctlyaccounting for the spatial information is important in the construction ofthese diffusivity measurements since the fiber tracts are typically spatiallystructured. This paper aims to establish test-based approaches to identifyanisotropic water diffusion areas in the human brain. These areas in turnindicate the areas passed by fiber tracts. Our proposed test statistic not onlytakes into account the bias components in eigenvalue estimates, but alsoincorporates the spatial information of neighboring voxels. Under mildregularity conditions, we demonstrate that the proposed test statisticasymptotically follows a $\chi^2$ distribution under the null hypothesis.Simulation and real DTI data examples are provided to illustrate the efficacyof our proposed methods.

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